Error Propagation of Capon’s Minimum Variance Estimator

The error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix which describes the location depence of the measurement positions is the key parameter for the error propagation, since the condition number of the shape matrix determines how the errors are amplified. Furthermore, the error resulting from a finite number of data samples is derived by regarding Capon’s estimator as a special case of the maximum likelihood estimator.

Combined Road Roughness and Vehicle Parameter Estimation Based on a Minimum Variance Unbiased Estimator

This paper deals with the simultaneous identification of road roughness and vehicle parameters, considering the effect of vehicle–structure interaction. The proposed technique avoids the use of bridge response data (which has practical implementation difficulties along with the high chances of corruption with environmental noises) and utilizes the vehicle response data (which is relatively easier to record). Further, vehicle calibration is not needed as the roughness is estimated simultaneously. The identification is carried out by the coupling of an unbiased minimum variance estimator with an optimization scheme. This study considers a quarter-car vehicle model and a half-car vehicle model, instrumented to measure the vehicle vibration data. The unbiased minimum variance estimator (MVE) allows a linear temporal evolution of the state variables, incorporating the roughness as an unknown input term such that the need for linearization is avoided, unlike the traditional nonlinear filters. The optimization scheme helps in choosing a set of optimal solutions for the vehicle parameters as designed in the coupled scheme. The best split of the available measurement data to be used in the two schemes (MVE and optimization scheme) is discussed. The effect of different objective functions is also studied. The proposed technique is successful in terms of simultaneously estimating the vehicle parameters, roughness profile and vehicle responses (states) accurately.

H∞-Property of the Continuous-Time Extended Kalman Filter

This work elucidates another theoretical property of the ubiquitous extended Kalman filter by analyzing the energy gain of the continuous-time extended Kalman filter used as a nonlinear observer in the presence of finite-energy disturbances. The analysis provides a bound on the ratio of estimation error energy to disturbance energy, which shows that the extended Kalman filter inherently has the H∞-property along with being the locally optimal minimum variance estimator. A special case of this result is also shown to be the H2-property of the extended Kalman filter.

Robust Human Machine Interface Based on Head Movements Applied to Assistive Robotics

This paper presents an interface that uses two different sensing techniques and combines both results through a fusion process to obtain the minimum-variance estimator of the orientation of the user’s head. Sensing techniques of the interface are based on an inertial sensor and artificial vision. The orientation of the user’s head is used to steer the navigation of a robotic wheelchair. Also, a control algorithm for assistive technology system is presented. The system is evaluated by four individuals with severe motors disability and a quantitative index was developed, in order to objectively evaluate the performance. The results obtained are promising since most users could perform the proposed tasks with the robotic wheelchair.