Allocating the weight to each local density is essential in generalized covariance intersection (GCI) fusion. However, such a problem has not been fully addressed in the existing literature and still remains an open issue. In this paper, we propose a deep learning enhanced framework that dynamically optimizes GCI fusion weights by leveraging sensor node dependent local variables, resulting in the GCINet for fusion of probability density functions (PDFs). The key innovation lies in the employment of contextual based variables (e.g., measurement noise) as input to a neural network, which is trained by minimizing a suitably defined cost function. The proposed approach eliminates the need for manual weight tuning and overcomes the limitations of traditional optimization-based methods reliant on, e.g., Shannon entropy or Chernoff information. Application of proposed GCINet to distributed extended object tracking (EOT) application is discussed. Simulation results show that the proposed GCINet achieves superior accuracy compared to GCI fusion under equal as well as heuristically designed fusion weights.

This paper discusses the problem of streaming coupled tensor factorization based on sensor networks, where each sensor observes only some features of the targets, and the measurements from sensors are provided in a streaming tensor fashion. Moreover, the observed features of different sensors might overlap (i.e., coupled tensor), and there is no central processing unit to collect all sensor data. Then, in our work, the canonical polyadic (CP) decomposition is exploited to perform local tensor decomposition based on the measurements of each sensor, and average consensus (AC) for diffusing information throughout the network. The proposed method is verified via simulations.

A key feature of extended target (ET) is that it can produce multiple measurements, thus providing detailed information such as size, orientation. However, due to the measurement number decrease, the ET tends to be a point target (PT) when it becomes far from the sensor, leading to disability of estimating the extensions. In this paper we consider the problem of distributed ETs tracking based on multiple sensors. In such a case the measurements decrease of an ET can be compensated by other sensors, so that the tracking performance can be maintained. In the proposed algorithm the targets are modeled by Poisson multi-Bernoulli (PMB) random finite set (RFS) and the state of each target consists of two parts representing the possibility of being ET and PT, respectively. In the local filtering state, interaction between ET and PT states is considered in the prediction step for target identity change between ET and PT, based on which the local PMB filter is achieved for seamlessly tracking ETs and PTs. In the fusion part a generalized covariance intersection (GCI) based criterion is proposed to fuse the posteriors of each sensor. The performance of proposed algorithm is verified via simulations.

In this article, we propose a novel approach to distributed joint detection, tracking, and classification (D-JDTC) of multiple targets by means of a multisensor network. The proposed approach relies on labeled multi-Bernoulli (LMB) random finite set modeling of the multisensor state, and consists of two main tasks, that is, local filtering in each individual node and data fusion among multiple nodes. For local filtering, the LMB filter is extended to JDTC by augmenting the target state to incorporate class and mode information. Further, the well-known generalized covariance intersection and recently developed minimum information loss fusion paradigms are exploited for data fusion among sensors. The effectiveness of the resulting algorithm, called D-JDTC-LMB, is assessed via simulation experiments.

With discrete modulation techniques, such as quadrature amplitude modulation and phase-shift keying, maximum likelihood (ML) signal detection in massive multi-input multi-output (MIMO) systems fundamentally relies on convex integer programming, executed efficiently through linear operations. However, for 1-bit massive MIMO systems, the nonlinearity introduced by 1-bit quantization impedes the linear realization of the ML detector. To achieve ML detector performance with manageable computational costs, researchers have proposed a two-stage strategy consisting of relaxed continuous convex programming followed by refinement using discrete search within the candidate solution set surrounding the optimal solution of the relaxed continuous convex programming. This article specifically examines the refinement stage. We demonstrate that it is possible to approximate the ML detection’s log-likelihood function using a 1-degree freedom quadratic function. We subsequently modify the decomposition algorithm for convex integer quadratic programming (CIQP) with a$d$-degree freedom matrix and box constraint. Finally, we employ the modified decomposition algorithm for refinement to obtain an initial candidate solution set, which is then expanded and pruned. This method is referred to as the improved CIQP-based algorithm. Numerical results indicate that the improved CIQP-based algorithm outperforms existing approaches in this domain.

Passive location and tracking of radio emitters is of great research value in civilian and defense applications. Among the existing methods, localization based on received signal strength indicator (RSSI) has been widely used due to its advantages in terms of low cost and easy implementation. However, most RSSI-based localization methods rely on the assumption that the emitter has been detected. Moreover, the emitter signal is supposed to propagate with the simplified path-loss model in which the shadow effects caused by obstacles are not considered. As a result, there are still gaps between the aforementioned methods and practical applications. In this paper, we consider the combined path-loss and shadowing model, which has been empirically confirmed in both outdoor and indoor radio propagation environments. Joint detection and tracking of an emitter is proposed by modeling the state of the emitter as Bernoulli random finite set, characterized by an existence probability and a spatial probability density function. Compared to existing studies, this paper works upon more practically appealing signal propagation model, and achieves better performance in real-time emitter detection and tracking. Moreover, the proposed method also provides explicit estimates of the unknown shadowing-related parameters, which can be adopted in further applications such as spectrum cartography and radio map construction. The feasibility of the proposed method is assessed via simulation experiments.

Target state estimation with Doppler-only sensors has attracted a lot of attention due to its wide potential applications in target localization and tracking. While existing Doppler-only tracking methods rely on the assumption that Doppler sensors have been correctly registered, in many practical cases there can be significant registration errors which imply measurement biases and thus performance degradation in target state estimation. Motivated by this issue, the present paper addresses the problem of jointly estimating target state and sensor biases based on Doppler-only measurements. The proposed method consists of two phases, i.e., (1) raw estimation of the target state without considering sensor biases, followed by (2) a bias compensation step that relies on linearization of the measurement function and joint estimation of target state-sensor biases via a least square method. The Cramer-Rao lower bound (CRLB) in estimating sensor biases is evaluated and the performance of the proposed method is also assessed via simulations.

In the wireless communication system, the pilot is essential for channel estimation. This paper study the pilot design of the 1-bit massive multi-input multi-output system with the flat Rayleigh fading channel. This paper aims to design the pilot matrix minimizing the estimation error of the Bussgang linear minimum mean squared error (BLMMSE) channel estimator, of which the estimation error is given by a closed-form formula. An approximate BLMMSE channel estimation error is derived in the low signal-to-noise ratio (SNR) region. The lower bound of the approximate channel estimation error for all possible pilot matrices is derived. The analysis shows that the pilot matrix with pairwise orthogonal and equal-norm row vectors and equal-norm column vectors is optimal in terms of approximate channel estimation error. The hypersphere-based steepest descent (HSD) algorithm is proposed to design the pilot matrix by optimizing the performance of the BLMMSE estimator. The numerical results show that the proposed HSD algorithm has a noticeable improvement in channel estimation compared with the DFT pilot and the random pilot. The HSD algorithm is also valid for the near maximum likelihood estimator and SNR mismatch.

A B-Spline implementation of the multi-target multi-Bernoulli (MeMBer) filter for nonlinear Gaussian/non-Gaussian models is proposed. Specifically, the spatial PDF (SPDF) of each Bernoulli component in the MeMBer density is represented by a B-Spline curve, which is characterized by the spline knots and control points. The spline knots and control points are then propagated via prediction and update steps of the MeMBer filter. Besides, a revised fitting algorithm is proposed so as to improve the implementation efficiency. The effectiveness of the proposed method is assessed via simulation experiments.

The interest of this paper is to detect an unmanned aerial vehicle (UAV) and then initialize its trajectory, if it exists. The difficulties of detecting a UAV mainly lie in two aspects: a) small radar cross section (RCS), which causes extremely low signal-to-noise ratio (SNR); and b) low velocity, which results in weak Doppler effect. In this case, traditional track-before-detect (TBD) algorithms cannot achieve the satisfying probability of detection. In this paper, we propose to solve the problem of detecting a UAV based on micro-Doppler aided dynamic programming TBD (MA-DP-TBD) algorithm where the effect of micro-Doppler caused by the blades of UAV is taken into consideration to aid the detection process. The performance of proposed algorithm is examined via simulations.

This paper focuses on reducing communication bandwidth and, consequently, energy consumption in the context of distributed target detection and tracking over a peer-to-peer sensor network. A consensus Bernoulli filter with event-triggered communication is developed by enforcing each node to transmit its local information to the neighbors only when a suitable measure of discrepancy between the current local posterior and the one predictable from the last transmission exceeds a preset threshold. Two information-theoretic criteria, i.e. Kullback-Leibler divergence and Hellinger distance, are adopted in order to measure the discrepancy between random finite set densities. The performance of the proposed event-triggered consensus Bernoulli filter is evaluated through simulation experiments.

In this work, the terrain data is exploited for passive source localization with Doppler frequency shift (DFS) measurements. The localization problem is modeled as a maximum likelihood estimation (MLE) problem. Firstly, in order to avoid carrying out optimization step on a highly nonlinear objective function, the likelihood function is reformulated as a constrained weighted least squares (CWLS) problem. Then it is further relaxed into the semidefinite programming (SDP) problem by a semidefinite relaxation (SDR) method, which can be solved by modern convex optimization methods. By incorporating the terrain data, the localization accuracy is promoted. The performance of the proposed algorithm is examined via simulations in a typical scenario.

This paper addresses the problem of target detection and tracking through a single frequency network with receiver position error. We consider the case that the SNR is low and it is hard to detect a target using the common detection algorithm like CFAR. The particle filter based track-before-detect algorithm is adopted to integrate the signal through sampling intervals to increase the SNR. The receiver is registered along with target detection and tracking. The performance of proposed algorithm is examined through simulations.

Several array systems along with algorithms based on sub-Nyquist sampling techniques have been extensively studied. This letter is committed to the joint frequency and direction-of-arrival estimation of more sources than sensors in a subband by using sparse arrays with sub-Nyquist sampling. The newly defined block vectorization eliminates the interference from sub-Nyquist sampling. Based on this, a novel augmented sample covariance matrix method is proposed, which enhances the spatial degrees of freedom and increases the number of identifiable sources. Simulations show that the joint estimation can be realized at a lower sampling rate with fewer sensors at the expense of a degradation in estimation performance. Such an algorithm provides a tradeoff between the expensive resource of sensors and channels, and the estimation performance.

In this paper, consensus-based Kalman filtering is extended to deal with the problem of joint target tracking and sensor self-localization in a distributed wireless sensor network. The average weighted Kullback-Leibler divergence, which is a function of the unknown drift parameters, is employed as the cost to measure the discrepancy between the fused posterior distribution and the local distribution at each sensor. Further, a reasonable approximation of the cost is proposed and an online technique is introduced to minimize the approximated cost function with respect to the drift parameters stored in each node. The remarkable features of the proposed algorithm are that it needs no additional data exchanges, slightly increased memory space and computational load comparable to the standard consensus-based Kalman filter. Finally, the effectiveness of the proposed algorithm is demonstrated through simulation experiments on both a tree network and a network with cycles as well as for both linear and nonlinear sensors.

This work focuses on the moving target localization problem in the noncoherent multiple-input multiple-output radar system with widely separated antennas. We assume that the time delay and Doppler shift between each transmit/receive element pair have already been measured by a preprocessing algorithm. Utilizing these measurements, an explicit method for jointly estimating the target position and velocity is proposed. It first divides the measurements into several groups based on the different transmitter elements or receive elements, and then employs two best linear unbiased estimators successively for each group to independently produce an estimate of target position and velocity. Finally, these results from different groups are combined to form a composite estimate. Simulation results show that the estimated accuracy of the proposed method achieves the Cramér-Rao lower bound at sufficiently small noise conditions.

Blind despreading of long-code direct sequence spread spectrum (DS-SS) signal with unknown carrier frequency offset (CFO) is considered. The maximum likelihood estimate (MLE) of spreading waveform is first derived, and to cope with the unknown CFO, we then use the semidefinite relaxation (SDR) technique to approximate our MLE problem as a convex semidefinite programming (SDP) problem, which can be solved efficiently using modern convex optimization methods. Simulation results demonstrate that the proposed approach significantly outperforms the dominant mode despreading estimator whether or not CFO exists at low signal to noise ratio (SNR).

In this study, the problem of estimating the spreading waveform of long-code direct sequence spread spectrum (DSSS) signals is considered. A novel spreading waveform estimation method based on a missing data model is proposed. By showing that the long-code DSSS signal can be equivalently represented as a short-code DSSS signal with missing data, the spreading waveform estimation problem can be viewed as a low-rank matrix approximation problem with missing data that can be approximately solved by the existing optimisation methods. To evaluate the performance of the author's proposed estimator, the authors also derive the Cramer–Rao lower bound (CRB) on the mean square error of spreading waveform estimators. The simulation results demonstrate that the proposed estimator approaches the CRB and provides significant performance improvement compared with the existing estimators in the case of low signal-to-noise ratio situations.