Attitude Estimation Using Biased Gyro and Vector Measurements With Time-Varying Reference Vectors

Abstract

Abstract-We present two results on attitude estimation using vector and rate gyro measurements. The first result concerns an observer previously presented by Hamel, Mahony, and Pflimlin, with proven stability results when (i) the reference vectors are stationary; or (ii) the gyro measurements are unbiased. We prove semiglobal stability without either of these assumptions when a parameter projection is added, and convergence from all initial attitudes when using a resetting strategy. The second result is an algorithm for estimation of bias in the body-fixed vector measurements, which is analyzed in combination with the attitude and gyro bias observer.

Design of inertial navigation systems for marine craft with adaptive wave filtering aided by triple‐redundant sensor packages

“…This is important since f n = −g n due to wave excitation of the vessel. The attitude observer, Σ 1 , by Grip et al [22], developed from [23], is given as…”

Observers for interconnected nonlinear and linear systems

“…Thus, we can apply our methodology with equal simplicity. Another possibility is to extend the attitude observer to include estimation of gyro bias, or to estimate accelerometer bias using the method of Grip, Fossen, Johansen, and Saberi (2011a), which also relies on the unmeasured variable a n . A disadvantage of our design is thatR is in general not a rotation matrix, even though it converges to one.…”

Hybrid observer for improved transient performance of a marine vessel in dynamic positioning**This work was supported by the Research Council of Norway through the Centres of Excellence funding scheme, project number 23254 - AMOS, and in part by NSF grant number ECCS-1508757 and AFOSR grant number FA9550-15-1-0155.

“…The reader is referred to Fossen and Strand (1999), Fossen (2011) for details on the model-based observer, and to Grip et al (2012), Grip et al (2013), Bryne et al (2014), and Bryne et al (2015) for details on the signal-based observer.…”

“…The signal-based estimation error dynamics (12) has the origin uniformly locally exponentially stable (ULES) with almost global attractivity (Grip et al (2012) and Bryne et al (2015)). The attractivity is almost global but not global; hence, the convergence rate from points near the boundary of the basin of attraction, particularly those corresponding to yaw estimation error equal to 180 degrees, is slow.…”

“…The signal-based observer, also referred to as a kinematic, or sensor-based observer, is based on the kinematic equations, see for instance Mahony et al (2008), Hua (2010), Grip et al (2012), and Bryne et al (2015). It is especially well suited during transients, as it uses linear acceleration measurements to predict velocity and position.…”