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In solving the non-myopic radar scheduling for multiple smart target tracking within an active and passive radar network, we need to consider both short-term enhanced tracking performance and a higher probability of target maneuvering in the future with active tracking. Acquiring the long-term tracking performance while scheduling the beam resources of active and passive radars poses a challenge. To address this challenge, we model this problem as a Markov decision process consisting of parallel restless bandit processes. Each bandit process is associated with a smart target, of which the estimation state evolves according to different discrete dynamic models for different actions - whether or not the target is being tracked. The discrete state is defined by the dynamic mode. The problem exhibits the curse of dimensionality, where optimal solutions are in general intractable. We resort to heuristics through the famous restless multi-armed bandit techniques. It follows with efficient scheduling policies based on the indices that are real numbers representing the marginal rewards of taking different actions. For the inevitable practical case with unknown transition matrices, we propose a new method that utilizes the forward Sarsa and backward Q-learning to approximate the indices through adapting the state-action value functions, or equivalently the Q-functions, and propose a new policy, namely ISQ, aiming to maximize the long-term tracking rewards. Numerical results demonstrate that the proposed ISQ policy outperforms conventional Q-learning-based methods and rapidly converges to the well-known Whittle index policy with revealed state transition models, which is considered the benchmark., Comment: 11 pages

In this article, the state estimation problems with unknown process noise and measurement noise covariances for both linear and nonlinear systems are considered. By formulating the joint estimation of system state and noise parameters into an optimization problem, a novel adaptive Kalman filter method based on conjugate-computation variational inference, referred to as CVIAKF, is proposed to approximate the joint posterior probability density function of the latent variables. Unlike the existing adaptive Kalman filter methods utilizing variational inference in natural-parameter space, CVIAKF performs optimization in expectation-parameter space, resulting in a faster and simpler solution. Meanwhile, CVIAKF divides optimization objectives into conjugate and non-conjugate parts of nonlinear dynamical models, whereas conjugate computations and stochastic mirror-descent are applied, respectively. Remarkably, the reparameterization trick is used to reduce the variance of stochastic gradients of the non-conjugate parts. The effectiveness of CVIAKF is validated through synthetic and real-world datasets of maneuvering target tracking., Comment: 13 pages

A smart target, also referred to as a reactive target, can take maneuvering motions to hinder radar tracking. We address beam scheduling for tracking multiple smart targets in phased array radar networks. We aim to mitigate the performance degradation in previous myopic tracking methods and enhance the system performance, which is measured by a discounted cost objective related to the tracking error covariance (TEC) of the targets. The scheduling problem is formulated as a restless multi-armed bandit problem (RMABP) with state variables, following the Markov decision process. In particular, the problem consists of parallel bandit processes. Each bandit process is associated with a target and evolves with different transition rules for different actions, i.e., either the target is tracked or not. We propose a non-myopic, scalable policy based on Whittle indices for selecting the targets to be tracked at each time. The proposed policy has a linear computational complexity in the number of targets and the truncated time horizon in the index computation, and is hence applicable to large networks with a realistic number of targets. We present numerical evidence that the model satisfies sufficient conditions for indexability (existence of the Whittle index) based upon partial conservation laws, and, through extensive simulations, we validate the effectiveness of the proposed policy in different scenarios., Comment: 14 pages

We address the challenge of tracking an unknown number of targets in strong clutter environments using measurements from a radar sensor. Leveraging the range-Doppler spectra information, we identify the measurement classes, which serve as additional information to enhance clutter rejection and data association, thus bolstering the robustness of target tracking. We first introduce a novel neural enhanced message passing approach, where the beliefs obtained by the unified message passing are fed into the neural network as additional information. The output beliefs are then utilized to refine the original beliefs. Then, we propose a classification-aided robust multiple target tracking algorithm, employing the neural enhanced message passing technique. This algorithm is comprised of three modules: a message-passing module, a neural network module, and a Dempster-Shafer module. The message-passing module is used to represent the statistical model by the factor graph and infers target kinematic states, visibility states, and data associations based on the spatial measurement information. The neural network module is employed to extract features from range-Doppler spectra and derive beliefs on whether a measurement is target-generated or clutter-generated. The Dempster-Shafer module is used to fuse the beliefs obtained from both the factor graph and the neural network. As a result, our proposed algorithm adopts a model-and-data-driven framework, effectively enhancing clutter suppression and data association, leading to significant improvements in multiple target tracking performance. We validate the effectiveness of our approach using both simulated and real data scenarios, demonstrating its capability to handle challenging tracking scenarios in practical radar applications., Comment: 15 pages

We track moving targets with a distributed multiple-input multiple-output (MIMO) radar, for which the transmitters and receivers are appropriately paired and selected with a limited number of radar stations. We aim to maximize the sum of the signal-to-interference-plus-noise ratios (SINRs) of all the targets by sensibly selecting the transmitter-receiver pairs during the tracking period. A key is to model the optimization problem of selecting the transmitter-receiver pairs by a restless multi-armed bandit (RMAB) model that is able to formulate the time-varying signals of the transceiver channels whenever the channels are being probed or not. We regard the estimated mean reward (i.e., SINR) as the state of an arm. If an arm is probed, the estimated mean reward of the arm is the weighted sum of the observed reward and the predicted mean reward; otherwise, it is the predicted mean reward. We associate the predicted mean reward with the estimated mean reward at the previous time slot and the state of the target, which is estimated via the interacting multiple model-unscented Kalman filter (IMM-UKF). The optimized selection of transmitter-receiver pairs at each time is accomplished by using Binary Particle Swarm Optimization (BPSO) based on indexes of arms, each of which is designed by the upper confidence bound (UCB1) algorithm. Above all, a multi-group combinatorial-restless-bandit technique taking into account of different combinations of transmitters and receivers and the closed-loop scheme between transmitter-receiver pair selection and target state estimation, namely MG-CRB-CL, is developed to achieve a near-optimal selection strategy and improve multi-target tracking performance. Simulation results for different scenarios are provided to verify the effectiveness and superior performance of our MG-CRB-CL algorithm., Comment: 13 pages

Deep convolutional neural network has made great achievements in sea-land clutter classification for over-the-horizon-radar (OTHR). The premise is that a large number of labeled training samples must be provided for a sea-land clutter classifier. In practical engineering applications, it is relatively easy to obtain label-free sea-land clutter samples. However, the labeling process is extremely cumbersome and requires expertise in the field of OTHR. To solve this problem, we propose an improved generative adversarial network, namely weighted loss semi-supervised generative adversarial network (WL-SSGAN). Specifically, we propose a joint feature matching loss by weighting the middle layer features of the discriminator of semi-supervised generative adversarial network. Furthermore, we propose the weighted loss of WL-SSGAN by linearly weighting standard adversarial loss and joint feature matching loss. The semi-supervised classification performance of WL-SSGAN is evaluated on a sea-land clutter dataset. The experimental results show that WL-SSGAN can improve the performance of the fully supervised classifier with only a small number of labeled samples by utilizing a large number of unlabeled sea-land clutter samples. Further, the proposed weighted loss is superior to both the adversarial loss and the feature matching loss. Additionally, we compare WL-SSGAN with conventional semi-supervised classification methods and demonstrate that WL-SSGAN achieves the highest classification accuracy., Comment: 9 pages

Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models. Due to the nonlinearity of the models and the non-conjugate prior, the state estimation problem is generally intractable as it involves integrals of general nonlinear functions and unknown process noise covariance, resulting in the posterior probability distribution functions lacking closed-form solutions. This paper presents a recursive solution for joint nonlinear state estimation and model parameters identification based on the approximate Bayesian inference principle. The stochastic search variational inference is adopted to offer a flexible, accurate, and effective approximation of the posterior distributions. We make two contributions compared to existing variational inference-based noise adaptive filtering methods. First, we introduce an auxiliary latent variable to decouple the latent variables of dynamic state and process noise covariance, thereby improving the flexibility of the posterior inference. Second, we split the variational lower bound optimization into conjugate and non-conjugate parts, whereas the conjugate terms are directly optimized that admit a closed-form solution and the non-conjugate terms are optimized by natural gradients, achieving the trade-off between inference speed and accuracy. The performance of the proposed method is verified on radar target tracking applications by both simulated and real-world data., Comment: 11 pages

In the sea-land clutter classification of sky-wave over-the-horizon-radar (OTHR), the imbalanced and scarce data leads to a poor performance of the deep learning-based classification model. To solve this problem, this paper proposes an improved auxiliary classifier generative adversarial network~(AC-GAN) architecture, namely auxiliary classifier variational autoencoder generative adversarial network (AC-VAEGAN). AC-VAEGAN can synthesize higher quality sea-land clutter samples than AC-GAN and serve as an effective tool for data augmentation. Specifically, a 1-dimensional convolutional AC-VAEGAN architecture is designed to synthesize sea-land clutter samples. Additionally, an evaluation method combining both traditional evaluation of GAN domain and statistical evaluation of signal domain is proposed to evaluate the quality of synthetic samples. Using a dataset of OTHR sea-land clutter, both the quality of the synthetic samples and the performance of data augmentation of AC-VAEGAN are verified. Further, the effect of AC-VAEGAN as a data augmentation method on the classification performance of imbalanced and scarce sea-land clutter samples is validated. The experiment results show that the quality of samples synthesized by AC-VAEGAN is better than that of AC-GAN, and the data augmentation method with AC-VAEGAN is able to improve the classification performance in the case of imbalanced and scarce sea-land clutter samples., Comment: 13 pages, 16 figures

Multitarget tracking in the interference environments suffers from the nonuniform, unknown and time-varying clutter, resulting in dramatic performance deterioration. We address this challenge by proposing a robust multitarget tracking algorithm, which estimates the states of clutter and targets simultaneously by the message-passing (MP) approach. We define the non-homogeneous clutter with a finite mixture model containing a uniform component and multiple nonuniform components. The measured signal strength is utilized to estimate the mean signal-to-noise ratio (SNR) of targets and the mean clutter-to-noise ratio (CNR) of clutter, which are then used as additional feature information of targets and clutter to improve the performance of discrimination of targets from clutter. We also present a hybrid data association which can reason over correspondence between targets, clutter, and measurements. Then, a unified MP algorithm is used to infer the marginal posterior probability distributions of targets, clutter, and data association by splitting the joint probability distribution into a mean-field approximate part and a belief propagation part. As a result, a closed-loop iterative optimization of the posterior probability distribution can be obtained, which can effectively deal with the coupling between target tracking, clutter estimation and data association. Simulation results demonstrate the performance superiority and robustness of the proposed multitarget tracking algorithm compared with the probability hypothesis density (PHD) filter and the cardinalized PHD (CPHD) filter., Comment: 21 pages, 21 figures

This paper optimizes path planning for a trunkand-branch topology network in an irregular 2-dimensional manifold embedded in 3-dimensional Euclidean space with application to submarine cable network planning. We go beyond our earlier focus on the costs of cable construction (including labor, equipment and materials) together with additional cost to enhance cable resilience, to incorporate the overall cost of branching units (again including material, construction and laying) and the choice of submarine cable landing stations, where such a station can be anywhere on the coast in a connected region. These are important issues for the economics of cable laying and significantly change the model and the optimization process. We pose the problem as a variant of the Steiner tree problem, but one in which the Steiner nodes can vary in number, while incurring a penalty. We refer to it as the weighted Steiner node problem. It differs from the Euclidean Steiner tree problem, where Steiner points are forced to have degree three; this is no longer the case, in general, when nodes incur a cost. We are able to prove that our algorithm is applicable to Steiner nodes with degree greater than three, enabling optimization of network costs in this context. The optimal solution is achieved in polynomialtime using dynamic programming.

This paper provides an optimized cable path planning solution for a tree-topology network in an irregular 2D manifold in a 3D Euclidean space, with an application to the planning of submarine cable networks. Our solution method is based on total cost minimization, where the individual cable costs are assumed to be linear to the length of the corresponding submarine cables subject to latency constraints between pairs of nodes. These latency constraints limit the cable length and number of hops between any pair of nodes. Our method combines the Fast Marching Method (FMM) and a new Integer Linear Programming (ILP) formulation for Minimum Spanning Tree (MST) where there are constraints between pairs of nodes. We note that this problem of MST with constraints is NP-complete. Nevertheless, we demonstrate that ILP running time is adequate for the great majority of existing cable systems. For cable systems for which ILP is not able to find the optimal solution within an acceptable time, we propose an alternative heuristic algorithm based on Prim's algorithm. In addition, we apply our FMM/ILP-based algorithm to a real-world cable path planning example and demonstrate that it can effectively find an MST with latency constraints between pairs of nodes., Comment: 11 pages, 7 figures

The ionosphere is the propagation medium for radio waves transmitted by an over-the-horizon radar (OTHR). Ionospheric parameters, typically, virtual ionospheric heights (VIHs), are required to perform coordinate registration for OTHR multitarget tracking and localization. The inaccuracy of ionospheric parameters has a significant deleterious effect on the target localization of OTHR. Therefore, to improve the localization accuracy of OTHR, it is important to develop accurate models and estimation methods of ionospheric parameters and the corresponding target tracking algorithms. In this paper, we consider the variation of the ionosphere with location and the spatial correlation of the ionosphere in OTHR target tracking. We use a Gaussian Markov random field (GMRF) to model the VIHs, providing a more accurate representation of the VIHs for OTHR target tracking. Based on expectation-conditional maximization and GMRF modeling of the VIHs, we propose a novel joint optimization solution, called ECM-GMRF, to perform target state estimation, multipath data association and VIHs estimation simultaneously. In ECM-GMRF, the measurements from both ionosondes and OTHR are exploited to estimate the VIHs, leading to a better estimation of the VIHs which improves the accuracy of data association and target state estimation, and vice versa. The simulation indicates the effectiveness of the proposed algorithm., Comment: 16 pages

Tracking an unknown number of targets based on multipath measurements provided by an over-the-horizon radar (OTHR) network with a statistical ionospheric model is complicated, which requires solving four subproblems: target detection, target tracking, multipath data association and ionospheric height identification. A joint solution is desired since the four subproblems are highly correlated, but suffering from the intractable inference problem of high-dimensional latent variables. In this paper, a unified message passing approach, combining belief propagation (BP) and mean-field (MF) approximation, is developed for simplifying the intractable inference. Based upon the factor graph corresponding to a factorization of the joint probability distribution function (PDF) of the latent variables and a choice for a separation of this factorization into BP region and MF region, the posterior PDFs of continuous latent variables including target kinematic state, target visibility state, and ionospheric height, are approximated by MF due to its simple MP update rules for conjugate-exponential models. With regard to discrete multipath data association which contains one-to-one frame (hard) constraints, its PDF is approximated by loopy BP. Finally, the approximated posterior PDFs are updated iteratively in a closed-loop manner, which is effective for dealing with the coupling issue among target detection, target tracking, multipath data association, and ionospheric height identification. Meanwhile, the proposed approach has the measurement-level fusion architecture due to the direct processing of the raw multipath measurements from an OTHR network, which is benefit to improving target tracking performance. Its performance is demonstrated on a simulated OTHR network multitarget tracking scenario., Comment: 40 pages, 23 figures

This paper considers the problem of detecting and tracking multiple maneuvering targets, which suffers from the intractable inference of high-dimensional latent variables that include target kinematic state, target visibility state, motion mode-model association, and data association. A unified message passing algorithm that combines belief propagation (BP) and mean-field (MF) approximation is proposed for simplifying the intractable inference. By assuming conjugate-exponential priors for target kinematic state, target visibility state, and motion mode-model association, the MF approximation decouples the joint inference of target kinematic state, target visibility state, motion mode-model association into individual low-dimensional inference, yielding simple message passing update equations. The BP is exploited to approximate the probabilities of data association events since it is compatible with hard constraints. Finally, the approximate posterior probability distributions are updated iteratively in a closed-loop manner, which is effective for dealing with the coupling issue between the estimations of target kinematic state and target visibility state and decisions on motion mode-model association and data association. The performance of the proposed algorithm is demonstrated by comparing with the well-known multiple maneuvering target tracking algorithms, including interacting multiple model joint probabilistic data association, interacting multiple model hypothesis-oriented multiple hypothesis tracker and multiple model generalized labeled multi-Bernoulli.