A Sequential Method for Passive Detection, Characterization, and Localization of Multiple Low Probability of Intercept LFMCW Signals

摘要

A method for passive Detection, Characterization, and Localization (DCL) of multiple low power, Linear Frequency Modulated Continuous Wave (LFMCW) (i.e., Low Probability of Intercept (LPI)) signals is proposed. We demonstrate, via simulation, laboratory, and outdoor experiments, that the method is able to detect and correctly characterize the parameters that define two simultaneous LFMCW signals with probability greater than 90% when the signal to noise ratio is -10 dB or greater. While this performance is compelling, it is far from the Cramer-Rao Lower Bound (CRLB), which we derive, and the performance of the Maximum Likelihood Estimator (MLE), whose performance we simulate. The loss in performance relative to the CRLB and the MLE is the price paid for computational tractability. The LFMCW signal is the focus of this work because of its common use in modern, low-cost radar systems.ududIn contrast to other detection and characterization approaches, such as the MLE and those based on the Wigner-Ville Transform (WVT) or the Wigner-Ville Hough Transform (WVHT), our approach does not begin with a parametric model of the received signal that is specified directly in terms of its LFMCW constituents. Rather, we analyze the signal over time intervals that are short, non-overlapping, and contiguous by modeling it within these intervals as a sum of a small number sinusoidal (i.e., harmonic) components with unknown frequencies, deterministic but unknown amplitudes, unknown order (i.e., number of harmonic components), and unknown noise autocorrelation function. It is this model of the data that makes the solution computationally feasible, but also what leads to a degradation in performance since estimates are not based on the full time series. By modeling the signal in this way, we reliably detect the presence of multiple LFMCW signals in colored noise without the need for prewhitening, efficiently estimate (i.e., characterize) their parameters, provide estimation error variances for a subset of these parameters, and produce Time-Difference-of-Arrival (TDOA) estimates that can be used to estimate the geographical location (i.e., localize) of each LFMCW source. We demonstrate the performance of our method via simulation and real data collections, which are compared to the CRLB.