A.V. Kalmykov1, V.A. Bulanov2, S.L. Ivanov3, A.A. Ispulov4

1-4 MESC of the Air Force “Air Force Academy n.a. Professor N.Ye. Zhukovsky and Yu.A. Gagarin”
(Voronezh, Russia)

2 Vac9Paroxod@yandex.ru; 3 st.iv.84@mail.ru; 4 ispulovy@yandex.ru

Formulation of the problem. The process of aiming with unguided aircraft missiles is a solution to a set of particular accounting problems: missile movement; own movement of the carrier; target movement. The trajectory and accuracy of missiles depends on the conditions of use at the time of launch (firing), which are determined by the parameters of the movement of the carrier and the target. Currently, the calculation of the rocket trajectory is based on the canonical motion model, which describes the change in speed, trajectory inclination angle, and rocket coordinates. The key parameter of the model is the speed of the rocket. In the case of a horizontal flight of the carrier, according to the laws of mechanics, the resulting initial velocity of the rocket is the sum of the carrier velocities and the muzzle velocity of the rocket. However, when the carrier is maneuvering, the resulting initial velocity of the rocket additionally depends on the angles of attack and slip of the carrier.

Goal. Development of an algorithm for estimating the resulting initial velocity of an unguided aircraft rocket using the Kalman nonlinear filtering method for a vertical carrier maneuver.

Results. A non-linear multidimensional Kalman filtering algorithm for the resulting initial velocity of an unguided aircraft rocket has been developed, which differs in that: the resulting initial velocity and acceleration of the rocket, the velocity and acceleration of the carrier, the angle of attack and its velocity are included in the state vector; corrective residuals are formed in the form of differences between the measured and extrapolated velocities and angles of attack according to the linear laws of changes in these parameters, as well as according to the nonlinear laws obtained from the expression of the resulting initial rocket velocity; the elements of the correlation matrix of errors of the initial estimates contain the variance of the resulting initial missile velocity, which is the sum of the squares of the partial derivatives of the resulting initial missile velocity with respect to the velocity and angle of attack of the carrier, taking into account the dispersion of their measurements.

Practical significance. The obtained results show the stable operation of the filter, which makes it possible to increase the accuracy of estimating the resulting initial velocity of an unguided aircraft missile up to 90% at the time of launch (firing).

Kalmykov A.V., Bulanov V.A., Ivanov S.L., Ispulov A.A. Algorithm for estimating the initial speed of an unguided aircraft missile with a vertical maneuver of the launch vehicle. Nonlinear World. 2023. V. 21. № 4. P. 5-14. DOI: https://doi.org/10.18127/j20700970-202304-01 (In Russian)

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