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The UD-based approach for designing pairwise Kalman filtering algorithms

Kulikova, Maria; Tsyganova, J.V.

IFAC-PapersOnLine, 50(1) (2017), 1619-1624

Over the past few years we have observed a growing interest in the class of Pairwise Markov Models (PMMs). In this paper, we explore the Pairwise Kalman Filter (PKF) intended for the hidden state estimation in linear PMMs in the presence of Gaussian noises. Previous works produced the robust square-root PKF algorithm for improving a numerical stability of the estimator with respect to roundoff errors. The square-root approach is, definitely, the most popular technique for designing numerically stable filter implementations. However, the use of the modified Cholesky decomposition of corresponding error covariance matrix together with the modified weighted Gram-Schmidt orthogonalization at each iteration step of the Kalman filter was shown to improve the estimation accuracy with the reduced computational cost compared to the square-root methods. Here, we propose the UD-based approach for designing the PKF implementations. As for the classical Kalman filter, we may anticipate a high accuracy of the new UD-based PKF implementation with the reduced CPU cost. The methodology is derived in terms of covariance quantities.