Since the initial developments in the state-space theory in the 1950s and 1960s, the state estimation has become an extensively researched and applied discipline. All systems that can be modelled mathematically are candidates for state estimators. The state estimators reconstruct the states that represent internal conditions and status of a system at a specific instant of time using a mathematical model and the information received from the system sensors. Moreover, the estimator can be extended for system parameter estimation. The resulting Kalman filter (KF) derivatives for state and parameter estimation also require knowledge about the noise statistics of measurements and the uncertainties of the system model. These are often unknown, and an inaccurate parameterization may lead to decreased filter performance or even divergence. Additionally, insufficient system excitation can cause parameter estimation drifts. In this chapter, a sensitivity-based adaptive square-root unscented KF (SRUKF) is presented. This filter combines a SRUKF and the recursive prediction-error method to estimate system states, parameters and covariances online. Moreover, local sensitivity analysis is performed to prevent parameter estimation drifts, while the system is not sufficiently excited. The filter is evaluated on two testbeds based on an axis serial mechanism and compared with the joint state and parameter UKF.
Part of the book: Kalman Filters