Document Type : Original Article

Authors

Department of Mechanical Engineering, Tarbiat Modares University

10.22034/jast.2024.428886.1170

Abstract

A complete miss distance analysis of true proportional navigation is carried out due to initial heading error, step target maneuver, and seeker noise sources assuming a first-order control system using forward and adjoint methods. For this purpose, linearized equations are utilized for deterministic and stochastic analyses. Worst case analysis shows that the maximum value of the final time-miss distance plots reduces by increasing the value of the effective navigation ratio due to initial heading error and step target acceleration. The number of peaks of these curves obeys the relation of the effective navigation ratio minus 1 (or 2) due to heading error (or step target maneuver). Moreover, the normalized miss coefficients due to seeker noise sources and miss due to random target maneuver are computed and approximate formulas are presented using the curve fitting method. This leads to an approximate formula for miss distance budget. Therefore, optimum values of the effective navigation ratio and control system time constant are obtained. Finally, the preferred values of these parameters are calculated for increased RMS miss of 5%, 10%, and 20% compared to its minimum value for two scenarios.

Keywords

Main Subjects

[1]  Nesline, F. W., and Zarchan, P., “Robust Instrumentation Configurations for Homing Missile Flight Control,” Guidance and Control Conference, August, 1980. 
 [2] Nesline, F. W., and Zarchan, P., “Miss Distance Dynamics in Homing Missile,” AIAA Paper 1984-1844, Aug. 1984.
[3]   Zarchan, P., “Complete Statistical Analysis of Nonlinear Missile Guidance Systems: SLAM,” Journal of Guidance and Control, Vol. 2, No. 1, 1979, pp. 71–78.
[4]  Nesline, F. W., and Nesline, M. L., “Wing Size vs Radome Compensation in Aerodynamically Controlled Radar Homing Missiles,” Journal of Guidance, Control and Dynamics, Vol. 9, No. 6, pp. 645–649, 1986.
[5]  Miwa, S., “Clutter Effect on the Miss Distance of a Radar Homing Missile,” Journal of Guidance, Control and Dynamics, Vol. 11, No. 4, pp. 336–342, 1988.
[6] Miwa, S., “Radome Effect on the Miss Distance of a Radar Homing Missile,” Electronics and Communications in Japan, Part 1, Vol. 81, No. 7, 1998.
[7] Arabian Arani, A. and Jalali-Naini, S. H., “Approximate Miss Distance Formulas of Proportional Navigation Due to Time Delay Based on Worst Case Analysis,” Aerospace Knowledge and Technology Journal, Vol. 7, No. 1, pp. 47-62, 2018 (in Persian).
[8] Zarchan, P., Tactical and Strategic Missile Guidance. American Institute of Aeronautics and Astronautics, Inc., 2012.
[9]  Nesline, F. W., and Zarchan, P., “Radome  Induced Miss Distance in Aerodynamically Controlled Homing Missiles,” 17th Fluid Dynamics, Plasma Dynamics, and Lasers Conference, June, 1984.
[10] Alpert, J., “Normalized Analysis of Interceptor Missiles Using the Four-State Optimal Guidance System,” Journal  of  Guidance,  Control, and Dynamics, Vol. 26, No. 6, pp. 838-845, 2003.
[11] Bucco, D., Zarchan, P. and Weiss, M., “On Some Issues Concerning the Adjoint Simulation of Guidance Systems,” in AIAA Guidance, Navigation, and Control Conference, 2012.
 [12] He, T., Chen, W., “A New Interpretation of Adjoint Method in Linear Time-Varying System Analysis,” presented at the 2017 IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), pp. 58-63, 2017.
[13] Alpert, J., “Adjoint Analysis of Guidance Systems for Time-Series Inputs Using Fourier Analysis,” Journal of Guidance, Control, and Dynamics, Vol. 43, No. 7, pp. 1359-1364, 2020.
[14] Donatelli, G. A., and Fleeman, E. L., “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA 20th Aerospace Sciences Meeting, Florida, 1982.
[15] Jalali-Naini, S. H., “Noise-Induced Miss Distance Formulas of First-Order Control System Under Proportional Navigation for Arbitrary Navigation Ratios,” presented at the 15th International Conference of Iranian Aerospace Society, Tehran, 2016.
[16]  Rusnak, I., “Bounds on the RMS Miss of Radar-Guided Missiles,” Journal of Guidance, Control, and Dynamics, Vol. 33, No. 6, pp. 1718–1723, 2010.
[17]   Rusnak, I., “Bounds on the RMS Miss of Radar-Guided Missiles Against Sinusoidal Target Maneuvers,” Journal of Guidance, Control, and Dynamics, Vol. 34, No. 4, pp. 1060–1069, 2011.
[18] Rusnak, I., “Bounds on the Miss of Radar-Guided Missiles with Discrete Guidance,” Journal of Guidance, Control, and Dynamics, Vol. 43, No. 4, 2020.
[19]  Rusnak, I., “Bounds on the Miss of Multiple-Model-Based Terminal Guidance Laws,” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 6, pp. 1001-1011, 2015.
[20] Jalali-Naini, S. H., Arabian Arani, A., “Proportional Navigation Guidance with Variable Navigation Ratio in Terms of the Angle of Relative Velocity with Respect to Line-of-Sight and its Rate,” Journal of Space Science and Technology, Vol. 13, Issue. 2, pp. 1-12, 2020 (in Persian)