Binary-encoding-based quantized Gaussian particle filtering for nonlinear systems with bit-flipping

This paper investigates the state estimation problem for nonlinear systems with binary-encoding-based quantization, bit-flipping and heavy-tailed noise. Due to the limitation of the communication channel bandwidth in a network environment, the measurement data collected by sensors must be quantized based on a limited number of bits and converted into binary codes for transmission, thus generating quantization errors. Meanwhile, during data transmission, the binary code output from quantization is affected by channel noise, signal distortion, signal interference, and other factors. It is prone to bit-flipping (i.e. 0 is flipped to 1, and 1 is flipped to 0), which leads to communication errors. For the problems of quantization error, heavy-tailed noise and bit-flipping, this paper aims to achieve the state estimation of such nonlinear systems by improving the particle filter algorithm, with the aid of the Bayesian formula and the Monte Carlo simulation method. To address the issue of particle degradation in particle filtering, this study employs a Gaussian approximation of the posterior probability density as the proposal distribution. In the design of the proposal distribution, a normalized innovation sequence is introduced to mitigate quantization errors and bit-flip effects. Based on this formulation, the mean, covariance of the proposal distribution, and likelihood function are analytically derived, yielding a complete proposal distribution. Subsequently, particles are sampled from the constructed proposal distribution, and an updated particle weighting scheme is rigorously derived. The optimal state estimate is obtained through a weighted summation of the particles. Numerical simulations are conducted to validate the efficacy of the proposed algorithm.