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—This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialised to systems on Lie groups. For invariant systems this leads to a general… (More)

— This paper considers the question of designing an attitude observer exploiting the structure of the Special Orthogonal Group SO(3) for both inertial and body-fixed-frame measurements. We consider measurements from a minimal sensor suite, typically a rate gyroscope along with several measurements of inertial and/or body-fixed vector directions. We propose… (More)

—This paper provides a comprehensive observability and stability analysis of a suite of non-linear attitude observers that have been developed over the last few years. The observers considered are based on vectorial measurements of an a-priori known reference direction. By treating the reference direction and the measurement in the same analysis framework,… (More)

—Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decom-pounding is a generalization of a similar classical problem. The proposed solution is based on a characteristic function method. The treated problem is important to recent models of… (More)

— In this paper, we provide a general method of state estimation for a class of invariant systems on connected matrix Lie groups where the group velocity measurement is corrupted by an unknown constant bias. The output measurements are given by a collection of actions of a single Lie group on several homogeneous output spaces, a model that applies to a wide… (More)

This paper considers the design of nonlinear observers for invariant systems posed on finite-dimensional connected Lie groups with measurements generated by a transitive group action on an associated homogeneous space. We consider the case where the group action has the opposite invariance to the system invariance and show that the group kinematics project… (More)

— In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in R n. We propose a gradient… (More)

This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias. The key contribution of the paper is to study the combined state and input bias estimation problem in the… (More)

This paper studies autonomous synchronization of k agent orientations ∈ SO(n) by using links that each convey (a priori different) partial state information between two agents: the latter compare the action of their states on a common link-dependent vector of R n. Such setting appears when each pair of agents compares the expression, in their respective… (More)