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In this paper we focus on deriving an approximate Cramer–Rao lower bound (CRLB) for the parameters of a multicomponent linear frequency modulated continuous wave (LFMCW) signal corrupted by complex additive white Gaussian noise. The approximation is necessary due to the discontinuities inherent in the mathematical model of the instantaneous phase of each LFMCW signal model. By comparing our approximate bound to a simulation of the maximum likelihood estimator (MLE) of the LFMCW parameters, we confirm our analysis. In general, the CRLB is a useful tool for feasibility studies or in evaluating the degree of suboptimality that non-MLE methods exhibit. For passive detection and estimation of LFMCW signals, the Generalized Likelihood Ratio Test and the associated MLE are difficult to implement in practice, primarily due to their large computational requirements. So, lower bounds on performance, such as those provided by the CRLB, are necessary to evaluate suboptimal methods that are more suited for practical implementations.

Many modern radar systems are overcoming the need for high-power transmitters by utilizing low peak-power, high duty-cycle waveforms, making noncooperative detection methods by traditional electronic surveillance a difficult task. This technological difficulty is driving a need for computationally tractable detection and characterization algorithms. Here, a practical method for detecting and fully characterizing an arbitrary number of low-power linear frequency modulated continuous wave (LFMCW) radar signals is achieved by dividing the time-domain signal into contiguous segments and treating each signal segment as a sum of harmonic components corrupted by noise with an unknown, time-varying power spectral density. This method is developed analytically and evaluated experimentally, revealing that the practicality of the method comes at the ex-pense of a loss in estimation accuracy when compared to the Cramer–Rao lower bound. Experimental results indicate that the parameters of two simultaneous LFMCW signals can be estimated to within $10\%$ of their true values with probability greater than $90\%$ when input signal-to-noise ratios are $-$ 10 dB and above with a 25 MHz bandwidth receiver.

We present an overview of the development of optimal detection methods using phase space (Wigner) distributions, and give a derivation for the detection of a known pulse in nonstationary noise. Application of the approach to detection of a pulse propagating with dispersion and absorption (or damping) is considered, using a recently developed Wigner-based approximation for pulse propagation.

This work considers the design of optimal, energy-constrained transmit signals for active sensing for the case when the designer has incomplete or uncertain knowledge of the target and/or environment. The mathematical formulation is that of a multi-objective optimization problem, wherein one can incorporate a plurality of potential targets, interference, or clutter models and in doing so take advantage of the wide range of results in the literature related to modeling each. It is shown, via simulation, that when the objective function of the optimization problem is chosen to maximize the minimum (i.e., maxmin) probability of detection among all possible model combinations, the optimal waveforms obtained are advantageous. The advantage results because the maxmin waveforms judiciously allocate energy to spectral regions where each of the target models respond strongly and each of the environmental models affect minimal detection performance degradation. In particular, improved detection performance is shown compared to linear frequency modulated transmit signals and compared to signals designed with the wrong target spectrum assumed. Additionally, it is shown that the maxmin design yields performance comparable to an optimal design matched to the correct target/environmental model. Finally, it is proven that the maxmin problem formulation is convex.

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) 1or 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 unknown frequencies, deterministic but unknown amplitudes, unknown order (i.e., number of harmonic components), and unknown 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 PFA 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 (i.e., localize) each LFMCW source. 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.

In this paper, the task of model-based transmit signal design for optimizing detection is considered. Building on past work that designs the spectral magnitude for optimizing detection, two methods for synthesizing minimum duration signals with this spectral magnitude are developed. The methods are applied to the design of signals that are optimal for detecting elastic objects in the presence of additive noise and self-noise. Elastic objects are modeled as linear time-invariant systems with known impulse responses, while additive noise (e.g., ocean noise or receiver noise) and acoustic self-noise (e.g., reverberation or clutter) are modeled as stationary Gaussian random processes with known power spectral densities. The first approach finds the waveform that preserves the optimal spectral magnitude while achieving the minimum temporal duration. The second approach yields a finite-length time-domain sequence by maximizing temporal energy concentration, subject to the constraint that the spectral magnitude is close (in a least-squares sense) to the optimal spectral magnitude. The two approaches are then connected analytically, showing the former is a limiting case of the latter. Simulation examples that illustrate the theory are accompanied by discussions that address practical applicability and how one might satisfy the need for target and environmental models in the real-world.

This paper develops an algorithm that can be used to solve the data association problem faced by a surveillance aircraft using Direction of Arrival angle measurements to locate a stationary RF signal source. The algorithm is based on statistical clustering of measurements with clusters being formed using a Mahalanobis distance association criterion. This approach accounts for angle measurement error statistics and avoids the computational complexity of an exhaustive combinatorial assignment. The optimal cluster is the one that maximized the target position log-likelihood function. This cluster is used to compute a target position estimate then removed from the set of measurements. The process is repeated until no additional clusters can be formed. Simulation results are shown where 100 measurements are distributed randomly across 7 target signal sources.

In this paper we overview the theory of Linear Time-Varying (LTV) filters and investigate via simulation their application to buried target classification in challenging nonstationary environments; in particular, environments where noise is not only nonstationary but exhibits statistical properties that are not known a priori. We then propose an extension of the Minimum Probability of Error (MPE) classifier (a/k/a Minimum Distance Receiver) by pre-processing the received data through a bank of LTV filters before the calculation of each test statistic via the MPE classifier. The proposed augmented MPE classifier is shown to outperform the conventional MPE classifier via simulation.

Some marine mammals as well as bats are known to emit sophisticated waveforms while searching for objects or hunting prey. Some dolphins have been observed to change their sonar pulse depending on the environment. Incorporating these strategies into sonar waveform and receiver design has become an active area of research. In this paper, we explore the application of an optimal waveform design scheme recently given by Kay, to the detection of elastic objects. We examine the benefits of optimal waveform design versus transmitting a linear FM waveform, as well as performance loss suffered by assuming a point target. The optimization approach designs the magnitude spectrum of the transmit waveform and, accordingly, there is an unlimited number of "optimal" transmit waveforms with the same magnitude spectrum. We propose a time domain optimization criterion to obtain the transmit waveform with the optimal magnitude spectrum and the smallest possible duration, as well as the waveform with the optimal magnitude spectrum and the longest possible duration. The former waveform allows for higher ping rates, but necessarily has higher time domain peak power, while the latter waveform has lower time domain peak power and lower ping rates. A method to obtain waveforms that are a blend of these two extremes is also presented, allowing a smooth trade-off between ping rate and peak power.

Idiopathic intracranial hypertension (IIH) is a syndrome of unknown etiology characterized by elevated intracranial pressure (ICP). Although a stenosis of the transverse sinus has been observed in many IIH patients, the role this feature plays in IIH is in dispute. In this paper, a lumped-parameter model is developed for the purpose of analytically investigating the elevated pressures associated with IIH and a collapsible transverse sinus. This analysis yields practical predictions regarding the degree of elevated ICPs and the effectiveness of various treatment methods. Results suggest that IIH may be caused by a sufficiently collapsible transverse sinus, but it is also possible that a stenosed sinus may persist following resolution of significant intracranial hypertension.

Detection, classification, and localization of underwater objects is a primary function of active sonar systems. Detection involves making a decision on whether or not an object of interest is present. Once a positive detection has been made, further information may be needed to classify the object as one among a set of possible objects of interest. Previous efforts have been directed at designing transmit sonar waveforms to maximize detection performance. In this work, we extend the optimal sonar design approach to enhance classification after detection. In particular, we present an optimal signal design approach that is aimed at maximizing the probability of correctly classifying the true target from among a set of assumed candidates. The approach is evaluated theoretically and via simulations, by which it is shown that waveform design can yield improvements in classification performance. [Work supported by ONR.]

Classification of submerged objects has traditionally been performed using high frequency sonars and imaging techniques. While this permits fine matching of target templates to images acquired in the field, HF methods are necessarily limited in range due to absorption of sound by the water. LF sonars, while offering increased detection range, come with some significant challenges related to the limited bandwidth available. Nonetheless, we show that it is feasible to estimate object size using nonimaging techniques. There are a number of low‐frequency phenomena that can be exploited to this end. Among these are edge diffraction in which sharply angled facets of objects (“edges”) act like independent, radiating point sources, and helical waves, which can be set up in cylindrical objects. We show that with appropriate postprocessing of these returns, object edges can be localized thus allowing object extent to be assessed. In this paper, we describe our processing system, and then give results when this syst...

In undersea environments, particularly shallow water, the sonar backscatter from objects of interest can be subject to propagation effects such as dispersion, attenuation, and multi‐path, which can confound detection and classification. Detection and classification of buried objects are further complicated by dramatic changes in the backscatter due to the sediment layer. These propagation and environmental effects can induce time‐varying (or nonstationary) characteristics in the received sonar signal. In addition, the object itself can induce nonstationarities, such as the inherent dispersion characteristics of some elastic objects. The processing and analysis of such signals for detection and classification can be enhanced by applying time‐varying methods to the received signal, such as time‐frequency analysis and linear time‐varying filters. Detection can also be enhanced by designing a transmit waveform to optimize some metric, such as received signal‐to‐interference/noise power. In this talk, we explo...

Animals that navigate and hunt by echolocation, such as some bats and marine mammals, have been observed to change their sonar pulse depending on the environment, as well as during hunting. It has become of interest to incorporate these strategies into man‐made sonar waveform and receiver design. We examine the benefits of optimal waveform design versus transmitting a linear FM waveform for detecting elastic objects. Performance loss suffered by assuming a point target is also examined. Our approach utilizes a method recently proposed by Kay to design the optimal power spectrum of the transmit waveform. Because there is an unlimited number of waveforms with the same power spectrum, we further impose a time domain constraint, in terms of the signal duration, to obtain a unique optimal waveform. [Work supported by ONR 321US.]