Theoretical Study On Location Algorithm And Error Analysis Of Lightning Targets

Lightning location systems have provided useful data for lightning scientific research and disaster prevention and mitigation in recent decades. Many kinds of lightning detection networks have been installed all over the world for different purposes. These networks are composed of multiple remote sensors located in different positions. The sensors can receive and record the time and angle of arrival of electromagnetic waves radiated by lightning events. Thus location systems can compute the occurred position and time of the lightning with the observed data. Fast and accurate computation of lightning sources is important to the early warning, emergency maintenance and scientific research of lightning disaster. On the basis of the characteristic of existing lightning detection networks, the mathematical principles of lightning location are induced in this dissertation. Moreover, passive location algorithm and location error analysis method are lucubrated and the performances of Wuhan lightning detection experimental network are assessed. The main contents and results are listed below:(1) Principles of Cloud-to-Ground and Intra-Cloud lightning location are introduced respectively. The basic equations are given for Cloud-to-Ground lightning location in 2-D plane and the earth surface, and time difference of arrival and angle of arrival Intra-Cloud lightning location in 3-D space and time. Many lightning location models have been summarized comprehensively. The criteria to find the maximum likelihood estimator of the unknown and the method to combine target location ellipses are given. The mathematical framework of lightning location problem is founded, which is the basis of subsequent study.(2) The iterative formulas based on Taylor series expansion for lightning location are given, and its convergence region and divergence region are investigated for the first time. The results show that an effective initial value is easy to obtain. If a point in the network is used as initial position, the iterative method will converge for most target, but the divergence region can not be eliminated, which declares that a universal initial value are not exist. In addition, grid search and particle swarm search algorithm are brought into lightning location research. These search algorithms are stable, but their data processing ability is constrained by computer power. Furthermore, a hybrid algorithm is given to combine particle swarm algorithm and iterative algorithm, which can significantly reduce the amount of calculation and fast converge to the right solution.(3) The statistical method of hypothesis test is used to detect and find out the gross error in the lightning observed data. The fitness cost function is used as assessment criteria, which obeys the chi-square distribution when there is no gross error. The requirement for detecting and finding out the gross error are analyzed, and it is shown that gross error can be eliminated only when there are redundancy observations. An example shows the feasibility of the gross error elimination. Continually combining the observed data and finding out the minimum fitness cost function can obtain the pure data that does not contain gross error, and it is proved that the location error decreases obviously when gross errors are eliminated.(4) The location errors caused by different location model are discussed. The earth is a flat ellipsoid, thus the plane and sphere location model are suitable for small network, and oblate spheroidal earth model is suitable for lightning location. Different computational formulas for distance and angle of geodetic line are compared; the results show that the computational accuracy is good enough for cloud-to-ground lightning location.(5) Location error parameters can be computed by Monte Carlo method, covariance matrix and CRB bounds. These computational methods are proved to be equivalent by numerical examples. Cloud-to-Ground and Intra-Cloud lightning location error are analyzed by those methods. For time of arrival positioning, triangle error model and tetrahedron error model are proposed to estimate location error of 2-D and 3-D target, respectively. These models can be used to evaluate target location error, illustrate the error distribution characteristics and guide the network installation. (6) The performances of Wuhan lightning detection experimental network are assessed. The evaluation indexes are location error and effective detection area. Cloud-to-ground lightning location error of Wuhan network is studied to prove that the angle data is very important for small network. Location error of intra-cloud lightning on different height is analyzed, and the results show that higher source can be located with higher accuracy, and the error increases as the range squared. The curvature of the earth surface and mountain blocking are considered to investigate the intra-cloud lightning detectivity. Height limits of the source which can be detected are computed. The results show that higher stations can improve the detectivity.