Attitude Estimation Based on Time-Varying Reference Vectors with Biased Gyro and Vector Measurements?

We present two results on attitude estimation using vector and rate gyro measurements, when both sets of measurements are biased. The first result concerns an observer for attitude and gyro bias that has previously been presented by Hamel and Mahony, and by Mahony, Hamel, and Pflimlin, with proven almost-global stability results when either (i) the reference vectors in the inertial frame are stationary; or (ii) the reference vectors are time-varying but the gyro measurements are unbiased. We prove that the same observer with an added parameter projection is semiglobally exponentially stable when bias estimation is included and the reference vectors are time-varying. The second result concerns estimation of bias in the body-fixed vector measurements. We show how the bias can be estimated in a manner that is decoupled from the attitude and gyro bias estimation, provided the measurements are sufficiently excited relative to the level of measurement noise.