Synthesis of Computationally Efficient Sequential Linear Estimators

The Kalman sequential linear estimation theory, although not always utilized because the number of computations required for many systems of practical importance becomes prohibitive, allows straight-forward synthesis of optimal estimators for many complex systems. Some systems designers have chosen to ignore variables and by such a reduction in system dimension have been able to economize with regard to the number of computations. The purpose of this paper is to demonstrate a method which allows economy of computation by partitioning the system state vector; the variables to be eliminated are placed in one subsystem and the remaining variables in one or more additional subsystems. The resultant system is computationally more efficient if some variables are eliminated. This is so because the remaining states have been partitioned into two or more subsystems. The number of computations for a subsystem varies approximately as the cube of the dimension of its state vector. By operating on several subsystems of lesser dimension than that of the unpartitioned system, the number of computations is decreased; performance will deteriorate. The method for determining the partitioning tends to keep this deterioration under control; it is illustrated by application to a marine-type inertial navigation system.