Periodic Chandrasekhar recursions

TL;DR

This paper develops periodic Chandrasekhar-type recursions for time-varying state-space models, offering potential computational benefits over traditional Kalman filtering methods.

Contribution

It extends existing Chandrasekhar recursions to periodic models, enabling efficient linear least squares estimation in time-varying systems.

Findings

Recursions satisfy specific properties for periodic models

Algorithms derived for linear least squares estimation

Potential computational advantages over Kalman Filter

Abstract

This paper extends the Chandrasekhar-type recursions due to Morf, Sidhu, and Kailath "Some new algorithms for recursive estimation in constant, linear, discrete-time systems, IEEE Trans. Autom. Control 19 (1974) 315-323" to the case of periodic time-varying state-space models. We show that the S-lagged increments of the one-step prediction error covariance satisfy certain recursions from which we derive some algorithms for linear least squares estimation for periodic state-space models. The proposed recursions may have potential computational advantages over the Kalman Filter and, in particular, the periodic Riccati difference equation.