REPUBLIC OF SERBIA

MINISTRY OF DEFENCE

www.mod.gov.rs

MINISTRY OF DEFENCE

Material Resources Sector

Defensive Technologies Department

Military Technical Institute

www.vti.mod.gov.rs

Performance evaluation of NONLINEAR optimization methods for TOA localization techniques

MAJA ROSIĆ

Faculty of Mechanical Engineering, University of Belgrade, Belgrade, mrosic@mas.bg.ac.rs

MIRJANA SIMIĆ

School of Electrical Engineering, University of Belgrade, Belgrade, mira@etf.rs

PREDRAG PEJOVIĆ

School of Electrical Engineering, University of Belgrade, Belgrade, peja@etf.rs

Abstract: Source localization based on the time of arrival (TOA) measurements is very important in military and civil applications such as Wireless Sensor Networks (WSNs), sonar, radar, security systems, health monitoring, etc. Some of the localization measurements are corrupted by errors which always exist no matter which localization techniques are used. Therefore, TOA source localization model, in the presence of additive noise, can be formulated as an optimization model with the sum of squared residuals as the objective function. This paper presents the application of three nonlinear optimization methods: the Steepest Descent, the Newton-Raphson and the Gauss-Newton methods and their performance is compared with each other in terms of localization accuracy. Numerical simulation results illustrate the performance comparison of these different proposed nonlinear optimization methods with different initial values and signal-to-noise ratio (SNR). The corresponding Cramer–Rao Lower Bound (CRLB) on the localization errors is derived, which gives a lower bound on the variance of any unbiased estimator. Finally, the simulation results analysis of the performance of the proposed gradient-based optimization methods are evaluated and compared with the CRLB and the closed-form LLS method.

Keywords: Wireless Seknsor Networks, Localization, Optimization, Time of Arrival, Signal-to-noise ratio