Correlative mean-field filter for sequential and spatial data processing

Accurate and robust state estimation is a fundamental problem in signal processing. Particle filter is an effective tool to solve the filtering problem in nonlinear stochastic dynamic systems. However, when the system is mean-field dependent and the data is high-dimensional in spatial and temporal domain, the estimator may become inaccurate or even diverge. In this paper, we propose a Correlative Mean-Field (CMF) filter for a general class of nonlinear systems. The algorithm iterates in four stages: decomposition, sampling, prediction, and correction. An expectation term is incorporated into system transition model to capture the mean-field property of the sequential data. By exploring the property of the circulant matrix and its relationship with Fast Fourier Transform (FFT), sufficient virtual samples are efficiently generated by cyclic shifts of original samples in the spacial domain. The correction is modeled as an online learning problem where the sample weights are updated by the correlation output of a regression function. Optimal states are estimated by the weighted sum. We perform simulations to illustrate that under some conditions our estimator converges while traditional mean-field-free filters diverge. Finally, we implement CMF in vehicle tracking tasks and tested on 12 traffic video sequences. Experiment results show that CMF outperforms the existing mean-field-free filters.