Spacecraft Angular Rate Estimation from Magnetometer Data Only Using an Analytic Predictor

Abstract

A method is presented for fast estimation of the angular rate of a tumbling spacecraft in a low-Earth orbit from sequential readings of Earth's magnetic eld. Useful as a backup algorithm in cases of rate gyro malfunctionsor during the initial acquisitionphase, the estimatorconsists of an extended Kalman lter, based on the assumptionthat the inertial geomagnetic eld vector does not signi cantly change during the short sampling time. As the external disturbance torque is neglected, an analytic solution of Euler's equations can be used in the lter's propagation phase, allowing a signi cant savings of computation time compared to numerical integration of Euler's equations. Contrary to most existing angular rate estimators, the spacecraft's attitude is neither used nor estimated within the proposed algorithm. Moreover, the body-referenced geomagnetic eld observations are not differentiated with respect to time as an external pre ltering procedure but are directly processed by the lter. This processing gives rise to a colored effective measurement noise, which is properly handled via approximate Markov modeling and application of Bryson and Henrikson's reduced-order ltering theory. A simulation study employing a standard tenth-order International Geomagnetic Reference Field model is presented to demonstrate the performance of the algorithm.

Gaussian Deterministic Recursive Estimator with Online Tuning Capabilities

“…Note that the differencing of TAM readings, which is performed to generate the effective measurement z k , makes the effective measurement noise colored, nonstationary, and state dependent. For the sake of simplicity, the procedure proposed in [14] to handle colored noise is not implemented here. Rather, it is assumed in our simulations that the measurements formed by differencing punctual magnetometer readings are affected by a zero-mean white Gaussian noise of known covariance.…”

“…In particular, the method presented in [14] for fast estimation of the angular rate of a tumbling spacecraft from sequential readings of the Earth's magnetic field is addressed.…”

Robust Adaptive Filter for Small Satellite Attitude Estimation Based on Magnetometer and Gyro

“…In the orbital state estimation stage, to avoid the influence of attitude errors, the modulus of geomagnetic field vector is taken as observed quantity. And in the attitude determination stage, orbital parameters are considered to be known; attitude optimal estimation is obtained by using the standard Kalman filtering algorithm, regardless of the influence of orbit determination errors [6].…”

Attitude and Rate Estimation of a Spacecraft by Using Magnetometers

“…A typical scenario is a batch estimation called the quaternion estimation (QUEST) for the attitude estimation 1,4,6) . The other typical scenario is a recursive estimation by applying an extended Kalman filter (EKF) technique for the attitude rate estimation 2,3) . In many cases, the Euler parameters representing the attitude or the angular velocity vector are directly estimated.…”

“…Although a similar problem was discussed by Psiaki 2) , the cost function is based on the trapezoidal integration of the Euler equation of motion. Moreover, in order to overcome the numerical differentiation problem 3) in the batch attitude rate estimation algorithm, we propose an alternative numerical differentiation method by combining the second order low pass filter with the time derivative filter.…”