This paper addresses the state estimation problem for new operation modes when there is insufficient measurement data available to learn model parameters. The proposed method, called the transfer state estimator, is formulated using variable-structure multiple model estimation, which enables one to improve estimation performance by transferring model knowledge from different source modes to the target mode. Specifically, first, to track system parameter changes, this work utilizes residuals, which represent the deviations between the actual state and the predicted state. These residuals play a crucial role in determining which knowledge needs to be updated. The transfer state estimator is then derived by integrating knowledge from source models. Through this fusion process, the estimator leverages the existing knowledge to handle the new mode in the target domain. Finally, we provide numerical examples and practical simulations to show the efficacy of the proposed method. The results illustrate that the proposed state estimator is a competitive alternative to various existing state estimation methods when dealing with state estimation in the presence of a new mode.

Effective state estimation is crucial for ensuring operational safety, environmental compliance, and efficient resource utilization in high-dimensional wastewater treatment plants (WWTPs). This study proposes a purely data-driven methodology based on dynamic mode decomposition (DMD) to construct a linear dynamic model capable of globally capturing the inherent nonlinearity and complexity of wastewater treatment processes. Moreover, DMD can generate system representations in both full-dimension and reduced-dimension forms and offers flexibility in modeling complex dynamics. Then, the Kalman filter and ensemble Kalman filter (EnKF) are implemented using the derived models for state estimation. A detailed analysis of estimation accuracy and computational cost is also provided. Furthermore, the performance of the proposed DMD-based method is comparatively evaluated against a traditional linearization-based approach, in which the process is linearized at a nominal operating point. Results from the high-dimensional WWTP demonstrate the effectiveness and superiority of the proposed method.

In the fifth-generation (5G) era, eliminating communication interference sources is crucial for maintaining network performance. Interference often originates from unauthorized or malfunctioning antennas, and radio monitoring agencies must address numerous sources of such antennas annually. Autonomous aerial vehicles (AAVs) can improve inspection efficiency. However, the data transmission delay in the existing cloud-only (CO) artificial intelligence (AI) mode fails to meet the low latency requirements for real-time performance. Therefore, we propose a computer vision-based AI of Things (AIoT) system to detect antenna interference sources for AAVs. The system adopts an optimized edge-cloud collaboration (ECC+) mode, combining a keyframe selection algorithm (KSA), focusing on reducing end-to-end latency (E2EL) and ensuring reliable data transmission, which aligns with the core principles of ultrareliable low-latency communication (URLLC). At the core of our approach is an end-to-end antenna localization scheme based on the tracking-by-detection (TBD) paradigm, including a detector (EdgeAnt) and a tracker (AntSort). EdgeAnt achieves state-of-the-art (SOTA) performance with a mean average precision (mAP) of 42.1% on our custom antenna interference source dataset, requiring only three million parameters and 14.7 GFLOPs. On the COCO dataset, EdgeAnt achieves 38.9% mAP with 5.4 GFLOPs. We deployed EdgeAnt on Jetson Xavier NX (TRT) and Raspberry Pi 4B (NCNN), achieving real-time inference speeds of 21.1 (1088) and 4.8 (640) frames/s (FPS), respectively. Compared with CO mode, the ECC+ mode reduces E2EL by 88.9%, increases accuracy by 28.2%. Additionally, the system offers excellent scalability for coordinated multiple AAVs inspections. The detector code is publicly available athttps://github.com/SCNU-RISLAB/EdgeAnt.

Accurate detection of leaks in underground water pipelines poses significant challenges due to the complexity of acoustic signals and environmental noise. The deep burial and widespread distribution of water supply pipelines in urban areas make current manual detection methods inefficient and time-consuming. This paper introduces the deep semi-supervised anomaly detection multiscale (DSMS) algorithm, which combines a multi-scale convolutional network with the deep semi-supervised anomaly detection (deep SAD) framework to address these challenges. The multi-scale convolutional network is specifically designed to extract both fine-grained and global acoustic features from Mel frequency cepstral coefficients (MFCCs), enabling effective differentiation between leakage sounds and background noise. Additionally, a pre-training module based on an autoencoder initializes the network weights, improving convergence and increasing the evaluation metric by 27%. The DSMS algorithm achieves state-of-the-art performance, with a test accuracy of 99.14% and a false positive rate of 0.89%. This approach offers a promising solution for efficient and precise leak detection in urban water distribution systems.

The Bayesian approach resulting in the Kalman filter (KF), often struggle with model uncertainties, particularly when noise statistics are inaccurate. Inspired by transfer learning, this letter presents a novel Bayesian transfer filtering framework that significantly enhances estimation accuracy by incorporating the unbiased finite impulse response (UFIR) structure for adaptive regularization. To adaptively adjust the UFIR filtering estimate, the statistical significance of the transfer-regularization is learned and the variational Bayesian method is applied to learn the regularization factor directly from the data. It is shown that this adaptive strategy not only improves the interpretability and transferability but also removes the need for heuristic selection, which is a common limitation in traditional regularization-based transfer methods. Numerical simulations and water tank experiments collectively confirm the effectiveness of the proposed framework under uncertain noise statistics.

This paper investigates the attitude tracking control problem for spacecraft. A tanh-type self-learning control (TSLC) approach with variable learning intensity (VLI) is proposed, which avoids saturation while overcoming previous algorithms’ long response time disadvantage. Unlike the previously introduced VLI method, the enhanced TSLC does not tweak the learning intensity based on the previous controller output. Instead, it relates learning intensity to an intermediate variable directly related to the system state and tunes the learning intensity using a tanh-type function. Since the system state reflects the tracking error in real-time, the transformed tanh-type function has a higher decay rate than the exponential function, which not only significantly reduces the saturation response but also improves the response speed and achieves higher steady-state accuracy. Simulation proved TSLC’s superiority, considering adverse actuator factors such as dead zone, bias torque, and saturation. The proposed approach has also been validated on the Quanser helicopter platform, confirming its better performance.

Integrating the advantage of the unbiased finite impulse response (UFIR) filter into the Kalman filter (KF) is a practical yet challenging issue, where how to effectively borrow knowledge across domains is a core issue. Existing methods often fall short in addressing performance degradation arising from noise uncertainties. In this article, we delve into a Bayesian transfer filter (BTF) that seamlessly integrates the UFIR filter into the KF through a knowledge-constrained mechanism. Specifically, the pseudo marginal measurement likelihood of the UFIR filter is reused as a constraint to refine the Bayesian posterior distribution in the KF. To optimize this process, we exploit the Kullback-Leibler (KL) divergence to measure and reduce discrepancies between the proposal and target distributions. This approach overcomes the limitations of traditional weight-based fusion methods and eliminates the need for error covariance. Additionally, a necessary condition based on mean square error criteria is established to prevent negative transfer. Using a moving target tracking example and a quadruple water tank experiment, we demonstrate that the proposed BTF offers superior robustness against noise uncertainties compared to existing methods.

This article investigates loosely coupled inertial navigation system/global positioning system (INS/GPS) integration for land vehicle navigation. To achieve navigation with higher accuracy and lower computational complexity, we present an integration solution using factor graph optimization (FGO) based on the graphical state-space model (GSSM). This solution is referred to as GSSM-FGO. Compared with traditional methods, the unique specialty of our work lies in both modeling and problem-solving aspects under the assumption of calibration parameter invariance. Specifically, we suggest that the time-series state-space model is not always suitable for widely existing constant calibration parameters. Thus, we propose GSSM as a more flexible and accurate state description by extracting the constant states as singular nodes. The FGO is adopted to manage this novel graphical model, while traditional filter-based algorithms fail when faced with the cyclic model structure. The universality of our approach is validated through a real-world land vehicle navigation dataset, featuring four distinct-grade inertial measurement units. Compared to the methods based on extended Kalman filter and FGO with the traditional state-space model, our approach demonstrates a substantial enhancement in estimation accuracy and computational speed.

To identify a reliable model for a dynamic system with nonideal measurements, this article develops a novel parameter transfer identification (PTI) algorithm that leverages the knowledge from a heterogeneous source system. Specifically, a mapping matrix is proposed to transform source parameters into intermediate parameters with dimensions matching the target parameters. By treating the intermediate parameter and mapping matrix as latent variables, variational Bayesian (VB) inference is introduced to efficiently approximate intractable posterior distributions of all unknown parameters, with variances reflecting their uncertainty levels. A probabilistic PTI is then proposed to derive the transfer posterior conditioned on the intermediate parameters, whose analytical form is vital for carrying out VB. Based on this, a heterogeneous PTI is established under the VB framework such that variational posterior distributions for all unknown parameters can be updated iteratively. Finally, an atmospheric fermenter example verifies that the proposed algorithm can bring in model accuracy improvement as high as 60% compared with the nontransfer identification approach, when dealing with nonideal measurements.

Rapidly recognizing water meter readings is crucial for intelligent water management systems. Despite the widespread availability of smart water meters, the lower cost of word-wheel water meters means they continue to be used in most cases. As a result, manual reading and data review processes persist, hindering efficient management of water resources. Traditional recognition methods have been hampered by complex algorithms and insufficient robustness. This paper proposes a deep learning-based detection and recognition method for word wheel water meters, which involves dividing the reading process into three stages: detection, correction, and recognition. We have targeted algorithm design to suit the unique environment where the water meter is located. We then made specific refinements and improvements to the recognition method to improve the performance. The method achieved an impressive segmentation accuracy of 98.2% and a recognition accuracy of 98.7% on a self-built dataset collected throughout Hangzhou, China. Additionally, it boasts a small model size and a short inference time, showcasing excellent efficiency. By streamlining manual meter reading and data review processes, our approach holds great potential for facilitating effective water resource management.

Due to record errors, transmission interruptions, etc., low-quality process data, including outliers and missing data, commonly exist in real industrial processes, challenging the accurate modeling and reliable monitoring of the operating statuses. In this study, a novel variational Bayesian Student's-t mixture model (VBSMM) with a closed-form missing value imputation method is proposed to develop a robust process monitoring scheme for low-quality data. First, a new paradigm for the variational inference of Student's-t mixture model is proposed to develop a robust VBSMM model, which optimizes the variational posteriors in an extended feasible region. Second, conditioned on the complete and partially missing data information, a closed-form missing value imputation method is derived to address the challenges of outliers and multimodality in accurate data recovery. Then, a robust online monitoring scheme that can maintain its fault detection performance in the presence of poor data quality is developed, where a novel monitoring statistic called the expected variational distance (EVD) is first proposed to quantify the changes in operating conditions and can be easily extended to other variational mixture models. Case studies on a numerical simulation and a real-world three-phase flow facility illustrate the superiority of the proposed method in missing value imputation and fault detection of low-quality data.

In this article, a composite control scheme, consisting of the conditional disturbance compensation controller and control allocation, is proposed for a manned submersible vehicle (MSV). First of all, a composite disturbance estimation method combining nonlinear disturbance observer (NDOB) and fuzzy logic system (FLS) is used to estimate the external disturbance and model uncertainty, which can acquire better accuracy than the conventional estimation method with a single NDOB. Second, a new disturbance characterization index (DCI) is proposed for the MSV, which not only indicates whether the disturbance/uncertainty is beneficial to MSV, but also reflects the beneficial degree of the disturbance/uncertainty. A conditional disturbance compensation controller is then developed on the basis of DCI, where the detrimental disturbance/uncertainty is eliminated and the favorable disturbance/uncertainty is reserved to further improve the system performance. Furthermore, a control allocation scheme is proposed to solve the overactuated problem of MSV, which can save energy consumption of the thruster system by making full use of the azimuth thrusters in MSV. Finally, the semiglobal asymptotic stability of the MSV system is rigorously analyzed. The effectiveness of the proposed composite control scheme is also verified by the simulations.

To design a finite impulse response (FIR) filter for Markov jump linear systems (MJLSs), a fundamental problem is to avoid constructing the extended state-space model without knowing the mode sequence. This article proposes a new FIR filtering algorithm for MJLSs to address this problem. Under each mode, the variational inference approximates the posterior distribution as a product of Gaussian distribution and inverse gamma distribution by minimizing the Kullback–Leibler divergence. A recursion is then derived over a predefined estimation horizon, where the influence of abandoning the measurements beyond the horizon is compensated. By setting the estimation horizon length as a fixed number, the recursion achieved becomes a new FIR filter for MJLSs, while a new suboptimal Bayesian estimator appears when the horizon length is determined as the full horizon. A Newtonian tracking example as well a three degree-of-freedom hover model is presented to demonstrate that the proposed FIR method has good immunity against unpredicted modeling uncertainties at the cost of extra computational resources and memories, and its full-horizon form does not show this feature and may lose to some exiting algorithms when the underlying model is accurate.

This letter aims to facilitate the identification proce-dure for dynamic systems by utilizing knowledge from different but related systems. By introducing the transfer gain matrix and constructing the transfer identification criterion, a novel parameters-transfer identification method is developed for the system with low-quality measurements. Meanwhile, the condi-tion for avoiding negative transfer is exploited to theoretically guarantee the effectiveness of knowledge transfer. Moreover, the size and elements of the transfer gain matrix depend on all measurements, a recursive form of the proposed method is derived to overcome the curse of dimensionality. Finally, a mass-spring-damper example and a continuous fermentation reactor example are simulated to demonstrate the advantages and capabilities of the proposed methods.

This article proposes a robust Bayesian inference approach for linear state-space models with nonstationary and heavy-tailed noise for robust state estimation. The predicted distribution is modeled as the hierarchical Student- t distribution, while the likelihood function is modified to the Student- t mixture distribution. By learning the corresponding parameters online, informative components of the Student- t mixture distribution are adapted to approximate the statistics of potential uncertainties. Then, the obstacle caused by the coupling of the updated parameters is eliminated by the variational Bayesian (VB) technique and fixed-point iterations. Discussions are provided to show the reasons for the achieved advantages analytically. Using the Newtonian tracking example and a three degree-of-freedom (DOF) hover system, we show that the proposed inference approach exhibits better performance compared with the existing method in the presence of modeling uncertainties and measurement outliers.

The robust online identification problem of linear systems is considered in this article using a faster robust recursive expectation–maximization (RREM) framework. To improve the convergence rate, the outliers, which would deteriorate the identified models, are accommodated with a Laplace distribution instead of Student's$t$-distribution. Then, the recursive transformation of the maximum likelihood function is realized with a recursive$Q$-function. The extensively recognized autoregressive exogenous (ARX) models are used for the description of general linear systems. As a result, the unknown parameters, including the regression coefficient vector of the ARX models, the variance of the noise without outliers, and the scale parameter of the Laplace distribution, are determined in a recursive manner. The performance of the proposed approach is tested with a simulated continuous fermentation reactor system example and a coupled-tank experiment.

Strictly nonwhite measurement noise (NMN) is observed in many industrial processes. Therefore, effective smoothing is often required to extract useful information about the process state with maximum accuracy. This article proposes a batch$q$-lag optimal finite impulse response (OFIR) smoother, operating under NMN with full block covariance matrices. It is shown that the OFIR smoother significantly outperforms the Rauch–Tung–Striebel (RTS) smoother and the unbiased FIR (UFIR) smoother. Testing is provided based on object tracking. The results are validated by a practical example of a three degree-of-freedom helicopter system, which confirms that OFIR smoothing provides better noise reduction than UFIR smoothing, RTS smoothing, and modified RTS smoothing using state augmentation and measurement differencing.

In most industrial processes, some measurements are sampled frequently while other measurements are available infrequently and often slow rate. To utilize the slow rate measurements better for improving the accuracy of estimation, this article proposes a powerful unifying estimation framework for Markovian jump linear systems with multirate measurements based on the transfer learning strategy. Specifically, the form of knowledge transferred is designated as the observation predictor derived using the slow rate measurements. We define the universal evaluation of relatedness between the distribution transferred knowledge and ideal posterior distribution from the perspective of Kullback–Leibler (KL) divergence. A smoothing method is then proposed to compute one-step-behind posterior estimates of the state since the estimates obtained using the slow rate measurements are less than the fast ones. Based on this, an iterative transfer state estimator that includes the transferred observation predictor derived using the slow rate measurements is developed, whenever the slow rate measurements are available. Finally, a moving-target example and an experiment with GPS tracking for the ship-board echo sounder show that the proposed approach can be regarded as a competitive alternative of various existing fusion methods when slow rate measurements arrive.

A new robust$q$-lag unbiased finite impulse response (UFIR) smoother is obtained in discrete-time state-space in batch and recursive forms for linear time-varying (LTV) systems under arbitrary zero mean noise and uncertainties. It is shown that recursive computation of the error covariance of the UFIR smoother is partly available for LTV systems and fully available for linear time-invariant systems. Examples of a polynomial model with colored noise and an uncertain harmonic process have proved that the$q$-lag UFIR smoother outperforms the Rauch-Tung-Striebel or Kalman smoother.

In this article, a new sensor fault estimation algorithm is proposed for industrial processes described by linear discrete-time systems, where the fault dynamics are modeled as a stochastic process. By performing the variational Bayesian inference, the potential sensor fault, as well as the system states, is estimated simultaneously in a probabilistic framework. It is shown that the target fault signal can be satisfactorily estimated through the proposed method, without knowing the statistics of measurement noise and fault coefficient matrix. The efficiency and superiority of the proposed method are demonstrated through numerical simulations and experimental tests performed on a hybrid tank system.

Despite rapid sensor technology developments, monitoring a biological process using regular sensor measurements is challenging, making the process very difficult to characterize. Designing an optimal estimator is an attractive alternative to soft-sensing for such complicated hybrid systems. In this article, the variational Bayesian learning algorithms are proposed to estimate the continuous fermenters' actual states. Special attention is given to the random transition probability matrix (TPM), which is a prerequisite to improving estimation performance. Under the assumption of a time-invariant but random TPM, the Dirichlet distribution is utilized to specify the property of TPM. We then estimate it together with the system state and modal state to approximate the conditional posterior joint distribution. Testing the proposed algorithms using the fermenter model shows that the variational Bayesian learning algorithm can satisfactorily estimate conditions and track TPM in high accuracy.

In this article, the multipass optimal finite impulse response (OFIR) filtering approach is developed for industrial processes with unknown initial conditions under temporary model mismatches. The forward and backward OFIR filters are derived in batch and fast iterative forms using recursions. The double-pass OFIR (DOFIR) filter supported by the unbiased FIR (UFIR) filter and triple-pass OFIR (TOFIR) filter starting with some initial values are designed and extensively investigated using simulations and experimental data. It is shown that the DOFIR and TOFIR filters are able to essentially improve the performance close to the initial values and are more robust against temporary model mismatches than the Kalman, OFIR, and UFIR filters.

State estimation is an important component for advance control and fault detection. This paper addresses the problem of smoother design for state estimation based on a finite number of measurements collected in a finite estimation horizon. Three different finite impulse response (FIR) smoothing algorithms are proposed using the maximum likelihood FIR estimation, which is robust against uncertain noise statistics and model parameters, and also independent of the initial states of each finite horizon. Moreover, we provide equivalent but iterative Kalman-like structures of these algorithms for practical implementation. The applications of the proposed smoothing algorithms to an object tracking and image processing examples are demonstrated, and it shows that they have better robustness against model uncertainties than traditional smoothing approaches.

Under coloured noise, known modifications of the Kalman filter (KF) exist only for discrete‐time state‐space models produced by the forward Euler (FE) method, which fits with feedback control. In this study, the authors modify the KF and unbiased finite impulse response (UFIR) filter using the backward Euler (BE) method for models with coloured measurement noise (CMN), which better fits systems without feedback. The FE‐ and BE‐based models differ by time indexes in the system input and noise that is essential for time‐varying and Markov jump systems. Employing measurement differencing, two KF algorithms and a unique UFIR algorithm are derived for time‐correlated and de‐correlated noise. An equivalence of the KF algorithms is proved analytically and confirmed by simulations. Numerical examples are given for target tracking and experimental verification is provided for visual object tracking. The high efficiency of the designed algorithms in removing CMN is demonstrated experimentally.

In this paper, an iterative finite impulse response (FIR) filter is proposed for discrete time-varying state-space models, with the purpose of a new initialization strategy for the iterative FIR structure as well as consideration of possible unexpected state dynamics in a finite horizon. A compensation variable that satisfies the Gaussian property is introduced into the state equation, and its probability density function (pdf) is estimated analytically together with the pdf of state variable using the variational Bayesian inference technique. Different from the existing methods, the proposed filter exploits the FIR structure from the perspective of pdf propagation, which provides a new efficient way to use the iterative FIR filtering structure without any particular initialization scheme. Moreover, the effects of uncertainties (caused by initialization and/or possible unmodeled state dynamics) on the filtering output are loosened adaptively. Two examples of applications demonstrate that the proposed algorithm can not only provide optimal estimates when the model used perfectly matches the measurements, but can also exhibit better robustness than the Kalman filter, optimal FIR filter, maximum likelihood FIR filter, and some commonly used robust and/or adaptive Kalman filters when the underlying process suffers from unpredicted uncertainties.

This letter develops the Kalman and unbiased finite impulse response filtering algorithms for linear discrete-time state-space models with Gauss-Markov colored process noise (CPN) employing state differencing. The approach avoids problems caused by matrix augmentation, but requires solving a nonsymmetric algebraic Riccati equation to specify the system matrix modified for CPN. Higher accuracy of the algorithms proposed is demonstrated by simulation. A comparative analysis of filtering estimates is provided based on navigation data of walking humans.

Feature extraction has become an essential prerequisite of developing data-based models, control and monitoring tools from massive industrial data. When the temporal correlation is significant, the latent feature is commonly described by a dynamic model, such as the state-space model. Industrial processes are widely subject to certain boundary constraints. However, most of the existing feature extraction methods have not considered the boundary constraints on the latent features. This study develops a learning approach with consideration of boundary constrained latent features. To retain dynamic behavior with a compact probability description, a novel state transition model is developed by using the Beta distribution for the constrained state. To learn the constrained dynamic feature from regularly observed data, a nonlinear observation function is incorporated, and the variational Bayesian inference is adopted for solving the problem. The effectiveness of the proposed method is demonstrated through numerical simulations along with industrial data sets.

The outlier is a common issue in the design of state estimators for an industrial process. In this paper, a robust finite impulse response (FIR) filter is proposed for time-invariant state-space models with its noise following the Student's t distributions. A batch solution is first derived by maximizing the likelihood, and then, an equivalent iterative realization is given to provide a clearer insight into the FIR structure. It shows that the essence of the proposed approach is the convergence of the maximum likelihood estimates in horizon scale through iterations, and the state estimate at each sampling instant is independent of the degree-of-freedom (DOF) parameter of the Student's t distribution. Based on this, a modified algorithm that updates the DOF parameter in each iteration is further proposed. Applications to a moving target tracking example and a 3-DOF helicopter system demonstrate that the proposed methods can exhibit good immunity against outliers during the filtering.

The demand of indoor localization has recently grown quickly in industries. In general, a localization system is required to be reliable, fast, and have high accuracy. In this paper, the ultrawideband (UWB) technique is combined with the inertial navigation sensor (INS) to form a coupled UWB/INS localization framework, which inherits the advantages from both components. A minimum variance unbiased finite impulse response (MVU FIR) method is then applied to obtain accurate position and velocity estimations from noisy measurements. Two experiments and several simulations are conducted. Compared with the traditional Kalman filter (KF) and particle filter, the MVU FIR filter exhibits better immunity to the errors about a priori knowledge of noise variances. It can handle the kidnapped problem, and recover from some extreme failures satisfactorily. Moreover, the MVU FIR filtering algorithm is fast and easily implementable. Its online computational time is even lower than that of the KF, which is favorable in localization applications.

It is proved that the iterative computation form for the mean square error (MSE) matrix of the batch unbiased finite impulse response (UFIR) filter exactly equals that of the iterative UFIR filter form, unlike what was previously thought. Based on the iterative MSE matrix form, we suggest two strategies for defining the optimal horizon length for the UFIR filter. The results are verified using the two-state polynomial and harmonic models.

Industrial processes are often organized using mechanical systems with multiple degrees-of-freedom (DOF). For real-time operation of such systems in noise environments, fast, optimal, and robust estimators are required. In this paper, information gathering about multi-DOF system states is provided using the optimal finite impulse response (OFIR) filter. To use this filter in real time, a fast iterative algorithm is developed with a pseudocode available for immediate use. Although the iterative algorithm utilizes Kalman recursions, it is more robust against uncertainties and model errors owing to the transversal structure. We use this algorithm to estimate state in the 1-DOF torsion system and the 3-DOF helicopter system.

In this survey, the authors examine the trade‐off between the unbiased, optimal, and in‐between solutions in finite impulse response (FIR) filtering. Specifically, they refer to linear discrete real‐time invariant state‐space models with zero mean noise sources having arbitrary covariances (not obligatorily delta shaped) and distributions (not obligatorily Gaussian). They systematically analyse the following batch filtering algorithms: unbiased FIR (UFIR) subject to the unbiasedness condition, optimal FIR (OFIR) which minimises the mean square error (MSE), OFIR with embedded unbiasedness (EU) which minimises the MSE subject to the unbiasedness constraint, and optimal UFIR (OUFIR) which minimises the MSE in the UFIR estimate. Based on extensive investigations of the polynomial and harmonic models, the authors show that the OFIR‐EU and OUFIR filters have higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.

In this letter, the maximum likelihood (ML) finite-impulse response (FIR) filter is proposed for discrete time-variant state-space models with nonsingular system matrix. The ML FIR filter has the deadbeat property and its form is universal for all known bias constrained FIR filters. By the identity weighting matrix, the ML FIR filter becomes the unbiased FIR filter, which ignores the noise statistics and the initial error statistics. Otherwise, the ML FIR filter is equivalent to the optimal FIR filter with embedded unbiasedness and to the minimum variance unbiased FIR filter. An example of a stochastic resonator demonstrates higher immunity of the ML FIR filter against errors in the imprecisely defined noise statistics than in the Kalman filter.

We propose a fast iterative algorithm for optimal finite impulse response (OFIR) filtering of linear discrete time-invariant state-space models in white Gaussian noise. The OFIR filter is known to have the BIBO stability and better robustness against the Kalman filter (KF). The iterative OFIR algorithm is KF-like; that is, its estimate appears much faster than in the batch OFIR filter. A dramatic reduction of computation time is demonstrated in the full-horizon iterative OFIR algorithm which operates as fast as KF. We also notice a considerable reduction of the computational resources allowed by iterations.

This study considers the minimum mean square error estimation problem for a class of jump Markov linear systems with unknown mode‐dependent state delays. In order to show the difficulties caused by the unknown delays, the online Bayesian equation of the investigated system is firstly developed by incorporating the time‐delay estimation into the recursion of system states. However, computing such optimal estimation causes an exponential increase in the requirement of computation and storage load. Therefore two different approximation techniques: interacting multiple‐model approximation and detection–estimation method are utilised to obtain two suboptimal but executable filtering algorithms, respectively. Simulation results of the proposed methods for a system are presented to illustrate the effectiveness.