Spacecraft-Doppler gravity-wave detection. I. Theory

It is the purpose of this paper to produce a self-contained summary of the methods which may be used to analyze data in the newly developing field of spacecraft-Doppler gravity-wave detection. Three algorithms are developed. The first is a near-optimal matched filter which produces a $\sqrt{2}$ improvement in signal-to-noise ratio for purposes of detecting short bursts of gravitational radiation. The second two methods are to be used in the search for the cosmic background, the one concentrating on the spectrum of the Doppler data and the other concentrating on the autocorrelation function. It is shown that these two methods are theoretically equivalent, although the autocorrelation method may be somewhat easier to use. The gain of these algorithms is shown to be $\propto \sqrt{n}$ where $n$ is the number of data points in the Doppler record.