Linear closed-form solution for wireless localisation with ultra-wideband/chirp spread spectrum signals based on difference of squared range measurements

In many practical applications of wireless localisation with ultra-wideband or chirp spread spectrum signals based on distance measurements, iterative least squares (ILS) method and direct solution (DS) method have been used. In these methods, some deployment conditions of reference nodes may cause problems such as: local minimum problem in the ILS method and red sea zone problem in the DS method. To overcome these problems, a linear closed-form solution based on difference of squared range measurements is presented in this study. The measurement used in this solution is the difference of squared range measurements instead of distance measurements. Also, it is shown that the proposed solution is equal to the range-difference measurements-based closed-form solution. Some Monte Carlo simulations were conducted to illustrate the proposed solution and demonstrate its performance. Through actual experiments, the validity of the proposed solution is confirmed.