Trade-Off Between Some State Space and FIR Algorithms in GPS-Based Optimal Control of a Local Crystal Clock

摘要

The report addresses a numerical investigation of the trade-off between some state space and FIR filtering algorithms intended to provide optimal time error steering of a local crystal clock employing the GPS reference time. For the sake of low-cost crystal clocks, we employ four most simple structures, namely (1) Two-state Kalman, (2) Three-state Kalman, (3) FIR with the constant kernel (simple MA), and (4) FIR with the linear kernel (optimally unbiased for linear phase drift). The optimal control problem is numerically solved in a sense of least mean squares for the GPS-based time error database and for different estimators tuned to have the same time constant. We study a digital control loop of a local clock, assuming the latter to be linear and inertialess with respect to the filter memory. We also compare the algorithms for the mean square error produced and for sensitivity to variations of the feedback coefficient.