Passive Detection, Characterization, and Localization of multiple LFMCW LPI signals

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. In contrast to other detection and characterization approaches, such as those based on the Wigner-Ville Transform (WVT) [1] or the Wigner-Ville Hough Transform (WVHT) [2], 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 sinusoidal (i.e., harmonic) components with deterministic but unknown frequencies, amplitudes, order (i.e., number of harmonic components), and noise autocorrelation function. Using this model of the signal, which we refer to as the Short-Time Harmonic Model (STHM), we implement a detection statistic based on Thompson's Method for harmonic analysis [3] which leads to a detection threshold that is a function of False Alarm Probability P_FA and not a function of the noise properties. By doing so 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-of-Arrival (TOA) estimates that can be used to estimate the geographical location of each LFMCW source (i.e., localize). Finally, by using the entire time-series we refine these parameter estimates by using them as initial conditions to the Maximum Likelihood Estimator (MLE), which was originally given in [1] and later found in [2] to be too computationally expensive for multiple LFMCW signals if accurate initial conditions were not available to limit the search space. We demonstrate the performance of our approach via simulation.