These following problems are extremely important to TDTCP wh

These following problems are extremely important to TDTCP which uses this type of scheme: accurate and quick prediction of impact point, real time calculation of lateral correction, minimum fire angle with respect to a determined lateral correction, and flight buy Tovok criterion analysis during the correction process. This paper mainly studies the above problems so as to lay a foundation for the extensively research of TDTC [1–5].
An impact point prediction method for TDTCP By taking the prediction efficiency and precision into consideration, a modified point mass trajectory model is used as the basic model for the identification of trajectory filter and aerodynamic coefficients:where v,v,v are the velocity components in the ground axis system, respectively; x,y,z are the position components in the ground axis system, respectively; w,w,w are the wind velocity components in the ground axis system, respectively; v is the relative velocity of the projectile; ρ is the atmospheric density; S is the reference area; m is the mass; g is the gravity acceleration; C is the drag coefficient; is the derivative of lift coefficient with respect to the angle of attack; δ, δ are the two components of the yaw of repose which can be calculated by using the formula described in Ref. [6]; K, K are the correction coefficients of the drag force and lift force, respectively, which reflect the difference between theoretical and real worlds. Let the projectile\'s position, velocity and the aerodynamic correction coefficients be the estimated states, namely , and K, K are regarded as the constants, namely. Thus the state equation can be described as follows:where ′ is the noise which is used to compensate the error between theoretical and real worlds. Observation equation under trajectory detection system is described as follows:where Z is the observation state, υ is the observation noise assumed as Gauss white noise. The Extended Kalman Filter [7] can be used to estimate the states based on the state and observation equations which are described above. The estimated states can be achieved as follows: In this case, not only the information measured directly from detection system is filtered, but also the aerodynamic coefficients with more accuracy are identified. Regarding the optimal estimated states as the initial values and parameters, the impact point of the projectile can be predicted fast and accurately. The simulation result is shown in Fig. 2. It can be seen from Fig. 2 that the proposed impact point prediction method has very high precision which is related to the tracking time of the measuring system. The longer the tracking time is, the higher the prediction precision is. However, the precision can not be improved when the tracking time reaches a certain level. Because a long tracking time may increase the amount of online computation and make an appropriate correction opportunity missed, it is very necessary to consider these factors synthetically and choose an appropriate tracking time.
A quick method for calculating the lateral correction According to the theory of exterior ballistics, the ballistic drift is caused by the yaw of repose Δp and mainly determined by the lateral component δ2p which is perpendicular to the vertical plane of fire direction. Suppose the angle between the fire direction and the tangent at any point of the ballistic drift curve is very small, the approximate formula of the ballistic drift can be established by integrating the lateral acceleration, which iswherewhere η is the twist of cannon, T is the flight time of projectile, k is the roll damping moment coefficient, is the average velocity, l is the reference length, d is the diameter, is the overturning moment coefficient, C is the polar moment of inertia, θ0 is the fire angle, and θ is the impact angle. The lateral ballistic drift at the impact point can be predicted without flight control,where Assuming that the unfolded moment of the damping disk equipped on the spin-stabilized projectile which can correct its trajectory is t1, the corresponding roll damping moment parameters are k, k (corresponding to u, u1),respectively, the lateral ballistic drift can be obtained through integration:where ; .