Research On SDP-based Outlier Automatic Identification Node Localization Algorithm

Wireless sensor network node positioning technology is commonly used in aviation,environmental monitoring and other fields.The positioning results are subject to errors due to communication range,power failure and strong interference.In this paper,algorithmic improvements are made to address the biases in node localisation in wireless sensor networks.In the first step,two low-rank matrix-completion algorithms,namely the edge semi-definite programming algorithm(ESDP)and the outlier self-identification algorithm(SDPS),are proposed to repair the distance matrix(EDM).The second step proposes two improved multi-source node localisation algorithms based on the repaired distance matrix(EDM),namely the squared distance observation-based node localisation algorithm(SDP-RLS)and the squared distance difference observation-based node localisation algorithm(SDP-SRLS).The research in this paper is divided into the following aspects.(1)In this paper,two low-rank matrix-completion algorithms,namely the edge semi-definite programming algorithm(ESDP)and the outlier self-identification algorithm(SDPS),are proposed to repair the distance matrix to obtain a low-rank matrix that approximates the target matrix.The edge semi-definite programming(ESDP)algorithm introduces the principle of semi-definite programming by exploiting the sparsity at the relaxation modelling level,and the constraint Y=~relaxed to≥~A convex optimisation transformation is carried out to extend the feasible set by adding the sparse condition-adjusted perturbation matrix P,which in turn enables the complementation of the distance matrix.The outlier self-identification(SDPS)algorithm introduces the error matrix E on the basis of matrix decomposition and adds iterative termination conditions,which can achieve automatic identification and replacement of outliers after repeated iterations.Simulation results show that the edge semi-definite planning(ESDP)algorithm,both in line-of-sight(LOS)and NLOS environments,uses convex optimisation methods without discarding any information to improve the accuracy of the estimated node position information,and compared with other algorithms,has a faster convergence and higher accuracy.The outlier self-identifying localisation algorithm has good fault tolerance in isolated point detection.Even if some normal entries are incorrectly regarded as’outliers’,the SDPS algorithm is robust enough to recover them to a certain extent.(2)Two node location algorithms based on squared distance observation and squared distance difference observationare proposed to improve the accuracy of multi-source node location algorithms.These two algorithms are algorithmic improvements based on the traditional range-based measurement and range-difference-based measurement combined with the theoretical knowledge of least squares.The SDP-RLS algorithm performs the solution of the global optimal solution without finding all the roots of the distance matrix and uses the bisection method to achieve the solution of the roots.The SDP-SRLS algorithm achieves higher order by adding a matrix constraint and discarding two constraints on the rank term of the reduced order.Simulation experiments show that the algorithm proposed in this paper outperforms conventional algorithms in terms of accuracy and robustness,even in the presence of high noise and outlier points.