A novel three-dimensional localization algorithm for Wireless Sensor Networks based on Particle Swarm Optimization

The paper presents a three-dimensional localization algorithm for Wireless Sensor Networks (WSN) based on Particle Swarm Optimization (PSO). According to a direct proportion relationship of the measured distance with the measuring errors, an improved three-dimensional localization objective function is defined with weighted the measured distance, and which is optimized by using PSO. In the process of solving the measured distance equations set which is an overdetermined system of equations, for reducing the order of the equations, the minimum distance equation in the system of equations is selected to subtract other equations instead of random selection. The simulation results show that the process can reduce localization errors. The effects of the amount and the distribution of the beacon nodes are analyzed, and the experimental results show that the localization errors under the marginal distribution of the beacon nodes are smaller than that one under the random distribution of the beacon nodes. The final simulation results indicate that the proposed three-dimensional localization algorithm has a higher accuracy and lower affection of the non-line-of-sight error than the least square algorithm and the BFGS (Broyden, Fletcher, Goldfarb, Shanno) algorithm, but the proposed algorithm is at cost of more localization time.