Time‐varying parameter estimation with application to trajectory tracking

PurposeThis paper is concerned with an online parameter estimation algorithm for nonlinear uncertain time‐varying systems for which no stochastic information is available.Design/methodology/approachThe estimation procedure, called nonlinear learning rate adaptation (NLRA), computes an individual adaptive learning rate for each parameter instead of using a single adaptive learning rate for all the parameters as done in stochastic approximation, each individual learning rate being controlled by a meta‐learning rate rule for the sake of minimizing the measurement prediction error. The method does not require stochastic information about the system model and the measurement noise covariance matrices contrarily to the Kalman filtering. Numerical results about aircraft navigation trajectory tracking show that the method is able to estimate reliably time‐varying parameters even in presence of measurement noise.FindingsThe proposed algorithm is practically insensitive to changes in the meta‐learning rate. Therefore, the performance of the method is stable with respect to the tuning parameter of the algorithm.Practical implicationsThe proposed NLRA method may be adopted for recursive parameter estimation of uncertain systems when no stochastic information is available. It may also be used for process regulation and dynamic system stabilization in feedback control applications.Originality/valueProvides a method for fast and practical computation of parameter estimates without requiring to know the model and measurement noise covariance matrices contrarily to existing stochastic estimation methods.