Estimations of frequency and its drift rate

This paper presents an analysis of frequency and its drift rate estimation by the difference method, the least-squares method, and the Kalman filter. Error formulas are derived for all five noise processes: white phase, flicker phase, white frequency, flicker frequency, and random walk frequency. The error formulas show the relationship between the estimate error and the noise spectral density coefficients, the same interval τ, and the data number N. Because of the existence of some nonstationary noise processes, a large data number may not yield a good estimation. One should choose an appropriate sample interval and data number so as to control the estimate error. An optimal solution based on the Kalman filter is presented