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The intercomparison between different atmospheric monitoring systems is key for instrument calibration and validation. Common cases involve satellites, radiosonde and atmospheric model outputs. Since instruments and/or measures are not perfectly collocated, miss-collocation uncertainty must be considered in related intercomparison uncertainty budgets. This paper is motivated by the comparison of GNSS-RO, the Global Navigation Satellite System Radio Occultation, with ERA5, the version 5 Reanalysis of the European Centre for Medium-range Weather Forecasts. We consider temperature interpolation observed at GNSS-RO pressure levels to the ERA5 levels. We assess the interpolation uncertainty using as 'truth' high-resolution reference data obtained by GRUAN, the Reference Upper-Air Network of the Global Climate Observing System. In this paper, we propose a mathematical representation of the interpolation problem based on the well-known State-space model and the related Kalman filter and smoother. We show that it performs the same (sometimes better) than linear interpolation and, in addition, provides an estimate of the interpolation uncertainty. Moreover, with both techniques, the interpolation error is not Gaussian distributed, and a scaled Student's t distribution with about 4.3 degrees of freedom is an appropriate approximation for various altitudes, latitudes, seasons and times of day. With our data, interpolation uncertainty results larger at the equator, the Mean Absolute Error being M A E ≅ 0.32 K, and smaller at a high latitude, M A E ≅ 0.21 K at −80° latitude. At lower altitudes, it is close to the measurement uncertainty, with M A E < 0.2 K below the tropopause. Around 300 hPa, it starts increasing and reaches about 0.8 K above 100 hPa, except at the equator, where we observed MAE about 1 K. [ABSTRACT FROM AUTHOR]

In this paper, the parameter estimation of bilinear state-space systems with missing outputs is studied. The bilinear model is transformed into a linear time-varying state-space model, and Kalman smoother with a time-varying gain is adopted to estimate missing outputs and unmeasurable states. Under the expectation-maximization (EM) algorithm scheme, an iterative estimation algorithm based on Kalman smoother is derived, in which the unknown parameters, missing outputs, and unmeasurable states can be estimated simultaneously. Two simulation examples, including a numerical example and a three-tank system experiment, are adopted to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper models an extensible catheter with an embedded magnet at its distal tip subject to an external magnetic field. We implement a control method coined observed control to perform model-based predictive control of the catheter using a Kalman smoother framework. Using this same smoother framework, we also solve for catheter shape and orientation given magnetic and insertion control using Cosserat rod theory and implement a disturbance observer for closed-loop control. We demonstrate observed control experimentally by traversing a 3D cube trajectory with the catheter tip. The catheter achieved positional accuracy of 3.3 mm average error in open-loop, while closed-loop control improved the accuracy to 0.33 mm. [ABSTRACT FROM AUTHOR]

Mathematical models that accurately simulate the physiological systems of the human body serve as cornerstone instruments for advancing medical science and facilitating innovative clinical interventions. One application is the modeling of the subglottal tract and neck skin properties for its use in the ambulatory assessment of vocal function, by enabling non-invasive monitoring of glottal airflow via a neck surface accelerometer. For the technique to be effective, the development of an accurate building block model for the subglottal tract is required. Such a model is expected to utilize glottal volume velocity as the input parameter and yield neck skin acceleration as the corresponding output. In contrast to preceding efforts that employed frequency-domain methods, the present paper leverages system identification techniques to derive a parsimonious continuous-time model of the subglottal tract using time-domain data samples. Additionally, an examination of the model order is conducted through the application of various information criteria. Once a low-order model is successfully fitted, an inverse filter based on a Kalman smoother is utilized for the estimation of glottal volume velocity and related aerodynamic metrics, thereby constituting the most efficient execution of these estimates thus far. Anticipated reductions in computational time and complexity due to the lower order of the subglottal model hold particular relevance for real-time monitoring. Simultaneously, the methodology proves efficient in generating a spectrum of aerodynamic features essential for ambulatory vocal function assessment. [ABSTRACT FROM AUTHOR]

The intercomparison between different atmospheric monitoring systems is key for instrument calibration and validation. Common cases involve satellites, radiosonde and atmospheric model outputs. Since instruments and/or measures are not perfectly collocated, miss-collocation uncertainty must be considered in related intercomparison uncertainty budgets. This paper is motivated by the comparison of GNSS-RO, the Global Navigation Satellite System Radio Occultation, with ERA5, the version 5 Reanalysis of the European Centre for Medium-range Weather Forecasts. We consider temperature interpolation observed at GNSS-RO pressure levels to the ERA5 levels. We assess the interpolation uncertainty using as ‘truth’ high-resolution reference data obtained by GRUAN, the Reference Upper-Air Network of the Global Climate Observing System. In this paper, we propose a mathematical representation of the interpolation problem based on the well-known State-space model and the related Kalman filter and smoother. We show that it performs the same (sometimes better) than linear interpolation and, in addition, provides an estimate of the interpolation uncertainty. Moreover, with both techniques, the interpolation error is not Gaussian distributed, and a scaled Student’s t distribution with about 4.3 degrees of freedom is an appropriate approximation for various altitudes, latitudes, seasons and times of day. With our data, interpolation uncertainty results larger at the equator, the Mean Absolute Error being MAE≅0.32 K, and smaller at a high latitude, MAE≅0.21 K at −80° latitude. At lower altitudes, it is close to the measurement uncertainty, with MAE<0.2 K below the tropopause. Around 300 hPa, it starts increasing and reaches about 0.8 K above 100 hPa, except at the equator, where we observed MAE about 1 K.

We propose a state estimation approach to time-varying magnetic resonance imaging utilizing a priori information. In state estimation, the time-dependent image reconstruction problem is modeled by separate state evolution and observation models. In our method, we compute the state estimates by using the Kalman filter and steady-state Kalman smoother utilizing a data-driven estimate for the process noise covariance matrix, constructed from conventional sliding window estimates. The proposed approach is evaluated using radially golden angle sampled simulated and experimental small animal data from a rat brain. In our method, the state estimates are updated after each new spoke of radial data becomes available, leading to faster frame rate compared with the conventional approaches. The results are compared with the estimates with the sliding window method. The results show that the state estimation approach with the data-driven process noise covariance can improve both spatial and temporal resolution. [ABSTRACT FROM AUTHOR]

In predictive geophysical model systems, uncertain initial values and model parameters jointly influence the temporal evolution of the system. This renders initial-value-only optimization by traditional data assimilation methods as insufficient. However, blindly extending the optimization parameter set jeopardizes the validity of the resulting analysis because of the increase of the ill-posedness of the inversion task. Hence, it becomes important to assess the potential observability of measurement networks for model state and parameters in atmospheric modelings in advance of the optimization. In this paper, we novelly establish the dynamic model of emission rates and extend the transport-diffusion model extended by emission rates. Considering the Kalman smoother as underlying assimilation technique, we develop a quantitative assessment method to evaluate the potential observability and the sensitivity of observation networks to initial values and emission rates jointly. This benefits us to determine the optimizable parameters to observation configurations before the data assimilation procedure and make the optimization more efficiently. For high-dimensional models in practical applications, we derive an ensemble based version of the approach and give several elementary experiments for illustrations. [ABSTRACT FROM AUTHOR]

We study the problem of semi-blind channel estimation and symbol detection in the uplink of multi-cell massive MIMO (multi-input multi-output) systems with spatially correlated time-varying channels. An algorithm based on expectation propagation (EP) is developed to iteratively approximate the joint a posteriori distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. This distribution is then used for direct estimation of the channel matrix and detection of data symbols. A modified version of the popular Kalman filtering algorithm referred to as KF-M is also proposed which emerges from our EP derivations. Performance of the Kalman smoothing algorithm followed by KF-M, referred here as KS-M, is also examined. Simulation results demonstrate that channel estimation error and the symbol error rate (SER) of the semi-blind KF-M, KS-M, and EP-based algorithms improve with the increase in the number of base station antennas and the length of the data symbols in the transmitted frame. In particular, by increasing the number of transmitted data symbols in the frame, the proposed semi-blind algorithms can mitigate the effects of pilot contamination as well as time-varying channels in a multi-cell massive MIMO system with pilot-overhead of around 5%.

We present a simple smoother designed for smooth data adjustments in sequentially generated reanalysis products by utilizing knowledge of future assimilation increments. A decay time parameter is applied to the smoother increments to account for memory decay timescales in the ocean. The result is different from simply time smoothing the reanalysis itself as only the increments are smoothed so the reanalysis product can retain high frequency variability that is being internally generated by the model and the atmospheric forcing. The smoother is applied first to the Lorenz 1963 model and then to the daily Met Office GloSea5 Global ¼° ocean reanalysis during 2016. Results show significant improvement over the original reanalysis in the 3D temperature and salinity state and variability, as well as in the sea surface height (SSH) and ocean currents. Comparisons are made directly against temperature, salinity and SSH observations, as well as independent 15 m drifter velocities. The impact on the time variability of conservative quantities, particularly ocean heat and salt content, as well as kinetic energy and the Atlantic Meridional Overturning Circulation (AMOC), is also demonstrated. Plain Language Summary: The ocean observing system is sparse and ocean circulation is slow relative to the atmosphere, giving the system a longer memory of state properties. Therefore an ocean reanalysis could seek to use more "future data" to help produce the best historical ocean state reconstruction for a given day. Conventional sequential assimilation approaches used operationally make no use of "future" data outside the window of current data analyzed for forecasting. Here we introduce a new approach for application to large global ocean reanalysis systems that have only been run in "forward mode" (using past data), using the history of stored data increments to produce a more physically plausible time‐evolving ocean state with smoother temporal adjustments toward the available observations. Key Points: A novel temporal smoother algorithm is designed for improving ocean reanalysis products by utilizing the stored history of assimilation incrementsHigh frequency variability internally generated by the model and the atmospheric forcing is retained in the outputThe smoother significantly improves the reanalysis temperature, salinity, velocity, and sea surface height fields [ABSTRACT FROM AUTHOR]

This paper models an extensible catheter with an embedded magnet at its distal tip subject to an external magnetic field. We implement a control method coined observed control to perform model-based predictive control of the catheter using a Kalman smoother framework. Using this same smoother framework, we also solve for catheter shape and orientation given magnetic and insertion control using Cosserat rod theory and implement a disturbance observer for closed-loop control. We demonstrate observed control experimentally by traversing a 3D cube trajectory with the catheter tip. The catheter achieved positional accuracy of 3.3 mm average error in open-loop, while closed-loop control improved the accuracy to 0.33 mm.

Air-pollution modelling at the local scale requires accurate meteorological inputs such as from the velocity field. These meteorological fields are generally simulated with microscale models (here Code_Saturne), which are forced with boundary conditions provided by larger scale models or observations. Local atmospheric simulations are very sensitive to the boundary conditions, whose accurate estimation is difficult but crucial. When observations of the wind speed and turbulence or pollutant concentration are available inside the domain, they provide supplementary information via data assimilation, to enhance the simulation accuracy by modifying the boundary conditions. Among the existing data assimilation methods, the iterative ensemble Kalman smoother (IEnKS) is adapted to urban-scale simulations. This method has already been found to increase the accuracy of wind-resource assessment. Here we assess the ability of the IEnKS method to improve scalar-dispersion modelling—an important component of air-quality modelling—by assimilating perturbed measurements inside the urban canopy. To test the data assimilation method in urban conditions, we use the observations provided by the Mock Urban Setting Test field campaign and consider cases with neutral and stable conditions, and the boundary conditions consisting of the horizontal velocity components and turbulence. We prove the capacity of the IEnKS method to assimilate observations of velocity as well as pollutant concentration. In both cases, the accuracy of pollutant concentration estimates is enhanced by 40–60%. We also show that assimilating both types of observations allows further improvements of turbulence predictions by the model. [ABSTRACT FROM AUTHOR]

A slide window variational adaptive Kalman filter is presented in this brief based on adaptive learning of inaccurate state and measurement noise covariance matrices, which is composed of the forward Kalman filtering, the backward Kalman smoothing, and the online estimates of noise covariance matrices. By imposing an approximation on the smoothing posterior distribution of slide window state vectors, the posterior distributions of noise covariance matrices can be analytically updated as inverse Wishart distributions by exploiting the variational Bayesian method, which avoids the fixed-point iterations and achieves good computational efficiency. Simulation comparisons demonstrate that the proposed method has better filtering accuracy and consistency than the existing cutting-edge method. [ABSTRACT FROM AUTHOR]

Abstract The classical Kalman smoother recursively estimates states over a finite time window using all observations in the window. In this paper, we assume that the parameters characterizing the second-order statistics of process and observation noise are unknown and propose an optimal Bayesian Kalman smoother (OBKS) to obtain smoothed estimates that are optimal relative to the posterior distribution of the unknown noise parameters. The method uses a Bayesian innovation process and a posterior-based Bayesian orthogonality principle. The optimal Bayesian Kalman smoother possesses the same forward-backward structure as that of the ordinary Kalman smoother with the ordinary noise statistics replaced by their effective counterparts. In the first step, the posterior effective noise statistics are computed. Then, using the obtained effective noise statistics, the optimal Bayesian Kalman filter is run in the forward direction over the window of observations. The Bayesian smoothed estimates are obtained in the backward step. We validate the performance of the proposed robust smoother in the target tracking and gene regulatory network inference problems.

With growing connection of distributed energy resources, availability of demand side response technologies, deployment of smart meters, the distribution system needs advanced network automation for running the system efficiently. State estimation is the core driver of network automation. While the output from SMs will make the state estimation more accurate, advanced metering infrastructures come with several challenges such as noisy, erroneous measurement including lost or missed measurements, exposure to cyber attack and so on. This study proposes a three-phase unbalanced distribution system state estimation which is robust against noisy distribution system measurements, bad data attacks and missing or delayed measurements. This method considers measurement from hybrid sources such as SCADA, micro-phasor measurement units (${\mu}$μ PMUs) and SMs. Kalman smoother is used to fill the missing measurements and expectation-maximisation based forecasting is used to interpolate the hybrid measurements to a common timestamp and compensate for the delay in SM measurements. Extensive numerical comparisons are made on IEEE 13, 37 and 123 bus systems to test the robustness of the proposed DSSE against delayed SM measurements and bad or noisy data. An IEEE 24 bus system is modelled and real-time measurement devices are interfaced to it in Hypersim. The data from the hybrid measurement devices of IIT Kanpur smart grid is also used to test the robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Objective: The objective of this paper is to obtain accurate estimation of breathing rate (BR), using only the electrocardiogram (ECG) or the photoplethysmogram (PPG) signals, to avoid wearing cumbersome and uncomfortable sensors for direct measurements. Methods: Several respiration waveforms are derived from ECG or PPG signals based on amplitude, frequency, and baseline wander modulations. It is, however, difficult to determine their optimal combination for BR estimation due to the noise and patient specificity. We first propose to quantify the quality of modulation waveforms using respiratory quality indices (RQIs). We then present two methods: the first automatically selects the modulation signal with highest RQI for BR estimation, and the second tracks the respiration signal using the Kalman smoother to fuse modulation signals with highest RQI. Results: These two methods are evaluated on two independent datasets, one benchmark database (DB) with immobilized patients recordings and the second with those performing daily activities. Our results outperform existing methods in the literature in both the cases. Conclusion: Experimental results show that the RQIs coupled with a fusion algorithm increases the accuracy for BR estimations in dealing with derived modulation signals. Significance: This work describes a robust Kalman Smoother method applicable in multiple clinical contexts to improve breathing rate estimation from data fusion. [ABSTRACT FROM AUTHOR]

This article proposes a development of detecting patches of additive outliers in autoregressive time series models. The procedure improves the existing detection methods via Gibbs sampling. We combine the Bayesian method and the Kalman smoother to present some candidate models of outlier patches and the best model with the minimum Bayesian information criterion (BIC) is selected among them. We propose that this combined Bayesian and Kalman method (CBK) can reduce the masking and swamping effects about detecting patches of additive outliers. The correctness of the method is illustrated by simulated data and then by analyzing a real set of observations. [ABSTRACT FROM AUTHOR]

Autonomous vehicles enable the development of smart warehouses and smart factories with an increased visibility, flexibility and efficiency. Thus, effective and affordable localisation methods for indoor vehicles are attracting interest to implement real-time applications. This paper presents an Extended Kalman Smoother design to both localise a mobile agent and reconstruct its entire trajectory through a sensor-fusion employing the UHF-RFID passive technology. Extensive simulations are carried out by considering the smoother optimal-window length and the effect of missing measurements from reference tags. Monte Carlo simulations are conducted for different vehicle trajectories and for different linear and angular velocities to evaluate the method accuracy. Then, an experimental analysis with a unicycle wheeled robot is performed in real indoor scenario, showing a position and orientation root mean square errors of 15 cm, and 0.2 rad, respectively.

The smooth variable structure filter (SVSF) is a new-type filter based on the sliding-mode concepts and has good stability and robustness in overcoming the modeling uncertainties and errors. However, SVSF is insufficient to suppress Gaussian noise. A novel smooth variable structure smoother (SVSS) based on SVSF is presented here, which mainly focuses on this drawback and improves the SVSF estimation accuracy of the system. The estimation of the linear Gaussian system state based on SVSS is divided into two steps: Firstly, the SVSF state estimate and covariance are computed during the forward pass in time. Then, the smoothed state estimate is computed during the backward pass by using the innovation of the measured values and covariance estimate matrix. According to the simulation results with respect to the maneuvering target tracking, SVSS has a better performance compared with another smoother based on SVSF and the Kalman smoother in different tracking scenarios. Therefore, the SVSS proposed in this paper could be widely applied in the field of state estimation in dynamic system.

The phase-reset model of oscillatory EEG activity has received a lot of attention in the last decades for decoding different cognitive processes. Based on this model, the ERPs are assumed to be generated as a result of phase reorganization in ongoing EEG. Alignment of the phase of neuronal activities can be observed within or between different assemblies of neurons across the brain. Phase synchronization has been used to explore and understand perception, attentional binding and considering it in the domain of neuronal correlates of consciousness. The importance of the topic and its vast exploration in different domains of the neuroscience presses the need for appropriate tools and methods for measuring the level of phase synchronization of neuronal activities. Measuring the level of instantaneous phase (IP) synchronization has been used extensively in numerous studies of ERPs as well as oscillatory activity for a better understanding of the underlying cognitive binding with regard to different set of stimulations such as auditory and visual. However, the reliability of results can be challenged as a result of noise artifact in IP. Phase distortion due to environmental noise artifacts as well as different pre-processing steps on signals can lead to generation of artificial phase jumps. One of such effects presented recently is the effect of low envelope on the IP of signal. It has been shown that as the instantaneous envelope of the analytic signal approaches zero, the variations in the phase increase, effectively leading to abrupt transitions in the phase. These abrupt transitions can distort the phase synchronization results as they are not related to any neurophysiological effect. These transitions are called spurious phase variation. In this study, we present a model to remove generated artificial phase variations due to the effect of low envelope. The proposed method is based on a simplified form of a Kalman smoother, that is able to model the IP behavior in narrow-bandpassed oscillatory signals. In this work we first explain the details of the proposed Kalman smoother for modeling the dynamics of the phase variations in narrow-bandpassed signals and then evaluate it on a set of synthetic signals. Finally, we apply the model on ongoing-EEG signals to assess the removal of spurious phase variations.

The phase-reset model of oscillatory EEG activity has received a lot of attention in the last decades for decoding different cognitive processes. Based on this model, the ERPs are assumed to be generated as a result of phase reorganization in ongoing EEG. Alignment of the phase of neuronal activities can be observed within or between different assemblies of neurons across the brain. Phase synchronization has been used to explore and understand perception, attentional binding and considering it in the domain of neuronal correlates of consciousness. The importance of the topic and its vast exploration in different domains of the neuroscience presses the need for appropriate tools and methods for measuring the level of phase synchronization of neuronal activities. Measuring the level of instantaneous phase (IP) synchronization has been used extensively in numerous studies of ERPs as well as oscillatory activity for a better understanding of the underlying cognitive binding with regard to different set of stimulations such as auditory and visual. However, the reliability of results can be challenged as a result of noise artifact in IP. Phase distortion due to environmental noise artifacts as well as different pre-processing steps on signals can lead to generation of artificial phase jumps. One of such effects presented recently is the effect of low envelope on the IP of signal. It has been shown that as the instantaneous envelope of the analytic signal approaches zero, the variations in the phase increase, effectively leading to abrupt transitions in the phase. These abrupt transitions can distort the phase synchronization results as they are not related to any neurophysiological effect. These transitions are called spurious phase variation. In this study, we present a model to remove generated artificial phase variations due to the effect of low envelope. The proposed method is based on a simplified form of a Kalman smoother, that is able to model the IP behavior in narrow-bandpassed oscillatory signals. In this work we first explain the details of the proposed Kalman smoother for modeling the dynamics of the phase variations in narrow-bandpassed signals and then evaluate it on a set of synthetic signals. Finally, we apply the model on ongoing-EEG signals to assess the removal of spurious phase variations. [ABSTRACT FROM AUTHOR]

This paper represents an integrated prognostics method dedicated to the wind turbine high-speed shaft bearing prognosis, which integrates physical degradation models and data driven approaches. In bearing failure prognostics, the excessive shaft vibration eventually leads to the system failure. In this case (crack growth prognostics), the measured data (crack size) is the same as a model prediction from Paris’s law. Indeed, we introduce an integrated prognostic approach based on usage model through Paris’s law and the use of a Kalman smoother to estimate the remaining useful life offering a solution to the inherent phase delay cancellation from Kalman filtering, providing a more accurate and smoother estimate with confidence bounds. The proposed method is validated on a real high-speed shaft bearing wind turbine generator. The used database contains one raw acquisition per day over 50 days of measurement at a high sample rate, 6 s each. The results show that the Kalman smoother is an effective way to improve trending and remaining useful life estimation. [ABSTRACT FROM AUTHOR]

We proposed a lower extremity exoskeleton for power amplification that perceives intended human motion via humanexoskeleton interaction signals measured by biomedical or mechanical sensors, and estimates human gait trajectories to implement corresponding actions quickly and accurately. In this study, torque sensors mounted on the exoskeleton links are proposed for obtaining physical human-robot interaction (pHRI) torque information directly. A Kalman smoother is adopted for eliminating noise and smoothing the signal data. Simultaneously, the mapping from the pHRI torque to the human gait trajectory is defined. The mapping is derived from the real-time state of the robotic exoskeleton during movement. The walking phase is identified by the threshold approach using ground reaction force. Based on phase identification, the human gait can be estimated by applying the proposed algorithm, and then the gait is regarded as the reference input for the controller. A proportional-integral-derivative control strategy is constructed to drive the robotic exoskeleton to follow the human gait trajectory. Experiments were performed on a human subject who walked on the floor at a natural speed wearing the robotic exoskeleton. Experimental results show the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

The parameter estimation for a class of single-input single-output (SISO) Hammerstein state space systems is considered in this paper. The nonlinear block in the discussed system is represented by a polynomial in the input signal with unknown coefficients. By applying the over-parameterization method, the SISO Hammerstein state space model is transformed to a multiple-input single-output linear state space model. The unknown system states and parameters are estimated interactively. The Kalman smoother is used to calculate the state estimates. Under the principle of the expectation maximization, an identification algorithm is derived to realize the joint estimation for the unknown model parameters and states. Although the over-parameterization method increases the number of redundant parameters, it simplifies the identification problem of the input nonlinear state space model in this paper. A numerical simulation example and an experiment carried out on the multitank system are provided to demonstrate that the derived identification method is effective. [ABSTRACT FROM AUTHOR]

High-frequency global navigation satellite system (GNSS) is one of the most effective means for structural health monitoring. At present, most of the GNSS-based structural health monitoring research focuses on the positioning method, however, the unmodeled error caused by the complex monitoring environment and the receiver are always ignored by such technology. Most of the displacement extraction algorithms based on GNSS kinematic positioning are based on the Kalman filter and its variants, and the research on the effective determination of the process noise matrix and the measurement noise matrix is still limited. This paper aims to explore a displacement extraction method with automatic parameter tuning for structural health monitoring. An auto-tuning Kalman smoother has been introduced for extracting vibration displacement from GNSS kinematic positioning. Specifically, we divide the GNSS kinematic positioning results into a training set and a validation set, then use non-convex optimization to obtain the hyperparameters of the Kalman smoother. Finally, we extract the displacement from Kalman smoother with the tuned hyperparameters. Simulation and field experiments were carried out to verify the proposed method. The results show the feasibility and effectiveness of the method for vibration displacement extraction. For real-time kinematic positioning, the displacement extraction accuracy is improved by 9.58% compared to the traditional Kalman smoother; for precise point positioning, the displacement extraction accuracy is improved by 15.36%. The influence of the proportion of training set on the proposed method is discussed, and suggestion for the training set proportion is given. [ABSTRACT FROM AUTHOR]

• A Kalman filter framework for finding the optimal response of digital IIR filters is proposed. • The presented theory shows that we can observe IIR filters as Wiener filters for optimal smoothing. • As an example, the output response of zero-phase digital Butterworth filter is computed using Kalman smoother. Recently, a unified framework was proposed for forward-backward filtering and penalized least-squares optimization. It was shown that forward-backward filtering can be presented as instances of penalized least-squares optimization. In other words, the output of a zero-phase digital infinite-impulse response (IIR) filter can be computed by solving a constrained optimization problem, in which the weight controlling the constraint is directly related to cutoff frequencies with closed-form equations. It was also shown that a zero-phase digital IIR filter can be formed as an optimal smoothing Wiener filter for a random process obtained from an autoregressive (AR) or AR-moving average (ARMA) model driven by input (innovation) noise in presence of an observation noise. In this paper, the problem of zero-phase digital IIR filtering is re-examined using Kalman filter/smoother. The paper shows that every zero-phase digital IIR filter can be viewed as a special case of an optimal smoothing Wiener filter. Based on the fact that the formulations of the optimum filter by Wiener and Kalman are equivalent in steady state, we present a Kalman filter/smoother framework to the design and implementation of digital IIR filters. As an example, the zero-phase digital Butterworth filter is designed using Kalman smoother and compared with the traditional design (forward filtering and backward smoothing) method. [ABSTRACT FROM AUTHOR]

We introduce fast implementations for the likelihood functions, telemetry error filters, probabilistic trajectory and velocity reconstructions, and movement-path simulations for a large class of continuous-time movement models. This class of models includes all of the basic continuous-time models that have been applied to animal movement. A diverse array of movement behaviors can be modeled from within this framework, including range residence, persistence of motion, migration, range shifting, and territorial patrol. The fast algorithms presented here, based upon the Kálmán filter, are critical for applying movement analyses to the evergrowing number of modern datasets that feature thousands or more observed animal locations, and they are key to the continuous-time movement modeling ( ctmm ) R package. [ABSTRACT FROM AUTHOR]

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A new stratospheric ensemble Kalman smoother (EnKS) system is introduced, and the potential of assimilating posterior stratospheric observations to better constrain the whole model state at analysis time is investigated. A set of idealised perfect-model Observation System Simulation Experiments (OSSE) assimilating synthetic limb-sounding temperature or ozone retrievals are performed with a chemistry–climate model. The impact during the analysis step is characterised in terms of the root mean square error reduction between the forecast state and the analysis state. The performances of (1) a fixed-lag EnKS assimilating observations spread over 48 hours and (2) an ensemble Kalman Filter (EnKF) assimilating a denser network of observations are compared with a reference EnKF. The ozone assimilation with EnKS shows a significant additional reduction of analysis error of the order of 10% for dynamical and chemical variables in the extratropical upper troposphere lower stratosphere (UTLS) and Polar Vortex regions when compared to the reference EnKF. This reduction has similar magnitude to the one achieved by the denser-network EnKF assimilation. Similarly, the temperature assimilation with EnKS significantly decreases the error in the UTLS for the wind variables like the denser-network EnKF assimilation. However, the temperature assimilation with EnKS has little or no significant impact on the temperature and ozone analyses, whereas the denser-network EnKF shows improvement with respect to the reference EnKF. The different analysis impacts from the assimilation of current and posterior ozone observations indicate the capacity of time-lagged background-error covariances to represent temporal interactions up to 48 hours between variables during the ensemble data assimilation analysis step, and the possibility to use posterior observations whenever additional current observations are unavailable. The possible application of the EnKS for reanalyses is highlighted.