The Auxiliary Extended and Auxiliary Unscented Kalman Particle Filters

Abstract

This paper proposes two new particle filters, namely, the auxiliary extended Kalman particle filter (AEKPF) and the auxiliary unscented Kalman particle filter (AUKPF). The theory governing the newly proposed filtering techniques is developed and the algorithms are described and contrasted. Next, a series of tests is presented in which the new filters are compared against the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and several existing particle filters. The test results are from simulations with synthetic mathematical models that incorporate elements that are nonlinear, non-stationary, and stochastic. Performance results are presented for various degrees of model nonlinearity including first, second, and third order systems. Furthermore, experimental results are also reported comparing the filters performances with different signal to noise ratios and noise models, including Gaussian, Cauchy, and Gamma distributions. Various metrics are used to compare the filters performances and to make conclusions about future work. It is shown to be advantageous to use certain particle filters depending on the noise distribution of the system of interest. In particular, the AUKPF and the AEKPF outperform existing particle filters in many cases.