The Kalman Like Particle Filter : Optimal Estimation With Quantized Innovations/Measurements

TL;DR

This paper introduces the Kalman Like Particle Filter (KLPF), a recursive estimation method combining Kalman filter structure with particle filtering for linear systems with quantized measurements, achieving near-optimal performance with fewer particles.

Contribution

The paper proposes the KLPF, a novel filter that effectively integrates Kalman filtering with particle filtering for quantized measurement systems, improving efficiency and accuracy.

Findings

KLPF delivers near-optimal estimation with fewer particles.

Conditional state density follows a generalized closed skew-normal distribution.

Separation property and LQG optimality hold for the proposed system.

Abstract

We study the problem of optimal estimation and control of linear systems using quantized measurements, with a focus on applications over sensor networks. We show that the state conditioned on a causal quantization of the measurements can be expressed as the sum of a Gaussian random vector and a certain truncated Gaussian vector. This structure bears close resemblance to the full information Kalman filter and so allows us to effectively combine the Kalman structure with a particle filter to recursively compute the state estimate. We call the resulting filter the Kalman like particle filter (KLPF) and observe that it delivers close to optimal performance using far fewer particles than that of a particle filter directly applied to the original problem. We show that the conditional state density follows a, so called, generalized closed skew-normal (GCSN) distribution. We further show that for such systems the classical separation property between control and estimation holds and that the certainty equivalent control law is LQG optimal.