Comparison of Recursive Algorithms for Emitter Localisation using TDOA Measurements from a Pair of UAVs NICKENS OKELLO, Member, IEEE NICTA Australia FIONA FLETCHER DSTO Australia DARKO MU ² SICKI, Member, IEEE Hanyang University BRANKO RISTIC DSTO Australia This paper presents a comparative analysis of three nonlinear filters for estimation of the location and velocity of a moving emitter, using time difference of arrival (TDOA) measurements received by two unmanned aerial vehicles (UAVs) as they traverse the surveillance region. The TDOA measurements are generated over time by comparing and subtracting leading edge time of arrivals (TOAs) of signals. The Cram ´ er Rao lower bound (CRLB) of estimation errors is derived and used as the benchmark in performance analysis. The three nonlinear filters considered in the comparison are: a Gaussian mixture measurement integrated track splitting filter (GMM-ITSF), a multiple model filter with unscented Kalman filters (UKFs) and a multiple-model filter with extended Kalman filters (EKFs). Manuscript received March 8, 2009; revised April 21, 2010; released for publication June 1, 2010. IEEE Log No. T-AES/47/3/941759. Refereeing of this contribution was handled by W. Koch. This work was completed under the Research Contract “Advanced Methods of Tracking and Fusion,” between ISR Division of DSTO and The University of Melbourne. D. Mu ² sicki was partially supported by FGAN-FKIE under Contract 4500035757. Authors’ current addresses: N. Okello, National ICT Australia (NICTA), Victoria Research Laboratory, Dept. of Electrical & Electronic Engineering, The University of Melbourne, Parkville, VIC 3010, Australia, E-mail: (nickens.okello@nicta.com.au); F. Fletcher, ISR Division, DSTO, PO Box 1500, Edinburgh, SA 5111, Australia; D. Mu ² sicki, Dept. of Electronic Systems Engineering, Sa 3 Dong 1271, Hanyang University, Room 407, 3rd Eng. Building, Ansan, Kyunggido 426-791, South Korea; B. Ristic, ISR Division, DSTO, 506 Lorimer St., Melbourne, VIC 3207, Australia. 0018-9251/11/$26.00 c ° 2011 IEEE I. INTRODUCTION Emitter geolocation using unmanned aerial vehicles (UAVs) is an important application [1]. The UAVs have passive sensors that are only able to measure the time of arrival (TOA) of signals at the receiver. A single sensor of this type is unable to infer any emitter location information from this measurement without knowing the time of emission of the signal. However, when two such sensors are available, and subjected to the same signal, the time difference of arrival (TDOA) may be calculated. In the absence of measurement noise, this TDOA defines a hyperbola in two-dimensional space 1 on which the emitter must be located. When measurements from n such sensors are available from a given emission, the emitter position is found as the intersection of n ¡ 1 independent hyperbolae defined by the TDOA measurements formed by selecting a reference sensor (referred to as sensor 1 in the remainder of the paper) and then pairing each of the remaining sensors with the reference sensor. 2 For a two-dimensional geolocation problem, only three sensors are required to find the emitter position, provided that the sensors are not located collinearly with the emitter [2, 3]. When measurements are noise corrupted, the hyperbolae will no longer intersect exactly at the emitter location. An estimate of emitter location can be found using least squares [4, 5]. The presence of further additional sensors can help improve the estimation of emitter location. Examples of applications include mobile positioning of wireless communication systems [6, 7] and geolocation of stationary or moving emitters using multiple UAVs [1, 4, 5, 8, 9]. These emitters may be tracked over time from position estimates calculated using these localisation techniques at each emission as measurements in a linear Kalman filter or other smoothing technique [6, 7, 9]. These localization techniques together with many others [10—14] can be classified as traditional methods in that they employ at least three noncollocated sensors that collect TDOAs of a single pulse from which emitter location estimate is obtained. This paper considers a scenario with two noncollocated mobile sensors where sensors measure TDOA over a number of emissions from a possibly moving emitter. The time history of received measurements, coupled with the assumption that emitter motion model is known (in the paper we assume constant velocity emitter motion), is sufficient to estimate target location over time. 1 In three dimensional space, the TDOA defines a hyperboloid on which the emitter must be located. 2 In practice, there are n(n ¡ 1)=2 pairings of sensors, but only n ¡ 1 are independent. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 3 JULY 2011 1723