Bilinear Observer/Kalman Filter Identification

Bilinear systems are important per se since several phenomena in engineering and other fields are inherently bilinear. Even more interestingly, bilinear systems can approximate more general nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems, such as satellite attitude control. This paper develops and demonstrates via numerical examples a method for discrete-time state-space model identification for bilinear systems in the presence of noise in the process and in the measurements. The formulation relies on a bilinear observer which is proven to have properties similar to the linear Kalman filter under the sole additional assumption of stationary white excitation input, and on a novel approach to system identification based on the estimation of the observer residuals. The latter are used to construct a new, noise-free identification problem, in which the observer is identified and the matrices of the system state-space model are recovered. The resulting method represents the bilinear counterpart of the Observer/Kalman filter Identification (OKID) approach for linear systems, originally developed for the identification of lightly-damped structures and distributed by NASA

Compensation of Magnetic Disturbances Improves Inertial and Magnetic Sensing of Human Body Segment Orientation

This paper describes a complementary Kalman filter design to estimate orientation of human body segments by fusing gyroscope, accelerometer, and magnetometer signals from miniature sensors. Ferromagnetic materials or other magnetic fields near the sensor module disturb the local earth magnetic field and, therefore, the orientation estimation, which impedes many (ambulatory) applications. In the filter, the gyroscope bias error, orientation error, and magnetic disturbance error are estimated. The filter was tested under quasi-static and dynamic conditions with ferromagnetic materials close to the sensor module. The quasi-static experiments implied static positions and rotations around the three axes. In the dynamic experiments, three-dimensional rotations were performed near a metal tool case. The orientation estimated by the filter was compared with the orientation obtained with an optical reference system Vicon. Results show accurate and drift-free orientation estimates. The compensation results in a significant difference (p<0.01) between the orientation estimates with compensation of magnetic disturbances in comparison to no compensation or only gyroscopes. The average static error was 1.4/spl deg/ (standard deviation 0.4) in the magnetically disturbed experiments. The dynamic error was 2.6/spl deg/ root means square

Online identification of a two-mass system in frequency domain using a Kalman filter

Some of the most widely recognized online parameter estimation techniques used in different servomechanism are the extended Kalman filter (EKF) and recursive least squares (RLS) methods. Without loss of generality, these methods are based on a prior knowledge of the model structure of the system to be identified, and thus, they can be regarded as parametric identification methods. This paper proposes an on-line non-parametric frequency response identification routine that is based on a fixed-coefficient Kalman filter, which is configured to perform like a Fourier transform. The approach exploits the knowledge of the excitation signal by updating the Kalman filter gains with the known time-varying frequency of chirp signal. The experimental results demonstrate the effectiveness of the proposed online identification method to estimate a non-parametric model of the closed loop controlled servomechanism in a selected band of frequencies

Optimal state estimation for cavity optomechanical systems

We demonstrate optimal state estimation for a cavity optomechanical system through Kalman filtering. By taking into account nontrivial experimental noise sources, such as colored laser noise and spurious mechanical modes, we implement a realistic state-space model. This allows us to obtain the conditional system state, i.e., conditioned on previous measurements, with minimal least-square estimation error. We apply this method for estimating the mechanical state, as well as optomechanical correlations both in the weak and strong coupling regime. The application of the Kalman filter is an important next step for achieving real-time optimal (classical and quantum) control of cavity optomechanical systems.Comment: replaced with published version, 5+12 page

A Nonparametric Adaptive Nonlinear Statistical Filter

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past observed data, and without making any assumptions of the system's prior distribution. The system's prior distribution at each time step is constructed from an ensemble of least-squares estimates on sub-sampled sets of the data via jackknife sampling. As new data is acquired, the state estimates, process uncertainty, and measurement uncertainty are updated accordingly, as described in this manuscript.Comment: Accepted at the 2014 IEEE Conference on Decision and Contro