This paper is concerned with the set-membership filtering problem for a class of linear time-varying systems with norm-bounded noises and impulsive measurement outliers. A new representation is proposed to model the measurement outlier by an impulsive signal whose minimum interval length (i.e., the minimum duration between two adjacent impulsive signals) and minimum norm (i.e., the minimum of the norms of all impulsive signals) are larger than certain thresholds that are adjustable according to engineering practice. In order to guarantee satisfactory filtering performance, a so-called parameter-dependent set-membership filter is put forward that is capable of generating a time-varying ellipsoidal region containing the true system state. First, a novel outlier detection strategy is developed, based on a dedicatedly constructed input-output model, to examine whether the received measurement is corrupted by an outlier. Then, through the outcome of the outlier detection, the gain matrix of the desired filter and the corresponding ellipsoidal region are calculated by solving two recursive difference equations. Furthermore, the ultimate boundedness issue on the time-varying ellipsoidal region is thoroughly investigated. Finally, a simulation example is provided to demonstrate the effectiveness of our proposed parameter-dependent set-membership filtering strategy.

/pdf/set-membership-filtering-subject-to-impulsive-measurement-1pt76dacem.pdf

Set-Membership Filtering Subject to Impulsive Measurement Outliers: A Recursive Algorithm

This paper is concerned with the ultimately bounded filtering problem for linear time-delay systems subject to norm-bounded disturbances and impulsive measurement outliers (IMOs). The considered IMOs are modeled by a sequence of impulsive signals with certain known minimum norm (i.e. the minimum of the norms of all impulsive signals). In order to characterize the occasional occurrence of IMOs, a sequence of independently and identically distributed random variables is introduced to depict the interval lengths (i.e. the durations between two adjacent IMOs) of the outliers. In order to achieve satisfactory filtering performance, a novel parameter-dependent filtering approach is proposed to protect the filtering performance from IMOs by using a special outlier detection scheme, which is developed based on a particular input-output model. The ultimate boundedness (in mean square) of the filtering error is investigated by using the stochastic analysis technique and Lyapunov-functional-like method. The desired filter gain matrix is derived through solving a constrained optimization problem. A simulation example is provided to demonstrate the effectiveness of our proposed

/pdf/ultimately-bounded-filtering-subject-to-impulsive-5epjy418mv.pdf

Ultimately Bounded Filtering Subject to Impulsive Measurement Outliers

This article is concerned with the ultimately bounded filtering problem for a class of linear time-delay systems subject to norm-bounded disturbances and impulsive measurement outliers (IMOs). The considered IMOs are modeled by a sequence of impulsive signals with certain known minimum norm (i.e., the minimum of the norms of all impulsive signals). In order to characterize the occasional occurrence of IMOs, a sequence of independent and identically distributed random variables is introduced to depict the interval lengths (i.e., the durations between two adjacent IMOs) of the outliers. In order to achieve satisfactory filtering performance, a novel parameter-dependent filtering approach is proposed to protect the filtering performance from IMOs by using a special outlier detection scheme, which is developed based on a particular input–output model. First, the ultimate boundedness (in mean square) of the filtering error is investigated by using the stochastic analysis technique and the Lyapunov-functional-like method. Then, the desired filter gain matrix is derived through solving a constrained optimization problem. Furthermore, the designed filtering scheme is applied to the case where the statistical properties about the interval lengths of outliers are completely unknown. Finally, a simulation example is provided to demonstrate the effectiveness of our proposed filtering strategy. 

/pdf/ultimately-bounded-filtering-subject-to-impulsive-4izfn1rw.pdf

This article is concerned with the energy-to-peak state estimation problem for a class of linear discrete-time systems with energy-bounded noises and intermittent measurement outliers (IMOs). In order to capture the intermittent nature, two sequences of step functions are introduced to model the occurrence of the IMOs. Furthermore, two special indices (i.e., minimum and maximum interval lengths) are adopted to describe the ``occurrence frequency'' of IMOs. Different from the considered energy-bounded noises, the outliers are assumed to have their magnitudes larger than certain thresholds. In order to achieve a satisfactory performance constraint on the energy-to-peak state estimation under the addressed kind of measurement outliers, a novel parameter-dependent (PD) state estimation strategy is developed to guarantee that the measurements contaminated by outliers would be removed in the estimation process. The proposed PD state estimation method is essentially a two-step process, where the first step is to examine the appearing and disappearing moments for each IMO by using a dedicatedly constructed outlier detection scheme, and the second step is to implement the state estimation task according to the outlier detection results. Sufficient conditions are obtained to ensure the existence of the desired estimator, and the gain matrix of the desired estimator is then derived by solving a constrained optimization problem. Finally, a simulation example is presented to illustrate the effectiveness of our developed PD state estimation strategy.

Energy-to-Peak State Estimation With Intermittent Measurement Outliers: The Single-Output Case

We study a three-species analogue of the Potts lattice gas model of nucleation from solution in a regime where partially disordered solute is a viable thermodynamic phase. Using a multicanonical sampling protocol, we compute phase diagrams for the system, from which we determine a parameter regime where the partially disordered phase is metastable almost everywhere in the temperature-fugacity plane. The resulting model shows non-trivial nucleation and growth behaviour, which we examine via multidimensional free energy calculations. We consider the applicability of the model in capturing the multi-stage nucleation mechanisms of polymorphic biominerals (e.g., CaCO3). We then quantitatively explore the kinetics of nucleation in our model using the increasingly popular "seeding" method. We compare the resulting free energy barrier heights to those obtained via explicit free energy calculations over a wide range of temperatures and fugacities, carefully considering the propagation of statistical error. We find that the ability of the "seeding" method to reproduce accurate free energy barriers is dependent on the degree of supersaturation, and severely limited by the use of a nucleation driving force Δμ computed for bulk phases. We discuss possible reasons for this in terms of underlying kinetic assumptions, and those of classical nucleation theory.

Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways

A method is developed for testing hypotheses on system availability and mean time to repair, under the assumption that the failure times and repair times are, respectively, independent exponential and gamma random variables. System is assumed to be in a steady state; availability is defined in usual manner as the ratio of mean time to failure to the sum of mean time to failure and mean time to repair. Testing hypotheses on system availability is achieved by simple application of the F distribution, provided: a) the system mean time to repair is known or determinable from other assumptions, or b) the ratio of system mean time to failure to the gamma scale parameter is known. Similarly, hypotheses on system mean repair time can be tested using the chi-square distribution, if the gamma scale parameter is known.

Simple Test of Hypotheses on System Availability and Mean Time to Repair

The Mellin convolution is used to derive in analytical form an exact 3-parameterprobabilitydensity function of the quotient of two noncentral normal random variables. In contrast with the 5-parameter probability density function previously derivedby Fieller (1932) and Hinkley (1969), this 3-parameter probability density function is feasible for computer evaluation of the mean and cumulative distribution function, which are needed, for example, when dealing with estimation and distribution problems in regression analysis and sampling theory. When the normal variables are independent, the probability density function reduces to a 2-parameter function, for which a computer program is operational. An illustrative example is given for one set of parameters when the normal variables are independent, in which themean and functional form of the probability density function are presented, together with a brief tabulation of the probability density function.

Distribution of the quotient of noncentral normal random variables

SYNOPTIC ABSTRACTThis paper exploits use of Mellin transforms in the study of product and quotient distributions by (a) identification of distributions (b) derivation of distributions (c) moment analysis of distributions (d) use of approximating functions (e) examples.

Serafettin Cabuk

Papers

Simple Test of Hypotheses on System Availability and Mean Time to Repair

Distribution of the quotient of noncentral normal random variables

Distribution Identification, Analysis and Approximation via Mellin Transforms