Parameterized gain-constrained Kalman Filtering via singular value decomposition

Gain-constrained Kalman filtering (KF) is an important estimation problem that has received much attention recently. It encompasses a few problems as special cases, including equality-constrained state estimation, filtering under unknown inputs, etc. In this paper, we propose a parameterized approach to gain-constrained KF by performing singular value decomposition (SVD) on the constraint condition. The filter equivalence between our results and the associated ones in the literature is established. Moreover, we show that the SVD-based approach has some computational advantages, compared to the existing methods in the literature. Specifically, on one hand, we show that with the aid of SVD, the proposed framework has computational advantages in certain situations (although it is not always the case), compared with the existing methods. On the other hand, for the case with network-induced effects, we show that the SVD-based approach is always more efficient than the existing methods, in terms of computational complexity. Finally, some numerical examples are presented to illustrate the obtained results.