Nanohertz frequency determination for the gravity probe B high frequency superconducting quantum interference device...

In this paper, we present a method to measure the frequency and the frequency change rate of a digital signal. This method consists of three consecutive algorithms: frequency interpolation, phase differencing, and a third algorithm specifically designed and tested by the authors. The succession of these three algorithms allowed a 5 parts in 10(10) resolution in frequency determination. The algorithm developed by the authors can be applied to a sampled scalar signal such that a model linking the harmonics of its main frequency to the underlying physical phenomenon is available. This method was developed in the framework of the gravity probe B (GP-B) mission. It was applied to the high frequency (HF) component of GP-B's superconducting quantum interference device signal, whose main frequency f(z) is close to the spin frequency of the gyroscopes used in the experiment. A 30 nHz resolution in signal frequency and a 0.1 pHz/s resolution in its decay rate were achieved out of a succession of 1.86 s-long stretches of signal sampled at 2200 Hz. This paper describes the underlying theory of the frequency measurement method as well as its application to GP-B's HF science signal.