Separate estimation of laser micro-Doppler parameters based on maximum likelihood schemes

Laser micro-Doppler (MD) effect is capable of obtaining obvious modulation in weak vibration detection. It helps to estimate target micro-motion parameters with high precision, which may extend the application field of MD to subtle identification and recognition. In laser detection, the multiple scattering points in the field of view will generate the single-channel multi-component (SCMC) signal. Moreover, the micro-Doppler features of each component will be overlapped in the time-frequency domain because of the similar micro-motion parameters. The overlapped SCMC signal makes the estimation of the MD parameters a very difficult problem, and there has been no good method so far. In this paper, a separate parameter estimator based on the maximum likelihood framework is proposed to deal with this underdetermined problem. First, the detailed period scanning method is presented to improve the estimation accuracy of micro-motion frequency from the singular value ratio (SVR) spectrum. Further, the amplitude ratio information of each component is extracted from the SVR spectrum. Then, the closed-form expressions of the maximum likelihood estimation (MLE) for the remaining micro-motion parameters are derived, where the mean likelihood estimation is used to approximate to the performance of MLE. The high nonlinearity and multi-peak distribution shape of the likelihood function (LF) in laser MD signal will lead to incorrect estimation result. To this end, a new LF based on the energy spectrum characteristics is designed. The new LF acts as a smoothing filter to the probability density function, through which the ideal PDF distribution form that has only one smooth peak is obtained. With this modification, the requirements for the initialization are reduced and the robustness in low SNR situation is increased. The Markov chain Monte Carlo sampling is employed to implement the MLE. The Gibbs method is chosen to solve the multi-dimensional parametric problems, and the detailed process is listed. In the end, the simulation results prove the feasibility and high efficiency of the proposed method. The accuracy of parameter estimation reaches the Cramer-Rao boundary. The inverse Radon transform is used as a comparison with the experiment, and the results show the precise estimation advantage of the presented method.