Particle filtering for Quantized Innovations

Abstract

In this paper, we re-examine the recently proposed distributed state estimators based on quantized innovations. It is widely believed that the error covariance of the Quantized Innovation Kalman filter [1, 2] follows a modified Riccati recursion. We present stable linear dynamical systems for which this is violated and the filter diverges. We propose a Particle Filter that approximates the optimal nonlinear filter and observe that the error covariance of the Particle Filter follows the modified Riccati recursion of [1]. We also simulate a Posterior CramerRao bound (PCRB) for this filtering problem.

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

“…It should be noted that for such separation results to be useful in practice, one needs a way to compute the MMSE estimate of the hidden state and this is primarily what we address through this work. The proposed filter requires far fewer particles than that of a particle filter applied directly to the original problem [15], as will be shown through various simulations. A preliminary version of this work appeared in [1].…”

“…For linear time invariant dynamical systems, if the Gaussian assumption of [11], [12] were realistic, convergence of the MLQ-Riccati must mean the convergence of the error of the MLQ-KF. [15] provides examples for which the actual error performance of MLQ-KF does not converge to the MLQ-Riccati which means that the assumption of Gaussianity is not generally true. Therefore, we present a closer examination of the conditional state density in this paper.…”

Target tracking in wireless sensor networks using particle filter with quantized innovations

“…This approach uses quantized sensor data and resource constrained WSN with non-ideal wireless channels. A Kalman like particle filter using quantized innovations has been proposed in [9]. Simulation results in this work show that the optimal performance can be achieved with moderate small number of particles.…”

Particle filtering with applications in networked systems: a survey

“…Taking advantage of the Gaussian properties, the authors design a Kalman-like particle filter (KLPF) where a group of Kalman filters are processing in parallel to obtain minimum mean square estimate of the state conditioned on perfect observations. One major advantage of KLPF is that the required number of particles is dramatically reduced compared with directly using particle filter as in [135].…”

“…Measurement quantization will induce big error to the filter system when the values of observed data are large. The filtering problem with innovation quantization has been studied in [135]. A counterexample is constructed to show that the Kalman filtering may perform below expectation or even diverge in the presence of quantized innovation.…”