Approximate Optimal Filter for Linear Gaussian Time-invariant Systems

03/09/2021
by   Kaiming Tang, et al.
0

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

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/06/2022

Continuous-Time Channel Gain Control for Minimum-Information Kalman-Bucy Filtering

We consider the problem of estimating a continuous-time Gauss-Markov sou...
research
01/06/2022

Well-Conditioned Linear Minimum Mean Square Error Estimation

Linear minimum mean square error (LMMSE) estimation is often ill-conditi...
research
04/01/2021

Task-Invariant Learning of Continuous Joint Kinematics during Steady-State and Transient Ambulation Using Ultrasound Sensing

Natural control of limb motion is continuous and progressively adaptive ...
research
10/05/2019

An Optimal Transport Formulation of the Ensemble Kalman Filter

Controlled interacting particle systems such as the ensemble Kalman filt...
research
12/24/2020

Distributed optimal steady-state regulation for high-order multi-agent systems with external disturbances

In this paper, a distributed optimal steady-state regulation problem is ...
research
07/11/2021

Statistical Estimation and Nonlinear Filtering in Environmental Pollution

This paper studies a nonlinear filtering problem over an infinite time i...
research
10/23/2021

Deep Structured Teams in Arbitrary-Size Linear Networks: Decentralized Estimation, Optimal Control and Separation Principle

In this article, we introduce decentralized Kalman filters for linear qu...

Please sign up or login with your details

Forgot password? Click here to reset