Position and Velocity Estimation Using TOA and FOA Based on Lagrange Programming Neural Network

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This paper addresses the problem of estimating the position and velocity of a moving source utilizing the time-of-arrival (TOA) and frequency-of-arrival (FOA) measurements. Since the concerned estimation problem is highly non-linear and non-convex, we propose to utilize a novel neural circuit, namely the Lagrange programming neural network (LPNN) framework, to solve this problem. LPNN equips the abilities of fast convergence and the robustness of resisting high noise level, and thus these two advantages have drawn much attention for it recently. Since LPNN is able to solve the optimization problem with constraint, we first reformulate the original non-linear and non-convex maximum likelihood (ML) problem by introducing additional variables and constraints, and thus a neural network is built up based on the LPNN framework. Subsequently, the convergence and stability of the proposed neural network is mathematically proved and then verified by the results of numerical experiments. Different from the conventional numerical algorithms, the analog neural network can be utilized to fulfil the task of real-time calculation, especially when there are limited computation resources in some applications. The simulation results demonstrate that the proposed LPNN model equips the basic properties of convergence and stability, and also show the superior localization accuracy of the proposed method than other numerical algorithms.