Point-mass Filter with Non-equidistant Grid Design

Abstract

State estimation is essential in engineering applications from navigation to control. While many estimation methods assume Gaussian probability density functions (PDFs), global filters can capture more complex, non-Gaussian PDFs. The point-mass filter (PMF) is a global filter that discretises the state-space into a grid and approximates the PDF as a piecewise constant function, known as the point-mass density (PMD). Unlike particle filters, the PMF produces deterministic estimates: given the same measurements, it will always generate identical outputs.This deterministic nature, combined with its structured representation of the entire distribution,higher robustness and better handling of abrupt changes, makes it valuable in high-reliabilityapplications like navigation systems.