Adaptive filter of non-linear systems with generalised unknown disturbances

This study presents the state estimation problem of discrete-time non-linear stochastic system with generalised unknown disturbance (GUD) in the measurements. To the best of our knowledge, there is no research result on the filter design dealing with such estimation problem. Here, an upper-bound filter is designed for the linear time-varying system with the GUD existing in the measurement equation, and optimal parameters are derived so that the minimum upper-bounds filter is obtained. The result is further extended to the non-linear case via the iterative optimisation of joint state estimation and parameter identification (the linearised measurement matrix). The simulation about tracking a target via one biased radar and one biased electronic support measure (ESM) shows the effectiveness and robustness of the proposed filter.