煤矿井下超宽带定位混合解算方法

Hybrid solution method for ultra-wideband positioning in coal mines

超宽带定位是根据基站测定的标记点距离,基于一组非线性定位方程组,通过泰勒(Taylor)级数展开算法、Chan算法或最小二乘法解算获得精确的设备位置。其中,Taylor级数展开算法的求解精度高,但是对初始值具有很强的依赖性,如果初始值选择不恰当,会导致算法不收敛。针对上述问题,提出了一种结合头脑风暴优化(BSO)和Taylor级数展开的混合解算(BSO-Taylor)方法。采用BSO算法求解移动站到基站的误差函数最小化的最优解,将最优个体的到达时间差(TDOA)值作为Taylor级数展开算法的初始值,进行Taylor展开解算得到定位信息,解决了Taylor级数展开算法需要较好初始值的问题。对Chan算法、Taylor级数展开算法和BSO-Taylor混合解算方法的结果进行了对比实验,结果表明,BSO-Taylor混合解算方法通过全局搜索策略,获得了接近于真实位置的迭代初始值,既可以获得接近真值的定位性能,又解决了Taylor级数展开算法对不良初始值的敏感性;相较于Chan算法,BSO-Taylor混合解算方法的解算结果更加稳定,且准确性更好;相较于初始位置为真实位置的Taylor级数展开算法,BSO-Taylor混合解算方法的解算误差稍大;定位距离的变化和TDOA测量值标准差的变化对Taylor级数展开算法和BSO-Taylor混合解算方法的影响基本一致,而对Chan算法的影响较大。

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.