SOURCE LOCALIZATION: ALGORITHMS AND ANALYSIS 閱讀記錄（2.1）

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.

根據一系列空間分離傳感器的測量結果找到無源信号源的位置一直是雷達，聲納和全球定位系統，移動通信，多媒體和無線傳感器網絡中的一個重要問題。

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.

到達時間（TOA），到達時間差（TDOA），接收信号強度（RSS）和發射信号的到達方向（DOA）是用于源定位的常用測量。

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提供源和傳感器之間的距離資訊，而DOA是相對于接收器的源方位。 然而，找到源位置并不是一項簡單的任務，因為這些測量與源位置具有非線性關系。

This chapter 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.

本章介紹了兩類基于TOA，TDOA，RSS和DOA測量的定位算法。 第一類研究直接從源和測量之間的非線性關系獲得的非線性方程。 将呈現相應的示例，即非線性最小二乘（NLS）和最大似然（ML）估計。

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. 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. 

第二類嘗試将方程轉換為線性，我們将讨論線性最小二乘（LLS），權重線性最小二乘（WLLS）和子空間方法。 此外，在足夠小的誤差條件下，我們為任何定位方法開發均值和方差表達式，這可以表示為無限制優化問題。

 Assuming that the disturbances in the measurements are zero - mean Gaussian distributed, the Cramér – 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.

假設測量中的幹擾是零 - 均值高斯分布，則還将提供Cramér-Rao下界（CRLB），其給出了使用相同資料的任何無偏位置估計器可獲得的方差的下界。

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

本章的預期學習成果包括：（1）使用TOA，TDOA，RSS和DOA測量來了解定位算法的開發; （2）了解位置估計的績效名額。

INTRODUCTION

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.

感興趣目标的位置可以通過利用其在空間上分離的接收器陣列處測量的具有先驗已知位置的發射信号來确定。

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] . 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.

事實上，源定位已經成為許多領域的核心問題之一，如雷達，聲納[1]，電信[2]，移動通信[3 - 5]，無線傳感器網絡[6,7]，以及人類 - 計算機互動[8]。 例如，可以在諸如視訊會議，自動場景分析和安全監視之類的應用中使用麥克風陣列來跟蹤活動講話者的位置。

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] .

另一方面, 移動終端的本地化受到了相當大的關注, 尤其是在美國聯邦通信委員會 (FCC) 通過了規則來改進911服務的時候, 強制定位一個緊急呼叫者在指定範圍内, 即使對于無線電話使用者 [9]。

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. 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.

除緊急援助外，移動位置資訊也是大量創新應用的關鍵推動因素，如個人本地化和監控，車隊管理，資産跟蹤，旅行服務，基于位置的廣告和計費。 最近，無線通信和微系統內建的技術進步使得能夠開發小型，廉價，低功率的傳感器節點，這些節點能夠收集周圍資料，執行小規模計算以及在其鄰居之間進行通信。

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.

這些無線連接配接節點在以協作方式工作時，在許多遠端監控和控制應用中具有巨大潛力，例如栖息地監控，醫療保健，樓宇自動化，戰場監控以及環境觀測和預測。 由于傳感器節點通常被任意放置，其位置未知，是以節點定位是傳感器網絡操作和管理的基本且關鍵的問題。

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.

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

我們假設測量中沒有異常值以實作可靠的位置估計; 也就是說，由RSS中的陰影和多徑傳播引起的誤差足夠小。 另一方面，假設視距（LOS）傳輸[10]，是以在估計TOA，TDOA和DOA時，源和每個接收器之間存在直接路徑。 值得指出的是，當源和接收器之間存在障礙物時會發生非視距（NLOS），這會在相應的距離資訊中産生較大的正偏差。 對于存在NLOS傳播的位置估計，感興趣的讀者可參考本書的第IV部分。

The rest of this chapter is organized as follows. The measurement models of TOA, TDOA, RSS, and DOA and their positioning principles are fi rst presented in Section 2.2 . Positioning algorithms based on the location - bearing information, which are classifi ed as nonlinear and linear approaches, are developed in Section 2.3 .

本章的其餘部分安排如下。 TOA，TDOA，RSS和DOA的測量模型及其定位原則首先在2.2節中介紹。 第2.3節開發了基于位置承載資訊的定位算法，這些算法被分類為非線性和線性方法。

The first category deals with the nonlinear equations directly constructed from the TOA, TDOA, RSS, or DOA measurements, which includes the NLS and ML estimators. On the other hand, the second approach converts the nonlinear equations to be linear, and LLS, WLLS, and subspace methods will be presented. Note that the WLLS estimator is, in fact, a generalized version of the LLS technique, where a weighting function is involved. Section 2.4 contributes to the algorithm analysis, and two important performance measures, namely, mean and variance, will be examined. Furthermore, the computation of CRLB, which is a lower bound on the variance attainable by any unbiased location estimator, will be presented. Finally, concluding remarks are given in Section 2.5 . Symbols that are used in this chapter are listed in Table 2.1 .

第一類涉及直接由TOA，TDOA，RSS或DOA測量建構的非線性方程，其中包括NLS和ML估計。 另一方面，第二種方法将非線性方程轉換為線性方程，并且将呈現LLS，WLLS和子空間方法。 注意，WLLS估計器實際上是LLS技術的通用版本，其中涉及權重函數。 第2.4節有助于算法分析，并将檢查兩個重要的性能名額，即均值和方差。 此外，将呈現CRLB的計算，CRLB是任何無偏位置估計器可獲得的方差的下限。 最後，第2.5節給出了結論性意見。 表2.1列出了本章中使用的符号。