Kalman filtering simulation via numerical solution of the associated matrix differential equations

Abstract

Abstract Using the fundamental relations of Kalman's approach to optimal filtering, a digital computer simulation of the Kalman filtering process is developed. The simulation consists of numerical integration of the solution of the matrix differential equations describing the linear system random process model and the optimum filter. As a prelude to this, a brief presentation of the fundamental concepts underlying the derivation of Kalman filtering theory is given. An assumption basic to this approach is that a sufficiently accurate model of the random process can be given by a linear, possibly time-varying, dynamic system excited by white Gaussian noise. The generation, by digital techniques, of the white Gaussian noise used in the simulation, is based upon a one-dimensional variable transformation and the assumption that a uniformly distributed uncorrelated random sequence of numbers from the interval [0, 1] is available. Tests are conducted to determine the validity of this technique which is used to convert the uniformly distributed random sequence to a Gaussianly distributed random sequence and to determine the validity of the assumption that the given sequence is actually uniformly distributed and uncorrelated.