Generalized Linear Covariance Analysis

• Published in: The Journal of the astronautical sciences 2009-01, Vol.57 (1-2), p.233-260
• Main Authors: Markley, F. Landis, Carpenter, J. Russell
• Format: Article
• Language: English
• Subjects: Accelerometers; Aerospace Technology and Astronautics; Confidence intervals; Covariance; Engineering; Error analysis; Errors; Estimators; Least squares method; Mathematical Applications in the Physical Sciences; Mathematical models; Monte Carlo methods; Mosaics; Noise; Orbit determination; Orbits; Partitioning; Permissible error; Sensitivity analysis; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Statistics; Subspaces; Variance
• ISSN: 0021-9142; 2195-0571
• DOI: 10.1007/BF03321503

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.