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This paper addresses the problem of simultaneously estimating the states, the state disturbances and the output disturbances of a linear time variant system. The objective is to develop a simple but optimal filter in the unbiased minimum-variance sense without depending extra complex system decomposition transformation. The derived filter bases on the assumption that no prior knowledge about the dynamical evolution of these disturbances is available. [ABSTRACT FROM AUTHOR]

Weather forecasts are essential for district heating (DH) utility operations as they prepare the utility for future consumption, thus ensuring optimal operation by supplying sufficient heat while keeping costs low. Weather forecasts are usually converted into heat demand forecasts, which are used for production planning and control of the temperatures in the network. Hence, increasing the accuracy of weather forecasts will lead to improvements in the system's operational performance. However, numerical weather predictions (NWPs) are computed over the earth as grid values, and NWPs are designed for rural areas, not urban areas. Therefore, we propose to localise the weather forecasts to the urban environment by calibrating them using Model Output Statistics. We show that localising weather forecasts (removing the bias) leads to enhanced accuracy in the heat demand forecasts. In our case study, localised weather forecasts lead to an error reduction between 1.5% and 2.5% when compared to forecasts using uncalibrated NWPs. [ABSTRACT FROM AUTHOR]

The controlled autoregressive autoregressive moving average (CARARMA) models are of popularity to describe the evolution characteristics of dynamical systems. To overcome the identification obstacle resulting from colored noises, this paper studies the identification of the CARARMA models by forming an intermediate correlated noise model. In order to realize the real-time prediction function of the models, the on-line identification scheme is developed by constructing the dynamical objective functions based on the real-time sampled observations. Firstly, a rolling optimization cost function is built based on the observation at a single sampling instant to catch the modal information at a single time point and a generalized extended stochastic gradient (GESG) algorithm is proposed through the stochastic gradient optimization. Secondly, a rolling window cost function is built in accordance with the dynamical batch observations within data window by extending the proposed GESG algorithm and the multi-innovation generalized extended stochastic gradient algorithm is derived. Thirdly, from the perspective of theoretical analysis, the convergence proof of the proposed algorithm is provided based on the stochastic martingale convergence theory. Finally, the simulation analysis and comparison studies are provided to show the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Abstract This article proposes an online solution to address the problem of closed‐loop system identification using multiple recursive least squares estimation protocols. Some control systems cannot be analysed in an open‐loop form for stability reasons or the requirement for online control system operation. So, it is necessary to identify plant dynamics and controller parameters based on input–output data from the feedback structure. The presented method identifies real‐time parameters of plant dynamics and controller parameters by utilising a series of recursive least square estimation algorithms that estimate open‐loop data from noisy input–output data measured from the closed‐loop feedback structure. The proposed method can effectively identify abrupt variations in both the controller parameters and plant dynamics. This capability makes it valuable for deployment as a supervisory component, enabling the detection of any faults that may arise in operating systems. Mathematical formulations and theorems are developed, and two numerical case studies are presented to examine the feasibility and performance of the presented closed‐loop system identification protocol.

The aim of this paper is to develop a new recursive identification algorithm for autoregressive (AR) models corrupted by additive white noise. The proposed approach relies on a set of both low-order and high-order Yule–Walker equations and on a modified version of the overdetermined recursive instrumental variable method, leading to the estimation of both the AR coefficients and the additive noise variance. The main motivation behind our proposition is introducing model identification procedures suitable for implementation on edge-computing platforms and programmable logic controllers (PLCs), which are known to have limited capabilities and resources when dealing with complex mathematical computations (i.e., matrix inversion). Indeed, our development is focused on condition monitoring systems, with particular attention paid to their integration onboard industrial machinery. The performance of the recursive approach is tested using both numerical simulations and a laboratory case study. The obtained results are very promising.

This article proposes an online solution to address the problem of closed‐loop system identification using multiple recursive least squares estimation protocols. Some control systems cannot be analysed in an open‐loop form for stability reasons or the requirement for online control system operation. So, it is necessary to identify plant dynamics and controller parameters based on input–output data from the feedback structure. The presented method identifies real‐time parameters of plant dynamics and controller parameters by utilising a series of recursive least square estimation algorithms that estimate open‐loop data from noisy input–output data measured from the closed‐loop feedback structure. The proposed method can effectively identify abrupt variations in both the controller parameters and plant dynamics. This capability makes it valuable for deployment as a supervisory component, enabling the detection of any faults that may arise in operating systems. Mathematical formulations and theorems are developed, and two numerical case studies are presented to examine the feasibility and performance of the presented closed‐loop system identification protocol. [ABSTRACT FROM AUTHOR]

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations.

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations. [ABSTRACT FROM AUTHOR]

We consider distributed recursive estimation of an unknown vector parameter θ* ∈ RM in the presence of impulsive communication noise. That is, we assume that interagent communication is subject to an additive communication noise that may have heavy-tails or is contaminated with outliers. To combat this effect, within the class of consensus+innovations distributed estimators, we introduce for the first time a nonlinearity in the consensus update. We allow for a general class of nonlinearities that subsumes, e.g., the sign function or componentwise saturation function. For the general nonlinear estimator and a general class of additive communication noises--that may have infinite moments of order higher than one--we establish almost sure convergence to the parameter θ*. We further prove asymptotic normality and evaluate the corresponding asymptotic covariance. These results reveal interesting tradeoffs between the negative effect of "loss of information" due to incorporation of the nonlinearity and the positive effect of communication noise reduction. We also demonstrate and quantify benefits of introducing the nonlinearity in high-noise (low signal-to-noise ratio) and heavy-tail communication noise regimes. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the forecasting performance associated with using machine learning, shrinkage, and variable selection methods during a historical period that contains the Great Recession of 2008. We find that these methods are most useful during "low" GDP growth periods, while simple autoregressive models are adequate during "high growth" periods. This finding stems from the introduction of very simple "hybrid" models that employ dynamic recursive (rolling) thresholding in order to switch between benchmark linear models and more complex index-driven models, depending on GDP growth conditions. In the context of predicting both quarterly real GDP growth and CPI inflation, these hybrid models are found to be superior, for all forecast horizons. When comparing the hybrid models against a host of alternatives, mean square forecast error gains reach as high as 35%, during the Great Recession, and remain significant throughout our entire prediction period. Additionally, the very best short-term GDP forecasting models contain variants of the Aruoba et al. (2009) business conditions index, although these models are most useful when diffusion indices are also incorporated. Thus, mixing mixed frequency and diffusion indices matters. Finally, across all experiments, we find strong new evidence of the usefulness of survey predictions, including those from the Survey of Professional Forecasters, and those from the Livingston Survey. While we leave the examination of alternative datasets, such as those including other recessionary periods, episodes of war, and epidemics to future research, we hypothesize that the findings in this paper point to the potential usefulness of machine learning, shrinkage, and variable selection methods during recessions, as well as to the usefulness of the hybrid models that we introduce. [ABSTRACT FROM AUTHOR]

This paper considers the recursive estimation of quantiles using the stochastic gradient descent (SGD) algorithm with Polyak-Ruppert averaging. The algorithm offers a computationally and memory efficient alternative to the usual empirical estimator. Our focus is on studying the non-asymptotic behavior by providing exponentially decreasing tail probability bounds under mild assumptions on the smoothness of the density functions. This novel non-asymptotic result is based on a bound of the moment generating function of the SGD estimate. We apply our result to the problem of best arm identification in a multi-armed stochastic bandit setting under quantile preferences. [ABSTRACT FROM AUTHOR]

Abstract The probability hypothesis density (PHD) filter and its cardinalised version PHD (CPHD) have been demonstratedasa class of promising algorithms for multi‐target tracking (MTT) with unknown,time‐varying number of targets. However, these methods can only be used in MTT systems with some prior information of multipletargets, such asdynamic model, newborn target distribution etc.;otherwise, the tracking performance will decline greatly. To solve this problem,an adaptive Grid‐driven technique is proposed based on the framework of the PHD/CPHD filter to recursively estimate the target states without knowing the dynamic model and the newborn target distribution. The grid size can be adaptively adjusted according to the grid resolution, and the dynamic tendencies of the grids can respond to the unknown dynamic models of each targets, including arbitrary manoeuvring models. The newborn targets outside the grid area can be identified by analysing the measurements, and some new grids are generated around them. The experimental results show that the proposed algorithm has a better performance than the traditional particle filter‐based PHD method in terms of average optimal sub‐pattern assignment distance and average target number estimation for tracking multiple targets with unknown dynamic parameters and unknown newborn target distribution.

Control augmentation can significantly boost the performance of systems with human-in-the-loop. However, the benefit of such designs has yet been fully realized because many parameters of human internal vehicle models are inaccurate. Here, a control augmentation framework is studied to assist human operators in controlling a system to precisely follow desired commands. There are two steps involved in this framework: (1) a Hidden Markov Model based estimator for unknown parameters in a human internal vehicle model; and (2) a regulator based on the identified human internal vehicle model to reduce tracking errors. A general form of the human internal vehicle model is applied to describe the operator’s understanding about the system dynamics. A recursive, closed-form solution is derived for a class of dynamical systems so that the computational cost can be significantly reduced. The algorithm is validated in a simulated, pilot-in-the-loop quadrotor scenario. [ABSTRACT FROM AUTHOR]

The paper deals with recursive estimation of financial time series with conditional volatility. It surveys the recursive methodology suggested in Hendrych and Cipra (2018) and adjusts it for various alternatives of GARCH models which are usual in financial practice. Such a recursive approach seems to be suitable for the dynamic estimation with high-frequency data. The paper verifies the applicability of recursive algorithms of particular models to high-frequency data from the Czech environment, particularly in the context of risk prediction.

Abstract Joint Cramér‐Rao lower bound (JCRLB) is very useful for the performance evaluation of joint state and parameter estimation (JSPE) of non‐linear systems, in which the current measurement only depends on the current state. However, in reality, the non‐linear systems with two‐adjacent‐states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non‐linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross‐correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems.

As a sparse data analysis algorithm, ensuring a reasonable model structure is an important challenge for grey models to identify the control mechanism of the uncertain system from observational data. To improve the intelligence and adaptability of the model, this study presents a synchronized optimization strategy for data prioritization and model structure for discrete polynomial grey prediction model. The proposed polynomial grey model contains two hyper-parameters: memory factor parameter and structural parameter. The memory factor is introduced into the discrete model to reconstruct the objective function of structural parameter optimization, thereby avoiding the problem of information superposition. The structural parameter is used to enhance the adaptability of grey prediction model in uncertain data analysis tasks. By employing a recursive estimation approach, an adaptive strategy for estimating model hyper-parameters is proposed, which focuses on minimizing prediction errors within the in-sample data. Additionally, a comparison is made between the proposed improved polynomial grey model and existing polynomial grey models in terms of data information mining, estimation stability, and robustness against measurement noise. The proposed model is applied to the practical engineering application of wear prediction, further validating the effectiveness of the proposed approach in non-equidistant time series prediction tasks. [ABSTRACT FROM AUTHOR]

This work presents an adaptive approach to cooperative aerial search and localization (SAL) which implements Lissajous search patterns and non-Gaussian observation likelihoods to preserve high target information. The adaptive component of the framework utilizes a simultaneous estimation and modeling technique to both estimate agent states and correct their motion models. In order to maximize the information available about a target even when it is not observed by a search agent, multi-Gaussian observation likelihoods are continuously generated for each agent and then fused across the search team. Monte Carlo simulation studies show that the proposed adaptive localization framework outperforms standard filtering techniques by significant margins, for a wide range of parameter values. The differential entropies of fused target likelihoods are studied for various multiagent Lissajous pattern configurations, leading to the derivation of optimal Lissajous parameters for cooperative SAL. This work has relevance for SAL applications in rescue, safety, and defense sectors, offering a robust solution to target localization when a priori target motion information is unavailable. [ABSTRACT FROM AUTHOR]

This article is concerned with a quasiperiodic disturbance estimation problem for dynamic control systems without prior knowledge on frequency. As a major challenge of our work, the quasiperiodic disturbance to be treated is always submerged by untargeted waves, leading to complicated coupling between disturbance separation and frequency identification. Existing approaches on quasiperiodic disturbance rejection have circumvented, rather than overcome, this challenge by assuming either a known frequency or a measurable disturbance signal. In this work, an expectation–maximization (EM) framework is proposed where disturbance signal separation and frequency identification are carried out in an iterative manner. In the E-step, the expected log-likelihood function is evaluated via reconstruction of the quasiperiodic signal based on the latest frequency estimate; and in the M-step, the frequency estimate is updated by maximizing the log-likelihood function obtained in the E-step. To facilitate recursive frequency estimation, an online EM algorithm is also developed based on the forward-only smoothing techniques. Furthermore, we show that the proposed method can be easily extended to deal with nonlinear system models and time-varying frequencies. [ABSTRACT FROM AUTHOR]

This article presents a novel state estimator for short-stroke reluctance actuators, intended for soft-landing control applications in which the position cannot be measured in real time. One of the most important contributions regards the system modeling for the estimator. The discrete state of the hybrid system is treated as an input. Moreover, the model is simplified to facilitate the identification of parameters and the implementation of the estimator. Thus, auxiliary variables are added to the state vector in order to indirectly account for modeling errors. Another important contribution is the state estimation approach. It is based on the Rauch–Tung–Striebel fixed-interval smoother, which allows refining past data from later observations. Numerous simulations are performed to analyze and compare the proposal and several alternatives. In addition, experimental testing is presented to evaluate and validate the estimator. As the simulated and experimental analyses demonstrate, the combined effect of the novel additions results in significantly smaller estimation errors of position and velocity. [ABSTRACT FROM AUTHOR]

The increasing penetration of intermittent distributed energy resources in power networks calls for novel planning and control methodologies which hinge on detailed knowledge of the grid. However, reliable information concerning the system topology and parameters may be missing or outdated for temporally varying electric distribution networks. This brief proposes an online learning procedure to estimate the network admittance matrix capturing topological information and line parameters. We start off by providing a recursive identification algorithm exploiting phasor measurements of voltages and currents. With the goal of accelerating convergence, we subsequently complement our base algorithm with a design-of-experiment procedure which maximizes the information content of data at each step by computing optimal voltage excitations. Our approach improves on existing techniques, and its effectiveness is substantiated by numerical studies on a modified IEEE testbed. [ABSTRACT FROM AUTHOR]

This article is concerned with the robust recursive filtering (RF) problem for a class of stochastic uncertain systems subject to time-correlated fading channels. The measurement received by the sensor is transmitted to the remote filter through the time-correlated fading channel where the channel coefficient evolves according to a certain dynamics and hence exhibits a time-correlated nature. The parameter uncertainties of the system are described by norm-bounded unknown matrices. By introducing a class of auxiliary variables, an augmented system is constructed to reflect the dynamics of the fading coefficient and state simultaneously. Then, a recursive filter is designed which is capable of online computation. Furthermore, an upper bound is guaranteed for the filtering error covariance (FEC) for the possible parameter uncertainties as well as the time-correlated fading channels. With the help of the completing-the-squares technique, filter gains are parameterized by minimizing the obtained upper bound. Finally, two examples are employed to verify the effectiveness of the proposed robust RF method. [ABSTRACT FROM AUTHOR]

This paper presents a technique to localize a stereo camera for in-crash toeboard deformation measurement. The proposed technique designed a sensor suite to install not only the stereo camera but also initial measurement units (IMUs) and a camera for localizing purpose. The pose of the stereo camera is recursively estimated using the measurement of IMUs and the localization camera through an extended Kalman filter. The performance of the proposed approach was first investigated in a stepwise manner and then tested in controlled environments including an actual vehicle crash test, which had successfully resulted in measuring the toeboard deformation during a crash. With the oscillation motion in the occurrence of the crash captured, the deformation of the toeboard measured by stereo cameras can be described in a fixed coordinate system. [ABSTRACT FROM AUTHOR]

In this paper, the recursive form of an optimal finite impulse response filter is proposed for discrete time-varying state-space models. The recursive form of the finite impulse response filter is derived by employing finite horizon Kalman filtering with optimally estimated initial conditions. The horizon initial state and its error covariance on the horizon are optimally estimated by using recent finite measurements, in the sense of maximum likelihood estimation, then initiating the finite horizon Kalman filter. The optimality and unbiasedness of the proposed filter are proved by comparison with the conventional optimal finite impulse response filter in batch form. Moreover, an adaptive FIR filter is also proposed by applying the adaptive estimation scheme to the proposed recursive optimal FIR filter as its application. To evaluate the performance of the proposed algorithms, a computer simulation is performed to compare the conventional Kalman filter and adaptive Kalman filters for the gas turbine aircraft engine model. [ABSTRACT FROM AUTHOR]

Objective: Real-time intramuscular electromyography (iEMG) decomposition, as an identification procedure of individual motor neuron (MN) discharge timings from a streaming iEMG recording, has the potential to be used in human-machine interfacing. However, for these applications, the decomposition accuracy and speed of current approaches need to be improved. Methods: In our previous work, a real-time decomposition algorithm based on a Hidden Markov Model of EMG, using GPU-implemented Bayesian filter to estimate the spike trains of motor units (MU) and their action potentials (MUAPs), was proposed. In this paper, a substantially extended version of this algorithm that boosts the accuracy while maintaining real-time implementation, is introduced. Specifically, multiple heuristics that aim at resolving the problems leading to performance degradation, are applied to the original model. In addition, the recursive maximum likelihood (RML) estimator previously used to estimate the statistical parameters of the spike trains, is replaced by a linear regression (LR) estimator, which is computationally more efficient, in order to ensure real-time decomposition with the new heuristics. Results: The algorithm was validated using twenty-one experimental iEMG signals acquired from the tibialis anterior muscle of five subjects by fine wire electrodes. All signals were decomposed in real time. The decomposition accuracy depended on the level of muscle activation and was $>90\%$ when less than 10 MUs were identified, substantially exceeding previous real-time results. Conclusion: Single channel iEMG signals can be very accurately decomposed in real time with the proposed algorithm. Significance: The proposed highly accurate algorithm for single-channel iEMG decomposition has the potential of providing neural information on motor tasks for human interfacing. [ABSTRACT FROM AUTHOR]

Active localization of a stationary target is one key issue in applications of bistatic sonar based on bistatic range (BR) measurement. However, the complex underwater environment makes achieving the synchronization between the transmitted station and the received station difficult. For solving the synchronization problem, this study relies on mobile bistatic sonar to acquire measurement information at multiple time steps. After that, the target location and clock bias are jointly estimated by solving a non‐linear least square problem. To this end, a recursive scheme is proposed to optimise the measurement cost and reduce the impact of the initial value to achieve accurate estimation by taking full advantage of the redundant measurement information. Orthogonal transformation is used to ensure computational efficiency and numerical reliability. The Cramer–Rao Lower Bound (CRLB) is also derived as a lower bound on the error in estimating the target position and clock bias. Simulation results show that the proposed method achieves the CRLB performance and optimises the measurement cost over the small error region under Gaussian noise. [ABSTRACT FROM AUTHOR]

Sensors for environmental perception are nowadays applied in numerous vehicles and are expected to be used in even higher quantities for future autonomous driving. This leads to an increasing amount of observation data that must be processed reliably and accurately very quickly. For this purpose, recursive approaches are particularly suitable in terms of their efficiency when powerful CPUs and GPUs are uneconomical, too large, or too heavy for certain applications. If explicit functional relationships between the available observations and the requested parameters are used to process and adjust the observation data, complementary approaches exist. The situation is different for implicit relationships, which could not be considered recursively for a long time but only in the context of batch adjustments. In this contribution, a recursive Gauss-Helmert model is presented that can handle explicit and implicit equations and thus allows high flexibility. This recursive estimator is based on a Kalman filter for implicit measurement equations, which has already been used for georeferencing kinematic multi-sensor systems (MSS) in urban environments. Furthermore, different methods for introducing additional information using constraints and the resulting added value are shown. Practical application of the methodology is given by an example for the calibration of a laser scanner for a MSS. [ABSTRACT FROM AUTHOR]

Point-mass filter (PMF) is a numerical Bayesian filtering algorithm that estimates the probability density of state variables using a deterministically defined grid on state space. An important factor that determines the performance of the PMF is how accurately one guesses the probabilistically significant region (called a nonnegligible region) where a grid will be placed. In this article, we introduce the concept of boundary to express the nonnegligible region and propose a method to define a grid tailored to the nonnegligible region of posterior density by transporting boundary according to log-homotopy induced flow. The proposed method ensures accurate estimation performance and robustness especially for uncertain prior information. Terrain referenced navigation (TRN) is composed of a nonlinear observation model defined by terrains and an uncertain initial position. Therefore, it is a major application of the PMF, which can handle nonlinearity and has a more robust characteristic than other numerical filters. In order to compare the proposed PMF with the conventional PMFs, this article applies the proposed method to TRN. Monte Carlo simulation results show that the proposed algorithm is more accurate and robust than the conventional PMFs. [ABSTRACT FROM AUTHOR]

Switching Kalman Filters (SKF) are well known for solving switching linear dynamic system (SLDS), i.e., piece-wise linear estimation problems. Practical SKFs are heuristic, approximate filters and require more computational resources than a single-mode Kalman filter (KF). On the other hand, applying a single-mode mismatched KF to an SLDS results in erroneous estimation. This letter quantifies the average error an SKF can eliminate compared to a mismatched, single-mode KF before collecting measurements. Derivations of the first and second moments of the estimators’ errors are provided and compared. One can use these derivations to quantify the average performance of filters beforehand and decide which filter to run in operation to have the best performance in terms of estimation error and computation complexity. We further provide simulation results that verify our mathematical derivations. [ABSTRACT FROM AUTHOR]

In this article, the distributed adaptive Kalman filtering is investigated for discrete-time stochastic nonlinear systems with gain perturbation as well as unknown covariance of process noises. For the adopted event-triggered communication scheduling, a distributed Kalman filter with an event timestamp is first constructed to effectively fuse the information from neighbors and itself while guaranteeing the unbiasedness. In light of stochastic analysis, the desired filter gain, achieving the suboptimality of filtering performance, is obtained recursively by solving two optimization issues with the form of Riccati-like difference equations. With the help of the fashionable weighted fusion conception combined with the well-known law of large numbers, a recursive estimation of process noise covariance is derived step by step and consequently suits for online computation. Finally, the effectiveness of the proposed filtering scheme is verified via a “lineland” system model. [ABSTRACT FROM AUTHOR]

The paper deals with dynamic modeling of currency portfolios. In contrast to univariate models of exchange rates and their returns one applies multivariate time series models of the type GARCH that are capable of capturing not only conditional heteroscedasticities (i.e. volatilities) but also conditional correlations for common movements of exchange rates (so called covolatilities). One makes use of recursive estimation algorithms suggested by authors for such models which enable to control, evaluate and manage currency investment portfolios in real time. The main task of the paper is to assess whether the recursive estimation procedures suggested by the authors are applicable for real currency portfolios. It is realized by performing an extensive numerical study for bivariate portfolios of the EU currencies and US dollar concentrating on the role of the Czech crown.

Featured Application: The production of algal biomass or of a product associated with biomass growth can be optimized by manipulating the dilution rate and the incident light intensity in indoor photo-bioreactors. However, model-based optimization is delicate in view of the time and experimental efforts required to develop sufficiently accurate dynamic models. Extremum seeking provides an alternative real-time optimization approach, where prior model knowledge is not required, and only a measurable (or estimable) performance index is needed online. This paper investigates the application of adaptive slope-seeking strategies to dual-input single output dynamic processes. While the classical objective of extremum seeking control is to drive a process performance index to its optimum, this paper also considers slope seeking, which allows driving the performance index to a desired level (which is thus sub-optimal). Moreover, the consideration of more than one input signal allows minimizing the input energy thanks to the degrees of freedom offered by the additional inputs. The actual process is assumed to be locally approachable by a Hammerstein model, combining a nonlinear static map with a linear dynamic model. The proposed strategy is based on the interplay of three components: (i) a recursive estimation algorithm providing the model parameters and the performance index gradient, (ii) a slope generator using the static map parameter estimates to convert the performance index setpoint into slope setpoints, and (iii) an adaptive controller driving the process to the desired setpoint. The performance of the slope strategy is assessed in simulation in an application example related to lipid productivity optimization in continuous cultures of micro-algae by acting on both the incident light intensity and the dilution rate. It is also validated in experimental studies where biomass production in a continuous photo-bioreactor is targeted. [ABSTRACT FROM AUTHOR]

Existing unsupervised monocular depth estimation methods resort to stereo image pairs instead of ground-truth depth maps as supervision to predict scene depth. Constrained by the type of monocular input in testing phase, they fail to fully exploit the stereo information through the network during training, leading to the unsatisfactory performance of depth estimation. Therefore, we propose a novel architecture which consists of a monocular network (Mono-Net) that infers depth maps from monocular inputs, and a stereo network (Stereo-Net) that further excavates the stereo information by taking stereo pairs as input. During training, the sophisticated Stereo-Net guides the learning of Mono-Net and devotes to enhance the performance of Mono-Net without changing its network structure and increasing its computational burden. Thus, monocular depth estimation with superior performance and fast runtime can be achieved in testing phase by only using the lightweight Mono-Net. For the proposed framework, our core idea lies in: 1) how to design the Stereo-Net so that it can accurately estimate depth maps by fully exploiting the stereo information; 2) how to use the sophisticated Stereo-Net to improve the performance of Mono-Net. To this end, we propose a recursive estimation and refinement strategy for Stereo-Net to boost its performance of depth estimation. Meanwhile, a multi-space knowledge distillation scheme is designed to help Mono-Net amalgamate the knowledge and master the expertise from Stereo-Net in a multi-scale fashion. Experiments demonstrate that our method achieves the superior performance of monocular depth estimation in comparison with other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Consider a sensor that reports whether or not an event has occurred somewhere along a path, but that has no conception of where along the path that event has occurred. We name this type of sensor a path-based sensor and describe the recursive Bayesian update that can be used to calculate posterior beliefs about the presence of a sensor triggering phenomenon given a path-based sensor observation. We show how the Bayesian update can be leveraged to calculate the expected Shannon information that will be gained along a particular path. We formalize two iterative information-gathering problems that result from this scenario and present path-planning algorithms to solve them. These include: 1) gathering information about the path-based sensor triggering phenomena and 2) assuming the path-based sensor triggering event is “robot destruction,” simultaneously gather information about: 1) hazards using a path-based sensor and 2) information about another environmental phenomenon using a standard sensor, such as the locations of search and rescue targets with a camera. We evaluate our methods using Monte Carlo simulations and observe that they outperform other techniques with respect to the new problems that we consider. Note to Practitioners—This work is motivated by the problem of searching for robot-destroying hazards that are otherwise invisible to the robots. That is, we can observe whether or not a robot survives a path, but, if a robot is destroyed, then we have no idea where, along the path, its destruction has occurred. A mathematically equivalent problem happens in any scenario, in which an agent is equipped with an event sensor that can only be set/triggered once, but that requires postprocessing to figure out if the sensor has been triggered or not. For example, postprocessing is needed if the determination of whether or not a biological specimen was obtained requires a manual laboratory inspection. We also consider an extension of the hazard detection problem, in which we simultaneously collect information about search-and-rescue victims using a “victim sensor,” such as a camera. In this problem, hazards indirectly affect information gathered about victims because new information about victims is lost whenever a robot is destroyed. We provide algorithms to solve these types of problems. The algorithms work even in cases with noise such that false positives and false negatives are possible. This work is useful in any application where observations take the form of a cumulative “yes” or “no” along a path. [ABSTRACT FROM AUTHOR]

The paper deals with recursive estimation of financial time series with conditional volatility. It surveys the recursive methodology suggested in Hendrych and Cipra (2018) and adjusts it for various alternatives of GARCH models which are usual in financial practice. Such a recursive approach seems to be suitable for the dynamic estimation with high-frequency data. The paper verifies the applicability of recursive algorithms of particular models to high-frequency data from the Czech environment, particularly in the context of risk prediction. [ABSTRACT FROM AUTHOR]

In this paper, the recursive state-of-charge (SOC) estimation problem is investigated for the Li-ion batteries. The uncertain parameters, which are used to account for the effects of the changing temperatures, the battery power and the drift current of current sensors, are considered in the modelling process of the Li-ion batteries. Moreover, the uncorrelated/correlated noises are also considered based on the engineering practice. The aim of the paper is to design a SOC estimation scheme such that an upper bound on the estimation error covariance is guaranteed, and such an upper bound is then minimised by appropriately designing the estimator gain. Finally, simulation experiments are carried out to demonstrate the effectiveness of our proposed SOC estimation scheme. [ABSTRACT FROM AUTHOR]

Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric empirical Bayesian estimation. Combined with Markov chain Monte Carlo algorithms, these stochastic optimisation methods have been successfully applied to a wide range of problems in science and industry. However, this strategy scales poorly to large problems because of methodological and theoretical difficulties related to using high-dimensional Markov chain Monte Carlo algorithms within a stochastic approximation scheme. This paper proposes to address these difficulties by using unadjusted Langevin algorithms to construct the stochastic approximation. This leads to a highly efficient stochastic optimisation methodology with favourable convergence properties that can be quantified explicitly and easily checked. The proposed methodology is demonstrated with three experiments, including a challenging application to statistical audio analysis and a sparse Bayesian logistic regression with random effects problem. [ABSTRACT FROM AUTHOR]

This article presents the estimation of electric and magnetic fields using the Kalman filter (KF). The electric and magnetic fields in the entire space have been estimated using the scalar and vector potential. For this estimation, the measurements at a sparse discrete set of spatial pixels have been used. To implement the KF, the state space model has been obtained using the wave equations with sources satisfied by the scalar and vector potential. The proposed method has been implemented on a Hertzian dipole antenna. The fields estimated using KF have been compared with the recursive least squares (RLS) method. The KF presents better estimation than RLS, as it is an optimal estimator. This work uses the Kronecker product for compact representation of discretized fields in the form of vectors and partial differential operators in the form of matrices. [ABSTRACT FROM AUTHOR]

In this paper, an accurate parameter identification algorithm is proposed for transient voltage profile calculation of the unknown transmission lines. This method is based on the virtual black-box method and uses single-ended data sampling, where the input data include voltage and current samples obtained by measuring at one end of the line in transient mode. A mathematical formulation is proposed to separate the sampled data and form a virtual black-box system with virtual inputs and outputs. The virtual black-box is designed, such that the system coefficients relating the virtual outputs and inputs are the known functions of transmission line parameters in the real world. The coefficient values are then calculated by employing the recursive least squares estimation method, which minimizes the sum of squared errors of observations. Using this method, transmission line parameters and transient voltage profile are calculated from only one terminal data with no need of measuring devices, data synchronization, and communication devices at both sides. The efficiency of the proposed method is tested and proved through the EMTP simulations.

In this paper, the recursive form of an optimal finite impulse response filter is proposed for discrete time-varying state-space models. The recursive form of the finite impulse response filter is derived by employing finite horizon Kalman filtering with optimally estimated initial conditions. The horizon initial state and its error covariance on the horizon are optimally estimated by using recent finite measurements, in the sense of maximum likelihood estimation, then initiating the finite horizon Kalman filter. The optimality and unbiasedness of the proposed filter are proved by comparison with the conventional optimal finite impulse response filter in batch form. Moreover, an adaptive FIR filter is also proposed by applying the adaptive estimation scheme to the proposed recursive optimal FIR filter as its application. To evaluate the performance of the proposed algorithms, a computer simulation is performed to compare the conventional Kalman filter and adaptive Kalman filters for the gas turbine aircraft engine model.

For an improved reduction of thermally induced wavefront aberrations associated with the projection lens in deep ultraviolet lithography, this article proposes a regularization-based recursive linear estimation strategy for the model parameters of a predictive control scheme. The linearity of estimation is ensured by estimating only the gains of an approximate exponential regression model that effectively describes the spatial cooling behavior, where the time constants are preset to specific values such that the actual exponentials are collectively well described. Owing to its suitability for recursive formulations, the corresponding solution involves the celebrated Tikhonov regularization, with its regularization term additionally consisting of a scaling term that relates to the magnitudes of parameters so that the same regularization parameter can be used at different exposure settings and time moments. Moreover, for a proper tuning of this regularization parameter, the method of generalized cross-validation is adopted. By means of comparative analysis with respect to both synthetic and real data, the treated method is demonstrated to outperform the traditional Kalman filter, as well as nonlinear approaches such as the extended and unscented Kalman filters. [ABSTRACT FROM AUTHOR]