Bounds on the Root-Mean-Square Miss of Radar-Guided Missiles Against Sinusoidal Target Maneuvers

In preliminary analysis of guided systems, it is required to assess the miss distance performance from some small set of parameters. Previous papers presented analytical formulas of bounds on the root-mean-square miss by a radar-guided missile against step- and exponential-type maneuvers. This paper presents formulas against harmonic-sinusoidal maneuvers. Moreover, a type of maneuver that is not treated in the literature, the continuously sinusoidal maneuver with uncertain-random frequency and magnitude, is introduced, and bound on the miss is presented. The formulas use a set of core parameters that affect the miss distance; thus, they can be used for synthesis and analysis of the performance of radar-guided tactical missiles. The bound is derived subject to assumption that the missile guidance law and estimator are fully matched to the missile dynamics, the target maneuver, and the glint noise. The glint is the dominant noise source, the missile applies frequency agility, there is no blind range or missile acceleration limit, and the terminal phase period is sufficiently long so that initial conditions fade away. No system can achieve smaller root-mean-square miss distance than the one presented, subject to the stated assumptions.

[1]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[2]  Robert Fitzgerald,et al.  Simple Tracking Filters: Closed-Form Solutions , 1981, IEEE Transactions on Aerospace and Electronic Systems.

[3]  Fumiaki Imado,et al.  Missile guidance algorithm against high-g barrel roll maneuvers , 1994 .

[4]  Joseph Z. Ben-Asher,et al.  Advances in Missile Guidance Theory , 1998 .

[5]  Ilan Rusnak.  Bounds on the RMS Miss of Radar-Guided Missiles , 2010 .

[6]  Ilan Rusnak,et al.  Optimal guidance for acceleration constrained missile and maneuvering target , 1990 .

[7]  Paul Zarchan,et al.  Tactical and strategic missile guidance , 1990 .

[8]  Ernest J. Ohlmeyer.  Root-mean-square miss distance of proportional navigation missile against sinusoidal target , 1996 .

[9]  P. Zarchan,et al.  Shaping filters for randomly initiated target maneuvers , 1978 .

[10]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[11]  Ilan Rusnak.  Bound on Root-Mean-Square Miss of Radar-Guided Missiles for Short Terminal Phase Period , 2012 .

[12]  K. Mehrotra,et al.  A jerk model for tracking highly maneuvering targets , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Pini Gurfil,et al.  Neoclassical Guidance for Homing Missiles , 2001 .

[14]  Joseph Lewin,et al.  Differential Games , 1994 .

[15]  W. Root,et al.  An introduction to the theory of random signals and noise , 1958 .

[16]  J. Holtzman,et al.  The sensitivity of terminal conditions of optimal control systems to parameter variations , 1965 .

[17]  Shaul Gutman,et al.  Applied min-max approach to missile guidance and control , 2005 .

[18]  Robert J. Fitzgerald.  Shaping Filters for Disturbances with Random Starting Times , 1979 .

[19]  Paul Zarchan.  Complete Statistical Analysis of Nonlinear Missile Guidance Systems - SLAM , 1979 .

[20]  P. Zarchan,et al.  Interception of spiraling ballistic missiles , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[21]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[22]  Ilan Rusnak.  Almost analytic representation for the solution of the differential matrix Riccati equation , 1988 .

[23]  R. Aggarwal.  Optimal missile guidance for weaving targets , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[24]  X. Rong Li,et al.  Survey of maneuvering target tracking: dynamic models , 2000, SPIE Defense + Commercial Sensing.

[25]  Joel Alpert.  Normalized Analysis of Interceptor Missiles Using the Four-State Optimal Guidance System , 2001 .

[26]  Paul Zarchan,et al.  Miss distance dynamics in homing missiles , 1984 .

[27]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[28]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[29]  J. P. Helferty.  Improved tracking of maneuvering targets: The use of turn-rate distributions for acceleration modeling , 1996 .

[30]  George A. Biernson.  Principles of feedback control , 1988 .

[31]  Geert Jan Olsder,et al.  Linear-quadratic stochastic pursuit-evasion games , 1981 .

[32]  Paul Zarchan,et al.  Fundamentals of Kalman Filtering: A Practical Approach , 2001 .

[33]  Paul Zarchan.  Representation of Realistic Evasive Maneuvers by the Use of Shaping Filters , 1979 .