J. Russell Carpenter

Libration Point Navigation Concepts Supporting the Vision for Space Exploration

This work examines the autonomous navigation accuracy achievable for a lunar exploration trajectory from a translunar libration point lunar navigation relay satellite, augmented by signals from the Global Positioning System (GPS). We also provide a brief analysis comparing the libration point relay to lunar orbit relay architectures, and discuss some issues of GPS usage for cis-lunar trajectories.

A Guidance and Navigation Strategy for Rendezvous and Proximity Operations with a Noncooperative Spacecraft in Geosynchronous Orbit

The feasibility and benefits of various spacecraft servicing concepts are currently being assessed, and all require that servicer spacecraft perform rendezvous, proximity operations, and capture operations with the spacecraft to be serviced. There are many high-value commercial and military spacecraft located in geosynchronous orbit (GEO) which may be candidates for servicing, but GEO is a regime in which rendezvous and capture operations are not commonplace; further, most GEO spacecraft were not designed to be cooperative rendezvous targets, and some may even be completely nonfunctional and therefore potentially tumbling. In this work we present elements of a guidance and navigation strategy for rendezvous and proximity operations with a noncooperative spacecraft in GEO. Translational Δv is assessed for a passively safe co-elliptic rendezvous approach sequence that is followed by injection into a safety ellipse about a noncooperative tumbling spacecraft and, ultimately, final approach to capture. Covariance analysis is presented for a simulation of range and bearing measurements throughout the rendezvous and proximity operations sequence.

PARTIALLY DECENTRALIZED CONTROL ARCHITECTURES FOR SATELLITE FORMATIONS

In a partially decentralized control architecture, more than one but less than all nodes have supervisory capability. This paper describes an approach to choosing the number of supervisors in such an architecture, based on a reliability vs. cost trade. It also considers the implications of these results for the design of navigation systems for satellite formations that could be controlled with a partially decentralized architecture. Using an assumed cost model, analytic and simulation-based results indicate that it may be cheaper to achieve a given overall system reliability with a partially decentralized architecture containing only a few supervisors, than with either fully decentralized or purely centralized architectures. Nominally, the subset of supervisors may act as centralized estimation and control nodes for corresponding subsets of the remaining subordinate nodes, processing all the measurement data from all their subordinates, or fusing the subordinates’ local estimates with a scheme that compensates for correlations among the local states estimates. The supervisors may then act as decentralized estimation and control peers with respect to each other. However, if the state estimates of each spacecraft are uncorrelated, the supervisors may command globally optimal maneuvers derived from simple differencing of the subordinates’ local estimates. Since the absolute positions and velocities of each spacecraft are unique, correlations may only occur through common biases, common process noise, or indirectly through common model errors. A simple example illustrates the discussion on the role of correlation.

Generalized Linear Covariance Analysis

This paper presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into “solve-for” and “consider” parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and a priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and a priori solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator’s epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the “variance sandpile” and the “sensitivity mosaic,” and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Navigation Filter Estimate Fusion for Enhanced Spacecraft Rendezvous

Techniques for optimally mixing the outputs from a pair of Kalman e lters are presented, generalizing previous results. These techniques are derived under the assumption that the designs of the e lters are e xed and cannot be modie ed to support fusion requirements. Conditions for using the optimally fused estimates to periodically reinitialize the Kalman e lters are described. The results are applied to an optimal spacecraft rendezvous problem, and simulated performance results indicate that use of the optimally fused data leads to signie cantly improved robustness to initial target vehicle state errors.

Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment

This paper shows how satellite owners/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies tolerances related to targeted false alarm and missed detection rates. This result is independent of the method one uses to compute the probability density that one integrates to compute collision probability. A well-established test case from the literature shows that this test yields acceptable results within the constraints of a typical operational conjunction assessment decision timeline. Another example illustrates the use of the test in a practical conjunction assessment scenario based on operations of the International Space Station.

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Precomputing Process Noise Covariance for Onboard Sequential Filters

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential ...