An Improved Phase-Derived Range Method Based on High-Order Multi-Frame Track-Before-Detect for Warhead Detection

It is crucial for a ballistic missile defense system to discriminate the true warhead from decoys. Although a decoy has a similar shape to the warhead, it is believed that the true warhead can be separated by its micro-Doppler features introduced by the precession and nutation. As is well known, the accuracy of the phase-derived range method, to extract micro-Doppler curves, can reach sub-wavelength. However, it suffers from an inefficiency of energy integration and high computational costs. In this paper, a novel phase-derived range method, using high-order multi-frame track-before-detect is proposed for micro-Doppler curve extraction under a low signal-to-noise ratio (SNR). First, the sinusoidal micro-Doppler range sequence is treated as the state, and the dynamic model is described as a Markov chain to obtain the envelopes and then the ambiguous phases. Instead of processing the whole frames, the proposed method only processes the latest frame at an arbitrary given time, which reduces the computational costs. Then, the correlation of all pairs of adjacent pulses is calculated along the slow time dimension to find the number of cells that the point scatterer crosses, which can be further used in phase unwrapping. Finally, the phase-derived range method is employed to get the micro-Doppler curves. Simulation results show that the proposed method is capable of extracting the micro-Doppler curves with sub-wavelength accuracy, even if SNR = -15 dB, with a lower computational cost.