Chandrasekhar recursion for structured time-varying systems and its application to recursive least squares problems

Chandrasekhar recursion of Kalman filtering for a time-varying system has not been fully studied while its counterpart for a time-invariant system has been around for decades. Sayed and Kailath (1992) have shown that Chandrasekhar recursion for a certain class of structured time-varying systems can be achieved. In this paper, the authors extend the traditional discrete-time Chandrasekhar recursion of Kalman filtering to derive an algorithm applicable to an even wider class of structured time-varying systems including those with so-called quasi-internally-invariant property. This extension makes it possible to update the Kalman filter of time-varying systems with a quasi-internally-invariant property, only with O(n(p+q)) flops instead of O(n³), where n, p and q are the number of states, the number of outputs and the displacement rank of Riccati solutions, respectively. It is also shown that the resulting algorithm can be applied to adaptive filtering (specifically, recursive least squares problems)