Conditionally Minimax Nonlinear Filter and Unscented Kalman Filter: Empirical Analysis and Comparison

Abstract

We present the results of the analysis and comparison of the properties of two concepts in state filtering problems for nonlinear stochastic dynamic observation systems with discrete time: sigma-point Kalman filter based on a discrete approximation of continuous distributions and conditionally minimax nonlinear filter that implements the conditionally optimal filtering method based on simulation modeling. A brief discussion of the structure and properties of the estimates and justifications of the corresponding algorithms is accompanied by a significant number of model examples illustrating both positive applications and limitations of the efficiency for the estimation procedures. The simplicity and clarity of the considered examples (scalar autonomous regressions in the state equation and linear observations) allow us to objectively characterize the considered estimation methods. We propose a new modification of the nonlinear filter that combines the ideas of both considered approaches.