(YIP) Information Collection and Fusion for Space Situational Awareness
Abstract
Significant progress has been made towards characterizing non-Gaussian state density function. Two new methods adaptive Gaussian mixture model (AGMM) and conjugate unscented transformation (CUT) have been developed for this purpose. AGMM method solves the Fokker-Planck-Kolmogorov equation associated with orbital dynamics model. Furthermore, sparse approximation tools have been used to identify the Gaussian kernels which best approximate the state pdf. CUT methodology provides efficient means to compute higher order moments of state density functions. Primary objective of CUT methodology is to find a fully symmetric sigma/cubature point set with reduced number of points that is equivalent to the set of cubature points of Gaussian quadrature product rule of same order. Equivalent to same order implies that for a polynomial of order 2m-1 in generic N-dimensions, both the new reduced sigma point set from the proposed method known as Conjugate Unscented Transform method (CUT) and the m^N quadrature points from the Gaussian quadrature product rule result in same order of relative percentage error. A closed form expression for these new sets of point is provided to satisfy up to 8 central moments. It is shown that the proposed method provides a significant reduction in function evaluations to compute multi-dimension expectation integrals. For example, the proposed method needs only 355 and 745 function evaluations to compute the expectation integral for a polynomial function of degree 8 in the 5- and 6-dimensional space, respectively whereas the Gaussian quadrature product rule would need 3,125 and 15,625 function evaluations for the same 5- and 6-dimensional space respectively. Finally, optimal control problem is posed to optimize sensor locations and other modalities to better track a target object. Main highlight of the work is to compute information theoretic metrics corresponding to non-Gaussian target state pdfs to describe current situation of the target state.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 30, 2014
- Accession Number
- AD1013204
Entities
People
- Shouhuai Xu
Organizations
- University at Buffalo