多输入多输出被动雷达的TDOA/AOA三维定位解析算法

雷达定位

需积分: 9 187 浏览量更新于2024-08-04 1 收藏 3.24MB PDF 举报

身份认证购VIP最低享 7 折!

领优惠券(最高得80元）

资源详情

资源推荐

IET Radar, Sonar & Navigation

Research Article

Algebraic solution for three-dimensional

TDOA/AOA localisation in multiple-input–

multiple-output passive radar

ISSN 1751-8784

Received on 31st March 2017

Revised 25th August 2017

Accepted on 3rd September 2017

E-First on 4th October 2017

doi: 10.1049/iet-rsn.2017.0117

www.ietdl.org

Ali Noroozi

, Mohammad Ali Sebt

Faculty of Electrical Engineering, K.N. Toosi University of Technology, Seyed-Khandan bridge, Shariati Avenue, Tehran, Iran

E-mail: ali_noroozi@ee.kntu.ac.ir

Abstract: The problem of estimating the location of a single target from time difference of arrival (TDOA) and angle of arrival

(AOA) measurements using multi-transmitter multi-receiver passive radar system with widely separated antennas is discussed.

A closed-form two-step target position estimator is presented and analysed. Using the measured AOAs, the method is able to

resolve the weakness of the TDOA-based methods in estimating the target height. Several weighted least-squares

minimisations are employed by the method to produce a location estimate. A weighting matrix in each step is employed to

provide a significant improvement in the performance of the algorithm. The Cramer–Rao lower bound (CRLB) for target

localisation accuracy is also developed. The proposed estimator is analytically shown to reach the CRLB for Gaussian TDOA

and AOA noises at moderate noise level. Simulation studies indicate that the proposed hybrid TDOA/AOA location scheme

performs better than any of the other algorithms, especially in the z-direction.

1 Introduction

Research on passive radars with multiple transmitters and multiple

receivers [known as multiple-input–multiple-output (MIMO)

passive radars] has received considerable attention in the past few

years [1–3]. MIMO passive radars can also play an important role

in improving the detection and localisation performances [4, 5].

This would be achieved by taking the advantage of the spatial

diversity provided by employing widely separated antenna

configuration [6, 7].

In passive radar systems, since the location of the target is

unknown, we are not able to compute the time of propagation

between transmitter–target–receiver triangles, namely the bistatic

triangle. Instead, we can measure the time difference between the

arrival of the direct and reflected signals collected from the

reference and surveillance channels, respectively. This delay is

determined by calculating the cross-ambiguity function (CAF)

between the reference signal and the reflected target echo. It can

then be converted to the bistatic range (BR), which is the sum of

transmitter–target and target–receiver ranges.

Several publications on target location estimation in the widely

distributed MIMO radars have appeared in recent years, which

indicate the importance of this issue. In general, the localisation

methods in these radars can be classified as either direct or indirect.

The former is based on processing simultaneously the observations

collected by the receivers to generate the target location estimate.

Although, the direct methods such as the maximum-likelihood

estimator (MLE) [7–9] and sparse recovery [10] are asymptotically

optimum, they, in addition to requiring high computational cost to

produce the desired results, cannot give a closed-form solution. On

the other hand, the indirect methods first measure the time delays

using the CAF. Then, by multiplying these delays by the speed of

signal propagation and performing some simple operations, the

corresponding BRs are calculated. These BRs form a set of elliptic

equations through which the target position is obtained. The best

linear unbiased estimator (BLUE) method is presented in [7, 8, 11],

which linearises the problem with a Taylor series expansion of the

non-linear equations. The major drawback of this approach is that

it requires an initial guess which is sufficiently close to the target

position. In [5], a least-squares solution is proposed in which only a

small number of the BR equations are utilised and then these

equations are changed to the range difference (RD) equations.

Using these RD equations yields the target location. Although this

approach has a closed-form solution, it does not exploit all the

possible equations. Furthermore, its performance is degraded by

converting the BR equations to the RD equations [12]. Another

solution to find the position of a moving target is presented in [13],

called the distributed approach. In this method, the measurements

are first divided into several groups based on the different

transmitters or receivers. Later, two weighted least-squares (WLSs)

estimators for each group are employed to independently generate

a target position estimate. The results from different groups are

then combined to produce the final estimate. In [14], a closed-form

two-step WLS method is proposed for finding the location of a

target. Under the conditions that the noise is small and the same in

all the measurements, this method can approximate the MLE. From

a practical viewpoint, however, they may never satisfy, especially

the second one. Recently, in [15, 16], a closed-form one-step WLS

method for target localisation in the general case of noise is

presented in two different conditions – when the measurement

noise is small, which leads to the MLE, and when it is not, which

results in the BLUE [17]. Although the method presented in [15,

16] is shown to outperform the previous works, generally it fails to

attain the Cramer–Rao lower bound (CRLB).

The major drawback of time difference of arrival (TDOA)-

based localisation with terrestrial transmitters and receivers is the

lack of accuracy in estimating the target height [16]. Although the

techniques using the TDOA measurements gathered from

terrestrial transmitters and receivers have a very good performance

in the x and y directions, they suffer from poor accuracy in the z-

direction. The main cause of this problem is the lack of the

diversity in the z-direction. To overcome this difficulty, a few

suggestions are put forward in [16], one of which is employing a

joint localisation scheme based on the TDOA and angle of arrival

(AOA) measurements. Thus, the aim of this paper is to improve the

localisation performance by utilising the measured AOAs as well

as the measured TDOAs.

This paper seeks to address the target localisation problem from

TDOA and AOA measurements in the presence of multiple

transmitters and multiple receivers. A closed-form two-step

solution is proposed, which is able to reach the CRLB under

Gaussian TDOA and AOA noise conditions. In this paper, we also

generate two weighting matrices which result in an approximate

MLE in each step under the condition that the measurement noise

is Gaussian and small. The covariance matrix of the location

estimate is derived. Analytically, we compare the covariance

IET Radar Sonar Navig., 2018, Vol. 12 Iss. 1, pp. 21-29

下载后可阅读完整内容，剩余8页未读，立即下载

这个夏天的你们

粉丝: 1
资源: 2

多输入多输出被动雷达的TDOA/AOA三维定位解析算法

最新资源