Sequential Wald Test Employing a Constrained Filter Bank: Application to Spacecraft Conjunctions

• Published in: Journal of optimization theory and applications Vol. 191; no. 2-3; pp. 440 - 458
• Main Authors: Carpenter, J. Russell, Markley, F. Landis
• Format: Journal Article
• Language: English
• Published: Goddard Space Flight Center Springer 01.12.2021; Springer US; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Constraints; Engineering; Filter banks; Hypotheses; Inequality; Kalman filters; Likelihood ratio; Mathematical And Computer Sciences (General); Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Spacecraft; Spacecraft maneuvers; Theory of Computation; 70F99; 62M99; Constrained Kalman filtering; Spacecraft conjunction analysis; Decision theory; 62C99
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-021-01847-6

A binary Wald sequential probability ratio test that uses the residuals of norm-inequality-constrained Kalman filters for its likelihood ratio may be employed for a class of compound hypothesis tests on non-stationary systems. The hypotheses concern an inequality constraint on the norm of some elements of the system state. Each of two filters minimizes the summed-squares of its estimation errors subject to one or the other direction of the inequality constraint. This solution is motivated by the problem of satellite conjunction assessment, wherein the constraint concerns the close approach distance between two space objects. The outcome of the test can inform decisions concerning risk mitigation maneuvers.