Estimation-Guided Guidance

This paper addresses the problem of guiding a missile towards an evading agile target in the presence of noisy measurements. Existing missile guidance law design methods are traditionally based on the separation theorem, which has never been proven for realistic guidance scenarios. In such cases, only the general separation theorem (GST) may be applied, implying a separately designed estimator, but a guidance law that takes into account the conditional probability density function resulting from this estimator. A new approach to fusion of estimation and guidance, under the guidelines of the GST, has been recently proposed by the authors. In the new approach, formulated in a discrete-time setting, particle flltering has been used to approximate the entire state conditional probability density function using the exact nonlinear dynamic models without constraining the analysis to the standard Gaussian noise assumptions. Geometry-based methodology has been utilized to derive necessary conditions for guaranteeing a hit. Furthermore, the notion of miss-set has been deflned, which enables the design of a new guidance law that complies with the GST. The new methodology has been recently reformulated by the authors for continuous-time dynamics, and extended into the realm where miss-set inclusion cannot be maintained. The new approach shows that the optimal control function is non-unique, indicating that an additional constraint may be imposed. The non-uniqueness feature of the optimal control function is exploited herein to generate an observability-enhancing trajectory shaping scheme, which improves the overall guidance performance. A nonlinear, non-Gaussian numerical study is presented, that demonstrates the performance of the proposed trajectory shaping scheme in a 3-D realistic engagement scenario with partial information.