Improved carrier tracking by smoothing estimators

Smoothing as a way to improve the carrier phase estimation is proposed and analyzed. The performance of first and second order Kalman optimum smoothers are investigated. This performance is evaluated in terms of steady state covariance error computation, dynamic tracking, and noise response. It is shown that with practical amounts of memory, a second order smoother can have a position error due to an acceleration or jerk step input less than any prescribed maximum. As an example of importance to the NASA Deep Space Network, a second order smoother can be used to track the Voyager spacecraft at Uranus and Neptune encounters with significantly better performance than a second order phase locked loop.