Robust ℋ∞-Filtering Design with Pole Placement Constraint via Linear Matrix Inequalities

The problem of robust filtering design for continuous-time systems with convex bounded uncertainties is addressed in this paper. The aim is to determine a stable linear filter such that the filtering error system remains quadratically stable within a prespecified -attenuation level. Necessary and sufficient conditions for the existence of such robust filter are provided in terms of linear matrix inequalities, which can be solved efficiently through standard convex optimization procedures guaranteeing global convergence. Furthermore, as an improvement of the strategy, the filter dynamics can be constrained to some specific regions inside the left-half complex plane.     

Convergence of the SMC Implementation of the PHD Filte

The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges in mean of order , and hence almost surely, to the true PHD filter. We also present a central limit theorem for the SMC approximation, show that the variance is finite under similar assumptions and establish a recursion for the asymptotic variance. This provides a theoretical justification for this implementation of a tractable multiple-object filtering methodology and generalises some results from sequential Monte Carlo theory.      

Linear Filtering for Time-Delay Systems

A linear filtering problem is studied in which the signal process(x(t):t 0) is described by a stochastic differential equationwhere time delays are present in both the noise input and thex variable. By means of a transformation new to the filteringliterature, we reduce the signal equation to a delay-free stochasticevolution equation; this permits us to solve the problem byapplication of the theory of infinite-dimensional linear filtering.     

Adaptive Filtering: Once More with Gusto

Adaptive filtering, when used as a forecasting method, proposes to be able to distinguish a "signal pattern" of a time series instead of just smoothing out the random noise introduced by the data. Adaptive filtering is claimed by its creators to "...always do as well if not better than either moving averages, exponential smoothing,...". In order to see whether this claim could be substantiated, the author has taken the approach of a casual user of forecasting methods and has sought to determine whether adaptive filtering is useful, or not, as a forecasting method. The method was used to compute forecasts for ten sets of data on monthly insurance payments in a Finnish insurance company, and the experience gained from this work is compared with criticisms of the method expressed by a number of writers. It is shown that the method performs quite well for practical purposes, despite the fact that it has some major theoretical shortcomings.     

Distributed event-triggered hybrid wired-wireless networked control with $${H_2}/{H_\infty }$$ filtering

Aiming at the fact that distributed multi-channel hybrid network-induced delays and noise interference may deteriorate the control performance of hybrid networked control systems, distributed event-triggered hybrid wired-wireless networked control with \({H_2}/{H_\infty }\) filtering is proposed. A distributed event-triggered mechanism is firstly employed to reduce communication burden, and two Markov chains are used to respectively describe different characters of network-induced delays of hybrid wired-wireless networks. Then, a \({H_2}/{H_\infty }\) filter is employed to improve the input signal precision of the controller, where a general closed-feedback filtering and control system model with distributed event-triggered parameters and network-induced delays of hybrid wired-wireless networks is proposed. Furthermore, the designed filter and controller enable the closed-feedback filtering and control system to be stochastic stability and to achieve a prescribed \({H_2}/{H_\infty }\) performance, and the relationships between the stability criteria and the maximum network-induced delays, distributed event-triggered parameters, the filter and controller parameters and the system performance parameter are established. Finally, simulation results confirm the effectiveness of the proposed method.     

Modulations of Deep Water Waves and Spectral Filtering

Modulations of deep water waves are studied by a new formalism of spectral filtering. For single-mode dynamics, spectral filtering results in computable equations, which are counterpart to the nonlinear Schrödinger (NLS) equations. An essential feature of new equations is that bandwidth limitation is decoupled from small-amplitude assumption. The filtered equations have a substantially broader range of validity than the NLS equations, and may be viewed as intermediate between the NLS and Zakharov equations. The new single-mode equations reproduce exactly the conditions for nonlinear four-wave resonance ("figure 8" of Phillips [ 1 ]) even for bandwidths greater than unity. Sideband instability for uniform Stokes waves is limited to finite bandwidths only, and agrees well with exact results of McLean [ 2 ].     

H{infty} filtering for linear continuous-time systems with sampled measurements

The problem of H filtering of continuous-time systems with sampledmeasurements has been investigated. Both finite-and infinite-horizoncases have been considered. It has bas been shown that the sampled-dataH filtering problem can be solved in terms of a differentialRiccati equation with finite discrete jumps. When the systemis time-invariant with zero initial condition, and an infinitehorizon is concerned, the solution to the above problem is equivalentto a solution to a discrete-time algebraic Riccati equation.     

Fourier analysis of frequency filtering decomposition preconditioners

In this paper, frequency filtering decomposition (FFD) preconditioner is analyzed by the approach of Fourier analysis. The condition number estimation of a preconditioned 2-D model problem is presented. Analysis reveals that condition number of the preconditioned matrix grows like O(h^-1), with h be the mesh size. By using the framework of FFD, a stabilized frequency filtering decomposition (SFFD) method is proposed and analyzed by Fourier method. Results show that SFFD preconditioner is superior to FFD preconditioner in the sense that . Numerical tests are performed to illustrate the theoretical results and the superiority of SFFD preconditioner.     

Optimal hedging and parameter uncertainty

Email: monoyios{at}maths.ox.ac.uk Received on 8 September 2006. Accepted on 15 March 2007. We explore the impact of drift parameter uncertainty in a basisrisk model, an incomplete market in which a claim on a nontradedasset is optimally hedged using a correlated traded stock. Usinganalytic expansions for indifference prices and hedging strategies,we develop an efficient procedure to generate terminal hedgingerror distributions when the hedger has erroneous estimatesof the drift parameters. These show that the effect of parameteruncertainty is occasionally benign, but often very destructive.In light of this, we develop a filtering approach in which thehedger updates her parameter estimates from observations ofthe asset prices, and we find an analytic solution to the hedger'scombined filtering and control problem in the case that thedrift of the traded asset is known with certainty.     

Robust H ∞ Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems

This paper considers the problem of the robust H filtering for a class of nonlinear discrete-time Markovian jump systems with real time-varying norm-bounded parameter uncertainty. For each mode, the nonlinearity is assumed to satisfy the global Lipschitz conditions and appears in both the state and measured output equations. The problem that we address is the design of a nonlinear filter which ensures robust stochastic stability and a prescribed H performance level of the filtering error system for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities; an explicit expression of a desired nonlinear H filter is also given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.     

A maximum a posteriori estimator for trajectories of diffusion processes

Let x _t be a diffusion process observed via a noisy sensor, whose output is y_t We consider the problem of evaluating the maximum a posteriori trajectory {x_s0≤ s ≤ t Based on results of Stratonovich [1] and Ikeda-Watanabe [2], we show that this estimator is given by the solution of an appropriate variational problem which is a slight modification of the "minimum energy" estimator. We compare our results to the non-linear filtering theory and show that for problems which possess a finite dimensional solution, our approach yields also explicit filters. For linear diffusions observed via linear sensors, these filters are identical to the Kalman-filter     

Data filtering for cluster analysis by $$\ell _0$$-norm regularization

A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted \(\ell _0\)-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed to approximate the \(\ell _0\)-norm. The convergence of the global minimum points of the approximating problems towards global minimum points of the original problem is stated. The proposed method also exploits a suitable technique to choose the penalty parameter. Numerical results on synthetic and real data sets are finally provided, showing how some existing clustering methods can take advantages from the proposed filtering strategy.     

Filtering of distributed parameter systems with pointwise disturbances

We consider in this article a filtering problem for a linear distributed parameter system where the input disturbances are located in points instead of being distributed. The observation process is assumed to be distributed inside the domain. Although formally one can derive equations for the Kalman filter and the Riccati equation, the complete justification of these equations leads to problems which cannot be solved by standard methods, in the sense that some new functional spaces need to be introduced. The objective of the paper is to give a rigorous treatment of this nonclassical filtering problem, which is relevant for applications.     

弹道测定中几种滤波方法的比较

在再入目标的弹道测定中,通常地面跟踪雷达的精度较高,采样率也较高,鉴于这一情形,在选择滤波方法时,除了要保证较高的滤波精度外,一个重要问题是降低计算量,以保证对弹道的实时跟踪.     

Particle filtering in the Dempster–Shafer theory

This paper derives a particle filter algorithm within the Dempster–Shafer framework. Particle filtering is a well-established Bayesian Monte Carlo technique for estimating the current state of a hidden Markov process using a fixed number of samples. When dealing with incomplete information or qualitative assessments of uncertainty, however, Dempster–Shafer models with their explicit representation of ignorance often turn out to be more appropriate than Bayesian models.The contribution of this paper is twofold. First, the Dempster–Shafer formalism is applied to the problem of maintaining a belief distribution over the state space of a hidden Markov process by deriving the corresponding recursive update equations, which turn out to be a strict generalization of Bayesian filtering. Second, it is shown how the solution of these equations can be efficiently approximated via particle filtering based on importance sampling, which makes the Dempster–Shafer approach tractable even for large state spaces. The performance of the resulting algorithm is compared to exact evidential as well as Bayesian inference.     

Linear Matrix Inequality Optimization Approach to Exponential Robust Filtering for Switched Hopfield Neural Networks

This paper is concerned with the delay-dependent exponential robust filtering problem for switched Hopfield neural networks with time-delay. A new delay-dependent switched exponential robust filter is proposed that results in an exponentially stable filtering error system with a guaranteed robust performance. The design of the switched exponential robust filter for these types of neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated using standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed filter.     

On a class of SGS filters for LES with shape preserving concatenation properties

We develop a class of filter functions for large-eddy simulation which have the key property that multiple successive application even with different filter widths is equal to a single filtering employing filters from the same class but at an extended or equal filter width. In the context of the filter class development we obtain a functional delay equation which for special cases may be solved completely general. The presently developed class of filters may be used in conjunction with certain sub-grid scale models such as the approximate deconvolution model [3] where explicit multiple filtering is needed. Hence utilizing filters from the present class computational cost of filter evaluation may be considerably reduced.     

Using local search to speed up filtering algorithms for?some NP-hard constraints

This paper proposes to use local search inside filtering algorithms of combinatorial structures for which achieving a desired level of consistency is too computationally expensive. Local search quickly provides supports for many variable-value pairs, thus reducing the effort required to check and potentially filter the rest of them. The idea is demonstrated on the SomeDifferent constraint, a graph coloring substructure. An experimental evaluation confirms its significant computational gain in many cases.     

Nonlinear filtering of semi-Dirichlet processes

Herein, we consider the nonlinear filtering problem for general right continuous Markov processes, which are assumed to be associated with semi-Dirichlet forms. First, we derive the filtering equations in the semi-Dirichlet form setting. Then, we study the uniqueness of solutions of the filtering equations via the Wiener chaos expansions. Our results on the Wiener chaos expansions for nonlinear filters with possibly unbounded observation functions are novel and have their own interests. Furthermore, we investigate the absolute continuity of the filtering processes with respect to the reference measures and derive the density equations for the filtering processes.