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

Putting reaction-diffusion systems into port-Hamiltonian framework

Reaction-diffusion systems model the evolution of the constituents distributed in space under the influence of chemical reactions and diffusion [6], [10]. These systems arise naturally in chemistry [5], but can also be used to model dynamical processes beyond the realm of chemistry such as biology, ecology, geology, and physics. In this paper, by adopting the viewpoint of port-controlled Hamiltonian systems [7] we cast reaction-diffusion systems into the portHamiltonian framework. Aside from offering conceptually a clear geometric interpretation formalized by a Stokes-Dirac structure [8], a port-Hamiltonian perspective allows to treat these dissipative systems as interconnected and thus makes their analysis, both quantitative and qualitative, more accessible from a modern dynamical systems and control theory point of view. This modeling approach permits us to draw immediately some conclusions regarding passivity and stability of reaction-diffusion systems. It is well-known that adding diffusion to the reaction system can generate behaviors absent in the ode case. This primarily pertains to the problem of diffusion-driven instability which constitutes the basis of Turing’s mechanism for pattern formation [11], [5]. Here the treatment of reaction-diffusion systems as dissipative distributed portHamiltonian systems could prove to be instrumental in supply of the results on absorbing sets, the existence of the maximal attractor and stability analysis. Furthermore, by adopting a discrete differential geometrybased approach [9] and discretizing the reaction-diffusion system in port-Hamiltonian form, apart from preserving a geometric structure, a compartmental model analogous to the standard one [1], [2] is obtaine