Robust H∞ filter design with variance constraints and parabolic pole assignment

Copyright [2006] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this letter, we consider a multiobjective filtering problem for uncertain linear continuous time-invariant systems subject to error variance constraints. A linear filter is used to estimate a linear combination of the system states. The problem addressed is the design of a filter such that, for all admissible parameter uncertainties, the following three objectives are simultaneously achieved: 1) the filtering process is P-stable, i.e., the poles of the filtering matrix are located inside a parabolic region; 2) the steady-state variance of the estimation error of each state is not more than the individual prespecified value; and 3) the transfer function from exogenous noise inputs to error state outputs meets the prespecified H∞ norm upper-bound constraint. An effective algebraic matrix inequality approach is developed to derive both the existence conditions and the explicit expression of the desired filters. An illustrative example is used to demonstrate the usefulness of the proposed design approach

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the 'perturbed Kalman filter' (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified

Deeply-Integrated Feature Tracking for Embedded Navigation

The Air Force Institute of Technology (AFIT) is investigating techniques to improve aircraft navigation using low-cost imaging and inertial sensors. Stationary features tracked within the image are used to improve the inertial navigation estimate. These features are tracked using a correspondence search between frames. Previous research investigated aiding these correspondence searches using inertial measurements (i.e., stochastic projection). While this research demonstrated the benefits of further sensor integration, it still relied on robust feature descriptors (e.g., SIFT or SURF) to obtain a reliable correspondence match in the presence of rotation and scale changes. Unfortunately, these robust feature extraction algorithms are computationally intensive and require significant resources for real-time operation. Simpler feature extraction algorithms are much more efficient, but their feature descriptors are not invariant to scale, rotation, or affine warping which limits matching performance during arbitrary motion. This research uses inertial measurements to predict not only the location of the feature in the next image but also the feature descriptor, resulting in robust correspondence matching with low computational overhead. This novel technique, called deeply-integrated feature tracking, is exercised using real imagery. The term deep integration is derived from the fact inertial information is used to aid the image processing. The navigation experiments presented demonstrate the performance of the new algorithm in relation to the previous work. Further experiments also investigate a monocular camera setup necessary for actual flight testing. Results show that the new algorithm is 12 times faster than its predecessor while still producing an accurate trajectory. Thirty-percent more features were initialized using the new tracker over the previous algorithm. However, low-level aiding techniques successfully reduced the number of features initialized indicating a more robust tracking solution through deep integration

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Robust H2 filtering for a class of systems with stochastic nonlinearities

Copyright [2006] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper addresses the robust H2 filtering problem for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities described by statistical means in this paper comprise some well-studied classes of nonlinearities in the literature. A technique is developed to tackle the matrix trace terms resulting from the nonlinearities, and the well-known S-procedure technique is adopted to cope with the uncertainties. A unified framework is established to solve the addressed robust H2 filtering problem by using a linear matrix inequality approach. A numerical example is provided to illustrate the usefulness of the proposed method

H ? filtering for stochastic singular fuzzy systems with time-varying delay

This paper considers the H? filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e?t - weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e?t -weighted iISSiM and the H? attenuation level from disturbance to estimation error is belowa prescribed scalar.Aset of sufficient conditions for the solvability of the H? filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

ObjectFlow: A Descriptor for Classifying Traffic Motion

Abstract—We present and evaluate a novel scene descriptor for classifying urban traffic by object motion. Atomic 3D flow vectors are extracted and compensated for the vehicle’s egomo-tion, using stereo video sequences. Votes cast by each flow vector are accumulated in a bird’s eye view histogram grid. Since we are directly using low-level object flow, no prior object detection or tracking is needed. We demonstrate the effectiveness of the proposed descriptor by comparing it to two simpler baselines on the task of classifying more than 100 challenging video sequences into intersection and non-intersection scenarios. Our experiments reveal good classification performance in busy traffic situations, making our method a valuable complement to traditional approaches based on lane markings. I

Image-Aided Navigation Using Cooperative Binocular Stereopsis

This thesis proposes a novel method for cooperatively estimating the positions of two vehicles in a global reference frame based on synchronized image and inertial information. The proposed technique - cooperative binocular stereopsis - leverages the ability of one vehicle to reliably localize itself relative to the other vehicle using image data which enables motion estimation from tracking the three dimensional positions of common features. Unlike popular simultaneous localization and mapping (SLAM) techniques, the method proposed in this work does not require that the positions of features be carried forward in memory. Instead, the optimal vehicle motion over a single time interval is estimated from the positions of common features using a modified bundle adjustment algorithm and is used as a measurement in a delayed state extended Kalman filter (EKF). The developed system achieves improved motion estimation as compared to previous work and is a potential alternative to map-based SLAM algorithms