Fixed point implementation of fast Kalman predictors

In this note we study scaling rules and roundoff 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 close to the floating point realization for relatively low-order ARMA time series that are not too narrow band. 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 written in Fortran. Experimental results were obtained by running the fixed- and floating-point filters on identical data sets. All experiments were carried out on an INTEL MIDS 230 development system.