Bilinear modeling and nonlinear estimation

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs

Application of modern control and nonlinear estimation techniques

Control and nonlinear estimation techniques applied to optimal guidance of low thrust spacecraft, planetary soft landings, and feedback systems desig

Smart Power Grid Synchronization With Fault Tolerant Nonlinear Estimation

Effective real-time state estimation is essential for smart grid synchronization, as electricity demand continues to grow, and renewable energy resources increase their penetration into the grid. In order to provide a more reliable state estimation technique to address the problem of bad data in the PMU-based power synchronization, this paper presents a novel nonlinear estimation framework to dynamically track frequency, voltage magnitudes and phase angles. Instead of directly analyzing in abc coordinate frame, symmetrical component transformation is employed to separate the positive, negative, and zero sequence networks. Then, Clarke\u27s transformation is used to transform the sequence networks into the αβ stationary coordinate frame, which leads to system model formulation. A novel fault tolerant extended Kalman filter based real-time estimation framework is proposed for smart grid synchronization with noisy bad data measurements. Computer simulation studies have demonstrated that the proposed fault tolerant extended Kalman filter (FTEKF) provides more accurate voltage synchronization results than the extended Kalman filter (EKF). The proposed approach has been implemented with dSPACE DS1103 and National Instruments CompactRIO hardware platforms. Computer simulation and hardware instrumentation results have shown the potential applications of FTEKF in smart grid synchronization

The Asymmetric Effects of Oil Shocks on an Oil-exporting Economy

We estimate the effects of unexpected changes in oil prices on output for the case of Venezuela, an oil-exporting economy. Following Hamilton (2003), Lee et al. (1995), and Mork (1989), we estimate measures of oil shocks and determine the effect of theseOil shocks, output fluctuations, nonlinear estimation

Nonlinear estimation for linear inverse problems with error in the operator

We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove their rate-optimality and adaptivity properties over Besov classes.Comment: Published in at http://dx.doi.org/10.1214/009053607000000721 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Recurrent backpropagation and the dynamical approach to adaptive neural computation

Error backpropagation in feedforward neural network models is a popular learning algorithm that has its roots in nonlinear estimation and optimization. It is being used routinely to calculate error gradients in nonlinear systems with hundreds of thousands of parameters. However, the classical architecture for backpropagation has severe restrictions. The extension of backpropagation to networks with recurrent connections will be reviewed. It is now possible to efficiently compute the error gradients for networks that have temporal dynamics, which opens applications to a host of problems in systems identification and control