Study Of Ill-posed Problem In Wireless Sensor Networks Node Localization

As the combination of computing, communications and sensors, Wireless Sensor Networks (Wireless Sensor Networks, WSNs) have huge potential and broad prospects in many fields such as in military, environment monitoring, home life, space exploration, medical and other fields. Wireless Sensor Networks have achieved the combination of the physical world, calculation world and the human society. WSNs positioning technology emphasis that sensor nodes must clear its own position when they receive information outside, which means that what event happens in what position. So that locating and tracking of target could be implemented. Therefore, WSNs location technology is one of the foundations of the WSNs technology.This article reviews the advantages and disadvantages of the positioning algorithm based on distance and the algorithm without distance, and the ranging method based on RSSI (Received Signal Strength Indicator, RSSI) is utilized in this article to calculate the distance between the unknown node and anchor nodes by using the wireless signal attenuation model. Method is proposed to overcome the ill-posed problems, and the positioning accuracy is improved.In three dimensional space positioning, the ranging error and the ill-posed distribution of the anchor nodes lead to the ill-posed problem in node positioning, which cause the serious deviation in sensor nodes locating. It is found that the ill-posed problem is caused by multiple collinearity of matrix. On this basis, this paper put forward the condition numbers to diagnose the strength of the ill-posed problem, if the ill-posed problem is relatively weak, Least Square Estimate method can be used to localize the unknown nodes. On the other hand, if the strength of ill-posed problem is serious, adding anchor nodes, biased estimate method and the direct measurement method are adopted in this paper to weaken the ill-posed problem.Experimental study shows that (1) increasing the anchor nodes could weaken the ill-posed degree, then the Least Square Estimate method can be utilized. However, because of the random selection of the anchor nodes, multiple anchor nodes may be added to weaken the ill-posed degree, and the impact is relatively weak.(2) Ridge estimation is an algorithm which modifies the eigenvalues of matrix closing to zero, so that it can overcome ill-posed problem. Choosing the ridge parameter is the key to use the ridge estimation, L-curve method and quasi optimal criterion method is proposed to choose the ridge parameter. Experimental data shows that choosing the proper ridge parameter can effectively weaken the degree of ill-posed problem, leading the positioning results more close to the real value. The best effect of positioning error can be reduced from81.3814to the revised2.893meters.(3) TSVD (Truncated Singular Value Decomposition, TSVD) is an algorithm which decompose design matrix, truncation the eigenvalue which is near to zero, and calculate the position. Statistics demonstrate that when the condition number is above1000, the minimum error is1.4648meters. However, when the condition number fluctuate between100and1000, position result of ridge estimation is much better than TSVD.