The Kalman filter (KF) has received a huge interest from the industrial electronics community and has played a key role in many engineering fields since the 1970s, ranging, without being exhaustive, trajectory estimation, state and parameter estimation for control or diagnosis, data merging, signal processing, and so on. This paper provides a brief overview of the industrial applications and implementation issues of the KF in six topics of the industrial electronics community, highlighting some relevant reference papers and giving future research trends.

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Industrial Applications of the Kalman Filter: A Review

A method is developed for the state estimation of linear time-varying discrete systems with unknown inputs. By making use of the two-stage Kalman filtering technique and a proposed unknown inputs filtering technique, a robust two-stage Kalman filter which is unaffected by the unknown inputs can be readily derived and serves as an alternative to the Kitanidis' (1987) unbiased minimum-variance filter. The application of this new filter is illustrated by optimal filtering for systems with unknown inputs.

Robust two-stage Kalman filters for systems with unknown inputs

The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bias is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

This paper presents a specific controller architecture devoted to obtain a permanent-magnet synchronous motor (PMSM) drive that is robust to mechanical sensor failure. In order to increase the reliability which is a key issue in industrial and transportation applications (electric or hybrid ground vehicle or aerospace actuators), two virtual sensors (a two-stage extended Kalman filter and a back-electromotive-force adaptive observer) and a maximum-likelihood voting algorithm are combined with the actual sensor to build a fault-tolerant controller (FTC). The observers are evaluated through simulation and experimental results. The FTC feasibility is proved through simulations and experiments on a 1.1-kW PMSM drive.

Design of a Fault-Tolerant Controller Based on Observers for a PMSM Drive

This is the fourth part of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I [1] and Part II [2] deal with target motion models. Part III [3] covers the measurement models and the associated techniques. This part surveys tracking techniques that are based on decisions regarding target maneuver. Three classes of techniques are identified and described: equivalent noise, input detection and estimation, and switching model. Maneuver detection methods are also included.

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A Survey of Maneuvering Target Tracking—Part IV: Decision-Based Methods

The two-stage Kalman estimator was originally proposed to reduce the computational complexity of the augmented state Kalman filter. It was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term. Except in certain restrictive conditions, the conventional two-stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter. In this paper, the authors propose a new two-stage Kalman estimator, i.e., new structure, which is an extension of Friedland's estimator and is optimal in general conditions. In addition, we provide some analytic results to demonstrate the computational advantages of two-stage estimators over augmented ones.

https://ir.nctu.edu.tw:443/bitstream/11536/31598/1/000077975300035.pdf

Optimal solution of the two-stage Kalman estimator

The optimal solution of estimating a set of dynamic state in the presence of a random bias employing a two-stage Kalman estimator is addressed. It is well known that, under an algebraic constraint, the optimal estimate of the system state can be obtained from a two-stage Kalman estimator. Unfortunately, this algebraic constraint is seldom satisfied for practical systems. This paper proposes a general form of the optimal solution of the two-stage estimator, in which the algebraic constraint is removed. Furthermore, it is shown that, by applying the adaptive process noise covariance concept, the optimal solution of the two-stage Kalman estimator is composed of a modified bias-free filter and an bias-compensating filter, which can be viewed as a generalized form of the conventional two-stage Kalman estimator.

/pdf/optimal-solution-of-the-two-stage-kalman-estimator-2bfenjcl09.pdf

A general two-stage Kalman filter that is equivalent to, but numerically more efficient than, the standard single-stage Kalman filter is developed for general, time-varying, linear discrete-time systems. Analytical results defining the reduction in computational burdens are presented. Simulation results that validate the predicted efficiency improvements are shown as well.

https://ir.nctu.edu.tw:443/bitstream/11536/30595/1/000087820100032.pdf

General two-stage Kalman filters

An optimal multistage Kalman estimator (OMSKE) is proposed as a generalization of the optimal two-stage Kalman estimator for the reduction of the computational burden of the Kalman estimator (KE) for discrete-time linear time-varying systems with triangular transition matrices. This new filer is obtained by applying a multistage U-V transformation to decouple the covariances of the KE. It is shown analytically that the computational complexity of the OMSKE is less than that of the KE and is minimum when the system transition matrix has the maximum stage number.

https://ir.nctu.edu.tw:443/bitstream/11536/30143/1/000165579300031.pdf

Optimal multistage Kalman estimators

This paper presents an attack-free time-distributed UIF approach to solve the secure state estimation (SSE) problem under malicious attacks. In this new approach, the malicious attacks are modeled as unknown inputs. This research investigates the SSE problem as the attack-resilient state estimation problem with sparse actuator and sensor attacks, and with both process and output noises. A sparse solution of the unknown inputs is sought to recast the SSE problem to a standard UIF problem. The existence and stability conditions of the optimal sparse solution are also provided to facilitate the design. An application of this new method to solve the chaotic synchronization problem is also addressed. Simulation results verify the usefulness of the proposed method.

Chien-Shu Hsieh

Papers

Optimal solution of the two-stage Kalman estimator

Optimal solution of the two-stage Kalman estimator

General two-stage Kalman filters

Optimal multistage Kalman estimators

Secure State Estimation Based on Unknown Input Filtering