Projectile Impact Point Prediction Based on Self-Propelled Artillery Dynamics and Doppler Radar Measurements

Abstract

Any trajectory calculation method has three primary sources of errors, which are model error, parameter error, and initial state error. In this paper, based on initial projectile flight trajectory data measured using Doppler radar system; a new iterative method is developed to estimate the projectile attitude and the corresponding impact point to improve the second shot hit probability. In order to estimate the projectile initial state, the launch dynamics model of practical 155 mm self-propelled artillery is defined, and hence, the vibration characteristics of the self-propelled artillery is obtained using the transfer matrix method of linear multibody system MSTMM. A discrete time transfer matrix DTTM-4DOF is developed using the modified point mass equations of motion to compute the projectile trajectory and set a direct algebraic relation between any two successive radar data. During iterations, adjustments to the repose angle are made until an agreement with acceptable tolerance occurs between the Doppler radar measurements and the estimated values. Simulated Doppler radar measurements are generated using the nonlinear sixdegree-of-freedom trajectory model using the resulted initial disturbance. Results demonstrate that the data estimated using the proposed algorithm agrees well with the simulated Doppler radar data obtained numerically using the nonlinear six-degree-offreedom model.

Advanced Top-Attack Trajectory Guidance Law with Impact Angle Constraints

“…The flight path angle at the interception point is evaluated like: (14) Where, (15) (16) ε imp is the desired impact angle, which is the angle between the missile velocity vector and the target at the moment of interception,γ mf and γ tf are the flight path angles of the missile and target respectively. When the missile and target on a collision stage, the Line-of-Sight angle is defined by ε f and the relation between the missile and target…”

“…Assuming that the missile is a rigid body that moves in the lower layers of the atmosphere (close to the earth's surface), the equations of its motion are as follows [14,15]…”

A Rapid Gun Firing Correction Algorithm Using Discrete Time Transfer Matrix Method

“…Based on discrete time transfer matrix method DTTMM-4DOF based on projectile modified point mass model stated in ref. [21], a two-dimensional iterative method is developed to obtain the projectile launching angle for desired target distance and direction.…”

“…To set a direct relation between the state errors S during any two successive time step, due to deviation of one or more state parameters for the reference trajectory, a state correction matrix  is deduced using a modified Jacobian J of the system mentioned in ref. [21]…”

“…43 are the first order projectile angle of repose derivative w.r.t. projectile velocity and spin rate respectively[21].Paper: ASAT-16-136-AE Finally, the elements of the transfer matrix , which maps the state error…”