A Magnetometer-Only Attitude Determination Strategy for Small Satellites: Design of the Algorithm and Hardware-in-the-Loop Testing

Abstract

Attitude determination represents a fundamental task for spacecraft. Achieving this task on small satellites, and nanosatellites in particular, is further challenging, because the limited power and computational resources available on-board, together with the low development budget, set strict constraints on the selection of the sensors and the complexity of the algorithms. Attitude determination is obtained here from the only measurements of a three-axis magnetometer and a model of the Geomagnetic field, stored on the on-board computer. First, the angular rates are estimated and processed using a second-order low-pass Butterworth filter, then they are used as an input, along with Geomagnetic field data, to estimate the attitude matrix using an unsymmetrical TRIAD. The computational efficiency is enhanced by arranging complex matrix operations into a form of the Faddeev algorithm, which is implemented using systolic array architecture on the FPGA core of a CubeSat on-board computer. The performance and the robustness of the algorithm are evaluated by means of numerical analyses in MATLAB Simulink, showing pointing and angular rate accuracy below 10° and 0.2°/s. The algorithm implemented on FPGA is verified by Hardware-in-the-loop simulation, confirming the results from numerical analyses and efficiency.

Precision Magnetometers for Aerospace Applications: A Review

“…Magnetometers are conventionally used onboard satellites as part of the attitude determination system for low-earth orbit satellites [ 12 ]. However, magnetometers cannot usually obtain three-axis attitude information with only a three-axis magnetometer, and the measurement is distorted by magnetized objects and current loops on board the satellite itself.…”

“…This can, in principle, be achieved by comparing magnetic field readings to an accurate model of the earth’s magnetic field. However, this method is computationally expensive [ 12 ]. Finally, disturbances onboard the satellite itself could be accounted for by either very careful calibration [ 59 ], or by using several magnetometers in different parts of the satellite, which would require further reduction of SWaP.…”

“…The information gathered from these instruments has been of great benefit in increasing our understanding of the composition and evolution of the Earth [ 1 , 2 , 3 , 4 , 5 ], other planets [ 6 , 7 , 8 , 9 ], and the interplanetary (heliospheric) magnetic field [ 10 , 11 ]. They are also widely used in technical aerospace applications, for instance, allowing attitude determination [ 12 ] and magnetic geological surveying [ 13 , 14 ]. Extensive overviews of space-based magnetometers have been previously performed by Acuña [ 15 ] in 2002, Díaz-Michelena [ 16 ] in 2009, and Balogh [ 17 ] in 2010, detailing the design, operation, and calibration of magnetometers flown from the Mariner missions of the early 1960s to the Lunar Prospector and Mars Global Surveyor missions of the turn of the century.…”

Strong tracking central difference Kalman filter for CubeSat attitude estimation with status mutation

“…where B g , k and S g , k are the geomagnetic field and sun vector derived from International Geomagnetic Reference Field model (Carletta et al, 2020) and mean elliptical orbit elements model (Rondão, 2016), respectively, expressed in the geocentric inertial coordinate system; T ( q ) is the direction cosine matrix represented by quaternion, denoted as…”

An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

“…The navigation and control operations in aerospace engineering usually require adequate accurate knowledge of spacecraft orientation in space, and attitude determination from vector observations is usually employed in astronautically applications [1][2][3][4]. The widely used Kalman type filters can infer the state in Euclidean vector space by fusing attitude dynamic and observation sensor according to their probabilities [5][6][7][8].…”