Yaakov Oshman

Liraz Mudrik, Yaakov Oshman

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.

Liraz Mudrik, Yaakov Oshman

Using Bayesian decision theory, we modify the perfect-information, differential game-based guidance law (DGL1) to address the inevitable estimation error occurring when driving this guidance law with a separately-designed state estimator. This yields a stochastic guidance law complying with the generalized separation theorem, as opposed to the common approach, that implicitly, but unjustifiably, assumes the validity of the regular separation theorem. The required posterior probability density function of the game's state is derived from the available noisy measurements using an interacting multiple model particle filter. When the resulting optimal decision turns out to be nonunique, this feature is harnessed to appropriately shape the trajectory of the pursuer so as to enhance its estimator's performance. In addition, certain properties of the particle-based computation of the Bayesian cost are exploited to render the algorithm amenable to real-time implementation. The performance of the entire estimation-decision-guidance scheme is demonstrated using an extensive Monte Carlo simulation study.

Liraz Mudrik, Yaakov Oshman

Classical guidance laws aim at minimizing the miss distance, thus implicitly determining the minimum warhead lethality radius required against nominal targets. However, nonnominal targets or scenarios might render the designed warhead insufficient, causing a significant degradation in the single-shot kill probability (SSKP). We propose a guidance methodology that shifts the interceptor's objective from minimizing the miss distance to directly maximizing the SSKP, while taking into account the warhead's probabilistic lethality model. Complying with the generalized separation theorem, the new paradigm is based on modifying deterministic differential-game-based guidance laws using Bayesian decision theory. Extensive Monte Carlo simulations demonstrate consistent SSKP improvement over the standard and recently introduced estimation-aware guidance laws, when tested against nominal and nonnominal evasively maneuvering targets.

Nitai Stein, Yaakov Oshman

A novel approach, based on the notion of altruism, is presented to cooperative parameter estimation in a system comprising two information-sharing agents. The underlying assumption is that the overall two-agent scheme can reach desired performance level even if only one of the agents performs satisfactorily, hence there exist two independent opportunities to estimate. The notion of altruism motivates a new definition of cooperative estimation optimality that generalizes the common definition of minimum mean squared error optimality. Fundamental equations are derived for two types of altruistic cooperative estimation problems, corresponding to heterarchical and hierarchical setups. Although these equations are, generally, hard to solve, their solution in the Gaussian case is straightforward and only entails the computation of the largest eigenvalue of the conditional covariance matrix and its corresponding eigenvector. Moreover, in the Gaussian case the performance improvement of the two altruistic cooperative estimation techniques over the conventional (egoistic) estimation approach is shown to depend on the problem's dimensionality and statistical distribution. In particular, the performance improvement grows with the dispersion of the spectrum of the conditional covariance matrix, rendering the new estimation approach especially appealing in ill-conditioned problems. The validity of the solution in the Gaussian case is illustrated numerically.