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CEAS EuroGNC 2019 |
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A Novel Multiplicative Quaternion Filter |
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| Abstract: This paper presents a novel quaternion filter from vector measurements that belongs to the realm of deterministic constrained least-squares estimation. Hinging on the interpretation of quaternion measurement errors as angular errors in a four-dimensional Euclidean space, a novel cost function is developed and a minimization problem is formulated under the quaternion unit-norm constraint. This approach sheds a new light on the Wahba problem and on the q-method. The optimal estimate can be interpreted as achieving the least angular distance among a collection of planes in R^4 that are constructed from the vector observations. The resulting batch algorithm is mathematically equivalent to the q-method. Taking advantage of the gained geometric insight, a recursive algorithm is developed, where the update stage consists of a rotation in the four-dimensional Euclidean space. The rotation angle is empirically designed as a fading memory factor. The quaternion update stage is multiplicative thus preserving the estimated quaternion unit-norm and no iterative search for eigenvalues is required, as opposed to the q-method. The two algorithms are extended to the case of time varying attitude, under the assumptions that the inertial angular rates are measured. Extensive Monte-Carlo simulations showed that the proposed filter asymptotically converges to the q-method solution. The performances are numerically investigated for a range of typical values of the noise intensities in the rate gyroscopes and the attitude sensing. | ||||
| Keywords: Parameter estimation; Spacecraft attitude determination | ||||
| CEAS-GNC-2019-025 PDF is not available online. Authors may distribute copies of their paper or contact the CEAS GNC TC chair to make their paper available through the EuroGNC paper archive. |
| Daniel Choukroun, Uri Tamir: A Novel Multiplicative Quaternion Filter. Proceedings of the 2019 CEAS EuroGNC conference. Milan, Italy. April 2019. CEAS-GNC-2019-025. |
| BibTeX entry: @Incollection{CEAS-GNC-2019-025, authors = {Choukroun, Daniel and Tamir, Uri}, title = {A Novel Multiplicative Quaternion Filter}, booktitle = {Proceedings of the 2019 {CEAS EuroGNC} conference}, address = {Milan, Italy}, month = apr, year = {2019}, note = {CEAS-GNC-2019-025} } |