Seminars

Abstract: The use of Gaussian mixture model representations is an attractive tool in nonlinear estimation, particularly for object tracking and orbit determination. It is the potential to reasonably balance estimator speed and performance that lends these models to applications which require effectiveness in both. This capability relies on intelligent management of the number of mixture components, a notion equivalent to model selection among the class of approximating mixtures. The purpose of replacing a state density with a mixture approximation is better representation of the mixture-generated density after a nonlinear transformation of the state. Knowing that use of a compact, linearized estimator is typically desired, this can be accomplished by anticipating and mitigating linearized solution weaknesses while still substantially capturing the pre-transformed density. The current work offers an automated algorithm for both inference and prediction filter steps. A key aspect is quantification of not only prior uncertainty but also nonlinearity associated with particular regions of the state-space. 

The second model selection domain addressed is sensor scheduling. Many applications have emerged that require configurability of rapid, real-time, plug-and-play sensing systems. Even with modern computational power, the underlying guidance, navigation, and control tasks can quickly overwhelm processing ability as complexity increases over time and/or the number of sensors. An efficient algorithm is offered to select among multiple sensors at all time-steps of a general dynamic linear system. This algorithm is the first in the literature to address the case of time-correlated measurement or process noises and one of the first for spatially-correlated sensors. By deriving an expression of the true scheduling objective explicit in all schedules (which was previously considered intractable), this method efficiently approximates the effects of accepting or rejecting each sensor measurement based on the underlying estimation and/or control tasks.