Brien Flewelling, ExoAnalytic Solutions
Keywords: Statistics, Initial Orbit Determination, Data Fusion, Model Estimation
Abstract:
The Random Sampling Consensus (RANSAC) algorithm is a robust model fitting approach for estimation of model parameters given a set of data. It is intended to be robust to the presence of outliers in measurements. The typical example of the simplest application of the RANSAC algorithm is the fitting of a line to 2D data. The implicit assumptions associated with processing a set of 2D points with a RANSAC line fitter is 1.) There is a sufficient number of meaningful inliers which map to a linear model such that a model can be determined and be best fit, and 2.) There is not a consistent set of outliers which fit a linear model and cause the algorithm to conclude that they are inliers. Extending this technique to determine the parameters of an orbit given angles only data requires the RANSAC algorithm to be combined with an orbit determination routine. In this case three right ascension and declination pairs are the minimal set to exercise an orbit determination process and obtain an estimate of the state vector at an associated time. The determination of the state vector at this time however does not uniquely guarantee that the deterministic solution based on three given measurements is the best one necessitating a need for a RANSAC solution. By applying a RANSAC approach, the Consensus Set within a candidate set of measurements is easily identified as the set of inliers to the model which contains the most inlier measurements. Furthermore, understanding the set of models which sufficiently contain a high fraction of inliers provides insight to the consistency of a set of measurements. Determining a set of RANSAC associated data points solves multiple problems at once. First, it provides a robust means to go from coarse initial orbit determination estimates to more refined precision OD solutions by increasing the confidence that the points used are all inliers. Second it has the potential ability to flag outliers which are potentially incorretly associated data, or indicative of the model changing within a given dataset requiring the model fit to change as well. This paper introduces a few demonstrative examples both constructed in simulation and applied to real data which illustrate the potential for methods based on RANSAC to inform an analyst of potential subtle challenges which may go undetected in the direct application of batch or sequential estimation methods and show up as structure in residuals. These challenges include various violations of assumptions that the data being processed represent a single object, moving ballistically, and are measured by a network of observers whose measurements can be expected to be zero-mean Gaussian distributed around the desired motion model to be determined. Examples will show the ways in which observations of space objects can routinely violate these assumptions including multiple closely spaced objects, maneuvering objects, and fusing multiple observation data sources of heterogeneous quality. A connectivity matrix is also defined which represents the association of models which fit a certain quality criteria and the measurements in a candidate set of data. Analysis of this matrix provides an efficient means to assess if a sufficiently confident consensus set exists.
Date of Conference: September 11-14, 2018
Track: Poster