Enhancing attitude estimation accuracy via system noise optimization

Abstract

It is well known to the Kalman filter design and estimation community that the values for the process noise, Q, and measurement noise, R, covariance matrices primarily dictate the filter performance. In addition, selecting proper values for Q and R is traditionally done in an ad-hoc manner. This paper provides a new look into the roles of the process noise and measurement noise matrices using the spacecraft attitude estimation problem as the design benchmark. This includes an interesting situation where the theoretical values of Q and R, derived as a function of gyro and star tracker noise parameters, are exactly matched with the noise characteristics employed on the sensor model side. However, the filter still exhibits poor attitude estimation performance, as measured against an attitude knowledge requirement, while subject to a high rate slew profile. A simulation based tuning methodology is developed to optimize the filter performance and bring the attitude estimation back to within the required attitude knowledge bound. IntroductionSolutions to the spacecraft Attitude Determination Subsystem (ADS) can be considered as proven and complete since the early 1980's for nominal missions involving low spacecraft rates [1]. Work conducted in the area of advanced ADS development, at various levels, during the past 20 years continues to excel [2]-[6]. These areas include unscented filtering [7], high order and adaptive filtering [3] and [8], and nonlinear observers [10]. Regardless of the filtering scheme selected by designers, the process noise, Q, and measurement noise, R, covariance matrices still dominate the overall performance of the ADS. It is a common misperception that setting the ADS filter noise parameters, in the Q and R matrices, to the actual sensor noise parameters provided by the hardware vendors will demonstrate acceptable ADS filter performance. However, due to the random nature of sensor noise parameters and on-orbit variation, the exact application of the hardware noise parameters in the ADS filter does not guarantee acceptable performance. This methodology certainly does not provide the optimal performance desired in an ADS design. A small amount of research and development work has been conducted in the area of Q and R parameterization for spacecraft ADS design. This paper provides a new look into optimization of the process noise and measurement noise matrices and presents an optimization approach designed to extend the ADS filter performance beyond its normally accepted levels and provide a greater level of performance margin. Background & Motivation on Kalman Filter Based OptimizationThe process noise covariance matrix, Q, is computed as a function of gyro random noise sources, spacecraft rate, and filter update cycle time. The measurement noise covariance matrix, R, is computed as a function of star tracker noise and the star tracker alignment matrix. An exact computed value of the Q and R matrices, based on vendor provided gyro

Performance Comparison Between Extended Kalman Filter and Sparse Grid Quadrature Filter for Spacecraft Attitude Estimation Using Low Grade Attitude Sensors

“…Also note that Q matrix design and selection for the estimation community has always been the active topic for many estimation applications (e.g., navigation design, target tracking, data fusion, etc) (see [12], [13], & [14]). Adaptive Q matrix has been extensively studied for the past decade and will remain to be the active topic for years to come.…”