A Novel Estimator for TDOA and FDOA Positioning of Multiple Disjoint Sources in the Presence of Calibration Emitters

Abstract

Multiple-target localization is extensively applied in wireless connected networks. However, sensor location uncertainty is known to degrade significantly the target localization accuracy. Fortunately, calibration emitters such as unmanned aerial vehicles (UAV) with known location can be used to reduce the loss in localization accuracy due to sensor location errors. This paper is devoted to the use of UAV calibration emitters for time differences of arrival (TDOA) and frequency differences of arrival (FDOA) positioning of multiple targets. The study starts with deriving the Cramér-Rao bound (CRB) for TDOA/FDOA-based target location estimate when several UAV calibration signals are available. Subsequently, the paper presents an iterative constrained weighted least squares (ICWLS) estimator for multiple-target joint localization using TDOA/FDOA measurements from both target sources and UAV calibration emitters. The newly proposed method consists of two stages. In the first phase, the sensor locations are refined based on the calibration measurements as well as the prior knowledge of sensor locations. The second step provides the estimate of multiple-target locations by combining the measurements of target signals as well as the estimated values in the first phase. An efficient ICWLS algorithm is presented at each stage. Both the two algorithms are implemented by using matrix singular value decomposition (SVD), which is able to provide a closed-form solution and update the weighting matrix at every iteration. Finally, the convergence behavior and estimation mean-square-error (MSE) of the new estimator are deduced. Both theoretical analysis and simulation results show that the developed method can improve the TDOA/FDOA localization accuracy obviously with the help of UAV calibration emitters. INDEX TERMS Target localization, unmanned aerial vehicle (UAV), time difference of arrival (TDOA), frequency difference of arrival (FDOA), multiple targets, calibration emitters, constrained weighted least squares (CWLS), Cramér-Rao bound (CRB), singular value decomposition (SVD).

A Survey for Recent Techniques and Algorithms of Geolocation and Target Tracking in Wireless and Satellite Systems

“…The simulation results demonstrated that the proposed algorithm could produce the optimal solution to the formulated constrained WLS problem. Additionally, its estimation RMSE can achieve CRLB with calibration emitters at common noise; from that, the analytical validation results verified that the proposed algorithm is better than some existing localization algorithms [90]. In [91], a simple algorithm is designed for movable target estimation using three or more stationary sensors.…”

“…In the first stage, the location of the sensors is enhanced based on the calibration measurements as well as the previous knowledge of the sensors position. In the second stage, the estimate of the multiple target geolocation is obtained by joining the measurements of emitted signals and the estimated values obtained in the first stage [90]. The simulation results demonstrated that the proposed algorithm could produce the optimal solution to the formulated constrained WLS problem.…”

Effectiveness of Mobile Emitter Location by Cooperative Swarm of Unmanned Aerial Vehicles in Various Environmental Conditions

“…Mobility and the lack of spatial restrictions in the UAV missions is a special property that determines the use of these vehicles both to create dynamically changing network structures and the implementation of additional communications services such as the location of emission sources. The prospects for using the UAVs to improve the quality and scope extension of communication services in fifth-generation (5G) mobile networks and in the localization systems of fixed emission sources are presented in [10,11] and [12], respectively.…”

“…Time and frequency differences of arrival (TDOAs and FDOAs) measurements performed by many sensors are some of the more commonly used techniques for estimating the position of mobile emitters [12][13][14][15]. Target tracking techniques based on the TDOA measurements in a WSN are described, i.a., in [16,17].…”

Method for Remote Determination of Object Coordinates in Space Based on Exact Analytical Solution of Hyperbolic Equations

“…Close in meaning to ToF is the algorithm ToA (Time of Arrival), which is based on distance calculation by measuring the signal transit time from the mobile terminal to the base station as the difference between the time the signal was sent and received [ 21 , 22 , 23 , 24 ]. The algorithm ToA is often used with TDoA (Time Difference of Arrival) [ 25 ] and FDoA (Frequency difference of arrival) [ 26 ], which are also often used together [ 27 , 28 , 29 , 30 ]. TDoA is a very popular algorithm for different applications and measures the difference in the time of arrival of a signal from an object to several base stations [ 31 , 32 , 33 ].…”