Trajectory optimization for well-conditioned parameter estimation

Andrew D. Wilson, Jarvis A. Schultz, Todd D. Murphey

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


When attempting to estimate parameters in a dynamical system, it is often beneficial to strategically design experimental trajectories that facilitate the estimation process. This paper presents an optimization algorithm which improves conditioning of estimation problems by modifying the experimental trajectory. An objective function which minimizes the condition number of the Hessian of the least-squares identification method is derived and a least-squares method is used to estimate parameters of the nonlinear system. A software-simulated example demonstrates that an arbitrarily designed trajectory can lead to an ill-conditioned least-squares estimation problem, which in turn leads to slower convergence to the best estimate and, in the presence of experimental uncertainties, may lead to no convergence at all. A physical experiment with a robot-controlled suspended mass also shows improved estimation results in practice in the presence of noise and uncertainty using the optimized trajectory.

Original languageEnglish (US)
Article number6823184
Pages (from-to)28-36
Number of pages9
JournalIEEE Transactions on Automation Science and Engineering
Issue number1
StatePublished - Jan 1 2015


  • Iterative methods in optimization
  • optimal control
  • parameter estimation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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