Design of Globally Exponentially Convergent Continuous Observers for\n Velocity Bias and State for Systems on Real Matrix Groups

2019/09/23 by Dong Eui Chang, Chang, Dong Eui
Engineering · Medicine · Computer Science · #Adaptive Control of Nonlinear Systems #Medical Imaging Techniques and Applications #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1909.10179

Abstract

We propose globally exponentially convergent continuous observers for\ninvariant kinematic systems on finite-dimensional matrix Lie groups. Such an\nobserver estimates, from measurements of landmarks, vectors and biased\nvelocity, both the system state and the unknown constant bias in velocity\nmeasurement, where the state belongs to the state-space Lie group and the\nvelocity to the Lie algebra of the Lie group. The main technique is to embed a\ngiven system defined on a matrix Lie group into Euclidean space and build\nobservers in the Euclidean space. The theory is illustrated with the special\nEuclidean group in three dimensions.\n

Related

• Globally exponentially convergent observer for systems evolving on matrix Lie groups
• Gradient-like observers for invariant dynamics on a Lie group
• Higher-Order Nonlinear Complementary Filtering on Lie Groups
• Observer design for invariant systems with homogeneous observations
• Intrinsic filtering on Lie groups with applications to attitude\n estimation