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Ph.D. Thesis: Deep Learning-based Marine Navigation.
M.Sc. Thesis: Integrated Guidance / Estimation in Linear Quadratic Differential Games.
I. “Adaptive Step Size Using a Covariance based Criterion”
Barak Or, Ben-Zion Bobrovsky, and Itzik Klein. IEEE - submitted.
The commonly used discrete Kalman filter is considered. There, the step size, defined as the difference between two successive time steps, is selected according to the scenario type and computational constraints. Generally, reducing the step size improves the estimation error accuracy with the cost of a high computational load. This trade-off raises the issue of choosing an appropriate step size. To avoid this conflict, we propose a criterion to act as a guideline for a reasonable choice of the step size. This criterion is based on the predictor-corrector error covariance matrices of the discrete Kalman filter. Furthermore, for the case of the time-varying measurement noise intensity, this criterion is elaborated to an adaptive algorithm, yielding a satisfactory, efficient, and stable step size. Two numerical examples and a field experiment for a vehicle tracking problem are demonstrated and analyzed to show the benefits of the proposed approach.
II. “Optimal Disturbance Attenuation Approach with Measurement Feedback to Missile Guidance” Barak Or, Joseph Z. Ben-Asher, and Isaac Yaesh. AIAA - submitted.
Pursuit-evasion differential games using the Disturbance Attenuation approach are revisited. Under this approach,the pursuer actions are considered to be control actions, whereas all external actions, such as target maneuvers, measurement errors, and initial position uncertainties, are considered to be disturbances. Two open issues have been addressed, namely the effect of noise on the control gains, and the effect of trajectory shaping on the solution. These issues are closely related to the question of the best choice for the disturbance attenuation ratio. Detailed analyses are performed for two simple pursuit-evasion cases: a Simple Boat Guidance Problem and Missile Guidance Engagement.
III. “Imperfect Information Game for a Simple Pursuit-Evasion Problem” Barak Or, Joseph Z. Ben- Asher and Isaac Yaesh. EuroGNC (5th CEAS Conference on GNC) AIAA co-sponsored conference. 2019.
Differential Games for pursuit-evasion problems have been investigated for many years. Differential games, with linear state equations and quadratic cost functions, are called Linear Quadratic Differential Game (LQDG). In these games, one defines two players a pursuer and an evader, where the former aims to minimize, and the latter aims to maximize the same cost function (zero-sum games). The main advantage of using the LQDG formulation is that one gets Proportional Navigation (PN) like solutions with continuous control functions. One approach which plays a main role in the LQDG literature is Disturbance Attenuation (DA), whereby target maneuvers and measurement error are considered as external disturbances. In this approach, a general representation of the input-output relationship between disturbances and output performance measures is the DA function (or ratio). This function is bounded by the control. This work revisits and elaborates upon this approach. We introduce the equivalence between two main implementations of the DA control. We then study a representative case, a “Simple Pursuit Evasion Problem”, with perfect and imperfect information patterns. By the derivation of the analytical solution for this game, and by running some numerical simulations, we develop the optimal solution based on the critical values of the DA ratio. The qualitative and quantitative properties of the Simple Pursuit Evasion Problem, based on the critical DA ratio, are studied by extensive numerical simulations and are shown to be different from the fixed DA ratio solutions.