Invex Relaxation Based Cooperative Localization Using RSS Measurements

Received signal strength (RSS)-based localization techniques have attracted a lot of interest as they are easy to implement and do not require any localization-specific hardware. However, maximum likelihood (ML) formulation of RSS-based localization problem is non-convex, non-linear, and discontinuous, and cannot be solved using standard optimization techniques. We propose techniques that converts the ML objective function into an invex (invariant convex) function and solve them using gradient descent. We also employ coordinate descent to solve the invex problem in a completely distributed manner without any synchronization requirements. The coordinate descent-based technique can be implemented on the sensor nodes as it has low computational complexity and scales very well to large networks. We prove the convergence theoretically, derive the convergence rate, and provide a detailed computational complexity and communication overhead analysis of the techniques. We perform extensive performance analysis and compare our techniques with centralized and distributed localization methods, and demonstrate the superior performance of the proposed techniques in terms of convergence rate, localization accuracy, and execution time.