Application of the Moore-Penrose generalized inverse to certain problems in linear and nonlinear estimation theory

The introductory chapters in this paper review the concept of a generalized inverse for arbitrary matrices. The Moore-Penrose definition of the generalized inverse is given and some of the properties of this generalized inverse are presented. A restatement of the linear least squares problem is given in terms of the generalized inverse. An application of the generalized inverse in a method of sequential least squares estimation is presented. A method is developed for generating a maximal set of estimable functions. A method of overcoming singularity problems in nonlinear estimation is discussed and an efficient method of calculating the generalized inverse on an electronic computer is given.