Linear least squares localization in sensor networks

Localization in sensor networks is critical for search and rescue. Linear least squares (LLS) estimation is a sub-optimum but low-complexity localization algorithm based on measurements of location-related parameters. Commonly, there are two types of LLS localization algorithms using range measurements; one is based on introducing a dummy variable (called LLS-I), and the other is based on the subtraction of the reference measured range (called LLS-II). Moreover, their respective weighted LLS (WLLS) algorithms (called WLLS-I and WLLS-II) can be adopted to further improve the localization accuracy. In addition, hybridization of different types of measurements can fix the deficiencies of one type of measurements. In this paper, we compare the localization performances of different LLS and WLLS algorithms in both non-hybrid time-of-arrival (TOA) and hybrid TOA/received signal-strength (RSS) networks. Simulation results show that if the variances of measurements are unavailable, the LLS-II localization algorithm should be adopted in both non-hybrid and hybrid networks using their respective reference selection criterions. If the variances of measurements are available, the two-step WLLS-I algorithm should be utilized to localize the agent in both non-hybrid and hybrid networks.