Bistatic Range Measurements Research Articles

Motion Modeling and State Estimation With Bistatic Range and Doppler Measurements

Motion Modeling and State Estimation With Bistatic Range and Doppler Measurements

An ADMM approach for elliptic positioning in non-line-of-sight environments

Elliptic positioning (EP) has recently emerged as a prevailing subject within localization research, holding significant relevance for a variety of multistatic systems including distributed multiple-input multiple-output radar, sonar, and wireless sensor networks. Mathematically, EP refers to estimating the location of a signal-reflecting/relaying target from the bistatic range (BR) measurements acquired by employing multiple spatially separated transmitters and receivers. BRs, as a specific type of range-based sensor observations, will however be positively biased when non-line-of-sight (NLOS) signal propagation occurs. Such a phenomenon is widespread across various localization scenarios, which can seriously degrade the positioning accuracy if not properly addressed. Through the alternating direction method of multipliers, this contribution introduces a computationally efficient iterative algorithm designed for error-mitigated EP in NLOS environments. In addition to target position coordinates, we incorporate a non-negatively bounded balancing parameter into the formulation and perform joint estimation, thereby achieving NLOS bias error reduction in a simple yet impactful manner. Numerical simulations are conducted to validate the functionality of the presented EP approach in NLOS situations.

Denoising of Bistatic Ranges for Elliptic Positioning

This letter considers the denoising of possibly unreliable bistatic range (BR) measurements for elliptic target positioning in multistatic systems. Built upon the BRs over all transmitter–target–receiver paths, the concept of BR matrix is introduced here to handle the problem in an algebraic manner. Specifically, the rank of the ideal BR matrix is proven to be at most 2, which constitutes the foundation of a low-rank matrix approximation (LRMA) formulation presented to enhance the quality of raw datasets. An alternating direction method of multipliers (ADMM) is subsequently devised to perform efficient optimization. Simulations validate the proposed LRMA scheme for denoising.

A cost‐efficient joint target location and clock bias estimation technique using multiple time step measurements in mobile bistatic sonar

Active localization of a stationary target is one key issue in applications of bistatic sonar based on bistatic range (BR) measurement. However, the complex underwater environment makes achieving the synchronization between the transmitted station and the received station difficult. For solving the synchronization problem, this study relies on mobile bistatic sonar to acquire measurement information at multiple time steps. After that, the target location and clock bias are jointly estimated by solving a non-linear least square problem. To this end, a recursive scheme is proposed to optimise the measurement cost and reduce the impact of the initial value to achieve accurate estimation by taking full advantage of the redundant measurement information. Orthogonal transformation is used to ensure computational efficiency and numerical reliability. The Cramer–Rao Lower Bound (CRLB) is also derived as a lower bound on the error in estimating the target position and clock bias. Simulation results show that the proposed method achieves the CRLB performance and optimises the measurement cost over the small error region under Gaussian noise.

Target localization in distributed MIMO radars via improved semidefinite relaxation

Target localization is an important problem in distributed multiple-input multiple-output (MIMO) radar systems. In this paper, a new algorithm using bistatic range measurements is developed for target localization in distributed MIMO radars. Unlike most existing schemes, the proposed algorithm firstly applies semidefinite relaxation to convert the maximum likelihood localization problem into a convex optimization problem. Subsequently, a novel procedure is devised to improve the solution accuracy of the convex optimization problem. Our scheme exhibits evidently better threshold behavior than the state-of-the-art approaches. Moreover, it does not require any initial estimate of the target position. Simulation results verify the superiority of the proposed algorithm over various existing methods.

Target Localization in Multistatic Systems Without the Bistatic Range Measurement Noise Power

This letter investigates the problem of determining the static target in multistatic systems using bistatic range (BR) measurements, which can be obtained by some local sensor signal processing methods. The localization problem is first formulated as a semidefinite programming problem by using the semidefinite relaxation technique. Then, an initial position estimate is given by augmenting the unknown parameter space, which is required for solving the SDP problem. Specifically, this initialization is also a closed-form solution. Compared with existing algorithms, the proposed estimator has the advantage of not relying on the prior knowledge of BR measurement noise power. Simulation results validate the performance of the proposed estimator.

3-D Target Localization Based on Bi-static Range Measurements in Widely Separated MIMO Radars

In this paper, a three-dimensional target localization problem in widely separated multiple-input multiple-output radars is solved using two specific techniques based on time difference of arrival measurements. These techniques are provided in terms of transmitter and receiver antennas, which are named as technique_t and technique_r, respectively. The localization problem is rewritten as a non-convex optimization problem which is based on a least-squares method without any initial estimation. Therefore, a convex semidefinite programming problem is obtained by utilizing the semidefinite relaxation method for the problem which can be performed via the CVX toolbox. Several simulations are provided to evaluate the positioning accuracy in terms of bi-static range error for 3 and 4 transmitter/receiver antennas, different antenna arrangements, and near/far target. In other simulations, the localization accuracy is evaluated in terms of the empirical cumulative density function of positioning error. The results show that the proposed techniques have better accuracy and performance in different scenarios in comparison with other compared methods. The last simulation also demonstrates that the computational time of the mentioned techniques is 0.69 s which is suitable for real-time processing.

Maritime Target Localization From Bistatic Range Measurements in Space-Based Passive Radar

In this article, localization of a maritime target using a passive multistatic radar system, consisting of a single receiver and a number of satellites as its transmitters, is investigated. The set of communication satellites and also the global navigation satellite system (GNSS), including GPS, Glonass, and Galileo, are employed as illuminators of opportunity. In the receiver, the reflected signals from the target along with the direct signal from the satellites are employed to extract a set of bistatic range measurements. Leveraging these measurements and the satellite’s position information, a novel localization method considering zero height of maritime target and appropriate combination of the measurement signals is presented. The proposed method is efficient for localization of maritime targets in cases with arbitrary bistatic range accuracy. The results of numerical simulations confirm the efficiency of the proposed method and its superior performance in comparison with the state-of-the-art methods.

Message Passing Based Target Localization Under Range Deception Jamming in Distributed MIMO Radar

Recent research shows that distributed radar has great potential in recognizing and countering deception jamming. In this letter, we investigate how to use deception bistatic range measurements to estimate the target location and deception ranges, and propose a message passing based method for target localization under range deception jamming in distributed MIMO radar. Firstly, the a posteriori distribution of the target location is derived, but its maximization is intractable. Then we represent the joint distribution of the relevant variables as a factor graph model and a highly efficient message passing algorithm is developed, where the target location and deception ranges are estimated iteratively. The Cramer-Rao bound is also derived and numerical simulations are provided to demonstrate the superiority of the proposed method.

LTE‐based multistatic passive radar system for UAV detection

Using the frequency-division duplex long-term evolution (LTE)-based multistatic passive radar system for unmanned aerial vehicle (UAV) detection is considered. The typical outdoor terrestrial LTE eNodeBs and the broadband direct air-to-ground communications network eNodeBs are used to cover the UAVs at the low altitude and at the medium-high altitude, respectively. The bistatic range measurements are obtained from multiple eNodeBs, and the hyperbolic positioning technique is used for target localisation. Since the existing LTE downlink signals are more suitable for the transmission of the communication data rather than target detection, a new LTE downlink signal feature termed as target localisation reference signals (TLRS) is designed exclusively for the passive radar application using the Costas frequency coding and the P4 phase coding. Compared with the existing LTE downlink signal features, the TLRS have better waveform properties and could potentially provide much higher target detection accuracy. Meanwhile, the TLRS occupy only 0.266% LTE downlink time–frequency resources within a time frame of 1 s when the bandwidth is 10 MHz and have no negative impact on the normal LTE downlink data transmission.

Closed-Form Solution for Elliptic Localization in Distributed MIMO Radar Systems With Minimum Number of Sensors

In this article, the problem of 3-D target localization from bistatic range measurements in multiple-input-multiple-output (MIMO) radars with distributed antennas is considered. A closed-form two-stage weighted least squares solution is developed, which is able to uniquely determine the target position with a smaller number of sensors (transmitters or receivers) compared to the other existing closed-form methods. The proposed method employs several weighted least-squares minimizations and does not require any initial solution guesses to give the target position estimate. A detailed theoretical performance analysis associated with the method as well as the Cramer-Rao lower bound (CRLB) are provided. The proposed estimator is shown theoretically to achieve the CRLB accuracy under small Gaussian noise. Computer simulations are included to corroborate the theoretical development and to compare the estimator performance with several previous approaches. The proposed algorithm in the considered example is shown to outperform the existing closed-form estimators. In the 3-D and in the case of a minimum number of sensors (i.e., two transmitters and two receivers) in a MIMO radar, the proposed method is also shown to be able to localize a target with high accuracy while the previous closed-form methods cannot uniquely determine the target position.

Target localisation from bistatic range measurements in multistatic passive radar using MDS

The target localisation in a multistatic passive radar system using bistatic range measurements from multiple transmitter–receiver pairs is considered. A novel closed-form solution employing multidimensional scaling (MDS) analysis technique is proposed, which is based on the optimisation of a cost function related to the scalar product matrix in the classical MDS framework. The proposed solution is robust to large measurement noise. Simulation results demonstrate the proposed solution achieves a significant performance improvement over existing spherical interpolation, spherical intersection and two-step weighted least squares methods, and attains the Cramer–Rao lower bound at a relatively higher measurement noise level before the threshold effect occurs.

New robust Taylor series method for target localisation based on external emitter radar

This study addresses the target localisation problem using bistatic range (BR) measurements in a multi-base system based on external emitter radar. An asymptotically efficient Taylor series method is proposed for target localisation. The initial value for Taylor series method is provided by some algebraic closed-form positioning algorithms, rather than priori initial guesses. The localisation convergence problem can also be avoided unless in an extremely large measurement noise. The proposed method can be applied to both critically determined and over-determined conditions. The performance is verified and evaluated through simulations. The results show that the method can realise Cramer-Rao lower bound (CRLB) precision under Gaussian measurement noise. In addition, the method is superior to the existing localisation estimation in positioning accuracy and robustness.

Target Localization Using Double-Sided Bistatic Range Measurements in Distributed MIMO Radar Systems.

We develop a novel approach improving existing target localization algorithms for distributed multiple-input multiple-output (MIMO) radars based on bistatic range measurements (BRMs). In the proposed algorithms, we estimate the target position with auxiliary parameters consisting of both the target–transmitter distances and the target–receiver distances (hence, “double-sided”) in contrast to the existing BRM methods. Furthermore, we apply the double-sided approach to multistage BRM methods. Performance improvements were demonstrated via simulations and a limited theoretical analysis was attempted for the ideal two-dimensional case.

Distributed MIMO radar target altitude estimation for ground‐based systems

This study presents novel target altitude estimation schemes optimised for ground-based multiple-input multiple-output (MIMO) radars with widely separated antennae, where the antennae are located in a plane so that the altitudes of the antennae are close together. For the ground-based systems, existing target localisation methods based on linear least squares such as least square (LS) and bistatic range measurement (BRM) suffer from performance degradation in target altitude estimation and eventually fail in altitude localisation for a perfect ground-based system where the altitude of antennae are the same. The authors propose three target altitude estimation schemes based on linear least squares for the ground-based systems resolving the drawback of existing algorithms for the ground-based systems; extended BRM approach, which estimates the square of target altitude from the auxiliary parameters produced by BRM algorithm, ellipsoid fitting approach, which directly estimates the square of target altitude with other target position information, and extended ellipsoid fitting approach, which utilise the estimation results of ellipsoid fitting approach to improve the target altitude estimation performance. Performance improvement of the proposed algorithms is analysed in terms of mean squared error and simulation results verify the performance.

Sequential Multi-Sensor JPDA for Target Tracking in Passive Multi-Static Radar With Range and Doppler Measurements

Target tracking in passive multi-static radar (PMSR) with bistatic range and Doppler frequency measurements from multiple transmit–receive pairs is gaining increasing interest. For the data association problem in this scenario, the parallel architecture of a multi-sensor joint probabilistic data association (P-MSJPDA) filter has been significantly investigated. As an alternative architecture, the sequential MSJPDA (S-MSJPDA) is rarely discussed in PMSR. In this paper, we evaluate the behaviors of S-MSJPDA in PMSR target tracking with bistatic range and Doppler frequency measurements. A comprehensive comparison between the S-MSJPDA and the P-MSJPDA in PMSR is provided. It can be found from the analysis that S-MSJPDA outperforms its parallel counterpart in terms of computational efficiency, given an acceptable degradation in position accuracy. The S-MSJPDA is further applied to an experimental passive multi-static radar for aircrafts tracking. The real data results obtained are rather close to the true trajectories of the targets. This demonstrates that the S-MSJPDA has great potentials in PMSR target tracking.

An Approximate Maximum Likelihood Algorithm for Target Localization in Multistatic Passive Radar

This paper addresses the problem of target localization using Bistatic range (BR) measurements in a distributed multistatic passive radar system. The rangebased positioning technique employs multiple transmitterreceiver pairs, which provide separate BR measurements. Based on the Maximum likelihood (ML) function, an efficient algebraic Approximate maximum likelihood (AML) algorithm for single target localization is proposed. The closed-form AML solution has neither initial condition requirements nor convergence difficulty. Simulations are included to compare its performance to that of the CramerRao lower bound (CRLB) and the Two-step Weighted least squares (TS-WLS) algorithm. The proposed method is shown to be able to achieve the CRLB accuracy under Gaussian measurement noise. It is more robust to noise than the TS-WLS method, and presents relative insensitivity to target-sensor geometry.

Effects of nuisance variables selection on target localisation accuracy in multistatic passive radar

The target localisation problem is considered using the bistatic range measurement in multistatic passive radar. The well-known two-step weighted least-squares algorithm is widely used to locate a single target, in which the nuisance variables are normally introduced in the first step. Whereas the nuisance variables can be categorised as either target–transmitter ranges based or target–receiver ranges based. The influence of nuisance variables selection on target positioning accuracy is investigated in this Letter. Some basic criteria on choosing nuisance variables are presented and validated through simulations.

Exact Solution for Elliptic Localization in Distributed MIMO Radar Systems

Elliptic localization is a range-based positioning technique exploiting multiple transmitter-receiver pairs, each of which provides separate bistatic range (BR) measurements. In this paper, a novel computationally efficient solution for locating a single target from BR measurements in distributed MIMO radar systems is proposed. Due to nonconvex nature of the associated maximum likelihood (ML) estimation problem, its globally optimal solution is difficult to obtain. We first reformulate the ML estimation as a nonconvex constrained weighted least squares problem. Owing to special structure of the resulting problem, it is recast as a convex problem, whose exact solution can be obtained in closed-form or near closed-form manner. Moreover, the proposed method is extended to localization in the presence of antenna location uncertainties. The positioning performance of the proposed method is shown to achieve the CRLB up to relatively high noise levels. Furthermore, numerical simulations demonstrate a significant performance improvement of the proposed method over the state-of-the-art algorithms.

Iterative Target Localization in Distributed MIMO Radar From Bistatic Range Measurements

This letter discusses the problem of determining the target position from bistatic range measurements in a multiple-input multiple-output radar system with widely separated antennas. By introducing nuisance parameters and taking the relationship between these parameters and the unknown target position into consideration, the problem is formulated as a constrained weighted least squares (CWLS) problem, which is a quadratically constrained quadratic programming problem. Since the constraints are nonconvex, finding the global solution is a difficult task. To solve this problem, an iterative CWLS method is developed in this letter. We iteratively approximate each nonconvex constraint as a linear constraint to convert the problem as a linearly constrained quadratic programming problem and then solve the problem. Numerical simulations are included to support and corroborate the theoretical developments.