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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.

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.

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.]