Trajectory Synthesis for Fisher Information Maximization
This work addresses the challenge of efficient parameter estimation for researchers and engineers in fields like robotics and control systems, offering a practical incremental improvement over existing trajectory optimization methods.
The paper tackles the problem of improving parameter estimation in nonlinear dynamic systems by optimizing experimental trajectories to maximize Fisher information, resulting in a three orders of magnitude increase in the minimum eigenvalue of the Fisher information matrix in simulation and an order of magnitude reduction in parameter estimate error experimentally.
Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix. A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the Fisher information matrix by three orders of magnitude compared to the initial trajectory. Experimental results show that this optimized trajectory translates to an order of magnitude improvement in the parameter estimate error in practice.