Direct Position Determination of Multiple Radio Signals
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Direct Position Determination of Multiple Radio Signals Anthony J. Weiss Department of Electrical Engineering – Systems, Tel Aviv University, Tel Aviv 69978, Israel Email: [email protected]
Alon Amar Department of Electrical Engineering – Systems, Tel Aviv University, Tel Aviv 69978, Israel Email: [email protected] Received 25 December 2003; Revised 8 June 2004 The most common methods for position determination of radio signal emitters such as communications or radar transmitters are based on measuring a specified parameter such as angle of arrival (AOA) or time of arrival (TOA) of the signal. The measured parameters are then used to estimate the transmitter’s location. Since the measurements are done at each base station independently, without using the constraint that the AOA/TOA estimates at different base stations should correspond to the same transmitter’s location, this is a suboptimal location determination technique. Further, if the number of array elements at each base station is M, and the signal waveforms are unknown, the number of cochannel simultaneous transmitters that can be localized by AOA is limited to M − 1. Also, most AOA algorithms fail when the sources are not well angularly separated. We propose a technique that uses exactly the same data as the common AOA methods but the position determination is direct. The proposed method can handle more than M − 1 cochannel simultaneous signals. Although there are many stray parameters, only a two-dimensional search is required for a planar geometry. The technique provides a natural solution to the measurements sources association problem that is encountered in AOA-based location systems. In addition to new algorithms, we provide analytical performance analysis, Cram´erRao bounds and Monte Carlo simulations. We demonstrate that the proposed approach frequently outperforms the traditional AOA methods for unknown as well as known signal waveforms. Keywords and phrases: angle of arrival, time of arrival, array processing, emitter localization.
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INTRODUCTION
The problem of emitter location attracts much interest in the signal processing, communications, and underwater acoustics literature. Defense oriented location systems have been reported since World War I. Civilian systems are now in use for the localization of cellular phone callers, spectrum monitoring, and law enforcement. Perhaps the first paper on the mathematics of emitter location, using angle of arrival (AOA), is due to Stansfield [1]. Many other publications followed including a fine review paper by Torrieri [2]. The papers by Krim and Viberg [3] and Wax [4] are comprehensive review papers on antenna array processing for location by AOA. Recently, Van Trees [5] published a book that is fully devoted to array processing. Positioning by time of arrival (TOA) and its derivatives (DTOA, EOTD) is used extensively in cellular phone localization [6], radar systems [7], and underwater acoustics [8]. In underwater acoustics, matched-field processing (MFP) is often proposed for source localization [9].
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