A Survey of Nonlinear Estimation Filters

The filtering problem, in which the state of a stochastic dynamical system is estimated using information from measurements, involves solving the Bayesian recursive relations (BRRs). The exact solution to the BRRs is almost always intractable in practical scenarios, leading to the need for approximations or simplifications. Various approaches have been proposed to approximate the solution to the BRRs. These approaches can be divided into two main categories: filters that incorporate measurement information linearly, such as the extended Kalman filter, and filters that use measurement information nonlinearly, such as particle filters. This survey provides a comprehensive overview of the latter, typically known as nonlinear filters. Three different classes of nonlinear filters are surveyed here: filters that use discrete representations of the probability density function (PDF), filters that assume a Gaussian mixture representation of the PDF, and filters that perform the measurement update using higher-order moments of the approximated PDF. © 2025 JAIF.