On the Recursive Algorithm of Weighted Least Squares Estimation with Non-Diagonal Weight Matrix

The recursive form for the standard least squares estimation cannot be applied to recursively compute the weighted least squares estimate if the weight matrix is not diagonal. The instrumental variable estimate obtained by the least squares solution of an over-determined system of equations can be viewed as one of the weighted least squares estimates with a non-diagonal weight matrix. In this paper, a recursive form for the weighted least squares estimation with a non-diagonal weight matrix is considered. A new effective and numerically stable recursive algorithm is proposed using QR factorization and J-orthogonal QR factorization for Isermann et al.'s weighted least squares estimate.