Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation

Abstract

Abstract-For applications with limited computational capacity, observers designed based on nonlinear stability theory offer an alternative to computationally demanding extended Kalman filters. In this paper, we present a semiglobally stable nonlinear observer for estimating position, velocity, attitude, and gyro bias by combining a GNSS receiver with an inertial measurement unit including a magnetometer. Previous work by the authors on this topic was based on local navigation equations that ignored the Earth's rotation and curvature. Moreover, the attitude was represented by an over-parameterized 9-degrees-of-freedom matrix. The current paper improves on these aspects by using navigation equations that take the Earth's rotation and curvature into account, and by representing the attitude estimate as a unit quaternion. Furthermore, the observer is tested experimentally on data from a light fixedwing aircraft.

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

“…Proj(·, ·) denotes the parameter projection, from [24, App. E], such that the gyro bias estimate is confined to a compact set, bb g ≤ M g , as with the previous results presented by Grip et al [22], [25], [16] and [26].…”

“…where (1)- (5) are obtained from Bryne et al [15], extending the formulation in Grip et al [16] with the integral of the vertical heave position, p n z , denoted p n I which is an auxiliary variable defined in order to utilize a virtual vertical reference (VVR) aiding measurement presented in Section 2.4. The strapdown equations applied in this paper are suitable for marine surface vessels employing local navigation.…”

“…From, q n b , the rotation matrix R n b ∈ SO(3) can be calculated according to R(q n b ) = I 3 + 2sS(r) + 2S(r) 2 , as in e.g. [16], where I 3 is the 3 × 3 identity matrix, while S(·) denotes the skew-symmetric matrix and is given such that b/n ∈ R 3 is the angular velocity given in {b}. Finally, the constant biases of the three-axis rate gyro is denoted b b g ∈ R 3 .…”

“…Bryne et al [15] have developed a six degree of freedom (DOF), time-varying nonlinear inertial navigation system (INS) observer, with USGES stability properties, exploiting the position reference system's quality indicator, customized for marine surface vessels, based on the results of Grip et al [16]. However, Bryne et al did not consider wave filtering.…”

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.…”