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Abstract: Three optimal linear attitude estimators are proposed for single-point real-time estimation of spacecraft attitude using a geometric approach. The final optimal attitude is represented by modified Rodrigues parameters (MRPs). After introducing incidental right-hand orthogonal coordinates for each pair of measured values, three error vectors are obtained by the use of dot or/and cross products. Corresponding optimality criteria are rigorously quadratic and unconstrained, which do not coincide with Wahba’s constrained criterion. The singularity, which occurs when the principal angle is close to π, can be easily avoided by one proper rotation. Numerical simulations show that the proposed three optimal linear estimators can provide a precision comparable with those complying with the Wahba optimality definition, and have faster computational speed than the famous quaternion estimator (QUEST).

[1]Angeles, J., 1988. Rational Kinematics. Springer-Verlag, New York, Vol. 34, Chapters 1-3.

[2]Bar-Itzhack, Y., 1996. REQUEST: A recursive QUEST algorithm for sequential attitude determination. Journal of Guidance, Control, and Dynamics, 19(5):1034-1038.

[3]Cheng, Y., Shuster, M.D., 2007. The Speed of Attitude Estimation. Proceedings of the Advances in the Astronautical Sciences, 127:101-116.

[4]Choukroun, D., 2009. Quaternion Estimation Using Kalman Filtering of the Vectorized K-matrix. AIAA Guidance Navigation, and Control Conference.

[5]Choukroun, D., Bar-Itzhack, I.Y., Oshman, Y., 2004. Optimal-REQUEST algorithm for attitude estimation. Journal of Guidance, Control, and Dynamics, 27(3):418-425.

[6]Farrell, J.L., Stuelpnagel, J.C., Wessner, R.H., Velman, J.R., 1966. A least squares estimate of satellite aatitude. SIAM Review, 8(3):384-386.

[7]Markley, F.L., 1988. Attitude determination using vector observations and the singular value decomposition. The Journal of the Astronautical Sciences, 36(3):245-258.

[8]Markley, F.L., 1993. Attitude determination using vector observations: a fast optimal matrix algorithm. The Journal of the Astronautical Sciences, 41(2):261-280.

[9]Markley, F.L., Mortari, D., 1999. How to Estimate Attitude from Vector Observations. AAS/AIAA Astrodynamics Conference.

[10]Markley, F.L., Mortari, D., 2000. Quaternion attitude estimation using vector measurements. The Journal of the Astronautical Sciences, 48(2&3):359-380.

[11]Mortari, D., 1997a. ESOQ: A closed-form solution to the Wahba problem. The Journal of the Astronautical Sciences, 45(2):195-204.

[12]Mortari, D., 1997b. ESOQ2: Single-point algorithm for fast optimal attitude determination. Advances in the Astronautical Sciences, 97(2):803-816.

[13]Mortari, D., 2000. Second estimator for the optimal quaternion. Journal of Guidance, Control, and Dynamics, 23(5):885-888.

[14]Mortari, D., Markley, F.L., Junkins, J.L., 2000. Optimal linear attitude estimator. Advances in the Astronautical Sciences, 105(1):465-478.

[15]Mortari, D., Markley, F.L., Singla, P., 2007. An optimal linear attitude estimator. Journal of Guidance, Control, and Dynamics, 30(6):1619-1627.

[16]Shuster, M.D., 1978. Approximate Algorithms for Fast Optimal Attitude Computation. Proceedings of AIAA Guidance and Control Conference, p.88-95.

[17]Shuster, M.D., 1989. A Simple Kalman filter and smoother for spacecraft attitude. Journal of the Astronautical Sciences, 37(1):89-106.

[18]Shuster, M.D., 2009. Filter QUEST or REQUEST. Journal of Guidance, Control, and Dynamics, 32(2):643-645.

[19]Shuster, M.D., OH, S.D., 1981. Three-axis attitude determination from vector observations. Journal of Guidance and Control, 4(1):70-77.

[20]Wahba, G., 1965. Problem 65-1: A least squares estimate of spacecraft attitude. SIAM Review, 7(3):409.