Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

Abstract

SUMMARYThe presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez-Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez-Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez-Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non-Gaussian distributions, is illustrated by intensive simulations.

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

“…These results are extended to develop a robust EKF by using a matrix forgetting factor in [21]. Simulations results in [18][19][20][21] show that robust filters outperform the standard EKF when the noise covariances used in the robust filters and the truth are mismatched. Although it is straightforward and simple to develop robust EKF, the EKF suffers from its own drawbacks such as instability due to linearization and costly calculation of Jacobian matrices.…”

“…For state estimation of nonlinear stochastic systems, extensions and generalizations have been proposed such as the robust extended Kalman filter (EKF) [18][19][20][21] and the Huber-based divideddifference filter [22,23]. In [18], the Masreliez-Martin method was used to develop a robust EKF in the case when the process noise has a Gaussian distribution and the measurement noise has a nonGaussian distribution.…”

“…The Masreliez-Martin EKF has been developed for such systems [18]. However, the process noise and the measurement noise covariance matrices should be known.…”

“…In [18], the Masreliez-Martin method was used to develop a robust EKF in the case when the process noise has a Gaussian distribution and the measurement noise has a nonGaussian distribution. In [19], an adaptive fading EKF was proposed by introducing a forgetting factor in the gain matrix. In [20], a robust EKF is proposed for the attitude estimation of small satellite.…”

Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements

“…Subsequently, the recursive estimation method was developed by employing the minimum mean square error principle and the projection theory. Accordingly, a considerable number of research results were reported to design the optimal filters in many practical systems [2][3][4][5][6][7].…”