Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.

Multiscale systems, Kalman filters, and Riccati equations

Abstract: An algorithm analogous to the Rauch-Tung-Striebel algorithm/spl minus/consisting of a fine-to-coarse Kalman filter-like sweep followed by a coarse-to-fine smoothing step/spl minus/was developed previously by the authors (ibid. vol.39, no.3, p.464-78 (1994)). In this paper they present a detailed system-theoretic analysis of this filter and of the new scale-recursive Riccati equation associated with it. While this analysis is similar in spirit to that for standard Kalman filters, the structure of the dyadic tree leads to several significant differences. In particular, the structure of the Kalman filter error dynamics leads to the formulation of an ML version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the Hamiltonian for the smoothing problem. In addition, the notion of stability for dynamics requires some care as do the concepts of reachability and observability. Using these system-theoretic constructs, the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation are analysed. >

A Derivative-Free Kalman Filtering Approach to State Estimation-Based Control of Nonlinear Systems

Abstract: For nonlinear systems, subject to Gaussian noise, the extended Kalman filter (EKF) is frequently applied for estimating the system's state vector from output measurements. The EFK is based on linearization of the systems' dynamics using a first-order Taylor expansion. Although EKF is efficient in several problems, it is characterized by cumulative errors due to the gradient-based linearization it performs, and this may affect the accuracy of the state estimation or even risk the stability of the state estimation-based control loop. To overcome the flaws of EKF, it has been proposed to use the unscented Kalman filter (UKF) as a method for nonlinear state estimation, which does not introduce linearization errors. Aiming also at finding more efficient implementations of nonlinear Kalman filtering, this paper introduces a derivative-free Kalman filtering approach, which is suitable for state estimation-based control of a class of nonlinear systems. The considered systems are first subject to a linearization transformation, and next state estimation is performed by applying the standard Kalman filter to the linearized model. Unlike EKF, the proposed method provides estimates of the state vector of the nonlinear system without the need for derivatives and Jacobians calculation and without using linearization approximations. The proposed derivative-free Kalman filtering approach has been compared to EKF and UKF in the case of state estimation-based control for a nonlinear DC motor model.

Extended Kalman Filter Based Learning Algorithm for Type-2 Fuzzy Logic Systems and Its Experimental Evaluation

Abstract: In this paper, the use of extended Kalman filter for the optimization of the parameters of type-2 fuzzy logic systems is proposed. The type-2 fuzzy logic system considered in this study benefits from a novel type-2 fuzzy membership function which has certain values on both ends of the support and the kernel, and uncertain values on other parts of the support. To have a comparison of the extended Kalman filter with other existing methods in the literature, particle swarm optimization and gradient descent-based methods are used. The proposed type-2 fuzzy neuro structure is tested on different noisy input-output data sets, and it is shown that extended Kalman filter has a better performance as compared to the gradient descent-based methods. Although the performance of the proposed method is comparable with the particle swarm optimization method, it is faster and more efficient than the particle swarm optimization method. Moreover, the simulation results show that the proposed novel type-2 fuzzy membership function with the extended Kalman filter has noise rejection property. Kalman filter is also used to train the parameters of type-2 fuzzy logic system in a feedback error learning scheme. Then, it is used to control a real-time laboratory setup ABS and satisfactory results are obtained.

Convergence Analysis of the Gaussian Mixture PHD Filter

Abstract: The Gaussian mixture probability hypothesis density (PHD) filter was proposed recently for jointly estimating the time-varying number of targets and their states from a sequence of sets of observations without the need for measurement-to-track data association. It was shown that, under linear-Gaussian assumptions, the posterior intensity at any point in time is a Gaussian mixture. This paper proves uniform convergence of the errors in the algorithm and provides error bounds for the pruning and merging stages. In addition, uniform convergence results for the extended Kalman PHD Filter are given, and the unscented Kalman PHD Filter implementation is discussed

Consensus+Innovations Distributed Kalman Filter With Optimized Gains

Abstract: In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus + innovations distributed linear estimator of the dynamic field termed as Consensus+Innovations Kalman Filter. We analyze the convergence properties of this distributed estimator. We prove that the mean-squared error of the estimator asymptotically converges if the degree of instability of the field dynamics is within a prespecified threshold defined as tracking capacity of the estimator. The tracking capacity is a function of the local observation models and the agent communication network. We design the optimal consensus and innovation gain matrices yielding distributed estimates with minimized mean-squared error. Through numerical evaluations, we show that the distributed estimator with optimal gains converges faster and with approximately 3dB better mean-squared error performance than previous distributed estimators.