Weak beat frequency extraction method for photon Doppler signal with low signal-to-noise ratio

In the window function spectrum of the low signal-to-noise ratio photon Doppler signal after the short-time Fourier transform, the weak beat frequency cannot be obtained by extracting the maximum amplitude spectrum frequency of each window because the amplitude of the noise spectrum exceeds the weak beat frequency. In this article, the value of the beat frequency is first estimated by the Kalman filter. Then, a multiple analytical bandpass filter is constructed to refine the spectrum of the high noise signal with the value of the beat frequency estimate as the spectrum band center. This technique extracts only the beat frequencies from the narrowband refinement spectrum by removing the interference spectrum band range. We use this technique to process the photon Doppler signals from the tiny high-speed flying fragments explosion experiment. After data processing, the beat frequency value heavily affected by high-frequency noise can reduce the error by up to 64.9%. The beat frequency value of the low noise signal can be accurate to 106 Hz, equivalent to 0.775 m/s after velocity demodulation. This method fully considers the positioning and protection of the beat frequency characteristics. It makes weak beat frequencies more obvious in the refined narrowband spectrum without changing the signal amplitude. This article describes a method for extracting the weak beat frequency of the photon Doppler signal or a signal optimization algorithm for needing high-precision beat frequencies in a test environment.