Constrained Quaternion Filtering for Single-Frame Attitude Determination

Abstract

This article presents two recursive quaternion filters for single-frame attitude determination from vector measurements. In the first filter, the estimate is sequentially projected on Null-space planes built from the measurements and normalized. The convergence analysis lends itself to a deterministic observability condition under which global exponential convergence is guaranteed. The update stage in the second filter consists of a planar rotation of the quaternion estimate. The rotation operator is a function of the measurements and is parameterized by a single angle. This rotational update enforces by design the unity constraint upon the quaternion estimate and lends itself to an intuitive tuning of the angle. The filter converges globally under fairly generic assumptions on the angular gain. No linearization is involved in both filters, which estimate the absolute quaternion rather than incremental corrections. A Monte Carlo (MC) numerical study illustrates the convergence characteristics of the filters and verifies their accuracy under various initial conditions, measurement sequences, and noise variances. With ideal noise-free measurements, the projection filter is the quickest and computationally the savviest. With noisy measurements, the rotational quaternion filter exhibits a better steady-state accuracy but is slower. This tradeoff is circumvented thanks to a time-varying angular gain that improves both transient and steady-state performances. Extensive MC simulations show that the rotational quaternion filter provides the same accuracy as the optimal REQUEST with a tenfold reduction in the computation load. An appealing characteristic of the proposed filters is that one can predict offline the transient duration for any predefined level of accuracy.