A Positioning And Orientation Method For Missile Truck By Observing Landmarks

The maneuvering launch of medium-range or long-range ballistic missiles requires rapid and accurate positioning and orientation methods.However,if only relying on the inertial navigation system on the missile truck,it is expensive and difficult to meet the requirements.Hence,other methods,such as traverse network and orientation joint measurement,astronomical orientation,gyro theodolite,and satellite navigation system,were used to solve the problem.However,these methods can not balance accuracy and speed well.This paper studies a positioning and orientation method by observing landmarks.This method,as an auxiliary and backup of the inertial navigation system on the missile truck,can determine the position and orientation of the missile at some specific site rapidly and accurately.Four aspects,including the positioning and orientation algorithm,the efficiency and stability of the algorithm,the error model,the precision estimation of the positioning and orientation results,and optimization of the layout of the landmarks are studied.The main works are as follows:(1)The planar positioning and orientation method by observing landmarks is studied.A area-based method to improve the computational efficiency of the error triangle positioning and orientation algorithm is proposed.In the improved algorithm,the measurement of the size of the error triangle is replaced from perimeter to area,thus the original algorithm is simplified by using the law of the change of the area inferred by the symbolic computation method.The simulation results show that,the improved algorithm can achieve higher numeric precision in a shorter execution time,which means more efficient.(2)The spatial positioning and orientation method by observing landmarks is studied.A spatial positioning and orientation algorithm is proposed,which can maintain numeric stability when the landmarks and the missile truck are coplanar or non-coplanar.The algorithm uses the variable projection framework to decompose the model parameters into plane parameters and vertical parameters.By selecting equations with stable coefficients during the parameter estimation process,the stable approximation to three-dimensional space by the planar positioning and orientation algorithm is realized.The simulation results show that the algorithm can solve the numerical insatiability problem that occurred in similar algorithms when the landmarks and the missile truck are coplanar.The experimental results show the performance of the positioning and orientation system with the algorithm: The position and azimuth precision are 2 cm(1σ)and 10 arc seconds(1σ),respectively.The time of the entire positioning and orientation process takes less than 100 seconds.The positioning and orientation method is comparable in accuracy to the reference side azimuth joint measurement method(optical transfer method),and it has a large advantage in the speed.(3)The error model and the error propagation law for the positioning and orientation method by observing landmarks are studied.An error model considers two sources of error,i.e.,optical angle measurement error and landmarks positioning error,is established,and a generalized least squares-based precision estimation method to estimate the precision of the positioning and orientation results is proposed.The method is verified by the simulation and experiment.The simulation results show that,unlike the pixel error model-based precision estimation method,the method can cope with any azimuth.(4)The optimization method of the layout of landmarks in plain and mountainous terrain is studied.For the plain terrain,from the perspective of theory and simulation,it is proven that the layout is optimal when the landmarks are placed on the vertices of the equilateral triangle which centered on the missile truck.For the mountainous terrain,a landmarks layout optimization algorithm that considers terrain occlusion is proposed.The algorithm computes the visibility of the landmarks according to digital elevation model,and searches for the layout of the landmarks with the smallest azimuth error by combining the visible landmarks exhaustively.The simulation results show the effectiveness of the algorithm.