Approximate multi-object filter with known SNR information for an optical sensor system.

In the image plane of an optical sensor, the amplitude information (AI) is very reliable for distinguishing returns generated by actual targets or coming from clutter generators. However, the majority of recently derived multi-object filters based on Mahler's finite set statistics (FISST) theory have ignored utilizing this information. This paper proposes an approximate multi-object filter with additive AI applied for optical sensor systems. The algorithm is operated on an image plane generated by the optical sensor, which has been pre-processed. After each prediction step, we sample multiple particles to approximate the prior multi-object density. Moreover, at the update step, we employ the amplitude feature likelihood for situations where the signal-to-noise ratio (SNR) information of targets is known. The loopy belief propagation (LBP) method with sequentially updated initialization messages is designed to solve the data association problem involved in the update step of the multi-object particle filter. We analyze the convergence performance of the LBP algorithm with additive AI and sequentially updated initialization messages; an ad hoc method for improving the performance of the AI-aided LBP is designed.

A Sparse-Based Off-Grid DOA Estimation Method for Coprime Arrays.

Recently, many sparse-based direction-of-arrival (DOA) estimation methods for coprime arrays have become popular for their excellent detection performance. However, these methods often suffer from grid mismatch problem due to the discretization of the potential angle space, which will cause DOA estimation performance degradation when the target is off-grid. To this end, we proposed a sparse-based off-grid DOA estimation method for coprime arrays in this paper, which includes two parts: coarse estimation process and fine estimation process. In the coarse estimation process, the grid points closest to the true DOAs, named coarse DOAs, are derived by solving an optimization problem, which is constructed according to the statistical property of the vectorized covariance matrix estimation error. Meanwhile, we eliminate the unknown noise variance effectively through a linear transformation. Due to finite snapshots effect, some undesirable correlation terms between signal and noise vectors exist in the sample covariance matrix. In the fine estimation process, we therefore remove the undesirable correlation terms from the sample covariance matrix first, and then utilize a two-step iterative method to update the grid biases. Combining the coarse DOAs with the grid biases, the final DOAs can be obtained. In the end, simulation results verify the effectiveness of the proposed method.

Two-Dimensional DOA Estimation for Three-Parallel Nested Subarrays via Sparse Representation.

Nested arrays are considered attractive due to their hole-free performance, and have the ability to resolve O ( N 2 ) sources with O ( N ) physical sensors. Inspired by nested arrays, two kinds of three-parallel nested subarrays (TPNAs), which are composed of three parallel sparse linear subarrays with different inter-element spacings, are proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation in this paper. We construct two cross-correlation matrices and combine them as one augmented matrix in the first step. Then, by vectorizing the augmented matrix, a hole-free difference coarray with larger degrees of freedom (DOFs) is achieved. Meanwhile, sparse representation and the total least squares technique are presented to transform the problem of 2-D DOA searching into 1-D searching. Accordingly, we can obtain the paired 2-D angles automatically and improve the 2-D DOA estimation performance. In addition, we derive closed form expressions of sensor positions, as well as number of sensors for different subarrays of two kinds of TPNA to maximize the DOFs. In the end, the simulation results verify the superiority of the proposed TPNAs and 2-D DOA estimation method.

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.

Real-Valued 2D MUSIC Algorithm Based on Modified Forward/Backward Averaging Using an Arbitrary Centrosymmetric Polarization Sensitive Array.

Two-dimensional multiple signal classification (MUSIC) algorithm based on polarization sensitive array (PSA) has excellent performance. However, it suffers a high computational complexity due to a multitude of complex operations. In this paper, we propose a real-valued two-dimensional MUSIC algorithm based on conjugate centrosymmetric signal model, which is applicable to arbitrary centrosymmetric polarization sensitive array. The modified forward/backward averaging, which can be applied to the PSA, is presented. Hence, the eigen-decomposition analysis process and spectrum function computation are converted into real domain, prominently reducing the computational complexity. Then, the direction-of-arrival (DOA) estimation is decoupled from the polarization parameter estimation so that the four-dimensional spectral peak search process is avoided. The theoretical computational complexity is discussed and the Cramer-Rao bound (CRB) of DOA estimation is derived in this paper. The simulation results indicate that the proposed algorithm achieves superior accuracy in DOA estimation and has low computational complexity.

Analysis of Maneuvering Targets with Complex Motions by Two-Dimensional Product Modified Lv's Distribution for Quadratic Frequency Modulation Signals.

For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed-referred to as the Two-Dimensional product modified Lv's distribution (2D-PMLVD)-for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.

DOA and Polarization Estimation Using an Electromagnetic Vector Sensor Uniform Circular Array Based on the ESPRIT Algorithm.

In array signal processing systems, the direction of arrival (DOA) and polarization of signals based on uniform linear or rectangular sensor arrays are generally obtained by rotational invariance techniques (ESPRIT). However, since the ESPRIT algorithm relies on the rotational invariant structure of the received data, it cannot be applied to electromagnetic vector sensor arrays (EVSAs) featuring uniform circular patterns. To overcome this limitation, a fourth-order cumulant-based ESPRIT algorithm is proposed in this paper, for joint estimation of DOA and polarization based on a uniform circular EVSA. The proposed algorithm utilizes the fourth-order cumulant to obtain a virtual extended array of a uniform circular EVSA, from which the pairs of rotation invariant sub-arrays are obtained. The ESPRIT algorithm and parameter pair matching are then utilized to estimate the DOA and polarization of the incident signals. The closed-form parameter estimation algorithm can effectively reduce the computational complexity of the joint estimation, which has been demonstrated by numerical simulations.

Multi-Target Tracking Using an Improved Gaussian Mixture CPHD Filter.

The cardinalized probability hypothesis density (CPHD) filter is an alternative approximation to the full multi-target Bayesian filter for tracking multiple targets. However, although the joint propagation of the posterior intensity and cardinality distribution in its recursion allows more reliable estimates of the target number than the PHD filter, the CPHD filter suffers from the spooky effect where there exists arbitrary PHD mass shifting in the presence of missed detections. To address this issue in the Gaussian mixture (GM) implementation of the CPHD filter, this paper presents an improved GM-CPHD filter, which incorporates a weight redistribution scheme into the filtering process to modify the updated weights of the Gaussian components when missed detections occur. In addition, an efficient gating strategy that can adaptively adjust the gate sizes according to the number of missed detections of each Gaussian component is also presented to further improve the computational efficiency of the proposed filter. Simulation results demonstrate that the proposed method offers favorable performance in terms of both estimation accuracy and robustness to clutter and detection uncertainty over the existing methods.

Multi-Target State Extraction for the SMC-PHD Filter.

The sequential Monte Carlo probability hypothesis density (SMC-PHD) filter has been demonstrated to be a favorable method for multi-target tracking. However, the time-varying target states need to be extracted from the particle approximation of the posterior PHD, which is difficult to implement due to the unknown relations between the large amount of particles and the PHD peaks representing potential target locations. To address this problem, a novel multi-target state extraction algorithm is proposed in this paper. By exploiting the information of measurements and particle likelihoods in the filtering stage, we propose a validation mechanism which aims at selecting effective measurements and particles corresponding to detected targets. Subsequently, the state estimates of the detected and undetected targets are performed separately: the former are obtained from the particle clusters directed by effective measurements, while the latter are obtained from the particles corresponding to undetected targets via clustering method. Simulation results demonstrate that the proposed method yields better estimation accuracy and reliability compared to existing methods.

Two-Dimensional DOA and Polarization Estimation for a Mixture of Uncorrelated and Coherent Sources with Sparsely-Distributed Vector Sensor Array.

This paper presents an L-shaped sparsely-distributed vector sensor (SD-VS) array with four different antenna compositions. With the proposed SD-VS array, a novel two-dimensional (2-D) direction of arrival (DOA) and polarization estimation method is proposed to handle the scenario where uncorrelated and coherent sources coexist. The uncorrelated and coherent sources are separated based on the moduli of the eigenvalues. For the uncorrelated sources, coarse estimates are acquired by extracting the DOA information embedded in the steering vectors from estimated array response matrix of the uncorrelated sources, and they serve as coarse references to disambiguate fine estimates with cyclical ambiguity obtained from the spatial phase factors. For the coherent sources, four Hankel matrices are constructed, with which the coherent sources are resolved in a similar way as for the uncorrelated sources. The proposed SD-VS array requires only two collocated antennas for each vector sensor, thus the mutual coupling effects across the collocated antennas are reduced greatly. Moreover, the inter-sensor spacings are allowed beyond a half-wavelength, which results in an extended array aperture. Simulation results demonstrate the effectiveness and favorable performance of the proposed method.

Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing.

This paper presents a novel off-grid direction of arrival (DOA) estimation method to achieve the superior performance in compressed sensing (CS), in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods.

Augmented lagrange based on modified covariance matching criterion method for DOA estimation in compressed sensing.

A novel direction of arrival (DOA) estimation method in compressed sensing (CS) is presented, in which DOA estimation is considered as the joint sparse recovery from multiple measurement vectors (MMV). The proposed method is obtained by minimizing the modified-based covariance matching criterion, which is acquired by adding penalties according to the regularization method. This minimization problem is shown to be a semidefinite program (SDP) and transformed into a constrained quadratic programming problem for reducing computational complexity which can be solved by the augmented Lagrange method. The proposed method can significantly improve the performance especially in the scenarios with low signal to noise ratio (SNR), small number of snapshots, and closely spaced correlated sources. In addition, the Cramér-Rao bound (CRB) of the proposed method is developed and the performance guarantee is given according to a version of the restricted isometry property (RIP). The effectiveness and satisfactory performance of the proposed method are illustrated by simulation results.

Joint estimation of 2D-DOA and frequency based on space-time matrix and conformal array.

Each element in the conformal array has a different pattern, which leads to the performance deterioration of the conventional high resolution direction-of-arrival (DOA) algorithms. In this paper, a joint frequency and two-dimension DOA (2D-DOA) estimation algorithm for conformal array are proposed. The delay correlation function is used to suppress noise. Both spatial and time sampling are utilized to construct the spatial-time matrix. The frequency and 2D-DOA estimation are accomplished based on parallel factor (PARAFAC) analysis without spectral peak searching and parameter pairing. The proposed algorithm needs only four guiding elements with precise positions to estimate frequency and 2D-DOA. Other instrumental elements can be arranged flexibly on the surface of the carrier. Simulation results demonstrate the effectiveness of the proposed algorithm.