Fixed Point Implementations of Fast Kalman Algorithms

摘要

In this paper the authors study scaling rules and round-off noise variances in a fixed point implementation of the Kalman predictor for an ARMA time series observed noise-free. The Kalman predictor is realized in a fast form that uses the so-called fast Kalman gain algorithm. The algorithm for the gain is fixed point. Scaling rules and expressions for rounding error variances are derived. The numerical results show that the fixed point realization performs very closely to the floating point realization for relatively low-order ARMA time series that are not too narrowband. The predictor has been implemented in 16-bit fixed point arithmetic on an INTEL 8086 microprocessor, and in 16-bit floating point arithmetic on an INTEL 8080. Fixed point code was written in ASSEMBLY language and floating point code was witten in FORTRAN. Experimental results were obtained by running the fixed and floating point filters on identical data sets. All experiments were carried out on a INTEL MDS 230 Development System.