An Efficient Nonlinear Filter for Spacecraft Attitude Estimation

Table 1

The improved computationally efficient attitude estimator.

Initialization	Step  1. Determine the vertexes of the polytopic linear model described as (50).
	Step  2. Search for optimal solutions (𝐺2,𝑆𝐴,𝑆𝐵,𝑆𝐶,𝑆𝐷) of LMIs (57); then calculate the constant filter coefficients (𝐴𝐹,𝐵𝐹,𝐶𝐹,𝐷𝐹) for the local attitude estimator by (59).
Estimator (one cycle)	Given 𝑞𝑘−1,𝑏̂𝑘−1,𝜔𝑘−1 and measurements 𝑢𝑘,𝑟𝑏𝑘, one has the following.
	Step  1. Compute the attitude predictions 𝑞𝑘/𝑘−1 and 𝑏̂𝑘/𝑘−1 by (20).
	Step  2. Compute measurement prediction errors Δ𝑟𝑏𝑘 by (21).
	Step  3. Compute the local error attitude estimation Δ𝑥𝑘 by (50).
	Step  4. Update the attitude estimations 𝑞𝑘 and 𝑏̂𝑘 by (26) and (27).
	Step  5. Update the angular velocity estimation: 𝜔𝑘=𝑢𝑘−𝑏̂𝑘.