Estimation of dual-mode nonlinear stochastic systems with unknown parameters

This article proposes the problem of state estimation for dual-mode nonlinear stochastic systems with unknown parameters, that is, the possible state evolution is described by unknown switch between normal and abnormal modes, and the mismatch term of abnormal mode deviating from the normal one is parameterized as a linear stochastic transformation of state with unknown transformation matrix and modeling error covariance to generalize various abnormal state evolution. For this complex estimation problem involving unknown states, modes, and parameters (i.e., transformation matrix and covariance), a Bayesian learning based filter is first derived to update the joint posterior of state and unknown parameters in abnormal mode by exploiting sequential Monte Carlo, conjugate prior and marginalization. Then a switching output strategy of normal/abnormal mode filters based on likelihood-ratio test is designed to reduce the conservatism of abnormal mode filter to normal mode state estimation. Finally, simulation study on a benchmark of maneuvering target tracking shows the superiority of the proposed method compared with existing ones.