Attitude-Independent Magnetometer-Bias Determination: A Survey
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Attitude-Independent Magnetometer-Bias Determination: A Survey Roberto Alonso! and Malcolm D. Shuster" Abstract The currently known algorithms for inflight magnetometer-bias determination without knowledge of the attitude are examined. The majority of these are shown to be limited either by poor convergence properties, significant statistical or analytical approximations, or the discarding of important data. The most robust and accurate of these algorithms is TWOSTEP, an algorithm recently developed which combines the best properties of the existing algorithms. Comparisons of algorithm performance are made both for spinning and inertially stabilized spacecraft. While TWOSTEP performs well in all cases, many of the other algorithms do not converge to the globally optimal estimate of the magnetometer-bias vector or even diverge.
Introduction A number of algorithms have been proposed for estimating the magnetometer bias when attitude information is not available. The simplest is to solve for the bias vector by minimizing the weighted sum of the squares of residuals which are the differences in the squares of the magnitudes of the measured and modeled magnetic fields [1]. This approach has the disadvantage that the cost function is quartic in the magnetometer bias and therefore admits multiple minima. Typically, one initiates the least-squares procedure by assuming that the initial magnetometer bias vector vanishes, which may lead to slow convergence or convergence only to a local minimum if the magnetometer bias is large compared to the ambient magnetic field. Gambhir [1, 2] advocated centering the data to remove the quartic dependence. This leads to a cost function which is quadratic is the bias and, therefore, has a unique solution. The algorithm embodying this centering is called RESIDG (supposedly, "G" for Gambhir) and has been employed for nearly two decades. The centering, however, necessarily discards part of the data, and the effect of this loss
I Jefe, Grupo de Control de Actitud, Comisi6n Nacional de Actividades Espaciales (CONAE), Avenida Paseo Colon 751, (1063) Buenos Aires, Argentina. 2Director of Research, Acme Spacecraft Company, 13017 Wisteria Drive, Box 328, Germantown, Maryland 20874. email: [email protected].
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of data on the accuracy of the algorithm was not studied. In addition, RESIDG does not make any attempt to treat the statistics correctly, so that it is not possible to assess the accuracy of the estimation adequately. A second approach has been put forth by Thompson et ale [3], who preferred to construct a fixed-point algorithm, which was called, with obvious reference, RESIDT. Fixed-point algorithms have the advantage of often converging quickly when one is far from the solution, but can become intolerably slow as one approaches the solution. Thompson's algorithm was successfully employed in support of the AMPTE spacecraft. Davenport et ale [4] have proposed another approach to solving the quartic cost function by computing first an approximate solution for
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