James S. McCabe

Particle Filter Methods for Space Object Tracking

An approach for space object tracking utilizing particle filters is presented. New methods are developed and used to construct a robust constrained admissible region given a set of angles-only measurements, which is then approximated by a finite mixture distribution. This probabilistic initial orbit solution is refined using subsequent measurements through a particle filter approach. A proposal density is constructed based on an approximate Bayesian update and samples, or particles, are drawn from this proposed probability density to assign and correct weights, which form the basis for a more accurate Bayesian update. A finite mixture distribution is then fit to these weighted samples to reinitialize the cycle. This approach is compared to methods that approximate all probability densities as finite mixtures and process them as such. Both approaches utilize recursive estimation based on Bayesian statistics, but the benefits of densely sampling the support probability based on incoming measurements is weighed against remaining solely within the finite mixture approximation and performing measurement corrections there.

Comparison of Factorization-Based Filtering for Landing Navigation

This paper develops and analyzes methods for fusing inertial navigation data with external data, such as data obtained from an altimeter and a star camera. The particular filtering techniques are based upon factorized forms of the Kalman filter, specifically the UDU and Cholesky factorizations. The factorized Kalman filters are utilized to ensure numerical stability of the navigation solution. Simulations are carried out to compare the performance of the different approaches along a lunar descent trajectory using inertial and external data sources. It is found that the factorized forms improve upon conventional filtering techniques in terms of ensuring numerical stability for the investigated landing navigation scenario.

Considering Uncertain Parameters in Non-Gaussian Estimation for Single-Target and Multitarget Tracking

Consider filtering is an estimation technique that emerged in the 1960s to account for uncertainties in system parameters while simultaneously reducing system dimensionality and (accordingly) the r...

Efficient multi-sensor data fusion for space surveillance

Multi-sensor networks can extend the sensing region of a single sensor in order to provide a more geometrically diverse and comprehensive view of the state of a dynamical system. The use of a multi-sensor network gives rise to the need for a fusion step that combines the outputs of all sensor nodes into a single probabilistic state description. This paper examines a fusion method based on logarithmic opinion pools and develops algorithms for multi-sensor data fusion as well as investigates weight selection schemes for the opinion pool using efficient quadrature integration methods. The proposed fusion rules are applied to the tracking of a space object using multiple ground-based optical sensors. It is shown that the multi-sensor fusion rule leads to an increase of nearly two orders of magnitude in the position tracking accuracy as compared to the traditional single-sensor tracking method.

Multi-Sensor Data Fusion in Non-Gaussian Orbit Determination

Multi-sensor networks can alleviate the need for high-cost, high-accuracy, single-sensor tracking in favor of an abundance of lower-cost and lower-accuracy sensors to perform multi-sensor tracking. The use of a multi-sensor network gives rise to the need for a fusion step that combines the outputs of all sensor nodes into a single probabilistic state description. When considering Gaussian uncertainties, the well-known covariance intersection technique may be used. In the more general, non-Gaussian case, covariance intersection is not sucient. This paper examines a fusion method based on logarithmic opinion pools and develops algorithms for multi-sensor data fusion as well as investigates weight selection schemes for the opinion pool. The proposed fusion rules are applied to the tracking of a space object using multiple ground-based optical sensors. Non-Gaussian orbit determination methods are applied to each sensor individually, and the fusion rule is applied to the combined outputs of each sensor node. It is shown that the multi-sensor fusion rule leads to an increase of nearly two orders of magnitude in the position tracking accuracy as compared to the traditional single-sensor tracking method.