Xudong Zhang

Bio: Xudong Zhang is an academic researcher from Stevens Institute of Technology. The author has contributed to research in topics: FDOA & Radar. The author has an hindex of 1, co-authored 4 publications receiving 15 citations.

Maximum Likelihood Delay and Doppler Estimation for Passive Sensing

Abstract: We consider the problem of delay and Doppler frequency estimation of a moving target in passive radar using a non-cooperative illuminator of opportunity (IO). The passive radar consists of a reference channel (RC), i.e., an antenna steered to the IO, and a surveillance channel (SC) that collects target echoes. We examine the maximum-likelihood estimator (MLE) for the passive estimation problem by modeling the unknown IO waveform as a deterministic process. Under this condition, the passive MLE is shown to reduce to a cross-correlation and search process using the surveillance signal and a delay-Doppler compensated version of the reference signal. We present two implementations for the passive MLE, including a direct and, respectively, a fast implementation based on a two-dimensional Fast Fourier Transform. In addition, the Cramer-Rao Bound is derived to benchmark the passive estimation performance. The passive MLE is compared via numerical simulation with its active counterpart, which has the exact knowledge of the waveform and uses it for cross-correlation. Our results show that the signal-to-noise ratio (SNR) in the RC relative to the SNR in the SC has a significant impact on the passive MLE. Specifically, if the former is notably higher than the latter (by, e.g., 5 dB), there is a minor difference between the passive and active MLEs for the delay and Doppler estimation; otherwise, the difference is non-negligible and increases with the SNR.

Maximum Likelihood and IRLS Based Moving Source Localization With Distributed Sensors

Abstract: In this article, we consider the problem of estimating the location and velocity of a moving source using a distributed passive radar sensor network. We first derive the maximum likelihood estimator (MLE) using direct sensor observations, when the source signal is unknown and modeled as a deterministic process. Since the MLE obtains the source location and velocity estimates through a search process over the parameter space and is quite computationally intensive, we also developed an efficient algorithm to solve the problem using a two-step approach. The first step finds the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimates for each sensor with respect to a reference sensor by using a two-dimensional fast Fourier transform and interpolation, while the second step employs an iterative reweighted least square (IRLS) approach with a varying weighting matrix to determine the source location and velocity. To benchmark the performance of the proposed methods, a constrained Cramer–Rao bound (CRB) for the considered source localization problem is derived. Numerical results show that the IRLS approach has a lower signal-to-noise ratio threshold phenomenon compared with several recent TDOA/FDOA-based methods, especially when the source is considerably farther away from some sensors than others, creating a larger disparity in the quality of sensors observations.

An Efficient Method for Cooperative Multi-Target Localization in Automotive Radar

Abstract: We consider the problem of locating multiple targets using automotive radar by exploiting a pair of cooperative vehicles, which form a mono- and bi-static sensing system to provide spatial diversity for localization. Each of the two sub-systems can measure the target echoes. The problem is to determine the locations of multiple targets in the surrounding area. A conventional approach is to directly estimate the target locations from the joint distribution of the mono- and bi-static observations, which is computationally prohibitive. In this paper, we propose a efficient two-step method that first uses the delay and angle estimates from each individual system to determine initial target locations, which are subsequently refined via an association and fusion step. Specifically, we use a 2-dimensional (2-D) fast Fourier transform (FFT) based approach to obtain the delay and angle estimates of each target in a sequential manner. The delay/angle estimates obtained by mono-static and bi-static systems lead to two sets of initial target location estimates, which are then sorted and paired via a minimum distance criterion. Finally, the initial location estimates are fused/weighted according to the target strength observed by each system. Simulation results show that our cooperative approach yields significant improved performance over non-cooperative approaches using only the mono-static or bi-static sensing system.

Covariance-Free TDOA/FDOA-Based Moving Target Localization for Multi-Static Radar

Abstract: In this paper, we consider the problem of estimating the location and velocity of a non-cooperative moving target using a multi-static radar, which consists of a set of spatially distributed sensors in listening mode. The moving target may be transmitting, or reflecting, a source signal that is assumed to be unknown and modeled as a deterministic process. We develop a computationally efficient two-step approach to solve the localization problem. The first step finds the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimates for each sensor with respect to a reference sensor by using a 2-dimensional Fast Fourier transform, and the second step employs an iterative reweighted least square (IRLS) approach with a varying weighting matrix to determine the target location and velocity. While most existing TDOA/FDOA-based methods require knowledge of the covariance matrix of the TDOA and FDOA estimates, which is usually unknown in practice, our proposed IRLS approach is covariance matrix-free. Numerical results show that the IRLS approach has a lower signal-to-noise ratio (SNR) threshold compared with a recent TDOA/FDOA-based method, especially when the target is considerably farther away from some sensors than others.

Multi-Aperture Space-Time Transmit and Receive Design for MIMO Radar

Abstract: We consider the joint transmit and receive design for multi-input multi-output radar with slow-time processing. The radar employs multiple transmit apertures to improve diversity. The design parameters include the spatial transmit code for each aperture, which varies from pulse to pulse to provide Doppler shaping, and the space-time receive filter, to jointly optimize the radar output signal-to-interference-and-noise ratio (SINR). To relieve the dependence on specific target parameters as required by some prior methods, we use the average SINR, averaged with respect to the target location/Doppler uncertainties, as the design metric. Simulation results show that our proposed multi-aperture solution outperforms a previous single-aperture based space-time transmit and receive design as well as the conventional phased-array radar.

Nonlinear Fractional Programming

Abstract: In this chapter we deal with the following nonlinear fractional programming problem: $$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$ where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Phase Design and Near-Field Target Localization for RIS-Assisted Regional Localization System

Abstract: This paper explores the near-field regional target localization problem with the reconfigurable intelligent surface (RIS) assisted system. Traditional near-field localization strategies typically estimate the position of the target through line-of-sight (LOS) signals transmitted from the anchor node. In practice, accurate location estimation is a challenging issue when the LOS link between the anchor node and target may be unavailable due to the obstacle. To this end, this paper investigates the possibility to confirm the position of the target node consisted in an area of interest (AOI) by retrieving information from the RIS reflection signals. Specifically, we establish a general framework for RIS-assisted regional localization, which consists of RIS phase design and position determination. By defining the average localization accuracy (ALA) of the AOI, we first present a discretization method to design the RIS phase. Then, a robust phase design problem is formulated via transforming the AOI into an uncertainty model of position parameters, and an efficient iterative entropy regularization (IER)-based algorithm is proposed to solve it. Using the designed RIS phase, we develop a near-field target localization algorithm and discuss the power optimization problem for the RIS-assisted localization system (RALS). Numerical results demonstrate the effectiveness of the proposed framework, in which both phase design strategies almost coincide with the optimal RIS phase, and the proposed localization method can attain the near-optimal localization performance by applying the designed RIS phase schemes.

Moving Target Localization in Multiple-Input Multiple-Output Radar Systems Without the Prior Knowledge of Measurement Noise Powers

Abstract: This letter investigates the problem of locating a moving target using bistatic range (BR) and bistatic range rate (BRR) measurements in multi-input and multi-output (MIMO) radar systems. The proposed estimator constructs two separate semidefinite programming (SDP) problems, in which both the BR and BRR measurement noise powers can be neglected. By utilizing the optimization toolbox, we efficiently solve the SDP problems and give the source position and velocity successively. Unlike the traditional techniques, the proposed method does not require the exact prior knowledge of the measurement noise powers. Simulation results validate the performance of the proposed method.

Maximum Likelihood and IRLS Based Moving Source Localization With Distributed Sensors

Abstract: In this article, we consider the problem of estimating the location and velocity of a moving source using a distributed passive radar sensor network. We first derive the maximum likelihood estimator (MLE) using direct sensor observations, when the source signal is unknown and modeled as a deterministic process. Since the MLE obtains the source location and velocity estimates through a search process over the parameter space and is quite computationally intensive, we also developed an efficient algorithm to solve the problem using a two-step approach. The first step finds the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimates for each sensor with respect to a reference sensor by using a two-dimensional fast Fourier transform and interpolation, while the second step employs an iterative reweighted least square (IRLS) approach with a varying weighting matrix to determine the source location and velocity. To benchmark the performance of the proposed methods, a constrained Cramer–Rao bound (CRB) for the considered source localization problem is derived. Numerical results show that the IRLS approach has a lower signal-to-noise ratio threshold phenomenon compared with several recent TDOA/FDOA-based methods, especially when the source is considerably farther away from some sensors than others, creating a larger disparity in the quality of sensors observations.

Phase Design and Near-Field Target Localization for RIS-Assisted Regional Localization System

Abstract: This paper explores the near-field regional target localization problem with the reconfigurable intelligent surface (RIS) assisted system. Traditional near-field localization strategies typically estimate the position of the target through line-of-sight (LOS) signals transmitted from the anchor node. In practice, accurate location estimation is a challenging issue when the LOS link between the anchor node and target may be unavailable due to the obstacle. To this end, this paper investigates the possibility to confirm the position of the target node consisted in an area of interest (AOI) by retrieving information from the RIS reflection signals. Specifically, we establish a general framework for RIS-assisted regional localization, which consists of RIS phase design and position determination. By defining the average localization accuracy (ALA) of the AOI, we first present a discretization method to design the RIS phase. Then, a robust phase design problem is formulated via transforming the AOI into an uncertainty model of position parameters, and an efficient iterative entropy regularization (IER)-based algorithm is proposed to solve it. Using the designed RIS phase, we develop a near-field target localization algorithm and discuss the power optimization problem for the RIS-assisted localization system (RALS). Numerical results demonstrate the effectiveness of the proposed framework, in which both phase design strategies almost coincide with the optimal RIS phase, and the proposed localization method can attain the near-optimal localization performance by applying the designed RIS phase schemes.