【 Notes 】SOURCE LOCALIZATION PREVIEW

FINDING THE  position of a passive source based on measurements from an array of spatially separated sensors has been an important problem in radar, sonar, and global positioning systems, mobile communications, multimedia, and wireless sensor networks.

根据一系列空间分离传感器的测量结果找到无源信号源的位置一直是雷达，声纳和全球定位系统，移动通信，多媒体和无线传感器网络中的一个重要问题。

The time of arrival ( TOA ), time difference of arrival ( TDOA ), received signal strength ( RSS ), and direction of arrival ( DOA ) of the emitted signal are commonly used measurements for source localization.

到达时间（TOA），到达时间差（TDOA），接收信号强度（RSS）和发射信号的到达方向（DOA）是用于源定位的常用测量。

Basically, TOAs, TDOAs, and RSSs provide the distance information between the source and sensors, while DOAs are the source bearings relative to the receivers. However, finding the source position is not a trivial task because these measurements have nonlinear relationships with the source position.

基本上，TOA，TDOA和RSS提供源和传感器之间的距离信息，而DOA是相对于接收器的方位。 然而，找到源位置并不是一项简单的任务，因为这些测量与源位置具有非线性关系。

we will introduces two categories of positioning algorithms based on TOA, TDOA, RSS, and DOA measurements. The first class works on the nonlinear equations directly obtained from the nonlinear relationships between the source and measurements. Corresponding examples, namely, nonlinear least squares ( NLS ) and maximum likelihood ( ML ) estimators, will be presented. The second category attempts to convert the equations to be linear, and we will discuss the linear least squares ( LLS ), weighted linear least squares ( WLLS ), and subspace approaches.

我们将介绍两类基于TOA，TDOA，RSS和DOA测量的定位算法。 第一类研究直接从源和测量之间的非线性关系获得的非线性方程。 将呈现相应的示例，即非线性最小二乘（NLS）和最大似然（ML）估计器。 第二类尝试将方程转换为线性，我们将讨论线性最小二乘（LLS），加权线性最小二乘（WLLS）和子空间方法。

In addition, under sufficiently small error conditions, we develop the mean and variance expressions for any positioning method, which can be formulated as an unconstrained optimization problem. Assuming that the disturbances in the measurements are zero - mean Gaussian distributed, the Cram é r – Rao lower bound ( CRLB ), which gives a lower bound on the variance attainable by any unbiased location estimator using the same data, will also be provided.

此外，在足够小的误差条件下，我们为任何定位方法开发均值和方差表达式，这可以表示为无约束优化问题。 假设测量中的干扰是零 - 均值高斯分布，则还将提供Cramér-Rao下界（CRLB），其给出了使用相同数据的任何无偏位置估计器可获得的方差的下界。

The intended learning outcomes  include (1) understanding the positioning algorithm development using TOA, TDOA, RSS, and DOA measurements; and (2) understanding the performance measures for position estimation.

预期的学习成果包括（1）使用TOA，TDOA，RSS和DOA测量来理解定位算法的开发; （2）了解位置估计的绩效指标。

The position of a target of interest can be determined by utilizing its emitted signal measured at an array of spatially separated receivers with a priori known locations.

感兴趣目标的位置可以通过利用其在空间上分离的接收器阵列处测量的具有先验已知位置的发射信号来确定。

这句话已经很重要了，这就是说，要想获得目标位置，我们得先知道测量站的位置，就是我们的测量站的位置是已知的，通过接收目标发射的信号来获得目标的位置。

In fact, source localization has been one of the central problems in many fields such as radar, sonar [1] , telecommunications [2] , mobile communications [3 – 5] , wireless sensor networks [6, 7] , as well as human – computer interaction [8] .

事实上，源定位已经成为许多领域的核心问题之一，如雷达，声纳[1]，电信[2]，移动通信[3 - 5]，无线传感器网络[6,7]，以及人类 - 计算机互动[8]。

For example, the position of an active talker can be tracked with the use of a microphone array in applications such as video conferencing, automatic scene analysis, and security monitoring. On the other hand, mobile terminal localization has been receiving considerable attention, especially after the Federal Communications Commission ( FCC ) in the United States has adopted rules to improve the 911 services by mandating the accuracy of locating an emergency caller to be within a specified range, even for a wireless phone user [9] .

例如，可以在诸如视频会议，自动场景分析和安全监视之类的应用中使用麦克风阵列来跟踪活动讲话者的位置。另一方面，移动终端本地化已经受到相当大的关注，特别是在美国联邦通信委员会（FCC）通过强制将紧急呼叫者，甚至对于无线电话用户[9]，定位在指定范围内的准确性来采用改进911服务的规则之后。

Apart from emergency assistance, mobile position information is also the key enabler for a large number of innovative applications such as personal localization and monitoring, fleet management, asset tracking, travel services, location - based advertising, and billing.

除紧急援助外，移动位置信息也是大量创新应用的关键推动因素，如个人定位和监控，车队管理，资产跟踪，旅行服务，基于位置的广告和计费。

More recently, technological advances in wireless communications and microsystem integration have enabled the development of small, inexpensive, low - power sensor nodes, which are able to collect surrounding data, perform small - scale computations, and communicate among their neighbors.

最近，无线通信和微系统集成的技术进步使得能够开发小型，廉价，低功率的传感器节点，这些节点能够收集周围数据，执行小规模计算以及在其邻居之间进行通信。

These wirelessly connected nodes, when working in a collaborative manner, have great potential in numerous remote monitoring and control applications, such as habitat monitoring, health care, building automation, battlefield surveillance, as well as environment observation and forecasting. Because sensor nodes are often arbitrarily placed with their positions being unknown, node positioning is a fundamental and crucial issue for the sensor network operation and management.

这些无线连接节点在以协作方式工作时，在许多远程监控和控制应用中具有巨大潜力，例如栖息地监控，医疗保健，楼宇自动化，战场监控以及环境观测和预测。 由于传感器节点通常被任意放置，其位置未知，因此节点定位是传感器网络操作和管理的基本且关键的问题。

TOA, TDOA, RSS, and DOA of the emitted signal are commonly used measurements [10] for source localization. Basically, TOAs, TDOAs and RSSs provide the distance information between the source and sensors, while DOAs are the source bearings relative to the receivers. However, finding the source position is not a trivial task because these measurements have nonlinear relationships with the source position. Given the TOA, TDOA, RSS, or DOA information, the main focus in this chapter is on positioning algorithm development and analysis. Although two dimensional (2 - D) source localization is considered, it is straightforward to extend the study to three dimensional space.

发射信号的TOA，TDOA，RSS和DOA是用于源定位的常用测量[10]。 基本上，TOA，TDOA和RSS提供源和传感器之间的距离信息，而DOA是相对于接收器的源方位。 然而，找到源位置并不是一项简单的任务，因为这些测量与源位置具有非线性关系。 鉴于TOA，TDOA，RSS或DOA信息，本章的主要重点是定位算法开发和分析。 虽然考虑了二维（2-D）源定位，但是将研究扩展到三维空间是直截了当的。

We assume that there are no outliers in the measurements in order to achieve reliable location estimation; that is, the errors due to shadowing and multipath propagation in the RSSs are sufficiently small. On the other hand, line - of - sight ( LOS ) transmission [10] is assumed, so that there is a direct path between the source and each receiver in estimating the TOAs, TDOAs, and DOAs. It is worthy to point out that non - line - of - sight ( NLOS ) occurs when there are obstructions between the source and receivers, which can cause large positive biases in the corresponding distance information.

我们假设测量中没有异常值以实现可靠的位置估计; 也就是说，由RSS中的阴影和多径传播引起的误差足够小。 另一方面，假设视距（LOS）传输[10]，因此在估计TOA，TDOA和DOA时，源和每个接收器之间存在直接路径。 值得指出的是，当源和接收器之间存在障碍物时会发生非视距（NLOS），这会在相应的距离信息中产生较大的正偏差。

For position estimation in the presence of NLOS propagation, the interested reader is referred to Part IV of this book.

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