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This paper considers the problem of direction-of-arrival (DOA) estimation of coherent signals on passive coprime arrays, where we resort to the fourth-order cumulants of the received signal to explore more information. A fourth-order cumulant matrix (FCM) is introduced for the coprime array. The special structure of the FCM is combined with the array configuration to resolve the coherent signals. Since each sparse array of a coprime array is uniform, a series of overlapping identical subarrays can be extracted. Using this property, we propose a generalized spatial smoothing scheme applied to the FCM. From the smoothed FCM, the DOAs of both the coherent and independent signals can be successfully estimated on the pseudo-spectrum generated by the fourth-order MUSIC algorithm. To overcome the problem of occasional false peaks appearing on the pseudo-spectrum, we use a supplementary sparse array whose inter-sensor spacing is coprime to that of either existing sparse array. From the combined spectrum aided by the supplementary sensors, the false peaks are removed while the true peaks remain. The effectiveness of the proposed methods is demonstrated by simulation examples.

This paper addresses the problem of modeling maneuvering target motion in tracking applications. A target trajectory can typically be divided into segments with different dynamic motion modes, such as a constant velocity motion, a constant acceleration motion or a constant turn rate motion. To integrate the different motion modes into a uniform model, a Constant Speed Changing Rate and Constant Turn Rate (CSCRCTR) model is proposed. A new state vector is defined, and the state transition function is derived. Based on the CSCRCTR model, we present a tracking algorithm using a particle filter. The performances of the CSCRCTR model, the uniform model (UM) and the interacting multiple model (IMM) for tracking a simulated maneuvering target are compared and show that the CSCRCTR model maintains a good consistency for different types of motions and achieves better accuracy than UM and IMM when maneuvers occur.

Error bounds for nonlinear filtering are very important for performance evaluation and sensor management. This paper presents a comparative study of three error bounds for tracking filtering, when the detection probability is less than unity. One of these bounds is the random finite set (RFS) bound, which is deduced within the framework of finite set statistics. The others, which are the information reduction factor (IRF) posterior Cramer-Rao lower bound (PCRLB) and enumeration method (ENUM) PCRLB are introduced within the framework of finite vector statistics. In this paper, we deduce two propositions and prove that the RFS bound is equal to the ENUM PCRLB, while it is tighter than the IRF PCRLB, when the target exists from the beginning to the end. Considering the disappearance of existing targets and the appearance of new targets, the RFS bound is tighter than both IRF PCRLB and ENUM PCRLB with time, by introducing the uncertainty of target existence. The theory is illustrated by two nonlinear tracking applications: ballistic object tracking and bearings-only tracking. The simulation studies confirm the theory and reveal the relationship among the three bounds.

The problem to be addressed in this paper is a phase-modulated waveform design for the detection of extended targets contaminated by signal-dependent noise (clutter) and additive noise in practical radar systems. An optimal waveform design method that leads to the energy spectral density (ESD) of signal under the maximum signal-to-clutter-and-noise ratio (SCNR) criterion is introduced first. In order to make full use of the transmission power, a novel phase-iterative algorithm is then proposed for designing the phase-modulated waveform with a constant envelope, whose ESD matches the optimal one. This method is proven to be able to achieve a small SCNR loss by minimizing the mean-square spectral distance between the optimal waveform and the designed waveform. The results of extensive simulations demonstrate that our approach provides less than 1 dB SCNR loss when the signal duration is greater than 1 μs, and outperforms the stationary phase method and other phase-modulated waveform design methods.

Sparse representation (SR) algorithms can be implemented for high-resolution direction of arrival (DOA) estimation. Additionally, SR can effectively separate the coherent signal sources because the spectrum estimation is based on the optimization technique, such as the L(1) norm minimization, but not on subspace orthogonality. However, in the actual source localization scenario, an unknown gain/phase error between the array sensors is inevitable. Due to this nonideal factor, the predefined overcomplete basis mismatches the actual array manifold so that the estimation performance is degraded in SR. In this paper, an adaptive SR algorithm is proposed to improve the robustness with respect to the gain/phase error, where the overcomplete basis is dynamically adjusted using multiple snapshots and the sparse solution is adaptively acquired to match with the actual scenario. The simulation results demonstrate the estimation robustness to the gain/phase error using the proposed method.

We address the problem of adaptive waveform design for extended target recognition in cognitive radar networks. A closed-loop active target recognition radar system is extended to the case of a centralized cognitive radar network, in which a generalized likelihood ratio (GLR) based sequential hypothesis testing (SHT) framework is employed. Using Doppler velocities measured by multiple radars, the target aspect angle for each radar is calculated. The joint probability of each target hypothesis is then updated using observations from different radar line of sights (LOS). Based on these probabilities, a minimum correlation algorithm is proposed to adaptively design the transmit waveform for each radar in an amplitude fluctuation situation. Simulation results demonstrate performance improvements due to the cognitive radar network and adaptive waveform design. Our minimum correlation algorithm outperforms the eigen-waveform solution and other non-cognitive waveform design approaches.

This article concerns the problem of the estimation bound for tracking an extended target observed by a high resolution sensor. Two types of commonly used models for extended targets and the corresponding posterior Cramer-Rao lower bound (PCRLB) are discussed. The first type is the equation-extension model which extends the state space to include parameters such as target size and shape. Thus, the extended state vector can be estimated through the measurements obtained by a high resolution sensor. The measurement vector is also an expansion of the conventional one, and the additional measurements such as target extent can provide extra information for the estimation. The second model is based on multiple target measurements, each of which is an independent random draw from a spatial probability distribution. As the number of measurements per frame is unknown and random, the general form of the measurement contribution to the Fisher information matrix (FIM) conditional on the number of measurements is presented, and an extended information reduction factor (EIRF) approach is proposed to calculate the overall FIM and, therefore, the PCRLB. The bound of the second extended target model is also less than that of the point model, on condition that the average number of measurements is greater than one. Illustrative simulation examples of the two models are discussed and demonstrated.

High range resolution (HRR) profiling using stepped-frequency pulse trains suffers from range shift and the attenuation/dispersion of range profiles while the target of interest is moving. To overcome these two drawbacks, a new algorithm based on the maximum likelihood (ML) estimation is proposed in this paper. Without altering the conventional stepped-frequency waveform, this algorithm can estimate the target velocity and thereby compensate the phase errors caused by the target's motion. It is shown that the velocity can be accurately estimated and the range profile can be correctly reconstructed.