Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

Abstract

This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group SE2(3), leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation (CRE). These observers are then extended to handle biased angular velocity measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observers.

Nonlinear Observers for Stereo-Vision-Aided Inertial Navigation

“…. These geometric estimation errors are motivated from [1], [15], [23], and are different from the standard errors used in classical EKF-based filters [2], [3]. The innovation term σ R in (7) can be rewritten as…”

“…Moreover, for any distinct non-negative scalars ρ i , i = 1, 2, 3, the matrix M is positive semi-definite with three distinct eigenvalues. From (15), one can notice that σ R has two terms: the first term k R ψ a (MR) is commonly used for the establishment of the stability proofs of the attitude estimation subsystem; see for instance [6], [17]. The second term depending on the estimation errorx is an asymptotically vanishing perturbation term as it will be shown later.…”

“…The second term depending on the estimation errorx is an asymptotically vanishing perturbation term as it will be shown later. In view of (3), (6) and (15), one obtains the following closed-loop system:…”

“…LetΦ(t, τ ) = exp(Ā(t − τ )) be the state transition matrix associated toĀ. Using similar steps as in the proof of [15,Lemma 3], the state transition matrix associated to A(t) can be written as…”

Nonlinear observer design on SL(3) for homography estimation by exploiting point and line correspondences with application to image stabilization

“…Time delay in output measurements is considered in (Khosravian et al 2016) for velocity-aided attitude observer design. Hybrid nonlinear attitude and pose observers are proposed in (Berkane et al 2017, Wang & Tayebi 2019 to overcome topological obstructions of Lie groups containing rotations (Bhat & Bernstein 2000) so that global asymptotical stability can be achieved. These are just a very nonexhaustive list of examples.…”