Title: Least Squares Estimation of Discrete Linear Dynamic Systems Using Orthogonal Transformations
Abstract:Kalman [9] introduced a method for estimating the state of a discrete linear dynamic system subject to noise. His method is fast but has poor numerical properties. Duncan and Horn [3] showed that the ...Kalman [9] introduced a method for estimating the state of a discrete linear dynamic system subject to noise. His method is fast but has poor numerical properties. Duncan and Horn [3] showed that the same problem can be formulated as a weighted linear least squares problem. Here we present a method which uses orthogonal transformations to solve the Duncan and Horn formulation by taking advantage of the special structure of the problem. This approach gives advantages in numerical accuracy over other related methods in the literature, and is similar in the number of computations required. It also gives a straightforward presentation of the material for those unfamiliar with the area.Read More