基于多元变量泰勒级数展开模型的定位算法

传统Taylor级数展开模型只考虑未知节点和锚节点之间的距离，没有考虑未知节点之间的距离，定位信息不够全面，从而导致定位精度不高。为了进一步提高定位精度，该文提出了一种新的基于多元变量Taylor级数展开模型的定位算法。首先考虑未知节点之间的距离信息，建立新的基于多元变量Taylor级数展开的定位模型。然后，在对新的定位模型求解过程中，采用粒子群算法对未知节点进行定位，获得其位置的初始值。再根据加权最小二乘法求出新模型的解，作为未知节点的估计位置。最后，为评价该算法的性能，对定位结果的克拉美罗界（CRLB）进行推导。仿真结果表明基于多元变量Taylor级数展开模型的定位精度更高，定位误差接近CRLB。

Localization Algorithm Based on Multivariable Taylor Series Expansion Model

Conventional Taylor series expansion model only considers the distances between unknown nodes and anchor nodes, without considering the distances between unknown nodes. As a result, the location information is not comprehensive enough to result in lower positioning accuracy. Thus, a novel localization algorithm based on multivariable Taylor series expansion model is proposed to further enhance positioning accuracy. Firstly, the new positioning model which considers the distances between unknown nodes in multivariable Taylor series expansion is established. In the process of model solution, the particle swarm algorithm is used to obtain the estimated position values of the unknown nodes. Then, the optimal position values are obtained by the weighted least squares method. Finally, the Cramer-Rao lower bound (CRLB) of the positioning result is derived to evaluate the performance of the proposed algorithm. Simulation results demonstrate that the proposed algorithm obtains a higher positioning accuracy, and its positioning error is very close to the CRLB.