Sharif Digital Repository

The Cramer-Rao lower bound for source localization based on Time Difference of Arrival and Frequency Difference of Arrival is investigated in this paper. The result is used for theoretical analysis of optimality in sensor placement. An optimal sensor-target geometry including sensors locations and velocities is presented and its properties is studied  

This paper proposes an algebraic solution for the position and velocity of a moving target in forward scatter radar based on a single step direct position determination method. Unlike the conventional two-step method, this direct technique does not require the joint estimation of the Doppler frequency and the angle of arrival, initialization step, convergence considerations and linearization approximations  

In this paper, a fundamental investigation on the performance of localization problem in a distributed multiple-input multiple-output radar system using bistatic range (BR) and angle of arrival (AOA) measurements is conducted. The study is based on the Cramer-Rao lower bound (CRLB) for the target position under Gaussian measurement noise. We attempt to approximately compute the CRLB separately in the cases of BR-only and joint BRlAOA localization schemes and determine which factors can affect the CRLB values. The three factors the transmitter/receiver placement, the number of transmitters and receivers, and noise power levels are shown to be effective on the localization performance.... 

In this paper, an algebraic solution for elliptic localization in multiple-input multiple-output (MIMO) radar systems is proposed by taking the uncertainties in antenna positions and their clock parameters into account. Through nonlinear transformation and multi-stage processing, the target position is estimated in closed-form by successively utilizing the weighted least squares estimator. Theoretical analysis demonstrates that the proposed method is able to attain the Cramer-Rao lower bound (CRLB) performance under mild Gaussian error. The conditions for achieving the CRLB are derived as well. The numerical simulations confirm the analytical results and demonstrate significant performance... 

This paper considers the localization of a moving target using a forward scatter radar consisting of a transmitter and an array antenna receiver. A direct positioning method based on maximum likelihood (ML) estimation is proposed and compared with the conventional two-step method in which the primary parameters, including Doppler shift and angle of arrival, should be determined in the first step. Moreover, closed-form expressions for Cramer-Rao lower bound of both methods are derived. The aforementioned methods are comprehensively compared in terms of positioning accuracy and computational complexity. Theoretical performance study, including determining the minimum required observation time... 

This letter addresses the problem of joint localization and clock synchronization in distributed multiple-input multiple-output (MIMO) radar systems. While the well-known two-stage weighted least squares (WLS) method provides an acceptable estimate of target position when a rough approximation of antennas clock parameters, the drifts and offsets, is available, its performance can degrade quickly if the level of uncertainty in these values increases. The proposed method offers a solution for synchronizing the clocks while simultaneously improving the target position estimate. The uncertainty in positions of antennas is also taken into account. The presented method is shown to be approximately... 

Multiple input multiple output (MIMO) radar is known for its superiority over conventional radar due to its antenna and waveform diversity. However, the increased hardware cost (due to multiple transmitters and receivers), power consumption (due to multiple transmitters and pulses), and computational complexity (due to numerous pulses) form the drawbacks of MIMO radar. On one hand, a higher estimation accuracy is required, but on the other hand, a lower number of active antennas/pulses is desirable. Therefore, in this paper, by proposing a convex optimization approach for the general case of transmitter-receiver-pulse selection, we will minimize the total number of active antennas/pulses in... 

In this paper, after introduction of symmetric multi- frequency signal, it will be presented how to estimate Doppler frequency from estimated frequency tones of returned echo. After that, three methods of Pisarenko, Prony and MUSIC for frequency estimation will be introduced, and then these methods are applied to estimate tone frequencies of a multi-carrier signal. It will be shown that estimation of Doppler frequency by multi-frequency signal transmission leads to less rms error than single-frequency signal, in the condition of equal SNR. Infact it will be suggested that distribution of the power of signal in spectrum instead of adding up all the power in one point, leads to less Doppler... 

In this study, the authors propose an algorithm to reduce the effect of antenna location uncertainty for locating moving targets in multiple-input multiple-output (MIMO) radar systems. The proposed method is a closed-form solution which employs the measurements of multiple independent targets to alleviate the antenna location uncertainties. The authors establish a pseudo-linear set of equations by using the range and the range-rate auxiliary parameters, which allows the problem to be solved using a two-stage weighted least squares estimator. The proposed method is shown analytically and confirmed by simulations to attain the Cramer-Rao lower bound under small error conditions. The... 

In this study, the optimal sensor placement problem for multi-source angle of arrival localisation is investigated. The authors adopt the A-optimality criterion, maximising the trace of Fisher information matrix, to determine the optimal sensor-target geometry under distance-dependent Gaussian noise model. A recursive representation of the Cramer-Rao lower bound is derived to recast the sensor placement problem into a sequential method, obtaining the optimal sensor geometries in a step by step manner. Note that the state-of-the-art methods are highly sensitive to the source location changes such that they should be relocated by any later changes in target geometries, which is practically... 

In this study, the optimal sensor placement problem for multi-source angle of arrival localisation is investigated. The authors adopt the A-optimality criterion, maximising the trace of Fisher information matrix, to determine the optimal sensor-target geometry under distance-dependent Gaussian noise model. A recursive representation of the Cramer-Rao lower bound is derived to recast the sensor placement problem into a sequential method, obtaining the optimal sensor geometries in a step by step manner. Note that the state-of-the-art methods are highly sensitive to the source location changes such that they should be relocated by any later changes in target geometries, which is practically... 

In this letter, we address the theoretical limitations in estimating the mixing matrix in noisy sparse component analysis (SCA) for the two-sensor case. We obtain the Cramer-Rao lower bound (CRLB) error estimation of the mixing matrix. Using the Bernouli-Gaussian (BG) sparse distribution, and some simple assumptions, an approximation of the Fisher information matrix (FIM) is calculated. Moreover, this CRLB is compared to some of the main methods of mixing matrix estimation in the literature. © 2008 IEEE  

This paper addresses the optimality of Network topology for localization purposes when measurements are range-only. Localization procedures based on TOA and TDOA range measurements are considered in this paper. As of now, the optimal placement of fixed terminals to locate mobile terminals has been studied based on Cramer-Rao Lower Bound (CRLB). CRLB is a universal bound on the variance of a general unbiased estimator and therefore is not dependent to the estimator and methods of localization. Here we introduce another algorithm dependent criterion, based on perturbation theory of linear equations. Different optimal topologies are presented using the new criterion. These optimal topologies,... 

An algebraic closed-form solution for locating a moving target using a distributed multiple-input multiple-output radar system is proposed. The position and velocity of the target are estimated by presenting a two-stage weighted least squares algorithm. In contrast to existing research, the proposed estimator is shown analytically to be approximately unbiased and its variance is equal to the Cramer-Rao lower bound. Numerical simulations corroborate the theoretical studies and demonstrate the superiority of this algorithm over the existing methods. © 1997-2012 IEEE  

Elliptic localization is an active range-based positioning technique that employs multiple transmitter-receiver pairs, each of which is able to provide separate bistatic range (BR) measurement. In this letter, an algebraic closed-form method for locating a single target from BR measurements using a distributed multiple-input multiple-output (MIMO) radar system is proposed. First, a set of linear equations is established by eliminating the nuisance parameters, and then, a weighted least squares estimator is employed to obtain the target position estimate. To refine the localization performance, the error in the initial solution is estimated in the sequence. The proposed method is shown... 

In this letter, the problem of target localization from bistatic range (BR) measurements in distributed multiple-input multiple-output radar systems is investigated. By introducing nuisance parameters, a pseudolinear set of BR equations is established. Then, a closed-form localization algorithm is developed, based on this pseudolinear set of equations and multistage weighted least squares estimation. This solution is shown analytically to attain the Cramer-Rao lower bound under the small Gaussian noise assumption. Simulations are included to support the theoretical studies. Unlike the existing studies where the variance of BR measurements is assumed to be independent of the corresponding... 

In this letter, the problem of source localization using time difference of arrival (TDOA) is investigated. Then, a closedform two-stage solution is proposed based on estimation of the range nuisance parameter in the first stage and refinement of initial solution in the next stage. The proposed solution is shown analytically and verified by simulations to be an efficient estimate, which can attain the CRLB performance under mild Gaussian noise assumption. This method is able to locate the source with the minimum number of sensors required for N-dimensional localization. Numerical simulations demonstrate significant performance improvement of the proposed method compared with the... 

In this paper, we focus on the moving target localization problem in a multiple-input multiple-output radar with widely separated antennas. By exploiting jointly different types of information including time delay, Doppler shift and azimuth and elevation angles of arrival, we develop an algebraic closed-form two-stage weighted least squares solution for the problem. The proposed algorithm is shown analytically to attain the CramerRao lower bound accuracy under the small Gaussian noise assumption. Numerical simulations are included to examine the algorithm's performance and corroborate the theoretical developments  

In this paper, a target parameter estimation problem is addressed for the recently emerging frequency diverse array multiple-input multiple-output (FDA-MIMO) radar system, utilizing sparse learning. The scene is modeled as a two dimensional (2D) angle-incremental range grid. To solve the resulting sparse problem, the recently proposed user-parameter free algorithms including block sparse learning via iterative minimization (BSLIM), iterative adaptive approach (IAA), sparse iterative covariance-based estimation (SPICE), likelihood-based estimation of sparse parameters (LIKES), and orthogonal matching pursuit (OMP) are applied which achieve excellent parameter estimation performance. However,... 

For several years, a substantial effort has been devoted to the study of 3-D source localization based on 2-D arrays by measuring the well-known azimuth and elevation angles. However, studies on 3-D source localization performed by 1-D arrays are still lacking. Perhaps, the most important drawback in the deployment of a 2-D array structure lies in the fact that it needs a planar space, which might not be available in some applications. This letter concentrates on the problem of 3-D source localization based on 1-D angle measurement provided by a linear array. Different from the traditional 2-D structures where each measurement induces a straight line, each measurement in the 1-D array...