Simultaneous State and Parameter Estimation using Robust Receding-horizon Nonlinear Kalman Filter

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

“…In this work, to minimize the effects of gross errors on the state estimates, two robust versions of receding horizon nonlinear Kalman filter (RNK) formulations are developed by modifying the update step of RNK with an M-estimator. 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 Mestimator as proposed by Rangegowda et al 22 A recursive update step is derived analytically and further used to arrive at a recursive rule for the associated covariance update using the Taylor series approximation. The second approach, referred to as 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.…”

“…If |ζ k , q | becomes greater than the threshold δ S , then the effect of ζ q , k is entirely neglected, and the influence function becomes zero, thereby the equation is robust to large measurement errors. Hampel estimator (or) redescending estimator: A three part redescending estimator is defined as follows: where variables ( a , b , c ) represent the tuning parameters that define four regions in the estimator satisfying the condition c ≥ b + 2 a . The influence function and its gradient of redescending estimator can be found in Rangegowda et al The redescending estimator behavior is plotted in Figures and . The performance of the redescending estimator depends on the three tuning parameters.…”

“…Through simulation studies, it has been shown that RNK is able to generate estimation performance comparable to that of MHE. , Thus, RNK can be an attractive alternative to MHE. Further, considering the advantages of the RNK algorithm, a robust RNK based simultaneous state and parameter estimation algorithm is developed by Rangegowda et al Taking motivation from Rangegowda et al, , Apio et al recently developed a robust moving window EKF, in which the update step is formulated in a QP formulation.…”

“…However, to illustrate features of the proposed estimation approaches the following representative M-estimators have been used: fair function, Welsch, Smith, and redescending estimators. The proposed work is a significantly enhanced version of the initial work of Rangegowda et al, and the main differences are as follows: Recursive expressions are developed for update of mean and covariance for Explicit M-RNK formulation. Implicit M-RNK formulation is proposed, eliminating the need of inclusion of the M-estimator in the cost function of the optimization problem. Recursive expressions are given for update of mean and covariance for the Implicit M-RNK formulation. In addition to the complete likelihood based robust state and parameter estimation, an innovation based simultaneous state and parameter estimation has been developed. The efficacy of the proposed robust estimation algorithms is demonstrated using two benchmark simulation case studies and using experimental data obtained from the benchmark quadruple tank system. …”

“…6 However, to illustrate features of the proposed estimation approaches the following representative M-estimators have been used: fair function, Welsch, Smith, and redescending estimators. The proposed work is a significantly enhanced version of the initial work of Rangegowda et al, 22 and the main differences are as follows:…”