Observer Design for Nonlinear Systems with Equivariance

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models mechatronic navigation systems. Such systems admit symmetry, the equivariance, that provides structure enabling design robust high-performance observers. A key insight to pose observer state lie in symmetry group rather than on system space. This allows one define global intrinsic equivariant error but poses challenge defining internal dynamics for observer. By choosing an lift model, we show have particularly nice form. Applying methodology extended Kalman filtering yields filter term filter. The geometry state-space manifold appears naturally as curvature modification classical Riccati equation filtering. exploits respects thus high-performance, filters wide range