Linear estimation in Krein spaces. Part II. Applications

We have shown that several interesting problems in H∞-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns

Convergence analysis of a family of robust Kalman filters based on the contraction principle

In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is sufficiently small, accordingly the filter converges

Array algorithms for H-infinity estimation

In this paper we develop array algorithms for H-infinity filtering. These algorithms can be regarded as the Krein space generalizations of H-2 array algorithms, which are currently the preferred method for implementing H-2 biters, The array algorithms considered include typo main families: square-root array algorithms, which are typically numerically more stable than conventional ones, and fast array algorithms which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H-infinity filters, as these conditions are built into the algorithms themselves. However, since H-infinity square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H-2 case, further investigation is needed to determine the numerical behavior of such algorithms

H∞ Estimation Approach to Active Noise Control: Theory, Algorithm and Real-Time Implementation

This paper presents an H∞ estimation approach to active control of acoustic noise inside an enclosure. It is shown how H∞ filter theory and algorithm can be effectively applied to active noise control to provide important robustness property. Real-time implementation of the algorithm is performed on Digital Signal Processor. Experimental comparison to conventional FxLMS algorithm for active noise control is presented for both single channel and multichannel cases. While providing some new results, this paper also serves as a brief review on H∞ filter theory and on active noise control

Krein Space-Based H

This paper investigates the finite-time H∞ fault estimation problem for linear time-delay systems, where the delay appears in both state and measurement equations. Firstly, the design of finite horizon H∞ fault estimation is converted into a minimum problem of certain quadratic form. Then we introduce a stochastic system in Krein space, and a sufficient and necessary condition for the minimum is derived by applying innovation analysis approach and projection theory. Finally, a solution to the H∞ fault estimation is obtained by recursively computing a partial difference Riccati equation, which has the same dimension as the original system. Compared with the conventional augmented approach, the solving of a high dimension Riccati equation is avoided

Receding horizon filtering for a class of discrete time-varying nonlinear systems with multiple missing measurements

This paper is concerned with the receding horizon filtering problem for a class of discrete time-varying nonlinear systems with multiple missing measurements. The phenomenon of missing measurements occurs in a random way and the missing probability is governed by a set of stochastic variables obeying the given Bernoulli distribution. By exploiting the projection theory combined with stochastic analysis techniques, a Kalman-type receding horizon filter is put forward to facilitate the online applications. Furthermore, by utilizing the conditional expectation, a novel estimation scheme of state covariance matrices is proposed to guarantee the implementation of the filtering algorithm. Finally, a simulation example is provided to illustrate the effectiveness of the established filtering scheme.This work was supported in part by the Deanship of Scientific Research (DSR) at King Abdulaziz University in Saudi Arabia [grant number 16-135-35-HiCi], the National Natural Science Foundation of China [grant number 61329301], [grant number 61203139], [grant number 61134009], and [grant number 61104125], Royal Society of the U.K., the Shanghai Rising-Star Program of China [grant number 13QA1400100], the Shu Guang project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation [grant number 13SG34], the Fundamental Research Funds for the Central Universities, DHU Distinguished Young Professor Program, and the Alexander von Humboldt Foundation of Germany