The Equivalence Between the Cholesky Decomposition and the Kalman Filter

Abstract

This is an expository article that develops the Kalman filter from a Cholesky factorization perspective. In particular, the Kalman filter is shown to be a modification of the Cholesky factorization that arises from efficient use of the intrinsic structure in state-space models.

KEY WORDS:

• Backward recursion
• Forward recursion
• Order n algorithm
• Smoothing