Hybrid solution method for ultra-wideband positioning in coal mines

Ultra-wideband positioning is based on the marked point distance measured by the base station and a set of non-linear positioning equations to obtain the precise device position by applying Taylor series expansion algorithm, Chan algorithm or least square solution. Among these algorithms, the Taylor series expansion algorithm has high solution accuracy, but has a strong dependence on the initial value. If the initial value is not selected properly, the algorithm will not converge. In order to solve the above problems, a hybrid solution (BSO-Taylor) method combining brain storm optimization (BSO) and Taylor series expansion is proposed. The BSO algorithm is used to solve the optimal solution for minimizing the error function from the mobile station to the base station. The time different of arrival(TDOA) value of the optimal individual is used as the initial value of the Taylor series expansion algorithm to carry out the Taylor expansion solution to obtain the positioning information.This method solves the problem that the Taylor series expansion algorithm requires better initial value. Moreover, the results of Chan algorithm, Taylor series expansion algorithm and the BSO-Taylor hybrid solution method are compared. The results show that the BSO-Taylor hybrid solution method obtains the iterative initial value close to the true position through the global search strategy. The method not only obtains the positioning performance close to the true value, but also solves the sensitivity of the Taylor series expansion algorithm to the bad initial values. Compared with the Chan algorithm, the solution of the BSO-Taylor hybrid solution method is more stable and more accurate. Compared with the Taylor series expansion algorithm, the initial position of which is the true position, the solution error of the BSO-Taylor hybrid solution is slightly larger. The effects of the variation of the positioning distance and the variation of the standard deviation of the TDOA measurements value on the Taylor series expansion algorithm and the hybrid BSO-Taylor solution method are basically the same. However, the effect on the Chan algorithm is greater.