Bearings-Only Initial Relative Orbit Determination

A method for performing bearings-only initial relative orbit determination of a nearby space object in the absence of any information regarding the space object’s geometry and relative orbit is presented. To resolve the range ambiguity characteristic of a single optical sensor system, a second optical sensor is included at a known baseline distance on the observing spacecraft. To formulate an initial estimate of the space object’s relative orbit and its associated uncertainty, the angle measurements from both sensors are used to bound a region for all possible relative positions of the space object. A parameterized probability distribution in relative position that reflects uniform relative range uncertainty across the bounded region is constructed at two unique times. Linkage of the positional distributions is performed using a second-order relative Lambert solver to formulate a full-state probability density function in relative position and velocity, which can be further refined through processing subs...

[1]  H. Sorenson,et al.  Nonlinear Bayesian estimation using Gaussian sum approximations , 1972 .

[2]  Chris Sabol,et al.  Search and Determine Integrated Environment (SADIE) for Space Situational Awareness , 2012 .

[3]  Tom E. Bishop,et al.  Blind Image Restoration Using a Block-Stationary Signal Model , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[4]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[6]  Initial Relative Orbit Determination using Stereoscopic Imaging and Gaussian Mixture Models , 2013 .

[7]  Srinivas R. Vadali,et al.  Model for Linearized Satellite Relative Motion About a J2-Perturbed Mean Circular Orbit , 2009 .

[8]  Keith A. LeGrand,et al.  Analysis of a Second-Order Relative Motion Lambert Solver , 2014 .

[9]  Rudolph van der Merwe,et al.  Gaussian mixture sigma-point particle filters for sequential probabilistic inference in dynamic state-space models , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[10]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[11]  Itzik Klein,et al.  Angles-Only Navigation State Observability During Orbital Proximity Operations , 2014 .

[12]  Gaurav S. Sukhatme,et al.  Bias Reduction and Filter Convergence for Long Range Stereo , 2005, ISRR.

[13]  Luc Van Gool,et al.  Speeded-Up Robust Features (SURF) , 2008, Comput. Vis. Image Underst..

[14]  Shai Segal,et al.  In-Orbit Tracking of Resident Space Objects: A Comparison of Monocular and Stereoscopic Vision , 2014, IEEE Transactions on Aerospace and Electronic Systems.

[15]  Kyle J. DeMars,et al.  Probabilistic Initial Orbit Determination Using Gaussian Mixture Models , 2013 .

[16]  Shai Segal,et al.  Vision-based relative state estimation of non-cooperative spacecraft under modeling uncertainty , 2011, 2011 Aerospace Conference.

[17]  Rudolph van der Merwe,et al.  The square-root unscented Kalman filter for state and parameter-estimation , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[18]  D.C. Woffinden,et al.  Observability Criteria for Angles-Only Navigation , 2009, IEEE Transactions on Aerospace and Electronic Systems.

[19]  Daniele Mortari,et al.  Multiplicative Measurement Model , 2009 .