Adaptive central difference filter for non-linear state estimation

A new algorithm for adaptive non-linear filter suitable for signal models with unknown measurement noise covariance is presented here. The proposed adaptive filter is based on numerically efficient central difference algorithm which is potentially suitable for on board implementation. Unlike some competing adaptation scheme the proposed method guarantees positive definiteness of the estimated covariance matrix and avoids consequent singularity. Superiority of the proposed filter in comparison with non-adaptive central difference filter (CDF), an adaptive unscented Kalman filter and also another CDF based adaptive filter with alternative adaptation scheme has been demonstrated by Monte Carlo simulations. The signal models used are a well-known reentry ballistic target tracking problem and a high dimensional, relatively complex spacecraft attitude determination problem. The algorithm has provisions for (i) iterative refinement, (ii) modulating the degree of adaptation and also (iii) for incorporating tradeoff mechanisms between computational load and estimation error.