Adaptive SVD-based Kalman filtering for state and parameter estimation of linear Gaussian dynamic stochastic models

In this talk, the recently published results on the robust adaptive Kalman filtering are presented. Such methods allow for simultaneous state and parameter estimation of dynamic stochastic systems. Any adaptive filtering scheme typically consists of two parts: (i) a recursive optimization method for identifying the uncertain system parameters by minimizing an appropriate performance index (e.g. the negative likelihood function, if the method of maximum likelihood is used for parameter estimation), and (ii) the application of the underlying filter for estimating the unknown dynamic state of the examined model as well as for computing the chosen performance index. In this paper we study the gradient-based adaptive techniques that require the corresponding performance index gradient evaluation. The goal is to propose the robust computational procedure that is inherently more stable (with respect to roundoff errors) than the classical approach based on the straightforward differentiation of the Kalman filtering equations.

Our solution is based on the SVD factorization. First, we have designed new SVD-based Kalman filter implementation method in [1]. Next, we have extended the obtained result on the gradient evaluation (with respect to unknown system parameters) and, hence, designed the SVD-based adaptive scheme in [2]. The newly-developed SVD-based methodology is algebraically equivalent to the conventional approach and the previously derived stable Cholesky-based methods, but outperforms them for estimation accuracy in ill-conditioned situations.

(joint work with Julia Tsyganova)

References:

[1] Kulikova M.V., Tsyganova J.V. (2017) Improved discrete-time Kalman filtering within singular value decomposition. IET Control Theory & Applications, 11(15): 2412-2418

[2] Tsyganova J.V., Kulikova M.V.(2017) SVD-based Kalman filter derivative computation. IEEE Transactions on Automatic Control, 62(9): 4869-4875