DRSS-Based Localization Using Convex Optimization in Wireless Sensor Networks

Localization with differential received signal strength measurement in recent years has been very much considered. Due to the fact that the probability density function is known for given observations, the maximum likelihood estimator is used. This estimator can be asymptotically represented the optimal estimation of the location. After the formation of this estimator, it is observed that the corresponding cost function is highly nonlinear and non-convex and has a lot of minima, so there is no possibility of achieving the global minimum with Newton method and the localization error will be high. There is no analytical solution for this cost function. To overcome this problem, two methods are existed. First, the cost function is approximated by a linear estimator. But this estimator has poor accuracy. The second method is to replace the non-convex cost function with a convex one with the aid of convex optimization methods, in which case the global minimum is obtained. In this paper, we proposed new convex estimator to solve cost function of maximum likelihood estimator. The results of the simulations show that the proposed estimator has up to 20 percent performance improvement compared with existing estimators, moreover, the execution time of proposed estimator is 30 percent faster than other convex estimators.