Guidance Without Assuming Separation

This paper addresses the problem of guiding a missile towards an evading agile target in the presence of noisy measurements. Existing guidance law design methods are all based on the separation theorem, which has never been proven for realistic guidance scenarios. Moreover, recent works in the fleld of guidance have suggested that in a 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 probability density function resulting from this estimator. A new approach to guidance, under the guidelines of the GST, is proposed herein. The full nonlinear dynamic models are used and the discussion is not limited to Gaussian noise assumptions. Utilizing a geometric approach, a new entity, termed the miss set, is identifled, which enables the design of a new guidance law that complies with the GST. From this analysis, a methodology to optimally guide a pursuer towards an evader is derived. A numerical study is provided which demonstrates the performance and viability of the proposed methodology in a realistic 3-D engagement scenario. A comparison between the proposed methodology and a difierential game-based guidance law is carried out, demonstrating a signiflcant improvement.

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