3D Localization and Tracking Methods for Multi-Platform Radar Networks

Multi-platform radar networks (MPRNs) are an emerging sensing technology due to their ability to provide improved surveillance capabilities over plain monostatic and bistatic systems. The design of advanced detection, localization, and tracking algorithms for efficient fusion of information obtained through multiple receivers has attracted much attention. However, considerable challenges remain. This article provides an overview on recent unconstrained and constrained localization techniques as well as multitarget tracking (MTT) algorithms tailored to MPRNs. In particular, two data-processing methods are illustrated and explored in detail, one aimed at accomplishing localization tasks the other tracking functions. As to the former, assuming a MPRN with one transmitter and multiple receivers, the angular and range constrained estimator (ARCE) algorithm capitalizes on the knowledge of the transmitter antenna beamwidth. As to the latter, the scalable sum-product algorithm (SPA) based MTT technique is presented. Additionally, a solution to combine ARCE and SPA-based MTT is investigated in order to boost the accuracy of the overall surveillance system. Simulated experiments show the benefit of the combined algorithm in comparison with the conventional baseline SPA-based MTT and the stand-alone ARCE localization, in a 3D sensing scenario.

New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both the strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cram\'er-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state of the art strategies.

Power-Aperture Resource Allocation for a MPAR with Communications Capabilities

Multifunction phased array radars (MPARs) exploit the intrinsic flexibility of their active electronically steered array (ESA) to perform, at the same time, a multitude of operations, such as search, tracking, fire control, classification, and communications. This paper aims at addressing the MPAR resource allocation so as to satisfy the quality of service (QoS) demanded by both line of sight (LOS) and non line of sight (NLOS) search operations along with communications tasks. To this end, the ranges at which the cumulative detection probability and the channel capacity per bandwidth reach a desired value are introduced as task quality metrics for the search and communication functions, respectively. Then, to quantify the satisfaction level of each task, for each of them a bespoke utility function is defined to map the associated quality metric into the corresponding perceived utility. Hence, assigning different priority weights to each task, the resource allocation problem, in terms of radar power aperture (PAP) specification, is formulated as a constrained optimization problem whose solution optimizes the global radar QoS. Several simulations are conducted in scenarios of practical interest to prove the effectiveness of the approach.

A Learning-Inspired Strategy to Design Binary Sequences with Good Correlation Properties: SISO and MIMO Radar Systems

In this paper, the design of binary sequences exhibiting low values of aperiodic/periodic correlation functions, in terms of Integrated Sidelobe Level (ISL), is pursued via a learning-inspired method. Specifcally, the synthesis of either a single or a burst of codes is addressed, with reference to both Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) radar systems. Two optimization machines, referred to as two-layer and single-layer Binary Sequence Correlation Network (BiSCorN), able to learn actions to design binary sequences with small ISL/Complementary ISL (CISL) for SISO and MIMO systems are proposed. These two networks differ in terms of the capability to synthesize Low-Correlation-Zone (LCZ) sequences and computational cost. Numerical experiments show that proposed techniques can outperform state-of-the-art algorithms for the design of binary sequences and Complementary Sets of Sequences (CSS) in terms of ISL and, interestingly, of Peak Sidelobe Level (PSL).

Large Deviations for Classification Performance Analysis of Machine Learning Systems

We study the performance of machine learning binary classification techniques in terms of error probabilities. The statistical test is based on the Data-Driven Decision Function (D3F), learned in the training phase, i.e., what is thresholded before the final binary decision is made. Based on large deviations theory, we show that under appropriate conditions the classification error probabilities vanish exponentially, as $\sim \exp\left(-n\,I + o(n) \right)$, where $I$ is the error rate and $n$ is the number of observations available for testing. We also propose two different approximations for the error probability curves, one based on a refined asymptotic formula (often referred to as exact asymptotics), and another one based on the central limit theorem. The theoretical findings are finally tested using the popular MNIST dataset.

Adaptive Radar Detection and Bearing Estimation in the Presence of Unknown Mutual Coupling

This paper deals with joint adaptive radar detection and target bearing estimation in the presence of mutual coupling among the array elements. First of all, a suitable model of the signal received by the multichannel radar is developed via a linearization procedure of the Uniform Linear Array (ULA) manifold around the nominal array looking direction together with the use of symmetric Toeplitz structured matrices to represent the mutual coupling effects. Hence, the Generalized Likelihood Ratio Test (GLRT) detector is evaluated under the assumption of homogeneous radar environment. Its computation leverages a specific Minorization-Maximization (MM) framework, with proven convergence properties, to optimize the concentrated likelihood function under the target presence hypothesis. Besides, when the number of active mutual coupling coefficients is unknown, a Multifamily Likelihood Ratio Test (MFLRT) approach is invoked. During the analysis phase, the performance of the new detectors is compared with benchmarks as well as with counterparts available in the open literature which neglect the mutual coupling phenomenon. The results indicate that it is necessary to consider judiciously the coupling effect since the design phase, to guarantee performance levels close to the benchmark.

Statistical Hypothesis Testing Based on Machine Learning: Large Deviations Analysis

We study the performance -- and specifically the rate at which the error probability converges to zero -- of Machine Learning (ML) classification techniques. Leveraging the theory of large deviations, we provide the mathematical conditions for a ML classifier to exhibit error probabilities that vanish exponentially, say $\sim \exp\left(-n\,I + o(n) \right)$, where $n$ is the number of informative observations available for testing (or another relevant parameter, such as the size of the target in an image) and $I$ is the error rate. Such conditions depend on the Fenchel-Legendre transform of the cumulant-generating function of the Data-Driven Decision Function (D3F, i.e., what is thresholded before the final binary decision is made) learned in the training phase. As such, the D3F and, consequently, the related error rate $I$, depend on the given training set, which is assumed of finite size. Interestingly, these conditions can be verified and tested numerically exploiting the available dataset, or a synthetic dataset, generated according to the available information on the underlying statistical model. In other words, the classification error probability convergence to zero and its rate can be computed on a portion of the dataset available for training. Coherently with the large deviations theory, we can also establish the convergence, for $n$ large enough, of the normalized D3F statistic to a Gaussian distribution. This property is exploited to set a desired asymptotic false alarm probability, which empirically turns out to be accurate even for quite realistic values of $n$. Furthermore, approximate error probability curves $\sim \zeta_n \exp\left(-n\,I \right)$ are provided, thanks to the refined asymptotic derivation (often referred to as exact asymptotics), where $\zeta_n$ represents the most representative sub-exponential terms of the error probabilities.

Multi-Spectrally Constrained Transceiver Design against Signal-Dependent Interference

This paper focuses on the joint synthesis of constant envelope transmit signal and receive filter aimed at optimizing radar performance in signal-dependent interference and spectrally contested-congested environments. To ensure the desired Quality of Service (QoS) at each communication system, a precise control of the interference energy injected by the radar in each licensed/shared bandwidth is imposed. Besides, along with an upper bound to the maximum transmitted energy, constant envelope (with either arbitrary or discrete phases) and similarity constraints are forced to ensure compatibility with amplifiers operating in saturation regime and bestow relevant waveform features, respectively. To handle the resulting NP-hard design problems, new iterative procedures (with ensured convergence properties) are devised to account for continuous and discrete phase constraints, capitalizing on the Coordinate Descent (CD) framework. Two heuristic procedures are also proposed to perform valuable initializations. Numerical results are provided to assess the effectiveness of the conceived algorithms in comparison with the existing methods.

Structured Covariance Matrix Estimation with Missing-Data for Radar Applications via Expectation-Maximization

Structured covariance matrix estimation in the presence of missing data is addressed in this paper with emphasis on radar signal processing applications. After a motivation of the study, the array model is specified and the problem of computing the maximum likelihood estimate of a structured covariance matrix is formulated. A general procedure to optimize the observed-data likelihood function is developed resorting to the expectation-maximization algorithm. The corresponding convergence properties are thoroughly established and the rate of convergence is analyzed. The estimation technique is contextualized for two practically relevant radar problems: beamforming and detection of the number of sources. In the former case an adaptive beamformer leveraging the EM-based estimator is presented; in the latter, detection techniques generalizing the classic Akaike information criterion, minimum description length, and Hannan-Quinn information criterion, are introduced. Numerical results are finally presented to corroborate the theoretical study.