Paul W. Schumacher

Initial Orbit Determination using Short-Arc Angle and Angle Rate Data

The population of space objects (SOs) is tracked with sparse resources and thus tracking data are only collected on these objects for a relatively small fraction of their orbit revolution (i.e., a short arc). This contributes to commonly mistagged or uncorrelated SOs and their associated trajectory uncertainties (covariances) to be less physically meaningful. The case of simply updating a catalogued SO is not treated here, but rather, the problem of reducing a set of collected short-arc data on an arbitrary deep space object without a priori information, and from the observations alone, determining its orbit to an acceptable level of accuracy. Fundamentally, this is a problem of data association and track correlation. The work presented here takes the concept of admissible regions and attributable vectors along with a multiple hypothesis filtering approach to determine how well these SO orbits can be recovered for short-arc data in near realtime and autonomously. While the methods presented here are explored with synthetic data, the basis for the simulations resides in actual data that has yet to be reduced, but whose characteristics are replicated as well as possible to yield results that can be expected using actual data.

Evaluation of the Naval Space Surveillance Fence Performance Using Satellite Laser Ranging

An experiment is described in which the performance of the Naval Space Command Fence Receiver Suite is evaluated using satellite laser ranging. Fence measurement accuracy and precision is presently assessed based on cataloged orbits,which are notsufe ciently accurateforrigorouscalibrationand trend identie cation. Satellitelaser ranging is a well-known high-precision data type, which can provide submeter reference positions routinely. Two methods of sensor evaluation are investigated. One is an ephemeris-based approach, where a truth reference orbit is determined from laser ranging data from a number of different satellites at different altitudes. Fence-based residuals are then computed from this truth. The second is a geometric method, which computes satellite positions directly using ranging data and angle data from the telescope. A mathematical treatment of the geometric dilution of precision for both methods is included in the discussion. The overall experiment showed that the fence sensor suite isoperating to within 14 ‐17 times its noisee oorof 10 πrad atzenith. We believe thatthis is the most extensive measurement of the fence performance utilizing an external and independent data type, and due to the precision of the data type, its overall response and error trends are identie ed.

Application Of Multi-Hypothesis Sequential Monte Carlo For Breakup Analysis With The Comparison Of Two Probabilistic Admissible Region Techniques

As more objects are launched into space, the potential for breakup events and space object collisions is ever increasing. These events create large clouds of debris that are extremely hazardous to space operations. Providing timely, accurate, and statistically meaningful Space Situational Awareness (SSA) data is crucial in order to protect assets and operations in space. The space object tracking problem, in general, is nonlinear in both state dynamics and observations, making it ill-suited to linear filtering techniques such as the Kalman filter. Additionally, given the multi-object, multi-scenario nature of the problem, space situational awareness requires multi-hypothesis tracking and management that is combinatorially challenging in nature. In practice, it is often seen that assumptions of underlying linearity and/or Gaussianity are used to provide tractable solutions to the multiple space object tracking problem. However, these assumptions are, at times, detrimental to tracking data and provide statistically inconsistent solutions. This paper details a tractable solution to the multiple space object tracking problem applicable to space object breakup events. Within this solution, simplifying assumptions of the underlying probability density function are relaxed and heuristic methods for hypothesis management are avoided. This is done by implementing Sequential Monte Carlo (SMC) methods for both nonlinear filtering as well as hypothesis management. This goal of this paper is to detail the solution and use it as a platform to discuss computational limitations that hinder proper analysis of large breakup events.

Implications of Hierarchies for RSO Recognition, Identification, and Characterization

Abstract : In our previous work, we demonstrated that hierarchical (taxonomical) trees can be used to depict hypotheses in a Bayesian object recognition and identification process using Figaro, an open source probabilistic programming language. We assume in this work that we have appropriately defined a satellite taxonomy that allows us to place a given space object (RSO) into a particular class of object without any ambiguity. Such a taxonomy allows one to assess the probability of assignment to a particular class by determining how well the object satisfies the unique criteria of belonging to that class. Furthermore, tree-based taxonomies delineate unique signatures by defining the minimum amount of information required to positively identify a RSO. Because of these properties of taxonomic trees, we can now explore the implications of RSO taxonomic trees for model distance metrics and sensor tasking. In particular, we seek to exploit the fact that taxonomic trees provide a model neighborhood that can be used to initiate a Monte Carlo or Multiple Hypothesis algorithm. We contend this feature of taxonomies will provide a quantifiable metric for model distances and the explicit number of models that should be considered, both of which currently do not exist. Additionally, the discriminating characteristics of taxonomic classes can be used to determine the kind of data and the associated sensor that needs to be tasked to acquire that data. We also discuss the concept of multiple interacting hierarchies that provide deeper insight into how object interact with one another.

Search and Determine Integrated Environment (SADIE) for Automated Processing of Space Surveillance Observations (Invited)

A new high-performance computing software applications package called the Search and Determine Integrated Environment (SADIE) is being developed and refined jointly by the Air Force and Naval Research Laboratories (AFRL and NRL). SADIE is designed to resolve uncorrelated tracks (UCTs) and build a more complete space object catalog for improved Space Situational Awareness (SSA), automatically. The motivation for SADIE is to address very challenging needs identified by Air Force Space Command (AFSPC) and other senior leaders and to develop this technology for the evolving Joint Space Operations Center (JSpOC) and Distributed Space Command and Control Center (DSC2)-Dahlgren. The SADIE suite includes modification and integration of legacy applications and software components that include Satellite Identification (SID) and Parallel Catalog (ParCat) as well as other utilities and scripts to enable end-to-end catalog building and maintenance in a parallel processing environment. SADIE is being developed to handle large catalog-building challenges in all orbit regimes and includes the automatic processing of radar and optical data. Promising real data results are provided for the processing of near-Earth radar and Space Surveillance Telescope optical data.

Using Fractional Gaussian Noise Models in Orbit Determination

Motivated by a recent requirement to provide accurate covariance matrices as well as orbit estimates for cata-loging space objects, a Bayesian estimator to handle autocorrelated process and measurement noises is presented. Although the application is orbit determination, the estimation method itself is general. Techniques are presented to model autocorrelated noises in terms of fractional Gaussian noise and increments of fractional Brownian motion. The Bayesian estimator is derived in both batch and sequential forms, along with explicit formulas for calculating the estimation error covariance matrix. The sequential form generalizes the Kalman filter to the case of autocorrelated noise processes. Also discussed is a batch least-squares estimator formulated with a whitening transformation that accounts for both measurement and process noise. Basic properties of the fractional Gaussian noise model are presented, showing how it contains the special case of white noise in a one-parameter family of self-similar random processes. The parameter characterizes the extent of the autocorrelation and is known as the Hurst parameter. When the measurement noise can be isolated from the process noise by appropriate sensor calibrations, statistical test-of-hypothesis techniques can be used to estimate the Hurst parameter by adjusting it to optimize thep value of the test. For a measurement noise sample that is sufficiently dense in time, the Hurst parameter can be calculated directly from the samples fractal dimension. In contrast, the process noise usually cannot be isolated from the total noise because the measurements are the only information available. However, assuming the Hurst parameter of the measurement noise is either estimated first or known a priori, test-of-hypothesis techniques can be used to estimate the Hurst parameters of the process noise.