A fuzzy-tuned adaptive Kalman filter

Abstract

In this research, fuzzy processing is applied to the adaptive Kalman filter. The filter gain coefficients are adapted over a 50 dB range of unknown signal/noise dynamics,, using fuzzy membership functions. Specific simulation results are shown for a dynamic system model which has position-velocity states, as in vehicle tracking applications such as the Global Positioning System (GPS). The filter is a single-input, single-output, driven by measurements of position, corrupted by additive (Gaussian) noise. The fuzzy adaptation technique is also applicable to multiple-input, multiple output applications for the cases where the states are higher-order moments of motion (position, velocity, acceleration. etc.). The fuzzy processing is driven by an inaccurate on-line estimate of signal-to-noise ratio (SNR) for the signal being tracked. A robust Bayes scheme would calculate the filter gain coefficients from the signal-to-noise estimate. In our implementation, the inaccurate signal-to-noise estimate is corrected by the use of fuzzy membership functions. The resulting adaptive filter produces near optimum performance in the GPS signal-noise environment. Performances are compared for fuzzy-tuned Kalman filter and fixed Kalman filter in case of optimum and suboptimum estimation in terms of Kalman gains (position and velocity in the second order system), SNR and tracking error.