An Adaptive Sigma Point Filter for Nonlinear Filtering Problems

In this paper a new Adaptive Unscented Kalman Filter (AUKF) is proposed and applied for the state estimation of a LEO (Low earth Orbit) satellite planar model. The Unscented Kalman Filter (UKF) is preferred here because of its derivative free calculation process and superior performance in highly non linear systems. Further the choice of adaptive filter gives the opportunity to estimate the states without any prior knowledge about the noise covariances. The measurement noise covariance (R) is changed here adaptively. Previously R adaptation techniques have been employed for linear and Extended Kalman Filters (EKF) but the use of R adaptation for sigma point filter is relatively newer trend. Two versions of R-adaptive UKF are presented here depending on the residual sequences and the innovation sequences. Positive definiteness of R is ensured in the proposed algorithm. The R matrix here has been constrained to have a diagonal structure as the measurement noise sources are normally independent of each other. Proposed scheme has also the provision to modulate the speed of adaptation. The simulation results show the superiority of the AUKF compared to the non-adaptive filters like EKF, UKF and CDF (Central Difference Filter). It is also found that the steady state performance of the residual based adaptive filter is robust to the initial value of R.