Louis L. Whitcomb

Andrew R. Spielvogel, Abhimanyu S. Shah, Louis L. Whitcomb

This article addresses the problem of dynamic on-line estimation and compensation of hard-iron and soft-iron biases of 3-axis magnetometers under dynamic motion in field robotics, utilizing only biased measurements from a 3-axis magnetometer and a 3-axis angular rate sensor. The proposed magnetometer and angular velocity bias estimator (MAVBE) utilizes a 15-state process model encoding the nonlinear process dynamics for the magnetometer signal subject to angular velocity excursions, while simultaneously estimating 9 magnetometer bias parameters and 3 angular rate sensor bias parameters, within an extended Kalman filter framework. Bias parameter local observability is numerically evaluated. The bias-compensated signals, together with 3-axis accelerometer signals, are utilized to estimate bias compensated magnetic geodetic heading. Performance of the proposed MAVBE method is evaluated in comparison to the widely cited magnetometer-only TWOSTEP method in numerical simulations, laboratory experiments, and full-scale field trials of an instrumented autonomous underwater vehicle in the Chesapeake Bay, MD, USA. For the proposed MAVBE, (i) instrument attitude is not required to estimate biases, and the results show that (ii) the biases are locally observable, (iii) the bias estimates converge rapidly to true bias parameters, (iv) only modest instrument excitation is required for bias estimate convergence, and (v) compensation for magnetometer hard-iron and soft-iron biases dramatically improves dynamic heading estimation accuracy.

Tyler M. Paine, Louis L. Whitcomb

This paper addresses the long-standing open problem of observability of mass and inertia plant parameters in the adaptive identification (AID) of second-order nonlinear models of 6 degree-of-freedom rigid-body dynamical systems subject to externally applied forces and moments. Although stable methods for AID of plant parameters for this class of systems, as well numerous approaches to stable model-based direct adaptive trajectory-tracking control of such systems, have been reported, these studies have been unable to prove analytically that the adaptive parameter estimates converge to the true plant parameter values. This paper reports necessary and sufficient conditions for the uniform complete observability (UCO) of 6-DOF plant inertial parameters for a stable adaptive identifier for this class of systems. When the UCO condition is satisfied, the adaptive parameter estimates are shown to converge to the true plant parameter values. To the best of our knowledge this is the first reported proof for this class of systems of UCO of plant parameters and for convergence of adaptive parameter estimates to true parameter values. We also report a numerical simulation study of this AID approach which shows that (a) the UCO condition can be met for fully-actuated plants as well as underactuated plants with the proper choice of control input and (b) convergence of adaptive parameter estimates to the true parameter values. We conjecture that this approach can be extended to include other parameters that appear rigid body plant models including parameters for drag, buoyancy, added mass, bias, and actuators.