Full-rank Model Research Articles

Online Decoupled Multi-Parameter Identification of Dual Three-Phase IPMSM Under Position-Offset and HF Signal Injection

Accurate and updated knowledge of electrical parameters is of great importance for high-performance control of motor drives. However, the common challenging issue in existing identification methods is to construct a full-rank model with low parameter coupling. In this paper, an online multi-parameter identification method has been proposed for the dual three-phase interior PMSM (IPMSM) drives with position-offset and high-frequency square-wave voltage injection. Thanking to the simplified amplitude extraction process, the inductance parameters can be conveniently calculated from HF current amplitude under HF square-wave voltage injection. On this basis, the position-offset injection based model has been developed for the individual identification of the rotor flux linkage. Finally, the resistance can be estimated according to the steady-state voltage equations in harmonic subspace with the aid of known inductance. With the constructed multi-source identification models, the rank-deficient problem of multi-parameter estimation can be solved. Furthermore, the additional control dimensions of dual three-phase IPMSM have been utilized to avoid the torque disturbance from position-offset injection. The experimental results are presented to verify performance of the proposed method.

D-optimal designs for a two-dimensional polynomial model

The influence of an affine transformation of the design space on the number of support points in the D-optimal design has been studied for a two-dimensional polynomial regression model. For a full rank model of degree n, a result was obtained that determines the structure of the D-optimal plan. It is proven that for a region of design space that is symmetric about zero, the optimal plan is symmetric as well. This result allows for a significant reduction in the dimensionality of the optimization problem and forms the basis of an algorithm developed by the author for finding D-optimal plans for models of incomplete rank in nonsymmetric design regions. The D-efficiency of designs concentrated at equidistant points was investigated.

Ambiguity-Fixing in Frequency-Varying Carrier Phase Measurements: Global Navigation Satellite System and Terrestrial Examples

<h3>Abstract</h3> Carrier phase signals are considered among the key observations in global navigation satellite systems (GNSSs) and several other high-precision interferometric measurement systems. However, these ultra-precise measurements are not fully exploited when the integerness of their inherent ambiguities is discarded during the estimation process. Provided that the integer-estimable functions of their phase ambiguities are properly identified, integer ambiguity resolution (IAR) can be utilized to benefit their parameter solutions. For the GNSS code division multiple access systems with transmitters that broadcast carrier phase signals on identical frequencies, these integer-estimable functions have been characterized and are well-known as double differenced ambiguities. However, this is not the case with “frequency-varying” carrier phase signals that are broadcast by GLONASS satellites, Low-Earth-Orbiting communication satellites, or cellular long-term evolution (LTE) transmitters. This study aims to present full-rank models that can be used to identify integer-estimable ambiguity functions, thereby bringing the observation equations of frequency-varying carrier phase measurements into an IAR-applicable form. Our analytical results are supported by several numerical examples, including GNSS and terrestrial-based IAR as well as a new set of “inter-frequency” integer ambiguities that this study discovers in Galileo multi-frequency carrier phase signals.

An alternative look at the linear regression model

An alternative look at the linear regression model is taken by proposing an original treatment of a full column rank model (design) matrix. In such a situation, the Moore–Penrose inverse of the matrix can be obtained by utilizing a particular formula which is applicable solely when a matrix to be inverted can be columnwise partitioned into two matrices of disjoint ranges. It turns out that this approach, besides simplifying derivations, provides a novel insight into some of the notions involved in the model and reduces computational costs needed to obtain sought estimators. The paper contains also a numerical example based on astronomical observations of the localization of Polaris, demonstrating usefulness of the proposed approach.

Tightly combined triple-frequency GPS and BDS for rapid wide-lane RTK positioning with consideration of carrier-phase differential inter-system bias

Multi-frequency signals have been accessible for most Global Navigation Satellite Systems . Existing studies have verified that using multi-frequency extra-wide-lane and wide-lane observations can realize decimeter, sub-decimeter and even centimeter rapid positioning. In this paper, a tightly combined wide-lane real-time kinematic positioning method using triple-frequency GPS and BDS is proposed. The differential inter-system bias is taken into consideration so that an inter-system differencing model is formed. Due to the influence of different frequencies between GPS and BDS, the double-difference wide-lane ambiguity between GPS and BDS reference satellites and the single-difference ambiguity of the BDS reference satellite are estimated jointly with the wide-lane differential inter-system bias. Thus, a full-rank model can be obtained without any external calibration. Using the stability of wide-lane differential inter-system bias in the estimation from epoch to epoch, redundant observations can be introduced, therefore the strength of the positioning model can be enhanced. Positioning performance under simulated obstructed environments is evaluated. The results show that the inter-system model can effectively improve the positioning compared with the conventional intra-system model for the severely obstructed situations.

On the problem of factor significance in the models of variance analysis

In analysis of variance models the hypotheses about factor significance form comparisons of the levels of the same factor. If there are no reasons according to the criterion for testing such hypotheses to reject the hypothesis about the equality of some levels of factors, then these levels are considered significantly different. The goal of the article is to find out whether the levels of factors have a significant effect on the response variable. Linear models of analysis of variance (AV) under conditions of complete and incomplete factor design are considered. As a computational scheme for processing the AV models the procedure for transforming incomplete rank models into a full rank models and representing the space of linear estimated forms as a direct sum of orthogonal subspaces corresponding to each of the qualitative facts of the model has been developed. Choosing different groups of linearly independent columns in the initial observation matrix and orthogonalizing this system of vectors (as columns of the matrix) we can obtain various orthogonal bases for the space of linear forms under estimation. Projections of the response vector to the vectors of orthogonal basis corresponding to the same basis determine the contribution of this factor to the total sum of squares obtained as a result of the response projection to the entire space of linear forms being estimated. With different orthogonal bases of the space of linear estimated forms, these contributions of factors change. Under conditions of incomplete factor design, one can distinguish an orthogonal basis of the space of linear estimated forms which provides the greatest significance of any comparison of one of the factors, and, consequently, of the factor itself. This allows determination of the best (in a certain sense) experimental design which ensures the greatest significance of the factors selected. To prove the results obtained the method of ranking factors LASSO was used.

PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK

PPP-RTK has the potential of benefiting enormously from the integration of multiple GNSS/RNSS systems. However, since unaccounted inter-system biases (ISBs) have a direct impact on the integer ambiguity resolution performance, the PPP-RTK network and user models need to be flexible enough to accommodate the occurrence of system-specific receiver biases. In this contribution we present such undifferenced, multi-system PPP-RTK full-rank models for both network and users. By an application of $$\mathcal {S}$$ -system theory, the multi-system estimable parameters are presented, thereby identifying how each of the three PPP-RTK components are affected by the presence of the system-specific biases. As a result different scenarios are described of how these biases can be taken into account. To have users benefit the most, we propose the construction of an ISB look-up table. It allows users to search the table for a network receiver of their own type and select the corresponding ISBs, thus effectively realizing their own ISB-corrected user model. By applying such corrections, the user model is strengthened and the number of integer-estimable user ambiguities is maximized.

Re‐evaluating the role of the Mahalanobis distance measure

AbstractIt is shown that the sum of squares of the standardised scores of all non‐zero principal components (PCs) equals the squared Mahalanobis distance. A new distance measure, the reduced Mahalanobis distance, is explored in which the number of PCs retained is less than the full rank model. It is illustrated by both one‐class and two‐class classifiers. Linear discriminant analysis can be employed as a soft model, and principal component analysis using the pooled variance‐covariance matrix is introduced as an intermediate view between conjoint and disjoint models allowing linear discriminant analysis to be used on these reduced rank models. By choosing the most discriminatory PCs, it can be shown that the reduced Mahalanobis distance has superior performance over the full rank model for discriminating via soft models. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Under-determined reverberant audio source separation using Bayesian Non-negative Matrix Factorization

In this paper, we address the task of audio source separation for a stereo reverberant mixture of audio signals. We use a full-rank model for the spatial covariance matrix. Bayesian Non-negative Matrix Factorization(NMF)frameworks are introduced for factorizing the time-frequency variance matrix of each source into basis components and time activations. We also propose to incorporate the temporal dependencies in the Bayesian model through (1) recursively updating the prior hyperparameters or (2) applying a prior with Markov chain structure to favor the smoothness of the solution and we compare the performance of these two schemes. The EM algorithm is applied to derive the update relations of the unknown parameters. The separation performance improvement over the non-Bayesian standard NMF method as well as the conventional full-rank unconstrained method are investigated by calculating objective separation evaluation metrics.

Principal component and factor analytic models in international sire evaluation.

BackgroundInterbull is a non-profit organization that provides internationally comparable breeding values for globalized dairy cattle breeding programmes. Due to different trait definitions and models for genetic evaluation between countries, each biological trait is treated as a different trait in each of the participating countries. This yields a genetic covariance matrix of dimension equal to the number of countries which typically involves high genetic correlations between countries. This gives rise to several problems such as over-parameterized models and increased sampling variances, if genetic (co)variance matrices are considered to be unstructured.MethodsPrincipal component (PC) and factor analytic (FA) models allow highly parsimonious representations of the (co)variance matrix compared to the standard multi-trait model and have, therefore, attracted considerable interest for their potential to ease the burden of the estimation process for multiple-trait across country evaluation (MACE). This study evaluated the utility of PC and FA models to estimate variance components and to predict breeding values for MACE for protein yield. This was tested using a dataset comprising Holstein bull evaluations obtained in 2007 from 25 countries.ResultsIn total, 19 principal components or nine factors were needed to explain the genetic variation in the test dataset. Estimates of the genetic parameters under the optimal fit were almost identical for the two approaches. Furthermore, the results were in a good agreement with those obtained from the full rank model and with those provided by Interbull. The estimation time was shortest for models fitting the optimal number of parameters and prolonged when under- or over-parameterized models were applied. Correlations between estimated breeding values (EBV) from the PC19 and PC25 were unity. With few exceptions, correlations between EBV obtained using FA and PC approaches under the optimal fit were ≥ 0.99. For both approaches, EBV correlations decreased when the optimal model and models fitting too few parameters were compared.ConclusionsGenetic parameters from the PC and FA approaches were very similar when the optimal number of principal components or factors was fitted. Over-fitting increased estimation time and standard errors of the estimates but did not affect the estimates of genetic correlations or the predictions of breeding values, whereas fitting too few parameters affected bull rankings in different countries.

Estimating intrinsic dimensionality using the multi-criteria decision weighted model and the average standard estimator

Information retrieval today is much more challenging than traditional small document retrieval. The main difference is the importance of correlations between related concepts in complex data structures. As collections of data grow and contain more entries, they require more complex relationships, links, and groupings between individual entries. This paper introduces two novel methods for estimating data intrinsic dimensionality based on the singular value decomposition (SVD). The average standard estimator (ASE) and the multi-criteria decision weighted model are used to estimate matrix intrinsic dimensionality for large document collections. The multi-criteria weighted model calculates the sum of weighted values of matrix dimensions which demonstrated best performance using all possible dimensions [1]. ASE estimates the level of significance for singular values that resulted from the singular value decomposition. ASE assumes that those variables with deep relations have sufficient correlation and that only those relationships with high singular values are significant and should be maintained [1]. Experimental results indicate that ASE improves precision and relative relevance for MEDLINE document collection by 10.2% and 12.9% respectively compared to the percentage of variance dimensionality estimation. Results based on testing three document collections over all possible dimensions using selected performance measures indicate that ASE improved matrix intrinsic dimensionality estimation by including the effect of both singular values magnitude of decrease and random noise distracters. The multi-criteria weighted model with dimensionality reduction provides a more efficient implementation for information retrieval than using a full rank model.

On InSAR Ambiguity Resolution For Deformation Monitoring

On InSAR Ambiguity Resolution For Deformation Monitoring

Reduced-rank hazard regression for modelling non-proportional hazards

The Cox proportional hazards model is the most common method to analyse survival data. However, the proportional hazards assumption might not hold. The natural extension of the Cox model is to introduce time-varying effects of the covariates. For some covariates such as (surgical)treatment non-proportionality could be expected beforehand. For some other covariates the non-proportionality only becomes apparent if the follow-up is long enough. It is often observed that all covariates show similar decaying effects over time. Such behaviour could be explained by the popular (gamma-) frailty model. However, the (marginal) effects of covariates in frailty models are not easy to interpret. In this paper we propose the reduced-rank model for time-varying effects of covariates. Starting point is a Cox model with p covariates and time-varying effects modelled by q time functions (constant included), leading to a pxq structure matrix that contains the regression coefficients for all covariate by time function interactions. By reducing the rank of this structure matrix a whole range of models is introduced, from the very flexible full-rank model (identical to a Cox model with time-varying effects) to the very rigid rank one model that mimics the structure of a gamma-frailty model, but is easier to interpret. We illustrate these models with an application to ovarian cancer patients.

A generalization of weighted subspace fitting to full-rank models

The idea of subspace fitting provides a popular framework for different applications of parameter estimation and system identification. Previously, some algorithms have been suggested based on similar ideas, for a sensor array processing problem where the underlying data model is not low rank. We show that two of these algorithms (DSPE and DISPARE) fail to give consistent estimates and introduce a general class of subspace fitting-like algorithms for consistent estimation of parameters from a possibly full-rank data model. The asymptotic performance is analyzed, and an optimally weighted algorithm is derived. The result gives a lower bound on the estimation performance for any estimator based on a low-rank approximation of the linear space spanned by the sample data. We show that in general, for full-rank data models, no subspace-based method can reach the Cramer-Rao lower bound (CRB).

Linear Models: A Mean Model Approach

Linear Algebra and Related Introductory Topics: Elementary Matrix Concepts. Kronecker Products. Random Vectors. Multivariate Normal Distribution: Multivariate Normal Distribution Function. Conditional Distributionsof Multivariate Normal Vectors. Distributions of Certain Quadratic Forms. Distributions of Quadratic Forms: Quadratic Forms of Normal Random Vectors. Independence. t and F Distributions. Bhats Lemma. Complete, Balanced Factorial Experiments: Models That Admit Restrictions (Finite Models). Models That Do Not Admit Restrictions (Infinite Models). Sum of Squares and Covariance Matrix Algorithms. Expected Mean Squares. Algorithm Applications. Least Squares Regression: Ordinary Least SquaresEstimation. Best Linear Unbiased Estimators. ANOVA Table for the Ordinary Least Squares Regression Function. Weighted Least Squares Regression. Lack of Fit Test. Partitioning the Sum of Squares Regression. The Model Y = X( + E in Complete, BalancedFactorials. Maximum Likelihood Estimation and Related Topics: Maximum Likelihood Estimators (MLEs) of ( and ( 2. Invariance Property, Sufficiency and Completeness. ANOVA Methods for Finding Maximum Likelihood Estimators. The Likelihood Ratio Test for H( = h. Confidence Bands on Linear Combinations of (. Unbalanced Designs and Missing Data: Replication Matrices. Pattern Matrices and Missing Data. Using Replication and Pattern Matrices Together. Balanced Incomplete Block Designs: General Balanced Incomplete Block Design. Analysis of the General Case. Matrix Derivations of Kempthornes Inter- and Intra-Block Treatment Difference Estimators. Less Than Full Rank Models: Model Assumptions and Examples. The Mean Model Solution.Mean Model Analysis When cov(E) = ( 2I n. Estimable Functions. Mean Model Analysis When cov(E) = ( 2V. The General Mixed Model: The Mixed Model Structure and Assumptions. Random Portion Analysis: Type I Sumof Squares Method. Random Portion Analysis: Restricted Maximum Likelihood Method. Random Portion Analysis: A Numerical Example. Fixed Portion Analysis. Fixed Portion Analysis: A Numerical Example. Appendixes. References. Subject Index.

HEDGING INTEREST RATE RISK UNDER TERM STRUCTURE EFFECTS: AN APPLICATION TO FINANCIAL INSTITUTIONS

AbstractIn this paper we investigate the use of the structured full rank model for hedging the balance sheet of a financial institution. Simulation results suggest that the optimal hedge is insensitive to changes in parameter estimates. In addition, we hedge a portfolio of Treasury bills using both the full information covariance matrix and the structured covariance matrix. We then contrast these results with those obtained from a duration‐based model. Empirical results suggest that the structured full rank model is generally more effective in hedging applications than either the full information model or duration‐based model.

Hedging Interest Rate Risk with Futures Portfolios Under Full-Rank Assumptions

A spot portfolio of rate-sensitive assets can be hedged by a portfolio of interest-sensitive futures contracts. The hedge ratios of minimum-variance portfolios are unique when the fixed cash flows of underlying instruments are linearly independent and when the covari? ance matrix of unexpected changes in spot rates over the term of the cash flows is of full rank. Hilliard's (1984) full-rank model has produced smaller portfolio variances than a duration model in a short-term hedging context. However, the methodology typically re? quires extensive econometric analysis. This paper develops a structured covariance matrix of full rank that requires only one parameter estimate. Hedging examples are provided.

An example of universal optimality in a full-rank model

If in the usual model for repeated measurements designs no period effect is present, then the information matrix for the estimation of residual effects no longer has row- and column-sums zero (see Cheng and Wu 1980, 1983). This means that the usual criterion for universal optimality cannot be applied.

A reduced-rank prediction model of stream-channel size response to traditional agricultural land-use practices in southwestern Nigeria

Stream-channel morphologic responses are found to be related to different parameters measuring traditional agricultural land-use patterns and practices in 50 small headwater basins in southwest Nigeria. The problem of intercorrelations among these parameters made it initially difficult to establish their precise channel enlargement effects and to calibrate an impact prediction model. Through factor analysis of the 22 land-use and morphometric parameters, six factors identified as measures of traditional land-use practice, farm size, planting activities, shortened fallow, relief and overland flow, were found to account for 86% of the variance in the data. The factor-defining variables are length of cropping period, areas in short fallow, farm-plot size, length of farm preparation, relief ratio and overland flow. In a multiple regression analysis, only the first three variables were found to be statistically significant in explaining stream-channel morphologic responses. Thus, areas in short fallows, average farm size and length of cropping period adequately described those aspects of the traditional farming practices that affect basin hydrologic and channel responses. Since these variables were orthogonally derived, they formed the basis for the evaluation of the channel impact status of traditional land-use activities. The duplication of information and effects in the original 22-variable full-rank model were removed while utilizing the three-factor reduced model.

A note on the universal optimality criterion for full rank models

The aim of this note is to suggest a revised formulation of the universal optimality criterion for full rank models as stated in Kiefer (1975). We have presented the relevant results with indications of some possible applications.