An Estimation Algorithm for Detecting and Reconstructing Optimal Maneuvers from Measurement Residuals

Tracking objects in Earth orbit is fraught with complications introduced by a large population from increased launching and debris accumulation, passive (i.e. no direct communication) and data-sparse observation, and the presence of maneuvers and dynamics mismodeling. Accurate orbit determination in this environment requires an algorithm to capture both a system’s state and its state dynamics in order to account for mismodelings. This research project focused on developing an algorithm to address this problem. Beyond typical methods for dealing with dynamically mismodeled system like process noise and Gauss-Markov processes [11, 16, 21], there are many methods for dealing with mismodeled dynamics. Input estimation techniques [2,4,7] append control estimates to the state when a maneuver is detected through residuals, however these methods are generally more applicable to highly dynamical systems with a lot of information. SSA focused methods [6, 9, 15, 20] are well adapted problems within the SSA community, but often they are limited in application to specific orbit and/or observation types. Many methods in the field of system identification focus on understanding the dynamics of an unknown system, but most methods require control of the observed system and data-rich measurement sets [1, 5, 17]. Other methods within system identification [3,22] lift these limitations, but they are often designed for specific systems that do not have overlap with SSA problems. Multiple model estimation methods [8, 14] offer yet another approach to this problem, but these methods limit mismodeling to a finite number of models and the complexity of these methods may limit automated implementation. What we desire is an algorithm that fills the hole in the existing literature. That algorithm is the Optimal Control Based Estimator (OCBE). The OCBE is an algorithm that simultaneously estimates a system’s state and optimal control policies that represent dynamic mismodeling in the system for an arbitrary orbit-observer setup. The control policies and state estimates may be used to identify the presence of dynamic mismodeling, characterize that mismodeling, and reconstruct that mismodeling. The stochastic properties of these estimated controls are then used to determine the presence of mismodelings (maneuver detection), as well as characterize and reconstruct the mismodelings. This method was automated in order to create an adaptive version of the estimator that was capable of real-time application to tracking problems. Below is a bulleted list of the capabilities of the OCBE. • State estimation • Control estimation where the controls represent the dynamic mismodeling within the system • Real-time implementation via the adaptive version of the algorithm, which automatically detects and compensates for mismodeling • Application to arbitrary observer-target setup as long as the system is observable • Maneuver (a.k.a. dynamics mismodeling) detection, compensation, characterization, and reconstruction • State and control estimate smoothing • Application to data sparse systems with non-cooperative observation • Linear and nonlinear estimation • Natural dynamics estimation No existing algorithm has these combined properties, which are important to solving problems in orbit determination for Space Situational Awareness applications. In the following section, we give a brief description of this estimator and how it is formed. After this we provide some brief conclusions detailing what was accomplished in the research project. It should be noted that the full algorithm and examples of its application are provided in the Ph.D. thesis defining this work as well as the journal and conference papers associated with this work.