טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentShaviv Ilan
SubjectA Stochastic Approach to Fusion of Estimation and Guidance
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Yaakov Oshman
Full Thesis textFull thesis text - English Version


Abstract

The problem of guiding a missile towards an evading agile target in the presence of noisy measurements is addressed. The full nonlinear dynamic models are used and the discussion is not limited to Gaussian noise processes.


Existing guidance methods are reviewed.  From the review it is apparent that all existing methods are designed utilizing the separation theorem, which has never been proven for realistic guidance scenarios. Moreover, recent works in the field of guidance have suggested that in realistic guidance scenarios the separation theorem is not applicable.  In such a case, only the general separation theorem (GST) may be applied, implying a separately designed estimator, but a guidance law that is to consider the conditional PDF resulting from this estimator.


A new approach to guidance, under the guidelines of the GST, is presented. The conventional notion of reachability sets is extended, introducing the notion of pursuer and evader miss-sets. Adopting a geometry-based approach, the necessary conditions for guaranteeing a capture are derived in the general case of nonlinear dynamic models without constraining the analysis to the standard Gaussian noise assumptions.


The devised methodology is derived in three stages. In the first stage, a deterministic approach is adopted, enabling to state a guidance law (formulated in the Miss-Set Inclusion Theorem) to guarantee a capture by the pursuer. Next, stochastic features are introduced rendering the optimal guidance law a product of a global optimization procedure. In the final stage, a sub-optimal guidance law, in a control-feedback configuration, is derived.  This law is termed the Maximum Inclusion Guidance Law.


The proposed methodology enables the pursuer to incorporate trajectory-shaping schemes. The trajectory-shaping scheme is intended to utilize the pursuer surplus agility to create a more advantageous geometry so as to better serve the needs of the estimator and the guidance loop. Two such trajectory-shaping schemes are addressed in this work: 1) Observability-Enhancing, and 2) Zero-Effort. Through the latter scheme, the relationship to DGL/1 is explored, while the former scheme demonstrates the benefit of this procedure in achieving enhanced engagement performance.


A nonlinear, non-Gaussian numerical study is presented, that demonstrates the performance of the proposed methodology in a 3-D realistic engagement scenario with partial information. The study compares the resulting performance with that of a conventional perfect-information guidance law, DGL/1, which is the best a designer can use assuming the availability of perfect information, or, at least, that the separation theorem holds.