This paper investigates the linear separation requirements for Angle-of-Arrival (AoA) and range sensors, in order to achieve the optimal performance in estimating the position of a target from multiple and typically noisy sensor measurements. We analyse the sensor-target geometry in terms of the Cramer–Rao inequality and the corresponding Fisher information matrix, in order to characterize localization performance with respect to the linear spatial distribution of sensors. Here in this paper, we consider both fixed and adjustable linear sensor arrays.
References
[1]
Abramovich, Y.; Spencer, N.; Gorokhov, A. Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays .I. Fully augmentable arrays. IEEE Trans. Signal Process. 2001, 49, 959–971.
[2]
Farina, A. Target tracking with bearing-Only measurements. Signal Process. 1999, 78, 61–78.
[3]
Weng, Y.; Xie, L.; Xiao, W. Total least squares method for robust source localization in sensor networks using TDOA measurements. Int. J. Distrib. Sens. Netw. 2011, 2011, 172902:1–172902:8.
[4]
Chia-Ho Ou, K.F.S.; Jiau, H.C. Range-free localization with aerial anchors in wireless sensor networks. Int. J. Distrib. Sens. Netw. 2006, 2, 1–21.
[5]
Stansfield, R. Statistical theory of DF fixing. J. IEEE 1947, 94, 762–770.
[6]
Nardone, S.; Lindgren, A.; Gong, K. Fundamental properties and performance of conventional bearings-only target motion analysis. IEEE Trans. Autom. Control 1984, 29, 775–787.
[7]
Foy, W. Position-location solutions by Taylor-series estimation. IEEE Trans. Aerosp. Electron. Syst. 1976, 12, 187–194.
[8]
Wylie, M.; Roy, S.; Messer, H. Joint DOA estimation and phase calibration of linear equispaced (LES) arrays. IEEE Trans. Signal Process. 1994, 42, 3449–3459.
[9]
Hoctor, R.; Kassam, S. The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging. Proc. IEEE 1990, 78, 735–752.
[10]
Dempster, A. Dilution of precision in angle-of-arrival positioning systems. Electron. Lett. 2006, 42, 291–292.
Martinez, S.; Bullo, F. Optimal sensor placement and motion coordination for target tracking. Automatica 2006, 42, 661–668.
[13]
Dogancay, K.; Hmam, H. Optimal angular sensor separation for AOA localization. Signal Process. 2008, 88, 1248–1260.
[14]
Fogel, E.; Gavish, M. Nth-order dynamics target observability from angle measurements. IEEE Trans. Aerosp. Electron. Syst. 1988, 24, 305–308.
[15]
Song, T. Observability of target tracking with bearings-only measurement. IEEE Trans. Aerosp. Electron. Syst. 1996, 32, 1468–1472.
[16]
Jauffret, C.; Pillon, D. Observability in passive target motion analysis. IEEE Trans. Aerosp. Electron. Syst. 1996, 32, 1290–1300.
[17]
Torrieri, D. Statistical theory of passive location systems. IEEE Trans. Aerosp. Electron. Syst. 1984, 20, 183–198.
[18]
Dogancay, K. Online optimization of receiver trajectories for scan based emmiter location. IEEE Trans. Aerosp. Electron. Syst. 2007, 43, 1117–1125.
[19]
Bishop, A.N.; Pathirana, P.N. Optimal Trajectories for Homing Navigation With Bearing Measurements. Proceedings of the International Federation of Automatic Control World Congress, COEX, Seoul, Korea, 6–11 July 2008.
[20]
Dogancay, K. Optimaized Path Planning for UAVs with AOA/SCAN Based Sensors. Proceedings of the 15th Europian Signal Processing Conference(EUSIPCO), Poznan, Poland, 3–7 September 2007.
[21]
Kim, M.; Chong, N.Y. Direction sensing RFID reader for mobile robot navigation. IEEE Trans. Autom. Sci. Eng. 2009, 6, 44–54.
[22]
Kim, M.; Kim, H.W.; Chong, N.Y. Automated Robot Docking Using Direction Sensing RFID. Proceedings of the 2007 IEEE International Conference on Robotics and Automation, Roma, Italy, 10–14 April 2007; pp. 4588–4593.
[23]
Sundaram, K.; Mallik, R.; Murthy, U. Modulo conversion method for estimating the direction of arrival. IEEE Trans. Aerosp. Electron. Syst. 2000, 36, 1391–1396.
[24]
Wong, K.; Zoltowski, M. Direction-finding with sparse rectangular dual-size spatial invariance array. IEEE Trans. Aerosp. Electron. Syst. 1998, 34, 1320–1336.
[25]
Oshman, Y.; Davidson, P. Optimization of observer trajectories for bearings-only target localization. IEEE Trans. Aerosp. Electron. Syst. 1999, 35, 892–902.
[26]
Kay, S. Fundamentals of Statistical Signal Processing: Estimation Theory; Prentice-Hall: Upper Saddle River, NJ, USA, 1993.
[27]
Wu, J.; Wang, T.; Bao, Z. Fast realization of maximum likelihood angle estimation with small adaptive uniform linear array. IEEE Trans. Antennas Propag. 2010, 58, 3951–3960.
[28]
Liao, B.; Chan, S.C. Direction finding with partly calibrated uniform linear arrays. IEEE Trans. Antennas Propag. 2012, 60, 922–929.
[29]
Hsu, Y.S.; Wong, K.; Yeh, L. Mismatch of near-field bearing-range spatial geometry in source-localization by a uniform linear array. IEEE Trans. Antennas Propag. 2011, 59, 3658–3667.
[30]
Chan, C.Y.; Goggans, P. Using bayesian inference for linear antenna array design. IEEE Trans. Antennas Propag. 2011, 59, 3211–3217.
[31]
Li, G.; Yang, S.; Nie, Z. Direction of arrival estimation in time modulated linear arrays with unidirectional phase center motion. IEEE Trans. Antennas Propag. 2010, 58, 1105–1111.
[32]
Vertatschitsch, E.; Haykin, S. Impact of linear array geometry on direction-of-arrival estimation for a single source. IEEE Trans. Antennas Propag. 1991, 39, 576–584.
[33]
Abramovich, Y.; Spencer, N.; Gorokhov, A. DOA estimation for noninteger linear antenna arrays with more uncorrelated sources than sensors. IEEE Trans. Signal Process. 2000, 48, 943–955.
[34]
Herath, S.; Nagahawatte, C.; Pathirana, P. Tracking Multiple Mobile Agents with Single Frequency Continuous Wave Radar. Proceedings of the 2009 5th International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Melbourne, Australia, 7–10 December 2009; pp. 163–167.
[35]
Irons, J.; Johnson, B.; Linebaugh, G. Multiple-angle observations of reflectance anisotropy from an airborne linear array sensor. IEEE Trans. Geosci. Remote Sens. 1987, GE-25, 372–383.
[36]
Abramovich, Y.; Spencer, N.; Gorokhov, A. Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays. II. Partially augmentable arrays. IEEE Trans. Signal Process. 2003, 51, 1492–1507.
[37]
Bresler, Y.; Macovski, A. On the number of signals resolvable by a uniform linear array. IEEE Trans. Acoust. Speech Signal Process. 1986, 34, 1361–1375.
[38]
Abramovich, Y.; Spencer, N.; Gorokhov, A. Resolving manifold ambiguities in direction-of-arrival estimation for nonuniform linear antenna arrays. IEEE Trans. Signal Process. 1999, 47, 2629–2643.
[39]
Pal, P.; Vaidyanathan, P. Nested arrays: A novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 2010, 58, 4167–4181.
[40]
Herath, S.C.K.; Pathirana, P.N. Optimal Sensor Separation for AoA Based Localization Via Linear Sensor Array. Proceedings of the 2010 6th International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Brisbane, Australia, 7–10 December 2010; pp. 187–192.
