A hybrid genetic optimization method for accurate target localization

Abstract

This paper considers the problem of estimating the position of a target based on the time of arrival (TOA) measurements from a set of receivers whose positions are known. The weighted least square (WLS) technique is applied as an efficient existing approach. The optimization problem is formulated by the minimization of the sum of squared residuals between estimated and measured data as the objective function. The hybrid Genetic Algorithm-Nelder-Mead (GA-NM) method is proposed that combines the global search and local search abilities in an effective way in order to improve the performance and the solution accuracy. The corresponding Cramer-Rao lower bound (CRLB) on the localization errors is derived as a benchmark. Simulation results show that the proposed hybrid GA-NM method achieves a significant performance improvement compared to existing methods

Time Difference of Arrival (TDoA) Localization Combining Weighted Least Squares and Firefly Algorithm

“…In this section, the results of the commonly used algorithms CWLS [31], Newton–Raphson (NR) [29], TSWLS [18], and GA [30], were compared with the hybrid-FA. The GA method is a search algorithm that is commonly used for optimization.…”

“…Usually, there are iterative methods, such as those mentioned in Section 1, to solve the equations, for which the computational burden is heavy. In this section, the WLS method is introduced based on TDoA measurements [29]. The sum of squares of residuals is defined as JNLS(x˜):JNLSfalse(x˜false)=mintrue∑i=1NRi2(x˜) where x˜ represents the optimization variable, and residual Ri(x˜) can be expressed as Ri(x˜)=r˜i,1−ri,1 where r˜i,1 is the measured value.…”

“…The firefly algorithm (FA) is one such nature-inspired algorithm, which was proposed in 2008. Using the FA for multimodal optimization applications with high efficiency has been proposed [28,29].…”

“…Research on algorithms that are robust and have low computational complexity is still worthy of study. Search algorithms for TDoA measurements can provide accurate results, although the efficiency will inevitably decrease when there are many estimated parameters [29]. Therefore, it is necessary to develop a highly efficient search algorithm for TDoA.…”