Approximate Optimal Filter for Linear Gaussian Time-invariant Systems
State estimation is critical to control systems, especially when the states cannot be directly measured. This paper presents an approximate optimal filter, which enables to use policy iteration technique to obtain the steady-state gain in linear Gaussian time-invariant systems. This design transforms the optimal filtering problem with minimum mean square error into an optimal control problem, called Approximate Optimal Filtering (AOF) problem. The equivalence holds given certain conditions about initial state distributions and policy formats, in which the system state is the estimation error, control input is the filter gain, and control objective function is the accumulated estimation error. We present a policy iteration algorithm to solve the AOF problem in steady-state. A classic vehicle state estimation problem finally evaluates the approximate filter. The results show that the policy converges to the steady-state Kalman gain, and its accuracy is within 2 %.
Code (0)
등록된 구현이 없습니다.
Tasks
State EstimationSimilar Papers 제목 키워드 기반
Nonlinear Bayesian Filtering with Natural Gradient Gaussian Approximation
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters su…
LEMMANear-Optimal Algorithms for Gaussians with Huber Contamination: Mean Estimation and Linear Regression
We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal an…
regressionCan a Transformer Represent a Kalman Filter?
Transformers are a class of autoregressive deep learning architectures which have recently achieved state-of-the-art performance in various vision, language, and robotics tasks. We revisit the problem of Kalman Filtering…
Design and Experimental Test of Datatic Approximate Optimal Filter in Nonlinear Dynamic Systems
Filtering is crucial in engineering fields, providing vital state estimation for control systems. However, the nonlinear nature of complex systems and the presence of non-Gaussian noises pose significant challenges to th…
Computational EfficiencyReinforcement Learning (RL)State EstimationGrid Based Nonlinear Filtering Revisited: Recursive Estimation & Asymptotic Optimality
We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two typ…
Quantization