Nonlinear State Estimation

This paper considers the joint estimation of population totals for different variables of interest in multi-purpose surveys using stratified sampling designs. When the finite population has a hierarchical structure, different methods of unbiased estimation are proposed. Based on Monte Carlo simulations, it is concluded that the proposed approach is better, in terms of relative efficiency, than other suitable methods such as the generalized weight share method.

In this paper we describe a new nonlinear estimator for filtering systems with nonlinear process and observation models, based on the optimization with RGO (Restricted Genetic Optimization). Simulation results are used to compare the performance of this method with EKF (Extended Kalman Filter), IEKF (Iterated Extended Kalman Filter), SNF (Second-order Nonlinear Filter), SIF (Single-stage Iterated Filter) and MSF (Monte-Carlo Simulation Filter) in the presence of diferents levels of noise.

The hydrodynamics of Newtonian fluids has been the subject of a tremendous amount of work over the past eighty years, both in physics and mathematics. Sadly, however, a mutual feeling of incomprehension has often hindered scientific contacts. This article provides a dictionary that allows mathematicians (including the author) to define and study the spectral properties of Kolmogorov-Obukov turbulence in a simple deterministic manner. In other words, this approach fits turbulence into the mathematical framework of studying the qualitative properties of solutions of PDEs, independently from any a-priori model of the structure of the flow. To check that this approach is correct, this article proves some of the classical statements that can be found in physics textbooks. This is followed by an investigation of the compatibility between turbulence and the smoothness of solutions of Navier-Stokes in 3D, which was the initial motivation of this study.

The Schwarz Alternating Method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an in nite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz Alternating Methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method of subsolutions and supersolutions) are given. In particular, an additive Schwarz method for scalar as well some coupled nonlinear PDEs are shown to converge to some solution on nitely many subdomains, even when multiple solutions are possible. In the coupled system case, each subdomain PDE is linear, decoupled and can be solved concurrently with other subdomain PDEs. These results are applicable to several models in population biology.

We study the asymptotic behavior of large data radial solutions to the focusing Schrödinger equation iut +∆u = -|u| 2 u in R 3 , assuming globally bounded H 1 (R 3 ) norm (i.e. no blowup in the energy space). We show that as t → ±∞, these solutions split into the sum of three terms: a radiation term that evolves according to the linear Schrödinger equation, a smooth function localized near the origin, and an error that goes to zero in the Ḣ1 (R 3 ) norm. Furthermore, the smooth function near the origin is either zero (in which case one has scattering to a free solution), or has mass and energy bounded strictly away from zero, and obeys an asymptotic Pohozaev identity. These results are consistent with the conjecture of soliton resolution. 1991 Mathematics Subject Classification. 35Q55. This work was conducted at Australian National University. The author is a Clay Prize Fellow and is supported by a grant from the Packard foundation. We thank Jim Colliander and Igor Rodnianski for helpful comments and corrections, and Wilhelm Schlag for pointing out that the author's original proof of Theorem 1.1 was incorrect. 1 It is likely that at least some of the results here also extend to other dimensions and exponents. However, we need to be in three and higher dimensions in order for the fundamental solution e it∆ to be "short range" (decaying faster than t -1 ), and the algebraic nature of the cubic nonlinearity is also somewhat convenient. Also much of the asymptotic analysis is restricted to the L 2 -supercritical regime p > 1 + 4 d in order for global Strichartz estimates to be useful. 2 As this is a vast field, we cannot hope to come close to an exhaustive description of results here, and the references given are not intended to be complete. We refer the reader to the books [10], [45], [6], for a more detailed survey.

The purpose of this paper is to describe and assess some methods for accounting for certainty primary sampling units (PSUs) when using a pseudo- replication procedure (specifically balanced repeated replication (BRR) procedure) for variance estimation 1 . We compare these alternatives to the variance estimation procedure using the explicit variance estimation equations with Taylor series linearization of nonlinear estimators. The

In the framework of denoising a function depending of a multidimensional variable (for instance an image), we provide a nonparametric procedure which constructs a pointwise kernel estimation with a local selection of the multidimensional bandwidth parameter. Our methodisageneralizationoftheLepski'smethodofadaptation,androughlyconsistsinchoosing the "coarsest" bandwidth such that the estimated bias is negligible. However, this notion becomes more delicate in a multidimensional setting. We will particularly focus on functions with inhomogeneous smoothness properties and especially providing a possible disparity of the inhomogeneous aspect in the different directions. We show, in particular that our method is able to exactly attain the minimax rate or to adapt to unknown degree of anisotropic smoothness up to a logarithmic factor, for a large scale of anisotropic Besov spaces.

In this paper, a new strategy to cope with unmeasurable premise variables in observer design for Takagi-Sugeno (TS) models is proposed. The guiding principles are the immersion techniques and auxiliary dynamics generation, allowing to immerge a given TS system with unmeasured state dependent weighting functions into a larger TS system with weighting functions depending only on measured variables. This result relaxes the strong conditions used in the design of observers for TS systems with unmeasurable premise variables. An example is provided to illustrate the performances of the proposed approach.

This paper presents a novel training method for estimating the parameters of retina models, such as integrateand-fire or Poisson-based. The presented models are constructed using a set of linear and nonlinear filters, described by basis functions and Taylor polynomials, respectively. This approach allows for the identification of a set of features that can be used for reproducing retina responses. By using the Bayesian-Laplace feature selection algorithm herein proposed, an efficient model with a reduced set of parameters is achieved. Experimental results show that the proposed algorithm is able to remove non-important features while still accurately reproducing retina responses. These results also show that the integrate-and-fire model is able to mimic the retina visual processing system using less parameters than the Poisson-based model.

This paper is concerned with the study of a nonlinear non-local equation that has a commutator structure. The equation reads with s ∈ (0, 1]. We are interested in solutions stemming from periodic positive bounded initial data. The given function F ∈ C ∞ (R + ) must satisfy F ′ > 0 a.e. on (0, +∞). For instance, all the functions F (u) = u n with n ∈ N * are admissible non-linearities. We construct global classical solutions starting from smooth positive data, and global weak solutions starting from positive data in L ∞ . We show that any weak solution is instantaneously regularized into C ∞ . We also describe the long-time asymptotics of all solutions. Our methods follow several recent advances in the regularity theory of parabolic integro-differential equations, in particular .

This paper is concerned with the study of a nonlinear non-local equation that has a commutator structure. The equation reads ∂t u−F (u) (−∆)u+ (−∆)(uF (u)) = 0, x ∈T , with s ∈ (0,1]. We are interested in solutions stemming from periodic positive bounded initial data. The given function F ∈C ∞(R+) must satisfy F ′ > 0 a.e. on (0,+∞). For instance, all the functions F (u) = u with n ∈N∗ are admissible non-linearities. We construct global classical solutions starting from smooth positive data, and global weak solutions starting from positive data in L∞. We show that any weak solution is instantaneously regularized into C ∞. We also describe the long-time asymptotics of all solutions. Our methods follow several recent advances in the regularity theory of parabolic integro-differential equations, in particular [19, 17]. 2010 Mathematics Subject Classification: 35B40; 35D30; 47G20.

We compare the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF), and particle filter (PF) for the angle-only filtering problem in 3D using bearing and elevation measurements from a single maneuvering sensor. These nonlinear filtering algorithms use discrete-time dynamic and measurement models. Two types of coordinate systems are considered, Cartesian coordinates and modified spherical coordinates (MSC) for the relative state vector. The paper presents new algorithms using the UKF and PF with the MSC. We also present an improved filter initialization algorithm. Numerical results from Monte Carlo simulations show that the EKF-MSC and UKF-MSC have the best state estimation accuracy among all nonlinear filters considered and have comparable accuracy with modest computational cost.

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In this article, we establish in the radial framework the $H^1$-scattering for the critical 2-D nonlinear Schr\"odinger equation with exponential growth. Our strategy relies on both the a priori estimate derived in \cite{CGT, PV} and the characterization of the lack of compactness of the Sobolev embedding of $H_{rad}^1(\R^2)$ into the critical Orlicz space ${\cL}(\R^2)$ settled in \cite{BMM}. The radial setting, and particularly the fact that we deal with bounded functions far away from the origin, occurs in a crucial way in our approach.

Estimations de dispersion et de Strichartz dans un domaine cylindrique convexe: Dans ce travail, nous allons établir des estimations de dispersion et des applications aux inégalités de Strichartz pour les solutions de l'équation des ondes dans un domaine cylindrique convexe Ω ⊂ R 3 à bord C ∞ , ∂Ω = ∅. Les estimations de dispersion sont classiquement utilisées pour prouver les estimations de Strichartz. Dans un domaine Ω général, des estimations de Strichartz ont été démontrées par Blair, Smith, Sogge . Des estimations optimales ont été prouvées dans lorsque Ω est strictement convexe. Le cas des domaines cylindriques que nous considérons ici généralise les resultats de dans le cas où la courbure positive dépend de l'angle d'incidence et s'annule dans certaines directions.

We consider the wave equation on Riemannian symmetric spaces of the noncompact type. We prove that the solutions of the homogeneous equation have dispersion properties and we deduce Strichartz-type estimates for these solutions. We use these estimates to treat nonlinear equations with power type. As a byproduct, we prove the global well-posedness for small energy.

Accurate generator modeling allows for more precise calculation of power system control and stability limits. In this paper a procedure using a set of measured data from Standstill Frequency Response (SSFR) test on Montazer-Ghaem gas power plant’s synchronous generator is used to obtain synchronous machine parameters. A novel approach is used to find d-axis which is different from standard SSFR scheme which can save the time in doing SSFR tests. Hook-Jeeves method is used for optimization purpose. The test procedure and identification results are reported.

accurate generator modeling allows for more precise calculation of power system control and stability limits. In this paper, a procedure using a set of measured data from Standstill Frequency Response (SSFR) test on MontazerGhaem gas power plant's synchronous generator is used to obtain dynamic parameters of the machine. A novel approach is used to find d-axis which is different from standard SSFR scheme which can save the time in performing SSFR tests. Hook-Jeeves optimization method is used for parameter estimation purpose. The test procedure and identification results are reported.

Accurate generator modeling allows for more precise calculation of power system control and stability limits. In this paper a procedure using a set of measured data from Standstill Frequency Response (SSFR) test on MontazerGhaem gas power plant's synchronous generator is used to obtain synchronous machine. A novel approach is used to find d-axis which is different from standard SSFR scheme which can save the time in doing SSFR tests. Hook-Jeeves method is used for optimization purpose. The test procedure and identification results are reported.

This paper presents a novel training method for estimating the parameters of retina models, such as integrateand-fire or Poisson-based. The presented models are constructed using a set of linear and nonlinear filters, described by basis functions and Taylor polynomials, respectively. This approach allows for the identification of a set of features that can be used for reproducing retina responses. By using the Bayesian-Laplace feature selection algorithm herein proposed, an efficient model with a reduced set of parameters is achieved. Experimental results show that the proposed algorithm is able to remove non-important features while still accurately reproducing retina responses. These results also show that the integrate-and-fire model is able to mimic the retina visual processing system using less parameters than the Poisson-based model.

This work studies the direct and inverse fixed energy scattering problem for the two-dimensional Schrödinger equation with rather general nonlinear index of refraction. In particular, using the Born approximation we prove that all singularities of the unknown compactly supported potential from L 2 space can be obtained uniquely by the scattering data with fixed positive energy. The proof is based on the new estimates for the Faddeev Green's function in L ∞ (R 2 ) space.

In this paper, a new structured approach for obtaining uniformly best non-Bayesian biased estimators, which attain minimum-mean-square-error performance at any point in the parameter space, is established. We show that if a uniformly best biased (UBB) estimator exists, then it is unique, and it can be directly obtained from any locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived. It is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and its closed-form expression is obtained. The proposed approach is exemplified in two nonlinear estimation problems, where uniformly minimum-variance-unbiased estimators do not exist. In the considered examples, we show that the UBB estimators outperform the corresponding maximum-likelihood estimators in the MSE sense. Index Terms-Locally best biased (LBB) estimators, minimummean-square-error (MMSE), non-Bayesian theory, parameter estimation, uniformly best biased (UBB) estimators. , is a branch of statistical mathematics, signal processing and information theory, which deals with estimating a set of underlying parameters based on measured data. This problem arises in many application areas, such as astronomy, biomedicine, communications, economics, image analysis, seismology, and speech analysis. There are three main categories of estimators: 1) non-Bayesian estimators, for cases where the parameters of interest are deterministic, 2) Bayesian estimators, for cases where the unknown parameters are random, and 3) hybrid estimators, for cases where the observation model contains deterministic and random parameters. Derivation of uniformly best non-Bayesian estimators, which attain minimum-mean-square-error (MMSE) performance at any point in the parameter space, is a fundamental problem in estimation theory. In similar to the Bayesian case, unconstrained minimization of the mean-square-error (MSE) is apparently a straightforward approach for obtaining such estimators. However, since in the non-Bayesian case the MSE is a function of the parameter to be estimated, then this approach yields the "trivial" estimator, which makes it inappropriate for this task.

This paper discusses estimation and guidance strategies for vision-based target tracking. Specific applications include formation control of multiple unmanned aerial vehicles (UAVs) and air-to-air refueling. We assume that no information is communicated between the aircraft, and only passive 2-D vision information is available to maintain formation. To improve the robustness of the estimation process with respect to unknown target aircraft acceleration, the nonlinear estimator (EKF) is augmented with an adaptive neural network (NN). The guidance strategy involves augmenting the inverting solution of nonlinear lineof-sight (LOS) range kinematics with the output of an adaptive NN to compensate for target aircraft LOS velocity. Simulation results are presented that illustrate the various approaches.

Many applications in science involve finding estimates of unobserved variables from observed data, by combining model predictions with observations. The sequential Monte Carlo (SMC) is a well‐established technique for estimating the distribution of unobserved variables that are conditional on current observations. While the SMC is very successful at estimating the first central moments, estimating the extreme quantiles of a distribution via the current SMC methods is computationally very expensive. The purpose of this paper is to develop a new framework using probability distortion. We use an SMC with distorted weights in order to make computationally efficient inferences about tail probabilities of future interest rates using the Cox–Ingersoll–Ross (CIR) model, as well as with an observed yield curve. We show that the proposed method yields acceptable estimates about tail quantiles at a fraction of the computational cost of the full Monte Carlo.

A n o vel model-based pose estimation algorithm is presented which estimates the motion of a three-dimensional object from an image sequence. The nonlinear estimation process within iteration is divided into two linear estimation stages, namely the depth approximation and the pose calculation. In the depth approximation stage, the depths of the feature points in three-dimensional space are estimated. In the pose calculation stage, the rotation and translation parameters between the estimated feature points and the model point set are calculated by a fast singular value decomposition method. The whole process is executed recursively until the result is stable. Since both stages can be solved e ciently, the computational cost is low. As a result, the algorithm is well-suited for real time computer vision applications. We demonstrate the capability o f t h i s algorithm by applying it to a real time head tracking problem. The results are satisfactory. keyword : Pose Estimation, singular value decomposition, real time vision and Human-computer Interface.

In this paper, a nonlinear estimation strategy for sensing the time-varying angular rate of a Z-axis MEMS gyroscope is presented. An off-line adaptive least-squares estimation strategy is first developed to accurately estimate the unknown model parameters. Both axes of a Z-axis MEMS gyroscope are then actively controlled utilizing an on-line controller/observer to facilitate time-varying angular rate sensing. The proposed nonlinear estimation strategy is developed based on a Lyapunov-based analysis, which proves that the time-varying angular rate experienced by the device can be estimated accurately. Two cases for angular rate are investigated which are time-varying and constant magnitudes. An adaptive controller/observer was also utilized for sensing the angular rate to investigate the performance of the proposed controller/observer. Representative numerical results are discussed to demonstrate the performance of the proposed nonlinear strategy in accurately sensing the applied angular rate. Overall, the proposed nonlinear controller/observer improves sensing the constant angular rate by 50% and the time-varying angular rate by 90% when compared with an adaptive controller/observer.

In this paper, a new strategy to cope with unmeasurable premise variables in observer design for Takagi-Sugeno (TS) models is proposed. The guiding principles are the immersion techniques and auxiliary dynamics generation, allowing to immerge a given TS system with unmeasured state dependent weighting functions into a larger TS system with weighting functions depending only on measured variables. This result relaxes the strong conditions used in the design of observers for TS systems with unmeasurable premise variables. An example is provided to illustrate the performances of the proposed approach.

The purchasing power parity puzzle, exchange rate disconnection to macroeconomic fundamentals and pricing to market are central issues of international macroeconomics. Recent research has suggested that these issues can be presented by nonlinear behaviour. In this dissertation, we examine and explain the nonlinearities in the form of regime switching behaviour in real exchange rate series, exchange rate and macroeconomic fundamentals relation and exchange rate pass-through into consumer and import prices. Overall, we find evidence that nonlinearities are important in analysing empirical exchange rate models. The dissertation consists of four self-contained empirical studies. In chapter 2 we examine whether the Markov switching models and exponential smooth transition autoregressive models can give any additional insights into real exchange rate behaviour for several OECD countries. The results show that there are long swings in the real exchange rate series, which can be characterize as a depreciation and an appreciation regime. These regimes are very persistent, although the processes are eventually mean reverting. We estimate a multivariate smooth transition autoregressive model for the euro/dollar exchange rate in chapter 3. The significant point of our analysis is the possibility that a nonlinear specification for the exchange rate series might reveal aspects of the exchange rate dynamics that cannot be picked up by linear models. We find that the euro/dollar exchange rate may display random walk or near random walk behaviour within a certain range but the ability of the exchange rate to wander without any bound is limited by long-term government bond interest rate differentials. In chapter 4 we examine nonlinear relationships between macroeconomic fundamentals and exchange rate for G-7 countries. We estimate a smooth transition error correction model that allows for parameter variation in the error correction form and interest rate differentials. The nonlinearity is determined by the inflation rate differentials between countries. We find significant error correction terms in monetary models. Our findings suggest the importance of nonlinear dynamics for examining deviations from the long-run equilibrium. We examine whether the degree of exchange rate pass-through is dependent on importing country inflation rate in chapter 5. Our model shows that import prices respond differently to exchange rate changes when we are in a high inflation regime compared to a low inflation regime. We also present empirical evidence by estimating pass-through elasticises for several OECD countries. We find that consumer prices are not very sensitive to exchange rate changes. For aggregate import prices, we find partial or full exchange rate pass-throughs. The tested nonlinear regime specific models proved appropriate for testing exchange rate dynamics for several currency pairs. Furthermore, we were able to present that macroeconomic fundamentals are important predictors of exchange rates.

The purchasing power parity puzzle, exchange rate disconnection to macroeconomic fundamentals and pricing to market are central issues of international macroeconomics. Recent research has suggested that these issues can be presented by nonlinear behaviour. In this dissertation, we examine and explain the nonlinearities in the form of regime switching behaviour in real exchange rate series, exchange rate and macroeconomic fundamentals relation and exchange rate pass-through into consumer and import prices. Overall, we find evidence that nonlinearities are important in analysing empirical exchange rate models. The dissertation consists of four self-contained empirical studies. In chapter 2 we examine whether the Markov switching models and exponential smooth transition autoregressive models can give any additional insights into real exchange rate behaviour for several OECD countries. The results show that there are long swings in the real exchange rate series, which can be characteriz...

This paper proposes a new approach to the analysis of the steady-state performance of constant modulus algorithms (CMA), which are among the most popular adaptive schemes for blind equalization. A major feature of the proposed feedback approach is that it bypasses the need for working directly with the weight error covariance matrix. In so doing, approximate expressions for the steady-state mean-square error of several CM algorithms are derived, including CMA2-2, CMA1-2, normalized CMA, and a new normalized CMA variant with less bias. A comparison among the various algorithms is also performed, along with several simulation results. The conclusions confirm the superior performance of CMA2-2.

Block diagram of an open-loop control system 1-2 Block diagram of a feedback control system 1-3 A representative learning control system 3-1 Block diagram of adaptive control algorithm 3-2 Block diagram of the iterated extended Kalman filter 4-1 Plots of ao, al and bo vs. Qp for Willscreek Basin 4-2 Estimation of time-invariant parameters by linear adaptive control approach 4-3 Estimate of direct runoff with and without control 4-4 Effect of adaptive estimation of model-error convariance matrix 4-5 Effect of rectification of nominal state 70 4-6 Estimation of time-invariant parameters by iterated extended Kalman filter 72

This paper concerns Gibbs measures ν for some nonlinear PDE over the D-torus T D. The Hamiltonian H = T D ∇u 2 − T D |u| p has canonical equations with solutions in Ω N = {u ∈ L 2 (T D) : |u| 2 ≤ N }. For D = 1 and 2 ≤ p < 6, Ω N supports the Gibbs measure ν(du) = Z −1 e −H(u) x∈T du(x) which is normalized and formally invariant under the flow generated by the PDE. The paper proves that (Ω N , • L 2 , ν) is a metric probability space of finite diameter that satisfies the logarithmic Sobolev inequalities for the periodic KdV , the focussing cubic nonlinear Schrödinger equation and the periodic Zakharov system. For suitable subset of Ω N , a logarithmic Sobolev inequality also holds in the critical case p = 6. For D = 2, the Gross-Piatevskii equation has H = T 2 ∇u 2 − T 2 (V * |u| 2)|u| 2 , for a suitable bounded interaction potential V and the Gibbs measure ν lies on a metric probability space (Ω, • H −s , ν) which satisfies LSI. In the above cases, (Ω, d, ν) is the limit in L 2 transportation distance of finite-dimensional (Ω n , • , ν n) given by Fourier sums.

Time-series segmentation algorithms, such as methods based on Principal Component Analysis (PCA) and fuzzy clustering, are based on input-output process data. However, historical process data alone may not be sufficient for the monitoring of process transitions. Hence, the key idea of this paper is to incorporate the first-principle model based state estimation into the segmentation algorithm to detect changes in the correlation among the state-variables. For this purpose, the homogeneity of the segments is measured using a PCA similarity factor calculated from the covariance matrices given by the state-estimation algorithm. The whole approach is applied to the monitoring of the industrial production of high-density polyethylene.

Time-series segmentation algorithms, such as methods based on Principal Component Analysis (PCA) and fuzzy clustering, are based on input-output process data. However, historical process data alone may not be sufficient for the monitoring of process transitions. Hence, the key idea of this paper is to incorporate the first-principle model based state estimation into the segmentation algorithm to detect changes in the correlation among the state-variables. For this purpose, the homogeneity of the segments is measured using a PCA similarity factor calculated from the covariance matrices given by the state-estimation algorithm. The whole approach is applied to the monitoring of the industrial production of high-density polyethylene.

We consider a system described by the Euler-Bernoulli beam equation. For stabilization, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the controller is a marginally stable positive real function which may contain poles on the imaginary axis. We then give various asymptotical and exponential stability results. We also consider the disturbance rejection problem.

For computing sampling variances of the Medical Expenditure Panel Survey (MEPS) Household Component estimates, the Taylor linearization method is generally used. The MEPS public use files include variance strata and cluster identifiers to facilitate variance computation using this method. Also a file containing a BRR replication structure (in the form of a set of half sample indicators) is also made available so that the users can form BRR replicate weights from the final MEPS weight to compute variances of MEPS estimates using either BRR or Fay's modified BRR (Fay 1989) methods. These replicate weights are useful to compute variances of complex non-linear estimators for which a Taylor linear form is not easy to derive and not available in commonly used software. However, the BRR replicates derived from the final weight represent a shortcut approach because the replicates are not produced starting with the base weight and all adjustments made in different stages of weighting are not applied independently in each replicate. So the variances computed using the one-step BRR do not capture the effects of all weighting adjustments. The Taylor approach, as implemented in most software, also does not fully capture the effects of different weighting adjustments. Of particular interest here is the effect of adjustments using external control totals which are expected to reduce the variance. To assess the effects of these adjustments on the variances of MEPS estimates, a set of proper Fay's BRR replicates were formed starting with the base weights and independently applying all weighting adjustments to each of these replicates. Variances of selected MEPS estimates were then computed from these properly created replicate weights and compared with those of the linearization method. This report presents the results of this comparison which shows that variance estimates are generally lower under the BRR method indicating that the net impact of various weighting adjustments on variance is generally downward. In most cases, relative standard errors based on BRR are at least 5-10% lower than that of Taylor approach. That means the variance estimates produced by the current recommended method are conservative and can be considered as compensating for the imputation variance and the variability in the control totals, which are unaccounted for under both methods of variance estimation.

The Medical Expenditure Panel Survey (MEPS) weighting procedures include several rounds of nonresponse and poststratification/raking adjustments. Although poststratifications/rakings using external control totals are generally applied for reducing bias due to nonresponse and coverage, an added benefit of these adjustments is variance reduction. The survey variances of control totals used in adjustments become zero while the variances of other estimates that are correlated to these totals decrease depending on the extent of correlation. However, this reduction in variance due to poststratification/raking is not captured in computing the variances of MEPS estimates. The Taylor linearization method is generally used for estimating variances in MEPS which is unable to account for the effect of these adjustments. A shortcut replication approach is also used sometimes for computing variances of MEPS estimates. Based on a published BRR replication structure, the users can form BRR or Fay’s...

For computing sampling variances of the Medical Expenditure Panel Survey (MEPS) Household Component estimates, the Taylor linearization method is generally used. The MEPS public use files include variance strata and cluster identifiers to facilitate variance computation using this method. Also a file containing a BRR replication structure (in the form of a set of half sample indicators) is also made available so that the users can form BRR replicate weights from the final MEPS weight to compute variances of MEPS estimates using either BRR or Fay’s modified BRR (Fay 1989) methods. These replicate weights are useful to compute variances of complex non-linear estimators for which a Taylor linear form is not easy to derive and not available in commonly used software. However, the BRR replicates derived from the final weight represent a shortcut approach because the replicates are not produced starting with the base weight and all adjustments made in different stages of weighting are not...

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels satisfy suitable and explicit growth conditions, given in terms of their distribution functions; natural conditions for sharpness are also given. Most of the known results about Moser-Trudinger inequalities can be easily adapted to our unified scheme. We give some new applications of our theorems, including: sharp higher order Moser-Trudinger trace inequalities, sharp Adams/Moser-Trudinger inequalities for general elliptic differential operators (scalar and vector-valued), for sums of weighted potentials, and for operators in the CR setting.

A novel on-line adaptive optimization algorithm is developed and applied to continuous biological reactors. The algorithm makes use of a simple nonlinear estimation model that relates either the cell-mass productivity or the cell-mass concentration to the dilution rate. On-line estimation is used to recursively identify the parameters in the nonlinear process model and to periodically calculate and steer the bioreactor to the dilution rate that yields optimum cell-mass productivity. Thus, the algorithm does not require an accurate process model, locates the optimum dilution rate online, and maintains the bioreactors at this optimum condition at all times. The features of the proposed new algorithm are compared with those of other adaptive optimization techniques presented in the literature [1-5]. A detailed simulation study using three different microbial system models [3, 6-7] was conducted to illustrate the performance of the optimization algorithm.

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to characterize the non-i.i.d. block-sparse signals commonly encountered in practice. The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal using the steepest-ascent based Expectation-Maximization (EM), and optimally selects the nonzero elements of the block-sparse signal by adaptive thresholding. The global convergence of Block-IBA is analyzed and proved, and the effectiveness of Block-IBA is demonstrated by numerical experiments and simulations on synthetic and real-life data.

The biological treatment is the most complex step in removing organic and inorganic pollutants from wastewaters, being very sensitive to input-flow oscillations, operating conditions, and biomass evolution. Sudden increases in substrate concentration or some inhibitory substances, deterioration of the biomass, or few observed species, all of these lead to a difficult process modelling and need repeated biokinetics identification for each waste and biomass type. However, the bioprocess numerical analysis is crucial for obtaining significant improvements in the wastewater treatment (WWT) plant performances and safety indices even under imperfect data. The paper exemplifies an advanced route to quickly on-line identify the biodegradation characteristics of new substrates processed by a series of perfectly mixed aeration basins with biomass recycle. The Monod kinetics is recursively identified by using the available collection of plant previous transient operating data and a robust shortcut estimator (MIP). The approximate solution is periodically refined with an exact nonlinear estimator (NLS), checked for consistency and significance versus prior information, and stored in databanks.