Spread spectrum code, Doppler, and multipath tracking using Gaussian sum filtering

The authors consider the problem of obtaining joint estimates of code delay, τ, multipath coefficient vector f, radial Doppler velocity ν_r, and carrier phase due to Doppler shift, φ, distorting a direct-sequence spread-spectrum signal during propagation. Parallel Kalman filtering is applied in the form of the Gaussian sum algorithm. The Gaussian sum filter is capable of updating the joint density of τ, f, ν_r, and φ given the measurements, Z^k. In particular, the authors are interested in obtaining an estimate of ν_r in the presence of a large initial uncertainty in that variable. A Gaussian sum filter that uses enough terms to approximate the joint density will be less susceptible to divergence than an estimator consisting of one Kalman filter. Bit error rate results are given to demonstrate the usefulness of the parameter estimates in a RAKE receiver for differential phase shift keyed (DPSK) encoded binary data