Accurate propagation of orbital uncertainty is essential to a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to increase resolution in areas of stronger nonlinearities, as well as by reducing mixands to prevent unnecessary computational effort. Recent work introduced novel splitting criteria and more sophisticated choices of splitting direction. These heuristics incorporate information from the system dynamics and initial uncertainty to determine optimal directions for splitting. This paper develops adaptive uncertainty propagation methods based on these robust splitting techniques. A deferred splitting algorithm tightly integrated with higher-order splitting techniques is proposed and shown to offer substantial gains in computational efficiency without sacrificing accuracy. Different initial and deferred splitting methods are compared in three representative orbit test cases, including a geostationary orbit, a Molniya orbit, and a periodic three-body orbit.

Probabilistic decentralized data fusion is the process of combining probabilistic beliefs from multiple sensors to reduce uncertainty and is broadly applicable to problems in aerospace, robotics, and wireless sensor networks. Fusing statistical information into a fused density is especially useful in distributed sensor networks, where each node or agent possesses only limited computation and sensing capabilities. The Chernoff fusion rule prevents information double-counting and produces a fused density that is equidistant from the input densities in an information-theoretic sense. This paper presents a novel approach to Gaussian mixture Chernoff fusion based on the progressive Bayes framework, where the optimal fused mixture is obtained through homotopy continuation. An advantage of the new approach is that it does not require fitting of Gaussian mixtures to lossy samples. A new and simple strategy for determining the optimal Chernoff weighting parameter is also presented and shown to outperform more complicated methods.

This paper addresses consensus-based networked estimation of the state of a nonlinear dynamical system. This paper first presents an information form of the recently proposed Bayesian recursive update filter (BRUF), a Kalman filter that uses a recursive update to incorporate information from nonlinear measurement systems. Under the assumptions that the system is collectively observable and the network is strongly connected, a distributed information Bayesian recursive update filter (DIBRUF), a distributed form of the information Bayesian recursive update filter (IBRUF), is proposed, which exploits consensus on information vectors and matrices. Compared to the distributed extended Kalman filter (DEKF), the DIBRUF reduces the linearization error of the extended Kalman filter (EKF) by dividing the measurement update into N steps. Unlike the BRUF and IBRUF, which require local observability, the DIBRUF requires only the network to be collectively observable, as the sensors can share information among the network. Simulation experiments demonstrate the validity of the proposed approach.

The role of negative information is particularly important to search-detect-track problems in which the number of objects is unknown a priori, and the size of the sensor field-of-view is far smaller than that of the region of interest. This paper presents an approach for systematically incorporating knowledge of the field-of-view geometry and position and object inclusion/exclusion evidence into object state densities and random finite set multi-object cardinality distributions. The approach is derived for a representative set of multi-object distributions and demonstrated through a sensor planning problem involving a multi-Bernoulli process with up to one-hundred potential targets.