Maximum Likelihood Delay and Doppler Estimation for Passive Sensing
TL;DR: The 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, and the Cramér-Rao Bound is derived to benchmark the passive estimation performance.
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.
Citations
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TL;DR: This letter investigates the problem of locating a moving target using bistatic range (BR) and bistatics range rate (BRR) measurements in multi-input and multi-output (MIMO) radar systems and efficiently solve the SDP problems and give the source position and velocity successively.
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.
12 citations
Cites methods from "Maximum Likelihood Delay and Dopple..."
...After some local processing algorithms such as [14], we can extract NtNr time delay (TD) and NtNr doppler shifts (DS) measurements....
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TL;DR: 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.
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.
12 citations
Additional excerpts
...According to [34], the maximum likelihood estimates of the TDOA and FDOA {τm1, fm1} for the mth (m = 2, ....
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TL;DR: In this paper , a 2-dimensional (2-D) fast Fourier transform (FFT) based approach was used to obtain the delay and angle estimates of each target in a sequential manner.
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.
6 citations
TL;DR: This article addresses the multistatic localization of an object by exploiting the direct-blast and object-reflected signals, where the transmitter location is not known and only the sensor positions are available, to determine the CRLB performance under Gaussian noise over the small error region.
Abstract: This article addresses the multistatic localization of an object by exploiting the direct-blast and object-reflected signals, where the transmitter location is not known and only the sensor positions are available. We study the cases that either the object or the transmitter is moving, in a noncooperative environment at which unknown offsets are present in the time delay and Doppler shift measurements. We analyze thoroughly by the Cramer–Rao lower bound (CRLB) if the direct-blast signals are useful in increasing the object localization performance, albeit doing so introduces extra parameters of the transmitter for estimation. Performance comparison with the fully dynamic moving object and moving transmitter modeling is established. Algebraic solutions are derived for the localization problem and analysis is made to validate that the proposed estimators are able to reach the CRLB performance under Gaussian noise over the small error region.
6 citations
TL;DR: In this paper, the problem of CRLB analysis for joint target location and velocity estimation in a multistatic passive radar system comprised of multiple noncooperative illuminators of opportunity (IOs) and multiple geographically separated receivers is addressed.
Abstract: This paper addresses the problem of Cramér–Rao lower bound (CRLB) analysis for joint target location and velocity estimation in a multistatic passive radar system comprised of multiple noncooperative illuminators of opportunity (IOs) and multiple geographically separated receivers. Unlike other existing studies, special attention in this paper is paid to a more ubiquitous scenario, in which no reference channel exists in receiver networks. Besides, the situation where the measurements collected at the receivers are contaminated by the interference directly illuminated from the IOs is taken into account. Namely, each receive station simultaneously obtains direct-path interference (DPI) from all the IOs and echo signals reflected by the target. Furthermore, the IO waveform is modeled as a stochastic process in which samples of the unknown IO waveform are treated as a complex Gaussian sequence. Finally, the effects of multipath clutter on the signal model and CRLB are well analyzed. The numerical results are provided to prove that the joint CRLB is not only a function of the signal-to-noise ratio (SNR), DPI-to-noise ratio (DNR), and clutter-to-noise ratio (CNR) but also associated with both IO waveform parameters and relative geographical distribution of the system.
5 citations
Cites background from "Maximum Likelihood Delay and Dopple..."
...INTRODUCTION Passive radar, also known as passive coherent location (PCL), utilizes existing noncooperative illuminators of opportunity (IOs) rather its own dedicated transmitter for target detection and estimation [1]–[6]....
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References
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03 Jun 2005
TL;DR: A bistatic form of the radar range equation specifically tailored to PCL systems is developed and realistic examples are used to examine and compare variations in sensitivity and coverage for three candidate transmitters of opportunity.
Abstract: Passive coherent location (PCL) systems are a variant of bistatic radar that exploit 'illuminators of opportunity' as their sources of radar transmission. Dispensing with the need for a dedicated transmitter makes PCL inherently low cost, and hence attractive for a broad range of applications. Although a number of experimental and development examples exist, relatively little has been reported on the detailed performance of these systems and the resulting effects that these will have on the interpretation of backscatter and exploitation of derived information. In the paper a bistatic form of the radar range equation specifically tailored to PCL systems is developed. Realistic examples are used to examine and compare variations in sensitivity and coverage for three candidate transmitters of opportunity. These are analogue FM radio, cellular phone base stations and digital audio broadcast (DAB). These examples show that a wide and extremely useful set of detection ranges are achievable and also highlight some of the key issues underpinning more detailed aspects of predicting detection performance.
608 citations
"Maximum Likelihood Delay and Dopple..." refers background in this paper
...g(θ) = (sR[1] + j sI [1]) − (a1 + ja2) = 0, (20)...
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...A useful CRB can be obtained by imposing a constraint that the first element s[1] = sR[1] + j sI [1] is known....
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...Unlike active radar systems that transmit probing waveforms and receive the reflections from objects of interest, a passive radar can detect and track targets without transmitting its own signal but utilizes existing transmission sources, referred to as noncooperative illuminators of opportunity (IOs) [1]–[3]....
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TL;DR: This paper presents a simple expression for the Cramer-Rao bound (CRB) for parametric estimation under differentiable, deterministic constraints on the parameters and shows that the constrained CRB formula reduces to the known expression when the FIM for the unconstrained problem is nonsingular.
Abstract: This paper presents a simple expression for the Cramer-Rao bound (CRB) for parametric estimation under differentiable, deterministic constraints on the parameters. In contrast to previous works, the constrained CRB presented does not require that the Fisher information matrix (FIM) for the unconstrained problem be of full rank. This is a useful extension because, for several signal processing problems (such as blind channel identification), the unconstrained problem is unidentifiable. Our expression for the constrained CRB depends only on the unconstrained FIM and a basis of the nullspace of the constraint's gradient matrix. We show that our constrained CRB formula reduces to the known expression when the FIM for the unconstrained problem is nonsingular. A necessary and sufficient condition for the existence of the constrained CRB is also derived.
331 citations
Additional excerpts
..., [27], [28]) Specifically, we construct a constraint function:...
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TL;DR: This study presents a scheme for pre-processing both the reference and surveillance signals obtained by the passive radar to mitigate the effects of the ambiguities and the clutter in range-Doppler processing.
Abstract: This paper provides a detailed overview of the Digital Video Broadcasting Terrestrial (DVB-T) signal structure and the implications for passive radar systems that use these signals as illuminators of opportunity. In particular, we analyze the ambiguity function and explain its delay and Doppler properties in terms of the underlying structure of the DVB-T signal. Of particular concern for radar range-Doppler processing are ambiguities consistent in range and Doppler with targets of interest. In this paper we adopt a mismatched filtering approach for range-Doppler processing. We also recognize that while the structure of the DVB-T signal introduces ambiguities, the structure can also be exploited to better estimate the transmitted signal and channel, as well as any mismatch between transmitter and receiver (e.g., clock offsets). This study presents a scheme for pre-processing both the reference and surveillance signals obtained by the passive radar to mitigate the effects of the ambiguities and the clutter in range-Doppler processing. The effectiveness of our proposed scheme in enhancing target detection is demonstrated using real-world data from an (Australian) 8k-mode DVB-T system. A 29 dB reduction in residual ambiguity levels over existing techniques is observed, and a 36 dB reduction over standard matched filtering; with only a 1 dB reduction in the zero-delay, zero-Doppler peak.
257 citations
"Maximum Likelihood Delay and Dopple..." refers background in this paper
...With the advances of wireless communication technologies, a variety of IOs can be used for passive sensing, including analog FM radio [4] and television stations [5], digital audio/video broadcasting [6], wireless cellular [7], WiFi signals [8], [9],...
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TL;DR: A compressed sensing algorithm is proposed to achieve supper resolution and better accuracy, using both the atomic norm and the -norm, to manifest the signal sparsity in the continuous domain.
Abstract: In this paper, we consider the problem of joint delay-Doppler estimation of moving targets in a passive radar that makes use of orthogonal frequency-division multiplexing communication signals. A compressed sensing algorithm is proposed to achieve supper resolution and better accuracy, using both the atomic norm and the $\ell _1$-norm. The atomic norm is used to manifest the signal sparsity in the continuous domain. Unlike previous works that assume the demodulation to be error free, we explicitly introduce the demodulation error signal whose sparsity is imposed by the $\ell _1$-norm. On this basis, the delays and Doppler frequencies are estimated by solving a semidefinite program (SDP) which is convex. We also develop an iterative method for solving this SDP via the alternating direction method of multipliers where each iteration involves closed-form computation. Simulation results are presented to illustrate the high performance of the proposed algorithm.
131 citations
"Maximum Likelihood Delay and Dopple..." refers background in this paper
...A recent study [18] considered this issue for passive radar using IO sources with orthogonal frequency division multiplexing (OFDM) modulation....
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TL;DR: This work addresses the problem of target detection in passive multiple-input multiple-output (MIMO) radar networks without utilization of direct-path reference signals, and a generalized likelihood ratio test is derived.
Abstract: This work addresses the problem of target detection in passive multiple-input multiple-output (MIMO) radar networks without utilization of direct-path reference signals. A generalized likelihood ratio test for this problem is derived, and the distribution of the test statistic is identified under both hypotheses. Equivalence is established between passive MIMO radar networks without references and passive source localization networks. Numerical examples demonstrate important characteristics of the detector, namely, the asymmetric contributions to detection performance from transmitters and receivers, and non-coherent integration gain as a function of signal length. The ambiguity properties of this detector are also investigated, and it is shown that the salient ambiguities can be explained in terms of the time-difference of arrival, frequency-difference of arrival, and angle-of-arrival of the target signals.
103 citations
"Maximum Likelihood Delay and Dopple..." refers background in this paper
...Then, the sampled signals in vector form can be written as [22], [23]...
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