This paper presents the anonymous, extent-informed (AEI) update for map-based localization. The presented approach builds upon anonymous feature processing (AFP) by introducing a new prior and landmark likelihood model such that extent-dependencies in the detection process are accounted for directly in the measurement update. The AEI update is applied to a lunar descent scenario, where the simulated vehicle collects optical observations of the lunar surface and compares them to an onboard map. The AEI update is compared to both a Gaussian mixture implementation of AFP and the standard extended Kalman filter (EKF). The results show that the AEI update is able to provide more precise and consistent estimates of the vehicle’s position and velocity than the other methods, while also requiring fewer components in the posterior mixture. The AEI update is also shown to be more robust to the presence of clutter and false detection processes.

A major challenge of applied Bayesian filtering is deriving estimates that are robust to misspecifications in the underlying statistical models, particularly when Bayes’ rule does not directly yield analytical posterior probability densities. Variational approaches present a promising alternative to “traditional,” closed-form Bayesian inference, wherein an approximate posterior is defined by minimizing the statistical dissimilarity to the conventional Bayesian posterior. There are, however, numerous realistic hurdles to defining an ideal dissimilarity measure, from which posteriors are derived using calculus of variations. This work utilizes a recently proposed framework, known as generalized variational inference (GVI), to define robust and tractable approximations of Bayes’ rule. The GVI framework is presented and accompanied by a novel sensitivity analysis and gradient-based solution method that is applicable for particle, Gaussian, and Gaussian mixture posterior representations. The proposed GVI filter is applied to a dynamic state estimation scenario with inaccurate measurement modeling and, via Monte Carlo analysis, demonstrates both statistical consistency and improvements over conventional robust filtering methods.

The incorporation of nonlinear measurement information plays an important role in Bayesian state estimation for real-word systems. While many methods exist for propagating states through continuous-time nonlinear dynamics, a complementary continuous solution for discrete-time nonlinear measurements has so far remained elusive. Building on intuition from our previous work, the Bayesian Recursive Update Filter, we formulate the nonlinear measurement update as an ordinary differential equation (ODE). This formulation naturally extends to particle flow. We define two particle flows: the first is a deterministic flow based on the ODE solution, and the second is stochastic; the numerical integration contains a diffusion term. The proposed particle flows demonstrate excellent performance on a system with deterministic dynamics and a highly accurate nonlinear measurement, a setting known to be challenging for particle filters.

Bayes’ rule provides an undoubtedly powerful framework for statistical inference; however, the assumptions inherent in Bayesian filtering often cannot be realized in physical systems. Oftentimes, the true Bayesian posterior probability density function (pdf) is infinite-dimensional and lacks tractable implementations, in addition to errors induced by inaccurate realizations of the prior and likelihood pdfs. Though particlebased methods can provide versatile and computationally efficient approximations of Bayes’ rule, they lack the theoretical ability to mitigate estimation errors incurred by erroneous measurement modeling. This work merges Stein Variational Gradient Descent, a nonlinear particle flow update scheme, with generalized variational inference, a method for formulating optimal non-Bayesian posteriors, to produce tractable variational posterior pdfs that remain robust to modeling errors. The new framework is demonstrated to outperform conventional filtering approaches in a simplified relative spacecraft navigation scenario.

Given that a single ground-based sensor, such as a radar or electro-optical telescope, is limited to observing only a small portion of an object's orbit, tracking accuracy can be greatly improved by collecting data with multiple geographically disparate sensors. Processing the data provided by such a distributed sensor network, however, poses complications in that full cooperation, i.e. direct sharing of raw measurement data, is usually implausible. Alternatively, cooperation within the network can be more feasibly established by instead sharing the posterior state densities produced by each sensor's tracking scheme and fusing these densities directly. This paper investigates the use of geometric averaging approaches to probability density fusion to exploit the diversity of a cooperative, distributed sensor network. These methods not only require approximate methods to perform sensor fusion, but they also require numerical procedures to determine an ideal weighting for each density. Computationally efficient approximations to these fusion techniques are formulated and compared to more expensive methods to determine the efficacy of the approximations. A numerical simulation considering the tracking of a space object in low Earth orbit with three cooperating ground-based radar stations is presented to produce conclusions on the discussed approaches.