Square-root algorithms for least-squares estimation

We present several new algorithms, and more generally a new approach, to recursive estimation algorithms for linear dynamical systems. Earlier results in this area have been obtained by several others, especially Potter, Golub, Dyer and McReynolds, Kaminski, Schmidt, Bryson, and Bierman on what are known as square-root algorithms. Our results are more comprehensive. They also show bow constancy of parameters can be exploited to reduce the number of computations and to obtain new forms of the Chandrasekhar-type equations for computing the filter gain. Our approach is essentially based on certain simple geometric interpretations of the overall estimation problem. One of our goals is to attract attention to non-Riccati-based studies of estimation problems.