Development of a Robust Receding-Horizon Nonlinear Kalman Filter Using M-Estimators

Abstract

The majority of Bayesian methods for the state estimation are based on the assumption that the measurements are corrupted only with random errors. In practice, however, the measurements are often corrupted with gross errors or biases, which leads to biased state estimates when the conventional Bayesian estimators are used. This, in turn, deteriorates the performance of model based process monitoring or control schemes that rely on the state estimator. In this work, to minimize the effects of gross errors on state estimates, two robust versions of the receding-horizon nonlinear Kalman filter (RNK) are developed by integrating M-estimators with the conventional RNK. In the first approach, referred to as Explicit M-RNK, the update step is recast as an optimization problem and further modified by explicitly including an M-estimator. Using the Taylor series approximation, a recursive update step is derived analytically and further used to arrive at a recursive rule for the associated covariance update. The second approach, referred to as the Implicit M-RNK, uses the gradient of the influence function of the chosen M-estimator for adaptive modification of the measurement model used in the update step. This approach facilities the use of the update step in conventional RNK without requiring explicit use of the M-estimator. The proposed robust RNK state estimation formulation is further used to develop a robust state and parameter estimation scheme. The efficacies of the proposed estimation schemes have been demonstrated by conducting simulation studies on some benchmark systems and experimental data sets. The simulation studies reveal that the proposed robust RNK estimators can estimate states and drifting parameter(s) accurately even with the gross errors in the measurements.