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Ensemble data assimilation methods, such as the Ensemble Kalman Filter (EnKF), are well suited for climate reanalysis because they feature flow‐dependent covariance. However, because Earth System Models are heavy computationally, the method uses a few tens of members. Sampling error in the covariance matrix can introduce biases in the deep ocean, which may cause a drift in the reanalysis and in the predictions. Here, we assess the potential of the hybrid covariance approach (EnKF‐OI) to counteract sampling error. The EnKF‐OI combines the flow‐dependent covariance computed from a dynamical ensemble with another covariance matrix that is static but less prone to sampling error. We test the method within the Norwegian Climate Prediction Model, which combines the Norwegian Earth System Model and the EnKF. We test the performance of the reanalyzes in an idealized twin experiment, where we assimilate synthetic sea surface temperature observations monthly over 1980–2010. The dynamical and static ensembles consist respectively of 30 members and 315 seasonal members sampled from a pre‐industrial run. We compare the performance of the EnKF to an EnKF‐OI with a global hybrid coefficient, referred to as standard hybrid, and an EnKF‐OI with adaptive hybrid coefficients estimated in space and time. Both hybrid covariance methods cure the bias introduced by the EnKF at intermediate and deep water. The adaptive EnKF‐OI performs best overall by addressing sampling noise and rank deficiencies issues and can sustain low analysis errors by doing smaller updates than the standard hybrid version. Plain Language Summary: Data assimilation is a statistical method that reduces uncertainty in a model, based on observations. Because of their ease of implementation, the ensemble data assimilation methods, that rely on the statistics of a finite ensemble of realizations of the model, are popular for climate reanalysis and prediction. However, observations are sparse—mostly near the surface—and the sampling error from data assimilation method introduces a deterioration in the deep ocean. We use a method that complements this ensemble with a pre‐existing database of model states to reduce sampling error. We show that the approach substantially reduces error at the intermediate and deep ocean. The method typically requires the tunning of a parameter, but we show that it can be estimated online, achieving the best performance. Key Points: Hybrid covariance handles sampling error and improves the update of deep water masses when assimilating surface observation with an Ensemble Kalman FilterThe method is well suited to provide a long coupled reanalysis of the past centuryHybrid covariance with adaptive hybrid coefficients explicitly estimated in space and time achieved the best performance [ABSTRACT FROM AUTHOR]

This study hybridizes the background error covariance (BEC) of the hourly atmospheric three-dimensional variational data assimilation (3DVar) in Local Analysis (LA) operated at Japan Meteorological Agency using the flow-dependent BEC derived from the singular vector-based Mesoscale Ensemble Prediction System (MEPS) and the static BEC. The impact of introducing the hybrid BEC into the 3DVar is examined, along with its sensitivities to various factors like the ensemble size that is augmented by using lagged ensemble forecasts, the weight given to the ensemble-based component of BEC, the localization scales, and the use (or not) of the cross-variable correlation. This hybrid 3DVar system can be operated with small additional computational cost because it has no coupling with another ensemble data assimilation system. In sensitivity experiments, this hybrid 3DVar is shown to yield smaller forecast root mean square errors than the pure 3DVar, especially for surface variables. Moreover, the hybrid 3DVar shows a better equitable threat score for strong precipitation. These improvements were greater in the experiments with larger ensemble sizes that were increased by using lagged ensemble forecasts because of the reduced sampling errors in the ensemble-based BEC. These results were sensitive to the weight given to the ensemble-based BEC and the horizontal localization scale, whose optimal values were found to be approximately 0.5 and 100 km, respectively. The longer vertical correlation scale and the cross-variable correlation were also found important to create dynamically-balanced analysis, which is especially true for heavy rain cases. [ABSTRACT FROM AUTHOR]

For Paleoclimate data assimilation (PDA), a hybrid gain analog offline ensemble Kalman filter (HGAOEnKF) is proposed. It keeps the benefits of the analog offline ensemble Kalman filter (AOEnKF) that constructs analog ensembles from existing climate simulations with joint information of the proxies. The analog ensembles can provide more accurate prior ensemble mean and "flow‐dependent" error covariances than randomly sampled ensembles. HGAOEnKF further incorporates the benefits of static prior error covariances that better capture large‐scale error correlations and mitigate sampling errors than the sample prior error covariances, through a hybrid gain approach within an ensemble framework. Observing system simulation experiments are conducted for various data assimilation methods, using ensemble simulations from the Community Earth System Model‐Last Millennium Ensemble Project. Results show that using the static prior error covariances estimated from a sufficiently large sample set is beneficial for the traditional offline ensemble Kalman filter (OEnKF) and AOEnKF. HGAOEnKF method is superior to the OEnKF and AOEnKF with and without static prior error covariances, especially for the reconstruction of extreme events. The advantages of HGAOEnKF over OEnKF and AOEnKF with and without static prior error covariances are persistent with varying sample sizes and presence of model errors. Plain Language Summary: Paleoclimate data assimilation (PDA) combines information from the climate simulations and proxy data, aiming to provide an optimal estimate of past climates. The relatively low predictive skill of the climate model and the noisy and sparse paleoclimate proxies have imposed great challenges on PDA. Previous studies have shown that offline ensemble assimilation methods are much more computationally efficient than online ensemble assimilation ones, and the offline analog ensemble can also provide "flow‐dependent" prior error covariances. However, the sample prior error covariances estimated from an ensemble with limited members can be contaminated by sampling errors. Hybridization of the "flow‐dependent" prior error covariances with the static ones can remedy the sampling error, and also infuse better representation of large‐scale error correlations from the static ones. Thus a hybrid gain analog offline ensemble Kalman filter (EnKF) is proposed, which retains the advantages of the analog ensemble and further adapts the benefits of static prior error covariances. The hybrid gain analog offline EnKF is superior to the traditional offline EnKF and the offline EnKF with analog ensembles. Key Points: Static B using sufficiently large samples can better capture large‐scale error correlations and mitigate sampling errors than the sampled BHybrid gain analog offline ensemble Kalman filter (HGAOEnKF) uses the ensemble mean prior from the analog ensemble and hybrid gains combining the static B and "flow‐dependent" BHGAOEnKF has advantages over OEnKF and analog offline ensemble Kalman filter with varying sample sizes and presence of model errors, especially for extreme years [ABSTRACT FROM AUTHOR]

The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman–Bucy filtering for continuous-time, linear-Gaussian signal and observation models. We present a system of equations that describe the flow of individual particles and the flow of the sample covariance and the sample mean in continuous-time ensemble filtering. We consider these equations and their characteristics in a number of popular ensemble Kalman filtering variants. Given these equations, we study their asymptotic convergence to the optimal Bayesian filter. We also study in detail some non-asymptotic time-uniform fluctuation, stability, and contraction results on the sample covariance and sample mean (or sample error track). We focus on testable signal/observation model conditions, and we accommodate fully unstable (latent) signal models. We discuss the relevance and importance of these results in characterising the filter's behaviour, e.g. it is signal tracking performance, and we contrast these results with those in classical studies of stability in Kalman–Bucy filtering. We also provide a novel (and negative) result proving that the bootstrap particle filter cannot track even the most basic unstable latent signal, in contrast with the ensemble Kalman filter (and the optimal filter). We provide intuition for how the main results extend to nonlinear signal models and comment on their consequence on some typical filter behaviours seen in practice, e.g. catastrophic divergence. [ABSTRACT FROM AUTHOR]

Flow‐dependent background error covariances estimated from short‐term ensemble forecasts suffer from sampling errors due to limited ensemble sizes. Covariance localization is often used to mitigate the sampling errors, especially for high dimensional geophysical applications. Most applied localization methods, empirical or adaptive ones, multiply the Kalman gain or background error covariances by a distance‐dependent parameter, which is a simple linear filtering model. Here two localization methods based on convolutional neural networks (CNNs) learning from paired data sets are proposed. The CNN‐based localization function (CLF) aims to minimize the sampling error of the estimated Kalman gain, and the CNN‐based empirical localization function (CELF) aims to minimize the posterior error of state variables. These two CNN‐based localization methods can provide localization functions that are nonlinear, spatially and temporally adaptive, and non‐symmetric with respect to displacement, without requiring any prior assumptions for the localization functions. Results using the Lorenz05 model show that CLF and CELF can better capture the structures of the Kalman gain than the best Gaspari and Cohn (GC) localization function and the adaptive reference localization method. For both perfect‐ and imperfect‐model experiments, CLF produces smaller errors of the Kalman gain, prior and posterior than the best GC and reference localization, especially for spatially averaged observations. Without model error, CELF has smaller prior and posterior errors than the best GC and reference localization for spatially averaged observations, while with model error, CELF has smaller prior and posterior errors than the best GC and reference localization for single‐point observations. Plain Language Summary: Ensemble Kalman filters have been widely used for high‐dimensional geophysical applications, with the advantages to provide flow‐dependent background error covariances based on short‐term ensemble forecasts. Due to the massive computational costs for advancing ensemble simulations, limited ensemble members are commonly adopted, which results in sample‐estimated background error covariances contaminated by spurious noisy correlations. To remedy the sampling error, covariance localization that tapers the observation impact on state variables with distance, is commonly used. There are pre‐defined localization functions with tuning parameters and adaptive localization functions that are often based on correlation statistics. Here two purely data‐driven localization methods based on convolutional neural networks are proposed. These newly proposed localization functions are spatially and temporally adaptive, non‐symmetric with respect to displacement, with better captured structures of the Kalman gain than the empirical and adaptive localization methods. When they are applied in cycling assimilation, the localization methods based on the convolutional neural networks can produce improved analyses and forecasts. Key Points: Two CNN‐based localization methods are proposed to minimize sampling errors of estimated Kalman gain or posterior errors of state variablesCNN‐based localizations are adaptive in space and time, non‐symmetric with respect to displacement, and able to fit nonlinear functionsCNN‐based localizations effectively represent the Kalman gain, and lead to improved analyses and forecasts in cycling assimilations [ABSTRACT FROM AUTHOR]

Localization is the key component to the successful application of ensemble data assimilation (DA) to high-dimensional problems in the geosciences. We study the impact of sampling error and its amelioration through localization using both analytical development and numerical experiments. Specifically, we show how sampling error in covariance estimates accumulates and spreads throughout the entire domain during the computation of the Kalman gain. This results in a bias, which is the dominant issue in unlocalized ensemble DA, and, surprisingly, we find that it depends directly on the number of independent observations but only indirectly on the state dimension. Our derivations and experiments further make it clear that an important aspect of localization is a significant reduction of bias in the Kalman gain, which in turn leads to an increased accuracy of ensemble DA. We illustrate our findings on a variety of simplified linear and nonlinear test problems, including a cycling ensemble Kalman filter applied to the Lorenz-96 model. Significance Statement: The dampening of long-range correlations has been the key to the success of ensemble data assimilation in global numerical weather prediction. In this paper, we show how noise in covariance estimates propagates through the state estimation process and corrupts state estimates. We show that this noise results in a bias and that this bias depends on the number of observations and not, as might be expected, on the state dimension. We go on to show how dampening long-range covariances through a process referred to as "localization" helps to mitigate the detrimental effects of this sampling noise. [ABSTRACT FROM AUTHOR]

For data assimilation to provide faithful state estimates for dynamical models, specifications of observation uncertainty need to be as accurate as possible. Innovation-based methods based on Desroziers diagnostics, are commonly used to estimate observation uncertainty, but such methods can depend greatly on the prescribed background uncertainty. For ensemble data assimilation, this uncertainty comes from statistics calculated from ensemble forecasts, which require inflation and localization to address under sampling. In this work, we use an ensemble Kalman filter (EnKF) with a low-dimensional Lorenz model to investigate the interplay between the Desroziers method and inflation. Two inflation techniques are used for this purpose: 1) a rigorously tuned fixed multiplicative scheme and 2) an adaptive state-space scheme. We document how inaccuracies in observation uncertainty affect errors in EnKF posteriors and study the combined impacts of misspecified initial observation uncertainty, sampling error, and model error on Desroziers estimates. We find that whether observation uncertainty is over- or underestimated greatly affects the stability of data assimilation and the accuracy of Desroziers estimates and that preference should be given to initial overestimates. Inline estimates of Desroziers tend to remove the dependence between ensemble spread–skill and the initially prescribed observation error. In addition, we find that the inclusion of model error introduces spurious correlations in observation uncertainty estimates. Further, we note that the adaptive inflation scheme is less robust than fixed inflation at mitigating multiple sources of error. Last, sampling error strongly exacerbates existing sources of error and greatly degrades EnKF estimates, which translates into biased Desroziers estimates of observation error covariance. Significance Statement: To generate accurate predictions of various components of the Earth system, numerical models require an accurate specification of state variables at our current time. This step adopts a probabilistic consideration of our current state estimate versus information provided from environmental measurements of the true state. Various strategies exist for estimating uncertainty in observations within this framework, but are sensitive to a host of assumptions, which are investigated in this study. [ABSTRACT FROM AUTHOR]

In this study, the local unscented transform Kalman filter (LUTKF) proposed in the previous study estimates the state of the Weather Research and Forecasting (WRF) model through local analysis. Real observations are assimilated to investigate the analysis performance of the WRF-LUTKF system. The WRF model as a regional numerical weather prediction (NWP) model is widely used to explain the atmospheric state for mesoscale meteorological fields, such as operational forecasting and atmospheric research applications. For the LUTKF based on the sigma-point Kalman filter (SPKF), the state of the nonlinear system is estimated by propagating ensemble members through the unscented transformation (UT) without making any linearization assumptions for nonlinear models. The main objective of this study is to examine the feasibility of mesoscale data assimilations for the LUTKF algorithm using the WRF model and real observations. Similar to the local ensemble transform Kalman filter (LETKF), by suppressing the impact of distant observations on model state variables through localization schemes, the LUTKF can eliminate spurious long-distance correlations in the background covariance, which are induced by the sampling error due to the finite ensemble size; therefore, the LUTKF used in the WRF-LUTKF system can efficiently execute the data assimilation with a small ensemble size. Data assimilation test results demonstrate that the LUTKF can provide reliable analysis performance in estimating the WRF model state with real observations. Experiments with various ensemble size show that the LETKF can provide better estimation results with a larger ensemble size, while the LUTKF can achieve accurate and reliable assimilation results even with a smaller ensemble size. [ABSTRACT FROM AUTHOR]

Kalman Filter (KF) based algorithms are the most frequently employed attitude estimation algorithms. Typically, a fully observable system necessitates the use of two distinct sensor types. Therefore, relying on a single sensor, such as a magnetometer, for spacecraft attitude estimation is deemed to be a challenge. The present investigation centers on utilizing magnetometers as the exclusive sensor. Several KF based estimation algorithms have been designed and evaluated to give the designer of spacecraft Attitude and Orbit Control System (AOCS) the choice of a suitable algorithm for his mission based on quantitative measures. These algorithms are capable of effectively addressing nonlinearity in both process and measurement models. The algorithms under examination encompass the Extended Kalman Filter (EKF), Sequential Extended Kalman Filter (SEKF), Pseudo Linear Kalman Filter (PSELIKA), Unscented Kalman Filter (USKF), and Derivative Free Extended Kalman Filter (DFEKF). The comparison of the distinct algorithms hinges on key performance metrics, such as estimation error for each axis, computation time, and convergence rate. The resulting algorithms provide numerous benefits, such as diverse levels of high estimation accuracy (with estimation errors ranging from 0.014o to 0.14o), varying computational demands (execution time ranges from 0.0536s to 0.0584s), and the capability to converge despite large initial attitude estimation errors (which reached 170o). These properties render the algorithms appropriate for utilization by spacecraft designers in all operational modes, supplying high-precision attitude estimations better than (0.5o) despite high magnetometer noise levels, which reached (200 nT). [ABSTRACT FROM AUTHOR]

The lithium iron phosphate (LiFePO4) blade battery is a long, rectangular-shaped cell that can be directly integrated into battery pack systems. It enhances volumetric power density, significantly reduces costs, and is widely utilized in electric vehicles. However, the flat open circuit voltage and significant polarization differences under wide operational temperatures are challenging for accurate voltage modeling of battery management systems (BMSs). In particular, inaccurate state of charge (SOC) estimation may cause overcharging and over-discharging risks. To accurately perceive the SOC of LiFePO4 blade batteries, a SOC estimation method based on the backpropagation neural network-extended Kalman filter (BPNN-EKF) algorithm is proposed. BPNN is a neural network model that utilizes the backpropagation algorithm to update model parameters, while EKF is an optimal estimation algorithm. Firstly, dynamic working condition tests, including the New European Driving Cycle (NEDC) and high-speed working (HSW) condition tests, are conducted under a wide temperature range (−25–43 °C). HSW conditions refer to a simulated operating condition that mimics the driving of an electric vehicle on a highway. The minimum voltage of the battery system is used as the output for training the BPNN model. We derive the Kalman gain by combining the BPNN output voltage. Additionally, the EKF algorithm is employed to correct the SOC value using voltage error information. Concerning long SOC calculation intervals, capacity errors, initial SOC errors, and current and voltage sampling errors, the maximum SOC estimation RMSE is 3.98% at −20 °C NEDC, 3.62% at 10 °C NEDC, and 1.68% at 35 °C HSW. The proposed algorithm can be applied to different temperatures and operations, demonstrating high robustness. This BPNN-EKF algorithm has the potential to be embedded in electric vehicle BMS systems for practical applications. [ABSTRACT FROM AUTHOR]

Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter's ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement: Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models. [ABSTRACT FROM AUTHOR]

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Copyright of Journal of Southeast University (English Edition) is the property of Journal of Southeast University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The satellite communication is embellished constantly by providing information, ensuring security, and enables the communication among huge at a particular time efficiently. The satellite navigation helps in determining the people's location. Global development, natural disasters, change in climatic conditions, agriculture crop growth, etc., are monitored using satellite observation. Hence, the satellite includes detailed information data, and it must be protected confidentially. The field of the satellite is enhanced at an astonishing pace. Satellite data play an important role in this modern world; hence, the onboard-satellite data must secure through the proper selection of error detection and estimation schema. Lightweight deep learning algorithm based on Extended Kalman Filter (KFK) is proposed to detect and estimate onboard pointing error such as an error in attitude and orbit. The Extended Kalman Filter (EKF) is widely used in the satellite system. EKF is utilized in this proposed model to detect the onboard pointing error such as attitude and orbit determination. An autonomous estimation of orbit position is possible through space-borne gravity. The information obtained through the observation of satellite data is compared with the accurate gravity model in detecting the error. The utilization of EKF reduces the dependence of the ground tracking system in satellite determination. The orbital altitude and orbital position are the most important challenges faced in the satellite determination system. The satellite model using the Extended Kalman Filter is an optimum method in estimating the orbital parameters. The errors in the linearization process are detected, and this can be overcome through the proper selection of linear expansion point with the EKF algorithmic model with the Jacobian matrix calculation. The results show that the EKF implementation helps in attaining better accuracy than other methodologies. Its contribution is enormous to many space missions, autonomous rendezvous and docking for manned and unmanned missions (e.g., ISS operations and beyond, in-orbit servicing, and in-orbit refueling), routine satellite OD operations, orbital debris removal systems, Space Situational Awareness (SSA) operations, and others. [ABSTRACT FROM AUTHOR]

Aiming at the problem that it is difficult to accurately estimate the state of charge (SOC) of lithium‐ion batteries in the strongly nonlinear interval, a novel algorithm based on a fuzzy control strategy is proposed. It integrates extended Kalman filter (EKF) and ampere‐hour (Ah) integration accurately estimate the SOC of lithium‐ion batteries. First, the algorithm uses the advantage that the EKF algorithm has high estimation accuracy in the nonlinear interval and can solve the problem of the large error caused by the inaccurate initial value of the Ah integral algorithm. Then the fuzzy‐EKF‐Ah (F‐EKF‐Ah) is used to fuse the two algorithms of EKF and Ah integral. The fused algorithm can effectively solve the problems of the cumulative error caused by the sampling accuracy of the Ah integral algorithm and the large estimation error of the EKF algorithm in the strong nonlinear interval. Finally, the equivalent circuit model is used for analysis. The experimental results show that the improved algorithm can achieve high estimation accuracy under three experimental conditions. [ABSTRACT FROM AUTHOR]

The ensemble-based Kalman filter requires at least a considerable ensemble (e.g., 10,000 members) to identify relevant error covariance at great distances for multidimensional geophysical systems. However, increasing numerous ensemble sizes will enlarge sampling errors. This study proposes a modified Cholesky decomposition based on the covariance localization (CL) scheme, namely a covariance localization scheme with modified Cholesky decomposition (CL-MC). Our main idea utilizes a modified Cholesky (MC) decomposition technique for estimating the background error covariance matrix; meanwhile, we employ the tunable singular value decomposition method on the background error covariance to improve the ensemble increment and avoid the imbalance of the system. To verify if the proposed method can effectively mitigate the sampling errors, numerical experiments are conducted on the Lorenz-96 model and large-scale model (SPEEDY model). The results show that the CL-MC method outperforms the CL method for different data assimilation parameters (ensemble sizes and localizations). Furthermore, by performing one year of assimilation experiments on the SPEEDY model, it is found that the 1-day forecast RMSEs obtained by the CL are approximately equal to the 5-day forecast RMSEs of CL-MC. So, the CL-MC method has potential advantages for long-term forecasting. Maybe the proposed CL-MC method achieves good prospects for widespread application in atmospheric general circulation models. [ABSTRACT FROM AUTHOR]

Accurate specification of error statistics required for data assimilation remains an ongoing challenge, partly because their estimation is an ill-posed problem that requires statistical assumptions. Even with the common assumption that background and observation errors are uncorrelated, the problem remains underdetermined. One natural question that could arise is: Can the increasing amount of overlapping observations or other datasets help to reduce the total number of statistical assumptions, or do they introduce more statistical unknowns? In order to answer this question, this paper provides a conceptual view on the statistical error estimation problem for multiple collocated datasets, including a generalized mathematical formulation, an exemplary demonstration with synthetic data as well as a formulation of the minimal and optimal conditions to solve the problem. It is demonstrated that the required number of statistical assumptions increases linearly with the number of datasets. However the number of error statistics that can be estimated increases quadratically, allowing for an estimation of an increasing number of error cross-statistics between datasets for more than three datasets. The presented optimal estimation of full error covariance and cross-covariance matrices between dataset does not accumulate uncertainties of assumptions among estimations of subsequent error statistics. [ABSTRACT FROM AUTHOR]

Covariance inflation is one of the necessary tools enabling the success of ensemble Kalman filters (EnKFs) in high‐dimensional spaces and in the presence of model error. Inflation maintains the ensemble variance to a sufficiently large value, counteracting the variance damping at analysis times and its underestimation arising from model and sampling errors. In this work, we investigate the effect of inflation on the dynamics of the EnKF ensemble. When the focus is on the recursive full cycle forecast–analysis–forecast, an apparently counterintuitive effect of multiplicative inflation appears in the span of the ensemble in the EnKF. In particular, we demostrate that multiplicative inflation changes the alignment of ensemble anomalies on to weakly stable backward Lyapunov vectors. Whereas the ensemble is expected to collapse on to the subspace corresponding to the unstable portions of the Lyapunov spectrum, the use of multiplicative inflation contributes to the retention of anomalies beyond that subspace. Given that the presence of model error implies that the analysis error is no longer fully confined in the local unstable subspace, this feature of multiplicative inflation is of paramount importance for optimal filtering. We propose hybrid schemes, whereby additive perturbations complement multiplicative inflation by suitably increasing the dimension of the subspace spanned by the ensemble. The use of hybrid schemes improves analysis root‐mean‐squared error in the Lorenz 96 model compared with the use of multiplicative inflation alone, emphasizing the role of model dynamics when designing additive inflation schemes. [ABSTRACT FROM AUTHOR]

Localization is an essential technique for ensemble-based data assimilations (DAs) to reduce sampling errors due to limited ensembles. Unlike traditional distance-dependent localization, the correlation cutoff method (Yoshida and Kalnay, 2018; Yoshida, 2019) tends to localize the observation impacts based on their background error correlations. This method was initially proposed as a variable localization strategy for coupled systems, but it can also can be utilized extensively as a spatial localization. This study introduced and examined the feasibility of the correlation cutoff method as an alternative spatial localization with the local ensemble transform Kalman filter (LETKF) preliminary on the Lorenz (1996) model. We compared the accuracy of the distance-dependent and correlation-dependent localizations and extensively explored the potential of the hybrid localization strategies. Our results suggest that the correlation cutoff method can deliver comparable analysis to the traditional localization more efficiently and with a faster DA spin-up. These benefits would become even more pronounced under a more complicated model, especially when the ensemble and observation sizes are reduced. [ABSTRACT FROM AUTHOR]

Linear transformations are widely used in data assimilation for covariance modeling, for reducing dimensionality (such as averaging dense observations to form "superobs"), and for managing sampling error in ensemble data assimilation. Here we describe a linear transformation that is optimal in the sense that, in the transformed space, the state variables and observations have uncorrelated errors, and a diagonal gain matrix in the update step. We conjecture, and provide numerical evidence, that the transformation is the best possible to precede covariance localization in an ensemble Kalman filter. A central feature of this transformation in the update step are scalars, which we term canonical observation operators (COOs), that relate pairs of transformed observations and state variables and rank-order those pairs by their influence in the update. We show for an idealized problem that sample-based estimates of the COOs, in conjunction with covariance localization for the sample covariance, can approximate well the true values, but a practical implementation of the transformation for high-dimensional applications remains a subject for future research. The COOs also completely describe important properties of the update step, such as observation-state mutual information, signal-tonoise and degrees of freedom for signal, and so give new insights, including relations among reduced-rank approximations to variational schemes, particle-filter weight degeneracy, and the local ensemble transform Kalman filter. Plain Language Summary Good estimates of the state of the Earth system rely on combining the latest observations with recent forecasts through a technique called data assimilation. To some degree, there is freedom to choose which variables are used in data assimilation and, before performing assimilation, to combine and transform the observations. Careful choices of variables and transformations of the observations not only have practical benefits, but also, by greatly simplifying the mathematical formulation of data assimilation, yield insights into how new observations influence Earth-system state estimates and common measures of the information provided by observations. [ABSTRACT FROM AUTHOR]

1. Metagenetic methods are commonplace within ecological and environmental research. One concern with these methods is the phenomenon of ‘critical mistagging’, where sequences from one sample are erroneously inferred to have originated from another sample due to errors in the attachment, PCR replication or sequencing of sample-specific dual-index tags. For studies using PCR-based library preparation on large sample sizes, the most cost-effective approach to limiting mistag-associated false detections involves using an unsaturated Latin square dual-indexing design. This allows researchers to estimate mistagging rates during sequencing but the statistical procedures for filtering out detections using this mistag rate have received little attention. 2. I propose a straightforward method to limit mistag-associated false discoveries during metabarcoding applications. I analysed two Illumina metabarcoding datasets produced using unsaturated Latin square designs to explore the distribution of mistagged sequences across dual-index combinations on a per taxon basis. I tested these data for conformity to the assumptions that (a) mistagging follows a binomial distribution (i.e. X ~ B(n, p)) where p, the probability of a sequence being mistagged, varies minimally across taxa and (b) mistags are distributed uniformly across dual-index combinations. I provide R functions that estimate the 95th percentile of expected mistags per dual-index combination for each taxon under these assumptions. 3. I show that mistagging rates were consistent across taxa within the datasets analysed and that modelling mistagging as a binomial process with uniform distribution across dual-index combinations enabled robust control of mistag-associated false discoveries. 4. I propose that this method of taxon-specific filtering of detections based on the maximum mistags expected per dual-index combination should be broadly accepted during metagenetic analysis, provided that control sample mistag abundances follow a near-uniform distribution. When this assumption is violated, data may be better fit by assuming that the distribution of mistags across combinations follows Poisson characteristics (i.e. X ~Pois(λ)), with λ empirically estimated from the abundance distribution of mistags among control samples. I provide a second R function for this case. [ABSTRACT FROM AUTHOR]

This study investigated the predictability and causes of the heavy rainfall event that brought severe disasters in Kyushu in July 2020 with a global numerical weather prediction system composed of the NICAM (non-hydrostatic icosahedral atmospheric model) and the LETKF (local ensemble transform Kalman filter). We performed ensemble data assimilation and forecast experiments using the NICAM-LETKF system with 1,024 members and 56-km horizontal resolution on the supercomputer Fugaku. The results showed that 1,024-member ensemble forecasts captured the probability of heavy rainfall in Kyushu about five days before it happens, although a 10-day-lead forecast is difficult. Ensemblebased lag-correlation analyses with the 1024-member ensemble showed very small sampling errors in the correlation patterns and showed that the moist air inflow in the lower troposphere associated with a low-pressure anomaly over the Baiu front was related to this heavy rainfall in Kyushu. [ABSTRACT FROM AUTHOR]

Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions. [ABSTRACT FROM AUTHOR]

Extended state observer (ESO) is featured with online estimating both the system's states and the total effect of external disturbance as well as nonlinear uncertain dynamics. The original ESO design, proposed for the cascade‐of‐integrator system without measurement noise, has been well studied with theoretical foundation and many successful applications. In the last years, multifarious modified ESOs have also been developed to handle many engineering systems captured by the models with general nonlinear structure, time‐delay, the noises with stochastic properties, and etc. This paper aims to comprehensively investigate the representative modified ESOs in recent years. Firstly, the ESO's design and tuning law are illustrated for general uncertain systems with multiple control inputs, multiple measured outputs and various uncertainties. The quantitative results regarding the estimation errors of ESO are also presented. Next, the extended state‐based Kalman‐typed filters to handle state estimation problem against both stochastic noises and uncertain dynamics are introduced. The consistency, stability, and asymptotic optimization of the proposed filters are rigorously shown. Furthermore, some novel designs of ESO to deal with the estimation problem of uncertain nonlinear systems with time‐delay and measurement biases are discussed. We believe this overview will be helpful for practitioners in applications of recent modified ESOs. [ABSTRACT FROM AUTHOR]

Model errors and sampling errors produce inaccurate sample covariances that limit the performance of ensemble Kalman filters. Linearly hybridizing the flow-dependent ensemble-based covariance with a time-invariant background covariance matrix gives a better estimate of the true error covariance. Previous studies have shown this, both in theory and in practice. How to choose the weight for each covariance remains an open question especially in the presence of model biases. This study assumes the weighting coefficient to be a random variable and then introduces a Bayesian scheme to estimate it using the available data. The scheme takes into account the discrepancy between the ensemble mean and the observations, the ensemble variance, the static background variance, and the uncertainties in the observations. The proposed algorithm is first derived for a spatially constant weight and then this assumption is relaxed by estimating a unique scalar weight for each state variable. Using twin experiments with the 40-variable Lorenz 96 system, it is shown that the proposed scheme is able to produce quality forecasts even in the presence of severe sampling errors. The adaptive algorithm allows the hybrid filter to switch between an EnKF and a simple EnOI depending on the statistics of the ensemble. In the presence of model errors, the adaptive scheme demonstrates additional improvements compared with standard enhancements alone, such as inflation and localization. Finally, the potential of the spatially varying variant to accommodate challenging sparse observation networks is demonstrated. The computational efficiency and storage of the proposed scheme, which remain an obstacle, are discussed. [ABSTRACT FROM AUTHOR]

The ensemble Kalman filter (EnKF) has been widely used in atmosphere, ocean, and land applications. The observing network has been significantly developed, and thus, observations with highly dense temporal resolutions have become available. To better extract information from dense temporal observations, one straightforward strategy is to increase the assimilation frequency. However, more frequent assimilation may exacerbate the model imbalance and result in degraded forecasts. To combat the imbalance caused by ensemble‐based data assimilation due to sampling error and covariance localization, three‐ and four‐dimensional incremental analysis update (IAU) were proposed, which gradually introduce the analysis increments into model rather than intermittently updating the state. The trade‐off between the assimilation frequency and imbalance is systematically explored here by using an idealized two‐layer model and the NOAA GFS. Results from the idealized two‐layer model show that increasing assimilation frequency can reduce errors for state variables that are not sensitive to imbalances. For state variable that carries the signal of the external gravity mode and is sensitive to imbalances, increasing assimilation frequency without (with) IAU reduces (increases) errors. Without IAU, more frequent updates result in smaller increments and less insertion noise, while the initialization of IAU cannot effectively mitigate the imbalances with increased assimilation frequency. Results with a low‐resolution version of the NOAA GFS demonstrate that increasing assimilation frequency from 6 to 2 h improves the errors and biases of forecasts verified with conventional and radiance observations, although gravity wave noise in the forecast is increased. Plain Language Summary: Data assimilation combines observations with prior information like model forecasts to produce the best estimate of the state for a dynamical system. For global prediction, a data assimilation interval of 6‐h has typically been used; but for high‐resolution regional models with dense spatial and temporal resolution observations such as radar and satellite data, shorter data assimilation intervals are often used. Given the significantly developed observing networks, observations with highly dense temporal resolutions and inhomogeneous spatial distributions have become available. Increasing the assimilation frequency may better extract information from dense temporal observations, but does not give the model enough time to adjust the updated state variables with potentially insertion shocks. This study systematically investigates the trade‐off between the data assimilation frequency and imbalance. Results reveal that increasing assimilation frequency can reduce errors for state variables, because more frequent updates can better fit the model to the observation and result in smaller increments/less imbalances to the model. When the incremental analysis update (IAU) is applied, increasing assimilation frequency reduces errors for state variables that are not sensitive to imbalances, but the opposite for state variables sensitive to imbalances, because the IAU with more frequent assimilation cannot effectively mitigate the imbalances. Key Points: Increasing assimilation frequency can reduce errors for state variables that are not sensitive to imbalancesFor variables sensitive to imbalances, increasing assimilation frequency without IAU results in less insertion noises and reduced errorsIncreasing assimilation frequency with IAU has lessened noise filtering and increases errors for state variables sensitive to imbalances [ABSTRACT FROM AUTHOR]

Localization is essential to effectively assimilate satellite radiances in ensemble Kalman filters. However, the vertical location and separation from a model grid point variable for a radiance observation are not well defined, which results in complexities when localizing the impact of radiance observations. An adaptive method is proposed to estimate an effective vertical localization independently for each assimilated channel of every satellite platform. It uses sample correlations between ensemble priors of observations and state variables from a cycling data assimilation to estimate the localization function that minimizes the sampling error. The estimated localization functions are approximated by three localization parameters: the localization width, maximum value, and vertical location of the radiance observations. Adaptively estimated localization parameters are used in assimilation experiments with the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model and the National Oceanic and Atmospheric Administration (NOAA) operational ensemble Kalman filter (EnKF). Results show that using the adaptive localization width and vertical location for radiance observations is more beneficial than also including the maximum localization value. The experiment using the adaptively estimated localization width and vertical location performs better than the default Gaspari and Cohn (GC) experiment, and produces similar errors to the optimal GC experiment. The adaptive localization parameters can be computed during the assimilation procedure, so the computational cost needed to tune the optimal GC localization width is saved. Plain Language Summary: Assimilation of satellite radiance observations is essential for numerical weather predictions, especially where conventional observations are limited. Satellite radiances effectively measure integrated quantities over an atmospheric column, but it is not straightforward to define the vertical location of such a nonlocal observation. This results in complexities for localizing the impact of radiance observations; however, localization is crucial to effectively assimilate satellite radiances. This study investigated an adaptive localization approach to estimate an effective vertical localization independently for each assimilated channel of every satellite platform. Three localization parameters, including the localization width, maximum value, and vertical location of the radiance observations, were examined. It is demonstrated that using the adaptive localization width and vertical location for radiance observations is more beneficial than also including the maximum localization value. The adaptive localization method performs similarly to the optimal Gaspri and Cohn (GC) function, but the adaptive localization has significant computational cost advantages because it does not require intensive tuning of the localization width like the GC localization function. Key Points: An adaptive method is proposed to estimate effective vertical localizations independently for each channel of every satellite platformUsing adaptive localization width and vertical location for radiances is more beneficial than including the maximum localization valueThe adaptive localization parameters outperform the default GC and produce similar results to the optimal GC but with less computations [ABSTRACT FROM AUTHOR]

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Multilevel ensemble-based data assimilation (DA) as an alternative to standard (single-level) ensemble-based DA for reservoir history matching problems is considered. Restricted computational resources currently limit the ensemble size to about 100 for field-scale cases, resulting in large sampling errors if no measures are taken to prevent it. With multilevel methods, the computational resources are spread over models with different accuracy and computational cost, enabling a substantially increased total ensemble size. Hence, reduced numerical accuracy is partially traded for increased statistical accuracy. A novel multilevel DA method, the multilevel hybrid ensemble Kalman filter (MLHEnKF) is proposed. Both the expected and the true efficiency of a previously published multilevel method, the multilevel ensemble Kalman filter (MLEnKF), and the MLHEnKF are assessed for a toy model and two reservoir models. A multilevel sequence of approximations is introduced for all models. This is achieved via spatial grid coarsening and simple upscaling for the reservoir models, and via a designed synthetic sequence for the toy model. For all models, the finest discretization level is assumed to correspond to the exact model. The results obtained show that, despite its good theoretical properties, MLEnKF does not perform well for the reservoir history matching problems considered. We also show that this is probably caused by the assumptions underlying its theoretical properties not being fulfilled for the multilevel reservoir models considered. The performance of MLHEnKF, which is designed to handle restricted computational resources well, is quite good. Furthermore, the toy model is utilized to set up a case where the assumptions underlying the theoretical properties of MLEnKF are fulfilled. On that case, MLEnKF performs very well and clearly better than MLHEnKF. [ABSTRACT FROM AUTHOR]

Accurate forecasting-aided state estimation plays a vital role in reliable and secure operation of power systems. However, most of existing methods are unable to deal with the uncertainties that might be caused by uncertain model parameters or uncertain noise statistics. Therefore, the performance of these methods may be inevitably degraded significantly. To address these issues, based on the robust control theory, in this paper, by incorporating the modified innovation based Sage-Husa estimator of noise statistics and the proposed estimation error covariance matrix adaptive technique, a novel adaptive $H_{\infty }$ extended Kalman filter (AHEKF) is developed to realize robust forecasting-aided state estimation for power system with model uncertainties. Extensive simulations carried out on several different test systems demonstrate the efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Sampling errors and model errors are major drawbacks from which ensemble Kalman filters suffer. Sampling errors arise because of the use of a limited ensemble size, while model errors are deficiencies in the dynamics and underlying parameterizations that may yield biases in the model's prediction. In this study, we propose a new time-adaptive posterior inflation algorithm in which the analyzed ensemble anomalies are locally inflated. The proposed inflation strategy is computationally efficient and is aimed at restoring enough spread in the analysis ensemble after assimilating the observations. The performance of this scheme is tested against the relaxation to prior spread (RTPS) and adaptive prior inflation. For this purpose, two model are used: the three-variable Lorenz 63 system and the Community Atmosphere Model (CAM). In CAM, global refractivity, temperature, and wind observations from several sources are incorporated to perform a set of assimilation experiments using the Data Assimilation Research Testbed (DART). The proposed scheme is shown to yield better quality forecasts than the RTPS. Assimilation results further suggest that when model errors are small, both prior and posterior inflation are able to mitigate sampling errors with a slight advantage to posterior inflation. When large model errors, such as wind and temperature biases, are present, prior inflation is shown to be more accurate than posterior inflation. Densely observed regions as in the Northern Hemisphere present numerous challenges to the posterior inflation algorithm. A compelling enhancement to the performance of the filter is achieved by combining both adaptive inflation schemes. [ABSTRACT FROM AUTHOR]

We previously performed local ensemble transform Kalman filter (LETKF) experiments with up to 10 240 ensemble members using an intermediate atmospheric general circulation model (AGCM). While the previous study focused on the impact of localization on the analysis accuracy, the present study focuses on the probability density functions (PDFs) represented by the 10 240-member ensemble. The 10 240-member ensemble can resolve the detailed structures of the PDFs and indicates that non-Gaussianity is caused in those PDFs by multimodality and outliers. The results show that the spatial patterns of the analysis errors are similar to those of non-Gaussianity. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions and storm track regions where highly nonlinear processes appear frequently. Therefore, we further investigate the life cycle of multimodal PDFs, and show that they are mainly generated by the on–off switch of convective parameterization in the tropical regions and by the instability associated with advection in the storm track regions. Sensitivity to the ensemble size suggests that approximately 1000 ensemble members are necessary in the intermediate AGCM-LETKF system to represent the detailed structures of non-Gaussian PDFs such as skewness and kurtosis; the higher-order non-Gaussian statistics are more vulnerable to the sampling errors due to a smaller ensemble size. [ABSTRACT FROM AUTHOR]

Ensemble‐based data assimilation systems typically use covariance localization to dampen spurious correlations associated with sampling error while increasing the rank of the covariance estimate. Variational methods use model‐space localization, in which localization is applied to ensemble estimates of covariances between model variables and is based on distances between those variables, while ensemble filters apply observation‐space localization to estimates of model‐observation covariances, based on distances between model variables and observations. It has been shown that for nonlocal observations, such as satellite radiances, model‐space localization can be superior. This paper demonstrates a new method for performing model‐space localization in serial ensemble filters using the linearized observation operators (or Jacobians). Results of radiance‐only assimilation in a global forecast system show the benefit of using model‐space localization relative to observation‐space localization. The serial ensemble square root filter with vertical model‐space localization gives results similar to those of the Ensemble Variational system (without outer loops or extra balance constraints) while increasing the runtime compared to the filter with observation‐space localization by a factor between 2 and 8, depending on how sparse the Jacobian matrices are. The results are also similar to another approach to model‐space localization in ensemble filters: ensemble Kalman filter with modulated ensembles. Key Points: A way to implement model‐space localization in a serial EnKF is presentedModel‐space localization outperforms observation‐space localization for radiance observations in the global atmospheric data assimilationImplementing model‐space localization in an EnKF allows to reach errors similar to those of EnVar with pure ensemble covariances [ABSTRACT FROM AUTHOR]

Ensemble transform Kalman filter (ETKF) is an extension of ensemble Kalman filter (EnKF), which avoids using "perturbed observations" to eliminate additional sampling errors. This paper demonstrates the capability of ETKF algorithm for sequentially correcting dynamically evolving fire perimeter positions at regular time intervals to enhance the prediction accuracy of wildfire spread. Forecast error covariance inflation scheme is adopted in the ETKF to address the underestimation problem of forecast error covariance of EnKF. Coupled to a widely-used fire spread simulator, FARSITE, the proposed approach is employed to a landscape with complex topography, where a fire barrier is also considered. The merits of ETKF algorithm for wildfire spread prediction are highlighted by simulation experiments using synthetically-generated observations. In order to quantitatively evaluate the prediction performance of ETKF, this paper has adopted a conservative index, Hausdorff distance, which is widely used in image processing area. This work is the first attempt of applying ETKF to wildfire spread simulation. The ETKF algorithm has been demonstrated to be more accurate than EnKF for a given ensemble size for wildfire spread simulation. The findings show that the ETKF-based data assimilation strategy is a promising tool for large-scale wildfire spread simulation. • Data assimilation of wildfires with fire perimeter positions in FARSITE using ETKF. • A wildfire barrier is considered in wildfire spread. • Hausdorff distance is applied to evaluate the prediction performance of the ETKF. • Comparison of the ETKF and EnKF algorithms for state estimation. • The ETKF algorithm is more accurate than EnKF given the same ensemble size. [ABSTRACT FROM AUTHOR]

We test an ensemble data assimilation system using the four‐dimensional Local Ensemble Transform Kalman Filter (4D‐LETKF) for a global numerical weather prediction (NWP) model with unstructured grids on the cubed‐sphere. It is challenging to selectively represent structures of dynamically growing errors in background states under system uncertainties such as sampling and model errors. We compute Ensemble Singular Vectors (ESVs) in an attempt to capture fast‐growing errors on the subspace spanned by ensemble perturbations, and use them as additive inflation to enlarge the covariance in the area where errors are flow‐dependently growing. The performance of the 4D‐LETKF system with ESVs is evaluated in real data assimilation, as well as Observing System Simulation Experiments (OSSEs). We find that leading ESVs help to capture fast‐growing errors effectively, especially when model errors are present, and that the use of ESVs as additive inflation significantly improves the performance of the 4D‐LETKF. Background error (contours, solid: positive, dash: negative) and analysis increment (shading) of zonal wind U (m/s) at the model level 45, around 850 hPa at 0600 UTC 20 February 2014 from the tests (a) ImPerfModel‐Random, and (b) ImPerfModel‐ESV. [ABSTRACT FROM AUTHOR]

This paper studies multiplicative inflation: the complementary scaling of the state covariance in the ensemble Kalman filter (EnKF). Firstly, error sources in the EnKF are catalogued and discussed in relation to inflation; nonlinearity is given particular attention as a source of sampling error. In response, the "finite‐size" refinement known as the EnKF‐N is re‐derived via a Gaussian scale mixture, again demonstrating how it yields adaptive inflation. Existing methods for adaptive inflation estimation are reviewed, and several insights are gained from a comparative analysis. One such adaptive inflation method is selected to complement the EnKF‐N to make a hybrid that is suitable for contexts where model error is present and imperfectly parametrized. Benchmarks are obtained from experiments with the two‐scale Lorenz model and its slow‐scale truncation. The proposed hybrid EnKF‐N method of adaptive inflation is found to yield systematic accuracy improvements in comparison with the existing methods, albeit to a moderate degree. This paper studies multiplicative inflation: the complementary scaling of the state covariance in the ensemble Kalman filter (EnKF). Firstly, error sources in the EnKF are catalogued and discussed in relation to inflation; nonlinearity is given particular attention as a source of sampling error. In response, the "finite‐size" refinement known as the EnKF‐N is re‐derived via a Gaussian scale mixture, again demonstrating how it yields adaptive inflation. An extension is proposed that hybridizes the EnKF‐N with an existing adaptive inflation scheme, making it suitable also in the presence of model error. [ABSTRACT FROM AUTHOR]

Purpose The successful use of the standard extended Kalman filter (EKF) is restricted by the requirement on the statistics information of the measurement noise. The covariance of the measurement noise may deviate from its nominal value in practical environment, and the filtering performance may decline because of the statistical uncertainty. Although the adaptive EKF (AEKF) is available for recursive covariance estimation, it is often less accurate than the EKF with accurate noise statistics.Design/methodology/approach Aiming at this problem, this paper develops a parallel adaptive EKF (PAEKF) by combining the EKF and the AEKF with an adaptive law, such that the final state estimate is dominated by the EKF when the prior noise covariance is accurate, while the AEKF is activated when the actual noise covariance deviates from its nominal value.Findings The PAEKF can reduce the sensitivity of the algorithm to the model uncertainty and ensure the estimation accuracy in the normal case. The simulation results demonstrate that the PAEKF has the advantage of both the AEKF and the EKF.Practical implications The presented algorithm is applicable for spacecraft relative attitude and position estimation.Originality/value The PAEKF is presented for a kind of nonlinear uncertain systems. Stability analysis is provided to show that the error of the estimator is bounded under certain assumptions. [ABSTRACT FROM AUTHOR]

This paper develops an efficient and parallel implementation of dynamically data-driven application systems inference using an ensemble Kalman filter based on shrinkage covariance matrix estimation. The proposed implementation works as follows: each model component is surrounded by a local box of radius size r and then, local assimilation steps are carried out in parallel at the different local boxes. Once local analyses are obtained, they are mapped back onto the global domain from which the global analysis state is obtained. Local background error correlations are estimated using the Rao–Blackwell Ledoit and Wolf estimator in order to mitigate the impact of spurious correlations whenever the number of local model components is larger than the ensemble size. The numerical atmospheric general circulation model (SPEEDY) is utilized for the numerical experiments with the T-63 resolution on the BlueRidge cluster at Virginia Tech. The number of processors ranges from 96 to 2048. The proposed implementation outperforms in terms of accuracy the well-known local ensemble transform Kalman filter (LETKF) for all the model variables. The computational time of the proposed implementation is similar to that of the parallel LETKF method (where no covariance estimation is performed) for the largest number of processors. [ABSTRACT FROM AUTHOR]

This paper is concerned with robust weighted state fusion estimation problem for a class of time-varying multisensor networked systems with mixed uncertainties including uncertain-variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, four weighted state fusion robust Kalman estimators (filter, predictor and smoother) are presented in a unified form that the robust filter and smoother are designed based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust local and fused steady-state Kalman estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method. Finally, a simulation example applied to uninterruptible power system (UPS) shows the correctness and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed filtering for discrete-time-invariant systems in sensor networks where each sensor's measuring system may not be observable, and each sensor can just obtain partial system parameters with unknown coefficients which are modeled by Gaussian white noises. A fully distributed robust Kalman filtering algorithm consisting of two parts is proposed. One is a consensus Kalman filter to estimate the system parameters. It is proved that the mean square estimation errors for the system parameters converge to zero if and only if, for any one system parameter, its accessible node subset is globally reachable. The other is a consensus robust Kalman filter to estimate the system state based on the system matrix estimations and covariances. It is proved that the mean square estimation error of each sensor is upper-bounded by the trace of its covariance. An explicit sufficient stability condition of the algorithm is further provided. A numerical simulation is given to illustrate the results. [ABSTRACT FROM AUTHOR]

We study in this work the mixed -filtering problem for Markov jump linear systems in a partial observation context. Rather than the Markov chain , we consider that only an estimation coming from a detector is available to the filter. We present a sufficient condition for the synthesis of a filter depending only on such that the estimation errors for the and filtering problems are bounded by given scalars. The robust mixed filtering considering that the transition and detection probabilities are uncertain, as well as the complete observation, cluster and mode-independent cases, are also studied. The results are given in terms of linear matrix inequalities and are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper presents a new method for the assessment of the process noise covariance matrix for three-phase dynamic state estimation in unbalanced active distribution networks which operate under normal conditions. The assessment is done in order to minimize the estimation error. The proposed assessment method, based on minimization of a particular cost function, enables the a priori assessment of covariance matrix by extracting information from previously observed measurements, without the need to simulate the true state of the system. The method was applied on two commonly used Kalman filter based estimation algorithms in nonlinear systems: Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). A comparative analysis was performed between two different cost functions based on average root mean square of innovations and maximum likelihood technique. Also, the importance of determining initial state vector and its error covariance matrix needed for the initialization of dynamic state estimation was examined, as well as the ability of UKF and EKF to handle measurement nonlinearities. The analysis was carried out and the proposed method was verified on modified IEEE 13- and 37-bus distribution test systems. [ABSTRACT FROM AUTHOR]

In this work, we consider the optimal sensory data scheduling of multiple process. A remote estimator is deployed to monitor S independent linear time-invariant processes. Each process is measured by a sensor, which is capable of computing a local estimate and sending its local state estimate wrapped up in packets to the remote estimator. The lengths of the packets are different due to different dynamics of each process. Consequently, it takes different time durations for the sensors to send the local estimates. In addition, only a portion of all the sensors are allowed to transmit at each time due to bandwidth limitation. We are interested in minimizing the sum of the average estimation error covariance of each process at the remote estimator under such packet transmission and bandwidth constraints. We formulate the problem as an average cost Markov decision process (MDP) over an infinite horizon. We first study the special case when S = 1 and find that the optimal scheduling policy always aims to complete transmitting the current estimate. We also derive a sufficient condition for boundedness of the average remote estimation error. We then study the case for general S . We establish the existence of a deterministic and stationary policy for the optimal scheduling problem. We find that the optimal policy has a consistent property among the sensors and a switching type structure. A stochastic algorithm is designed to utilize the structure of the policy to reduce computation complexity. Numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, robust Kalman filtering problem is investigated for a class of two-dimensional (2-D) shift-varying uncertain systems with both additive and multiplicative noises over a finite horizon. The measurement outputs suffer from randomly occurring degradations obeying certain probabilistic distributions, and the norm-bounded parameter uncertainties enter into both the state and the output matrices. The main aim of this paper is to design a robust Kalman filter such that, in the presence of parameter uncertainties and degraded measurements, certain upper bound of the generalized estimation error variance is locally minimized in the trace sense at each shift step. Recursion of the generalized estimation error variances for the addressed 2-D system is first established via the introduction of a 2-D identity quadratic filter, based on which an upper bound of the generalized estimation error variance is obtained. Subsequently, such an upper bound is minimized in the trace sense by properly designing the filter parameters. The design scheme of the robust Kalman filter is presented in terms of two Riccati-like difference equations which can be recursively computed for programmed applications. Finally, a numerical example is provided to demonstrate effectiveness of the proposed filter design method. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed federated Tobit Kalman filter fusion problem for a class of discrete-time systems subject to measurement censoring and packet delays. The censored measurement is characterized by the Tobit measurement model and the packet delay obeys the Poisson distribution. At the input terminal of each local estimator, a censoring detection device and a buffer with finite length are exploited to tackle the censored/delayed measurements. The filtering fusion is carried out in two steps: in the first step, every sensor in the network collects and sends its measurements to the corresponding local estimator via an unreliable network with probabilistic packet delays and, in the second step, the estimates from local estimators are further collected by the fusion center to form a fused estimate. The local estimator runs a modified Tobit Kalman filtering algorithm, which is designed based on the modified Tobit regression model, while the fusion center performs a distributed federated modified Tobit Kalman filtering algorithm, which is devised on the basis of the federated Kalman fusion rule. Given the buffer length, the prescribed bound on the estimation error covariance and the probability distribution of the packet delay, the stability performance of the proposed filtering fusion algorithm is evaluated via a probabilistic approach. Simulation results are provided to show the feasibility of the proposed filter. [ABSTRACT FROM AUTHOR]

In this paper, a fractional-order unscented Kalman filter (FUKF) is introduced at first. Then, its convergence is analyzed based on Lyapunov functions for nonlinear fractional-order systems. Specific conditions are obtained that guarantee the boundedness of the FUKF estimation error. In addition, an adaptive noise covariance is suggested to overcome huge estimation errors. Since the adaptation law plays a crucial role in the performance of the proposed method, a fuzzy logic based method is also presented to improve the adaptive noise covariance. Therefore, a modified FUKF is proposed to increase the convergence and the accuracy of the estimation. Finally, the proposed algorithm is implemented to estimate the states of a two electric pendulum system and its performance is analyzed. Simulation results show that a huge estimation error leads to the FUKF divergence; however, the modified fractional-order unscented Kalman filter with fuzzy performs an accurate state estimation. [ABSTRACT FROM AUTHOR]

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that the gain parameter optimization in a networked Kalman filter requires a centralized framework. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, an upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor’s measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios. [ABSTRACT FROM AUTHOR]

The convergence of nonlinear Kalman filters has conventionally been analyzed in terms of the estimation error. In this paper, we present a new method for investigating the convergence performance of a class of nonlinear Kalman filters based on deterministic sampling. The systems considered here are described by nonlinear state equations with linear measurements. For this type of systems, our proposed convergence analysis is performed using “innovation”, which is defined as the error between the measurement and its prediction. Specifically, we obtain a linear relationship between the innovation and the estimation error, and derive a set of sufficient conditions that ensures the convergence of nonlinear Kalman filters. Compared with the conventional convergence analysis method based on the estimation error, the proposed innovation-based method can obtain sufficient conditions for convergence more directly and readily. Simulation results show that the convergence of innovation generates the convergence of nonlinear Kalman filters. [ABSTRACT FROM AUTHOR]