A Novel Maneuvering Target Tracking Approach by Stochastic Volatility GARCH Model

Abstract: In this paper, we introduce a new single model maneuvering target tracking approach using stochastic differential equation (SDE) based on GARCH volatility. The traditional input estimation (IE) techniques assume constant acceleration level which do not cover all the possible acceleration quintessence. In contrast, the multiple model (MM) algorithms that take care of some IE's shortcomings, are sensitive to the transition probability matrices. In this paper, an innovative model is proposed to overcome these drawbacks by using a new generalized dynamic modeling of acceleration and a Bayesian filter. We utilize SDE to model Markovian jump acceleration of a maneuvering target through GARCH process as the SDE volatility. In the proposed scheme, the original state and stochastic volatility (SV) are estimated simultaneously by a bootstrap particle filter (PF). We introduce the bootstrap resampling to obtain the statistical properties of a GARCH density. Due to the heavy-tailed nature of the GARCH distribution, the bootstrap PF is more effective in the presence of large errors that can occur in the state equation. We show analytically that the target tracking performance is improved by considering GARCH acceleration model. Finally, the effectiveness and capabilities of our proposed strategy (PF-AR-GARCH) are demonstrated and validated through simulation studies.