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A Comprehensive Approach to Directly Addressing Estimation Delays in Stochastic Guidance

Liraz Mudrik, Yaakov Oshman

Abstract

In realistic pursuit-evasion scenarios, abrupt target maneuvers generate unavoidable periods of elevated uncertainty that result in estimation delays. Such delays can degrade interception performance to the point of causing a miss. Existing delayed-information guidance laws fail to provide a complete remedy, as they typically assume constant and known delays. Moreover, in practice they are fed by filtered estimates, contrary to these laws' foundational assumptions. We present an overarching strategy for tracking and interception that explicitly accounts for time-varying estimation delays. We first devise a guidance law that incorporates two time-varying delays, thereby generalizing prior deterministic formulations. This law is driven by a particle-based fixed-lag smoother that provides it with appropriately delayed state estimates. Furthermore, using semi-Markov modeling of the target's maneuvers, the delays are estimated in real-time, enabling adaptive adjustment of the guidance inputs during engagement. The resulting framework consistently conjoins estimation, delay modeling, and guidance. Its effectiveness and superior robustness over existing delayed-information guidance laws are demonstrated via an extensive Monte Carlo study.

A Comprehensive Approach to Directly Addressing Estimation Delays in Stochastic Guidance

Abstract

In realistic pursuit-evasion scenarios, abrupt target maneuvers generate unavoidable periods of elevated uncertainty that result in estimation delays. Such delays can degrade interception performance to the point of causing a miss. Existing delayed-information guidance laws fail to provide a complete remedy, as they typically assume constant and known delays. Moreover, in practice they are fed by filtered estimates, contrary to these laws' foundational assumptions. We present an overarching strategy for tracking and interception that explicitly accounts for time-varying estimation delays. We first devise a guidance law that incorporates two time-varying delays, thereby generalizing prior deterministic formulations. This law is driven by a particle-based fixed-lag smoother that provides it with appropriately delayed state estimates. Furthermore, using semi-Markov modeling of the target's maneuvers, the delays are estimated in real-time, enabling adaptive adjustment of the guidance inputs during engagement. The resulting framework consistently conjoins estimation, delay modeling, and guidance. Its effectiveness and superior robustness over existing delayed-information guidance laws are demonstrated via an extensive Monte Carlo study.
Paper Structure (32 sections, 2 theorems, 105 equations, 11 figures, 1 algorithm)

This paper contains 32 sections, 2 theorems, 105 equations, 11 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Nonlinear Kinematics and Dynamics
  4. Measurement Model
  5. Linearized Model Used for Guidance
  6. DGLCC with Time-Varying Delays
  7. Time-Varying Delayed Information Game
  8. Necessary Conditions for Optimality
  9. Game Space Decomposition
  10. Particle Filtering and Smoothing for Delayed Interception
  11. The IMMPF Algorithm
  12. Uncertainty Interval Estimation
  13. Simplified Modeling of the Detection Delay
  14. Probabilistic Modeling of the Uncertainty Interval
  15. Semi-Markovian Switching Model
  16. ...and 17 more sections

Key Result

Theorem III.1

If $\bar{u}^{*}(\tau)$ and $\bar{v}^{*}(\tau)$ are the optimal controls, and $\varphi^{*}(\zeta)$ is the optimal initial condition of the delayed information differential game, then

Figures (11)

  • Figure 1: Planar engagement geometry
  • Figure 2: Linearized planar engagement geometry
  • Figure 3: Game Space, $\mu > 1$
  • Figure 4: Simplified physical model for estimation delay generation. hexner_temporal_2008
  • Figure 6: Estimated (red) and true (blue) $\dot{\xi}$ vs $t_{go}$. The evader changes its maneuver at $t_{go}= 0.6$ s.
  • ...and 6 more figures

Theorems & Definitions (7)

  • Remark 1
  • Theorem III.1
  • proof
  • Lemma III.2
  • proof
  • Remark 2
  • Definition 1