Research On Numerical Algorithm Of Airborne Optical Sighting System Simulation

In recent years,the research on airborne optical sighting system in China has continued to strengthen.The numerical simulation based on airborne optical sighting system has become an important development direction which is a research method not limited by the original system scale and structure complexity.The system numerical simulation algorithm can affect the effectiveness of simulation directly on system performance detection and evaluation,so it has become an indispensable part of the airborne optical sighting system research.Airborne optical sighting system is a stiff system with low dynamic and high dynamic.The general numerical algorithm use a very small step to ensure the numerical stability in the numerical simulation on airborne optical sighting system.The small simulation step can increase the calculation amount and accumulated error multiplied,which will affect the real-time performance and accuracy of the simulation.On the other hand,if the high dynamic part of the system is modified to adapt to the simulation step in order to make the numerical solution steadily,the simulation accuracy of system will be reduced.Based on the stiff dynamic characteristics of airborne optical sighting system and the limitation of traditional simulation algorithm,this paper studies the numerical simulation algorithm of airborne optical sighting system.A numerical simulation algorithm with high stability,high precision and less computation is proposed.The main research work of this paper is as follows:(1)This paper modeled the airborne optical sighting system,and the kinematic mathematical model is established by studying the structure,function and working principle of airborne optical sighting system.In addition,this paper analyzes the mathematical model of airborne optical sighting system,which can be expressed as a stiff system of differential equations.In this paper,the numerical simulation problem of airborne optical sighting system is transformed into the problem of solving the stiff ordinary differential equations,which provides the basis for the research of numerical algorithm of airborne optical sighting system simulation.(2)According to the requirement of numerical simulation and rigid dynamic characteristics of airborne optical sighting system,this paper proposed a banded implicit Runge-Kutta numerical algorithm with high accuracy,high stability and small calculation efforts by studying the limitations of traditional numerical simulation algorithm.Some traditional numerical algorithms with high accuracy and high stability have a large calculation efforts and the usage are limited.However,the general improved numerical algorithm improved the calculation speed by reduces the computation,which makes the low accuracy and poor stability.Based on the single-step method of Gauss quadrature formula with multi-stage and multi-order,this paper transformed the full coefficient iterative matrix into a banded matrix,which reduces the computation on the basis of ensuring its high accuracy and high stability.The construction,implementation,stability,accuracy and computation of the banded implicit Runge-Kutta algorithm are discussed in this paper.(3)Based on the proposed banded implicit Runge-Kutta numerical algorithm,this paper proposed a numerical algorithm with variable step size by approximating the local truncation error to the difference between the high-order method and the low-order method at the same point.The proposed method can change the integration step of the numerical algorithm according to whether the accuracy of the airborne optical sighting system simulation is achieved,and improve the efficiency of the system numerical simulation.(4)The mathematical model of the airborne optical sighting system is simulated by using the fixed-step banded implicit Runge-Kutta method and variable-step banded implicit Runge-Kutta method,and the simulation results are compared with other commonly used numerical algorithms.Simulation results show that the banded implicit Runge-Kutta algorithm constructed in this paper is superior to the traditional numerical simulation algorithm,and the larger the system is,the higher the efficiency will be.In this paper,the implicit Runge-Kutta algorithm with variable step size is proposed to improve the numerical simulation efficiency of airborne optical viewing system.In addition,the numerical algorithm constructed in this paper has good robustness and can also be applied to the simulation of other complex large-scale systems.