Low complexity improvement on linear least-squares localization

In this paper, a low complexity way to improve the Linear Least-Squares (LLS) method is introduced. The n-dimensional (n-D) positioning problem is first reduced to 1-D and then solved iteratively. Compared to the classic Gauss-Newton method, the n×n matrix inversion/factorization in each iteration is reduced to the inversion of a scalar. Simulations are performed to compare the Gauss-Newton, the LLS and the improved LLS method versus the Cramer-Rao Lower Bound (CRLB). The Mean Squared Error (MSE) of the obtained estimator is very close to that of the Gauss-Newton method, while the computational complexity is kept at almost the same level of the LLS approach.