Simplified Solution for a Class of Fading Memory Filters

A fading memory filter is a least squares estimator (LSE) thatapplies an exponentially decaying weight to past measurements.When compared with a standard Kalman filter, its key advantagesare asymptotic stability and reduced sensitivity to modeling errors.This paper derives a simple solution for a class of fading memoryfilters, resulting in a reduction in computational complexity. Steadystate filter solutions are obtained for second-and third-order filtersused in a global positioning system (GPS) receiver for high dynamicvehicles.