Emanuele Grossi

Compressed sensing of time-varying signals

Compressed sensing (CS) lowers the number of measurements required for reconstruction and estimation of signals that are sparse when expanded over a proper basis. Traditional CS approaches deal with time-invariant sparse signals, meaning that, during the measurement process, the signal of interest does not exhibit variations. However, many signals encountered in practice are varying with time as the observation window increases (e.g., video imaging, where the signal is sparse and varies between different frames). The present paper develops CS algorithms for time-varying signals, based on the least-absolute shrinkage and selection operator (Lasso) that has been popular for sparse regression problems. The Lasso here is tailored for smoothing time-varying signals, which are modeled as vector valued discrete time series. Two algorithms are proposed: the Group-Fused Lasso, when the unknown signal support is time-invariant but signal samples are allowed to vary with time; and the Dynamic Lasso, for the general class of signals with time-varying amplitudes and support. Performance of these algorithms is compared with a sparsity-unaware Kalman smoother, a support-aware Kalman smoother, and the standard Lasso which does not account for time variations. The numerical results amply demonstrate the practical merits of the novel CS algorithms.

A Novel Dynamic Programming Algorithm for Track-Before-Detect in Radar Systems

In this paper we present a novel procedure for multi-frame detection in radar systems. The proposed architecture consists of a pre-processing stage, which extracts a set of candidate alarms (or plots) from the raw data measurements (e.g., this can be the Detector and Plot-Extractor of common radar systems), and a track-before-detect (TBD) processor, which jointly elaborates observations from multiple scans (or frames) and confirms reliable plots. A computationally efficient dynamic programming algorithm for the TBD processor is derived, which does not require a discretization of the state space and operates directly on the input plot-lists. Finally, a simple algorithm to solve possible data association problems arising at the track-formation step is given, and a thorough complexity and performance analysis is provided, showing that large detection gains with respect to the standard radar processing are achievable with negligible complexity increase.

Sequential Along-Track Integration for Early Detection of Moving Targets

This paper concerns the joint multiframe sequential target detection and track estimation in early-warning radar surveillance systems. The rationale for applying sequential procedures in such a scenario is that they promise a sensitivity increase of the sensor or, alternatively, a reduction in the time needed to take a decision. Unlike previous works on sequential radar detection, the attention is not restricted to stationary targets, namely position changes during the illumination period are allowed. Starting from previous sequential rules, different truncated sequential strategies are proposed and assessed: they are aimed at orienting the sensor resources towards either the detection or the track estimation or the position estimation. Bounds on the performances of the proposed procedures in terms of the system parameters are derived and computational complexity is examined. Also, numerical experiments are provided to elicit the interplay between sensor-target parameters and system performances, and to quantify the gain with respect to other fixed-sample-size procedures.

Track-before-detect for multiframe detection with censored observations

In this work, we address the problem of target detection from multiple noisy observations produced by a generic sensor. A two-step approach is considered, wherein a censoring stage retains the significant measurements (i.e., those whose likelihood ratio exceeds a primary threshold) in each frame, while a multiframe detector elaborates the preprocessed observations and takes the final decision through a generalized likelihood ratio test. A dynamic programming algorithm to form the decision statistic, which exploits the sparse nature of the censored observations, is proposed. A closed-form complexity analysis is provided, and a thorough performance assessment is undertaken to elicit the tradeoffs among censoring level, system complexity, and achievable performance.

Space-Time Code Design for MIMO Detection Based on Kullback-Leibler Divergence

The focus of the paper is on the design of space-time codes for a general multiple-input, multiple-output detection problem, when multiple observations are available at the receiver. The figure of merit used for optimization purposes is the convex combination of the Kullback-Leibler divergences between the densities of the observations under the two hypotheses, and different system constraints are considered. This approach permits to control the average sample number (i.e., the time for taking a decision) in a sequential probability ratio test and to asymptotically minimize the probability of miss in a likelihood ratio test: the solutions offer an interesting insight in the optimal transmit policies, encapsulated in the rank of the code matrix, which rules the amount of diversity to be generated, as well as in the power allocation policy along the active eigenmodes. A study of the region of achievable divergence pairs, whose availability permits optimization of a wide range of merit figures, is also undertaken. A set of numerical results is finally given, in order to analyze and discuss the performance and validate the theoretical results.

A Track-Before-Detect Algorithm With Thresholded Observations and Closely-Spaced Targets

In this letter, we consider the detection architecture in , where a track-before-detect processor elaborates the plot-lists provided on a scan-by-scan basis by the detector and plot-extractor of a radar system. We derive a novel track formation procedure in order to provide improved performance in the presence of multiple, closely-spaced targets. Numerical examples are provided to assess the detection capabilities and the accuracy in the estimation of the target position.

Sequential Detection of Markov Targets With Trajectory Estimation

The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair signal-observation forms a hidden Markov model (HMM)), a sequential procedure is proposed, wherein the detection part is a sequential probability ratio test (SPRT) and the estimation part relies upon a maximum a posteriori probability (MAP) criterion, gated by the detection stage (the parameter to be estimated is the trajectory of the state evolution of the system itself). A thorough analysis of the asymptotic behavior of the test in this new scenario is given, and sufficient conditions for its asymptotic optimality are stated, i.e., for almost sure minimization of the stopping time and for (first-order) minimization of any moment of its distribution. An application to radar surveillance problems is also examined.

Track-before-detect for sea clutter rejection: tests with real data

Track-before-detect (TBD) is a popular incoherent energy integration technique aimed at improving detectability of weak targets. A number of studies are available in the literature demonstrating its efficacy against disturbance (whether noise or clutter), but most of them refer to synthetic data, i.e., relying on computer simulations. In this paper, we tackle the problem of assessing the TBD performance with real data and in a particularly severe clutter environment, i.e., sea-clutter. Precisely, using a set of real data from a ground-based sea-search radar, we implement TBD directly on the plot-lists coming from the radar plot extractor (this be can done with acceptable complexity by using an ad hoc dynamic programming algorithm), and demonstrate its effectiveness in reducing sea-clutter. As a further contribution, we also develop an improved decision logic for plot confirmation.

Min-max waveform design for MIMO radars under unknown correlation of the target scattering

The problem of robust waveform design for multiple-input, multiple-output radars equipped with widely-spaced antennas is addressed here. Robust design is needed as a number of parameters may be unknown, e.g., the target scattering covariance matrix (at both transmit and receive side). A min-max approach is adopted, and the code matrix is designed to minimize the worst-case cost under all possible target covariance matrices. Surprisingly, the same min-max solution applies to many commonly adopted performance measures. Examples illustrating the behavior of the min-max codes are provided for the mutual information.

A Heuristic Algorithm for Track-Before-Detect With Thresholded Observations in Radar Systems

We consider here the two-stage, multi-frame detection architecture proposed in in the context of radar systems, wherein the Detector and Plot Extractor provides a list of candidate detections (or plots) on a scan-by-scan basis to a Track-before-detect (TBD) Processor, which correlates data over multiple scans before taking the final decision as to the target presence. We propose a heuristic algorithm to implement the TBD processor, and we show that its computational complexity is smaller than that of the algorithm proposed in . Numerical examples demonstrate that the detection and estimation performance obtained with the new algorithm is almost coincident with that obtained with the algorithm in .