Least Squares

The design of flood control structures requires rainfall intensity estimation for design discharge computation. To make the rainfall intensity values easily available in Warri, Delta state of Nigeria, this research developed rainfall models. Rainfall intensity data were collected and analysed. The statistical method of least squares was used to fit the curves generated. Intensityduration models were developed and presented in graphical curves. Quotient method was adopted in the modeling. Another set of models developed are intensity-frequency models which gave correlation coefficient values of between 0.8694 and 0.9689 showing good fit. These models were used to produce rainfall intensity values for durations of 30, 60, 90 and 120 minutes and some return periods between 5 years and 30 years.

An extended least-squares method is described which allows us to model the location and scale of a process parametrically without specifying any parametric form for the distribution of the errors. The degree of the associated polynomials is chosen using a step-down method on a table of p-values. A pseudo-likelihood ratio test is given. The concepts of upper and lower return levels are extended to non-stationary series. The method is applied to annual means and extremes of Auckland temperatures. Evidence is found that the mean is changing non-linearly and the variance is also changing for all three series.

1] We present a new statistical method to construct a model for the chemical composition of Earth's primitive mantle along with its variance. Earth's primitive mantle is located on the melting trend exhibited by the global compilation of mantle peridotites, using cosmochemical constraints on the relative abundances of refractory lithophile elements (RLE). This so-called pyrolite approach involves the least amount of assumptions, thereby being probably most satisfactory compared to other approaches. Its previous implementations, however, suffer from questionable statistical treatment of noisy geochemical data, leaving the uncertainty of model composition poorly quantified. In order to properly take into account how scatters in peridotite data affect this geochemical inference, we combine the following statistical techniques: (1) modeling a nonlinear melting trend in the multidimensional compositional space through the principal component analysis, (2) determining the primitive mantle composition on the melting trend by simultaneously imposing all of cosmochemical constraints with least squares, and (3) mapping scatters in original data into the variance of the final model through the bootstrap resampling technique. Whereas our model is similar to previous models in terms of Mg, Si, and Fe abundances, the RLE contents are at $2.16 ± 0.37 times the CI chondrite concentration, which is lower than most of previous estimates. The new model is depleted by >20% in a number of incompatible elements including heat-producing elements, U, Th, and K, and this depleted nature is further amplified (up to 60%) in terms of predicted composition for the present-day mantle.

The Illinois State Water Survey performed a study to assess the streamgaging network in the State of Illinois. One of the important aspects of the study was to assess the regional value of each station through an assessment of the information transfer among gaging records for low, average, and high flow conditions. This analysis was performed for the main hydrologic regions in the State, and the stations were initially evaluated using a new approach based on entropy analysis. To determine the regional value of each station within a region, several information parameters, including total net information, were defined based on entropy. Stations were ranked based on the total net information. For comparison, the regional value of the same stations was assessed using the generalized least square regression (GLS) method, developed by the US Geological Survey. Finally, a hybrid combination of GLS and entropy was created by including a function of the negative net information as a penalty function in the GLS. The weights of the combined model were determined to maximize the average correlation with the results of GLS and entropy. The entropy and GLS methods were evaluated using the high-flow data from southern Illinois stations. The combined method was compared with the entropy and GLS approaches using the high-flow data from eastern Illinois stations.

1] The goal of this study is to quantify the world's wind power potential for the first time from data. Wind speeds are calculated at 80 m, the hub height of modern, 77-m diameter, 1500 kW turbines. Since relatively few observations are available at 80 m, the Least Square extrapolation technique is utilized and revised here to obtain estimates of wind speeds at 80 m given observed wind speeds at 10 m (widely available) and a network of sounding stations. Tower data from the Kennedy Space Center (Florida) were used to validate the results. Globally, $13% of all reporting stations experience annual mean wind speeds ! 6.9 m/s at 80 m (i.e., wind power class 3 or greater) and can therefore be considered suitable for low-cost wind power generation. This estimate is believed to be conservative. Of all continents, North America has the largest number of stations in class ! 3 (453), and Antarctica has the largest percent (60%). Areas with great potential are found in northern Europe along the North Sea, the southern tip of the South American continent, the island of Tasmania in Australia, the Great Lakes region, and the northeastern and northwestern coasts of North America. The global average 10-m wind speed over the ocean from measurements is 6.64 m/s (class 6); that over land is 3.28 m/s (class 1). The calculated 80-m values are 8.60 m/s (class 6) and 4.54 m/s (class 1) over ocean and land, respectively. Over land, daytime 80-m wind speed averages obtained from soundings (4.96 m/s) are slightly larger than nighttime ones (4.85 m/s); nighttime wind speeds increase, on average, above daytime speeds above 120 m. Assuming that statistics generated from all stations analyzed here are representative of the global distribution of winds, global wind power generated at locations with mean annual wind speeds ! 6.9 m/s at 80 m is found to be $72 TW ($54,000 Mtoe) for the year 2000. Even if only $20% of this power could be captured, it could satisfy 100% of the world's energy demand for all purposes (6995-10177 Mtoe) and over seven times the world's electricity needs (1.6-1.8 TW). Several practical barriers need to be overcome to fully realize this potential.

Soil Organic Carbon (SOC) is one of the key soil properties, but the large spatial variation makes continuous mapping a complex task. Imaging spectroscopy has proven to be an useful technique for mapping of soil properties, but the applicability decreases rapidly when fields are partially covered with vegetation. In this paper we show that with only a few percent fractional maize cover the accuracy of a Partial Least Square Regression (PLSR) based SOC prediction model drops dramatically. However, this problem can be solved with the use of spectral unmixing techniques. First, the fractional maize cover is determined with linear spectral unmixing, taking the illumination and observation angles into account. In a next step the influence of maize is filtered out from the spectral signal by a new procedure termed Residual Spectral Unmixing (RSU). The residual soil spectra resulting from this procedure are used for mapping of SOC using PLSR, which could be done with accuracies comparable to studies performed on bare soil surfaces (Root Mean Standard Error of Calibration = 1.34 g/kg and Root Mean Standard Error of Prediction = 1.65 g/kg). With the presented RSU approach it is possible to filter out the influence of maize from the mixed spectra, and the residual soil spectra contain enough information for mapping of the SOC distribution within agricultural fields. This can improve the applicability of airborne imaging spectroscopy for soil studies in temperate climates, since the use of the RSU approach can extend the flight-window which is often constrained by the presence of vegetation.

Dissolved organic carbon (DOC) is a key parameter in lakes that can affect numerous features, including microbial metabolism, light climate, acidity, and primary production. In an attempt to understand the factors that regulate DOC in lakes, we assembled a large database (7,514 lakes from 6 continents) of DOC concentrations and other parameters that characterize the conditions in the lakes, the catchment, the soil, and the climate. DOC concentrations were in the range 0.1-332 mg L 21 , and the median was 5.71 mg L 21. A partial least squares regression explained 48% of the variability in lake DOC and showed that altitude, mean annual runoff, and precipitation were negatively correlated with lake DOC, while conductivity, soil carbon density, and soil C : N ratio were positively related with lake DOC. A multiple linear regression using altitude, mean annual runoff, and soil carbon density as predictors explained 40% of the variability in lake DOC. While lake area and drainage ratio (catchment : lake area) were not correlated to lake DOC in the global data set, these two factors explained significant variation of the residuals of the multiple linear regression model in several regional subsets of data. These results suggest a hierarchical regulation of DOC in lakes, where climatic and topographic characteristics set the possible range of DOC concentrations of a certain region, and catchment and lake properties then regulate the DOC concentration in each individual lake.

In this paper we present a novel on-line method
to recursively align point clouds. By considering each point
together with the local features of the surface (normal and
curvature), our method takes advantage of the 3D structure
around the points for the determination of the data association
between two clouds. The algorithm relies on a least squares
formulation of the alignment problem, that minimizes an error
metric depending on these surface characteristics. We named
the approach Normal Iterative Closest Point (NICP in short).
Extensive experiments on publicly available benchmark data
show that NICP outperforms other state-of-the-art approaches.

Abstract: Among the search engines, Google is one of the most powerful. It uses an accurate ranking algorithm to order web pages in search results. In this paper, it is shown that a simple linear model can approximately model the dynamics governing the behaviour of Google. Least Squares is used for the system identification procedure. Identification results are provided to show the effectiveness of the identified system. Copyright © 2003 IFAC

Jan. 8, 2016: Perhaps wherever I noted "the estimated standard error of the random factors of the estimated residuals," I should have said "the estimated standard deviation of the random factors of the estimated residuals." I saw some things by a couple of people that made me realize my language was sloppy here. But I also read where this may be fairly common. At any rate, this is a fixed value to be estimated. It is a standard deviation.
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Previous notes:
The classical ratio estimator (CRE) is very simple, has a long history, and has a stunningly broad range of application, especially with regard to econometrics, and to survey statistics, particularly establishment survey statistics. The CRE has a number of desirable properties, one of which is that the sum of its estimated residuals is always zero. It is easily extended to multiple regression, and a property shown in Sarndal, Swensson and Wretman (1992) may be used to indicate the desirability of this zero sum of estimated residuals feature when constructing regression weights for multiple regression. In the single regressor form, the zero sum of estimated residuals property is related to an interesting phenomenon expressed in Fox (1997). Finally, relationships of the CRE to some other statistics are also considered.
-- Note added November 2014: As noted in other works I have done, and elsewhere, for this model, only the individual values of x corresponding to individual y values need to be known, as long as the sum of the remaining x (for out-of-sample cases) is known, and then one can still estimate variance. If we do not know the sum of those remaining N-n x-values (where n is sample size selected minus cases to be imputed), but we know a range for that subtotal of x's, then we know a range of estimated variances for the estimated y-totals to go with that range. --

Two Matlab TM software packages for strain field computation, starting from displacements of experimental points (EPs), are here presented. In particular, grid_strain estimates the strain on the nodes of a regular planar grid, whereas grid_strain3 operates on the points of a digital terrain model (DTM). In both cases, the computations are performed in a modified least-square approach, emphasizing the effects of nearest points. This approach allows users to operate at different scales of analysis by introducing a scale factor to reduce or also exclude points too far from grid nodes. The input data are displacements (or velocities) that can be provided by several techniques (e.g. GPS, total topographical station, terrestrial laser scanner). The analysis can be applied to both regional-and local-scale phenomena, to study tectonic crustal deformations (strain E10 À8 À10 À6 ) or rapid landslide collapses (10 À4 À10 2 ), and to characterize the kinematics of the studied system. Errors on strains and geometric significance of the results are also provided. r

The use of GPS for the estimation of orthometric heights in a given region, with the help of existing levelling data requires the determination of a local geoid and the bias between the local levelling and the one implicitly defined when the geoid is calculated which is generally based on the gravity anomalies data. The heights of new data can

In 1907, Erhard Schmidt published a paper in which he introduced an orthogonalization algorithm that has since become known as the classical Gram-Schmidt process. Schmidt claimed that his procedure was essentially the same as an earlier one published by J. P. Gram in 1883. The Schmidt version was the first to become popular and widely used. An algorithm related to a modified version of the process appeared in an 1820 treatise by P. S. Laplace. Although related algorithms have been around for almost 200 years, it is the Schmidt paper that led to the popularization of orthogonalization techniques. The year 2007 marked the 100th anniversary of that paper. In celebration of that anniversary, we present a comprehensive survey of the research on Gram-Schmidt orthogonalization and its related QR factorization. Its application for solving least squares problems and in Krylov subspace methods are also reviewed. Software and implementation aspects are also discussed. squares solution if and only if the corresponding residual vector r D b Ax is orthogonal to span.a 1 , : : : , a n /. This condition is equivalent to

A technique for reconstructing a class of quadric surfaces from 3D data is presented. The technique is driven by a linear least-squaresbased fitting mechanism. Previously, such fitting was restricted to recovery of central quadrics; here, extension of that basic mechanism to allow recovery of one commonly-occurring class of non-central quadric, the elliptic paraboloids, is described. The extension uses an indirect solution approach that involves introducing a variable to the basic mechanism that is a function of a quadric surface invariant. Results from fitting real and synthetic data are also exhibited.

Image and template matching is probably the most important function in digital photogrammetry and also in automated modelling and mapping. Many approaches for matching have evolved over the years, but the problem is still unsolved in general terms. This paper describes the development of image matching techniques in photogrammetry over the past 50 years, addresses the results of some empirical accuracy studies and also provides a critical account of some of the problems that remain. Although automated approaches have quite a number of advantages, the quality of the results is still not satisfactory and, in some cases, far from acceptable. Even with the most advanced techniques, it is not yet possible to achieve the quality of results that a human operator can produce. There is an urgent need for further improvements and innovations, be it through more powerful multi-sensor approaches, thereby enlarging the information spectrum, and/or through advancements in image understanding algorithms, thus coming closer to human capabilities of reading and understanding image content.

We have developed a least-squares method to determine simultaneously the depth and the width of a buried thick dipping dike from residualized magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the half-width of the source and a combination of windowed observations. The relationship represents a family of curves (window curves). For a fixed window length, the depth is determined for each half-width value by solving one nonlinear equation of the form f (z) = 0 using the least-squares method. The computed depths are plotted against the width values representing a continuous curve. The solution for the depth and the width of the buried dike is read at the common intersection of the window curves. The method involves using a dike model convolved with the same moving average filter as applied to the observed data. As a result, this method can be applied to residuals as well as to measured magnetic data. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to theoretical data with and without random errors. The validity of the method is tested on airborne magnetic data from Canada and on a vertical component magnetic anomaly from Turkey. In all cases examined, the model parameters obtained are in good agreement with the actual ones and with those given in the published literature.

Multiples contain valuable information about the subsurface, and if properly migrated can provide a wider illumination of the subsurface compared to imaging with VSP primary reflections. In this paper we review three different methods for migrating multiples. The first method is model-based, and it is more sensitive to velocity errors than primary migration; the second method uses a semi-natural Green's function for migrating multiples, where part of the traveltimes are computed from the velocity model, and part of the traveltimes (i.e., natural traveltimes) are picked from the data to construct the imaging condition for multiples; the third method uses cross-correlation of traces. The last two methods are preferred in the sense that they are significantly less sensitive to velocity errors and statics because they use "natural data" to construct part of the migration imaging conditions. Compared with the interferometric (i.e., crosscorrelation) imaging method the semi-natural Green's function method is more computationally efficient and is sometimes less prone to migration artifacts.

The calibration parameters of a vector magnetometer are estimated only by the use of a scalar reference magnetometer. The method presented in this paper differs from those previously reported in its linearized parametrization. This allows the determination of three offsets or signals in the absence of a magnetic field, three scale factors for normalization of the axes and three non-orthogonality angles which build up an orthogonal system intrinsically in the sensor. The advantage of this method compared with others lies in its linear least squares estimator, which finds independently and uniquely the parameters for a given data set. Therefore, a magnetometer may be characterized inexpensively in the Earth's magnetic-field environment. This procedure has been used successfully in the pre-flight calibration of the state-of-the-art magnetometers on board the magnetic mapping satellites Ørsted, Astrid-2, CHAMP and SAC-C. By using this method, full-Earth-field-range magnetometers (±65536.0 nT) can be characterized down to an absolute precision of 0.5 nT, non-orthogonality of only 2 arcsec and a resolution of 0.2 nT.

En métrologie tridimensionnelle, la détermination d'une surface idéale associée à une surface réelle n'est pas facile. Depuis les années 1970, le critère des moindres carrés a été le plus utilisé, car il peut être traité par un simple calcul matriciel. De nos jours le critère minimax et le critère enveloppe sont facilement accessibles à l'aide des solveurs. Cet article propose des méthodes d'identification des surfaces géométriques basées sur un solveur sans l'hypothèse des petits déplacements. Le choix du critère d'association et le calcul du défaut de forme est alors conforme aux normes ISO 5459 et ISO 1101. L'analyse de la mesure des points pour les surfaces réputées planes et les surfaces réputées cylindriques est traitée sur des pièces réelles et validée à l'aide de tests disponibles dans la littérature. L'application porte sur deux cas difficiles à traiter avec les méthodes classiques : la construction d'un système de références et le contrôle d'une spécification au maximum de matière.  2003 Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés.

MEMS gyroscopes and accelerometers are designed to measure angular rate of rotation and acceleration forces, respectively. In many applications, a measurement of the angle itself is needed but gyroscopes have a drift error occurred by integrating the angular rate output and accelerometers have errors due to translation forces. In this paper, we present a method of designing a complementary filter to estimate the angle using both an accelerometer and a gyroscope. First, we show that the estimation of the angle using single sensor of a gyroscope or an accelerometer has a lack of accuracy in some experiments. And we propose a design method of the complementary filter using linear least squares to estimate the angle. Experimental results of the proposed method are compared with the cut-off frequency method in a practical rotary inverted pendulum system.

We present a method to estimate Time of Concentration (T c ) and Storage Coefficient (R) to develop Clark's Instantaneous Unit Hydrograph (CIUH). T c is estimated from Time Area Diagram of the catchment and R is determined using optimization approach based on Downhill Simplex technique (code written in FOR-TRAN). Four different objective functions are used in optimization to determine R. The sum of least squares objective function is used in a novel way by relating it to slope of a linear regression best fit line drawn between observed and simulated peak discharge values to find R. Physical parameters (delineation, land slope, stream lengths and associated drainage areas) of the catchment are derived from SPOT satellite imageries of the basin using ERDAS: Arc GIS is used for geographic data processing. Ten randomly selected rainfall-runoff events are used for calibration and five for validation. Using CIUH, a Direct surface runoff hydrograph (DSRH) is developed. Kaha catchment (5,598 km 2 ), part of Indus river system, located in semiarid region of Pakistan and dominated by hill torrent flows is used to demonstrate the applicability of proposed approach. Model results during validation are very good with model efficiency of more than 95% and root mean square error of less than 6%. Impact of variation in model parameters T c and R on DSRH is investigated. It is identified that DSRH is more sensitive to R compared to T c . Relatively equal values of R and T c reveal that shape of DSRH for a large catchment depends on both runoff diffusion and translation flow effects. The runoff diffusion effect is found to be dominant.

Abstract One of the most important steps in solving Multi-Attribute Decision Making (MADM) problems is to derive the weights of importance of the attributes. The decision maker is requested to compare the importance for each pair of attributes. The result expressed in numbers is written in a pairwise comparison matrix. The aim is to determine a weight vector w=(w1, w2,, wn), which reflects the preferences of the decision maker, in the positive orthant of the n-dimensional Euclidean space.

ABSTRAK Model regresi linear adalah model yang digunakan untuk mengetahui hubungan antara satu atau lebih variabel bebas dengan variabel terikat. Pada makalah ini, model regresi log-log linear berganda akan digunakan untuk mengetahui pengaruh banyaknya permintaan soft drink berdasarkan pada harga soft drink itu sendiri, harga minuman dan barang/jasa lainnya serta pendapatan keluarga/masyarakat dengan estimasi parameter menggunakan metode Ordinary Least Square (OLS) dan Monte Carlo. Penaksiran parameter dilakukan terhadap parameter tanpa retriksi, dengan retriksi dari non-sample information dari teori ekonomi dan dengan retriksi parameter yang mempunyai kekeliruan sedikit. Dari penaksiran tersebut, dilakukan pengujian hipotesis untuk masing-masing parameter yang diperoleh dan terhadap model secara keseluruhan (goodness of fit). Selanjutnya, akan ditentukan parameter mana yang paling baik bagi model untuk mampu mewakili permasalahan ini. Hasil yang diperoleh bahwa harga soft drink itu sendiri, harga minuman dan barang/jasa lainnya serta pendapatan keluarga/masyarakat memiliki pengaruh dalam menentukan banyaknya permintaan soft drink dengan penaksir parameter terbaik adalah penaksir parameter dengan retriksi yang didukung oleh teori ekonomi. Kata Kunci: Model regresi log-log linear, Estimasi parameter, Ordinary Least Square (OLS), Monte Carlo

Ingeniar intervalos de calibración para satisfacer los requisitos de calidad que orientan las organizaciones que rigen la metrología y las normas de calidad se discute en este trabajo. Se proponen dos métodos diferentes para el establecimiento de un intervalo de calibración óptimo para los instrumentos patrones del laboratorio de Metrología del Grupo Nacional de Validación.

The usual way of the implementation of on-line discrete Hilbert transformers is the design of linear phase finite impulse response (FIR) filters. Recently, a method has been published for the design of infinite impulse response (IIR) Hilbert transformers as well.

The use of GPS for the estimation of orthometric heights in a given region, with the help of existing levelling data requires the determination of a local geoid and the bias between the local levelling and the one implicitly defined when the geoid is calculated which is generally based on the gravity anomalies data. The heights of new data can be collected swiftly without using the orthometric heights from levelling; it is what one calls commonly levelling by GPS. In this framework, the Least Squares Collocation method (LSC) has been used to evaluate the quality of the available GPS-Levelling data, to determine a gravimetric geoid in the North region of Algeria and to estimate the constant datum bias. The data used in the setting of this study are: The geopotential model EGM96, a total number of 2534 gravity anomalies, as well as 43 GPS points connected to the geodetic network levelling present on the whole North part of Algerian.

Iran is a mountainous country with large lateral density variations of its crust. Constant density value is commonly used to determine the geoid models as well as topographic corrections. The effect of lateral density variation in the geoid can reach up to 14 cm in Iran which is not negligible in a precise geoid modelling. Also, the current height datum of Iran is based on the orthometric system but the effect of gravity variation was not applied in height parameter. Furthermore, the height systems of most neighbouring countries are defined as normal height. Connection of networks can be useful for the unification of height datum, geodynamics researches and optimal adjustment of levelling network. The new quasi-geoid model based on a recent EGM2008 global geo-potential model was created to solve the mentioned problem. The main purpose of the present study is to discuss the results of a research project in which a gravimetric quasi-geoid model for Iran was computed based on the least-squares modification of Stokes' formula. The evaluation is made using 475 GPS/levelling height anomalies covering the major parts of the country except the mountainous areas to the North and West. After a 7-parameter fit, the most promising attempt achieved a RMS value of 19 cm for the residuals based on the GPS/levelling data.

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the number of variables (i.e., entries in the matrix) is modest, say, under 1000. Since the number of variables is n(n + 1)/2, this corresponds to a limit around n = 45. Malick [SIAM J. Matrix Anal. Appl., 26 (2005), pp. 272-284] studies a closely related problem and calls it the semidefinite least-squares problem. In this paper we formulate a dual problem that has no matrix inequality or matrix variables, and a number of (scalar) variables equal to the number of equality and inequality constraints in the original least-squares covariance adjustment problem. This dual problem allows us to solve far larger least-squares covariance adjustment problems than would be possible using standard methods. Assuming a modest number of constraints, problems with n = 1000 are readily solved by the dual method. The dual method coincides with the dual method proposed by Malick when there are no inequality constraints and can be obtained as an extension of his dual method when there are inequality constraints. Using the dual problem, we show that in many cases the optimal solution is a low rank update of the original matrix. When the original matrix has structure, such as sparsity, this observation allows us to solve very large least-squares covariance adjustment problems.

A least-squares meshfree method (LSMFM) based on the first-order velocity-pressure-vorticity formulation for two-dimensional steady incompressible viscous flow is presented. The discretization of all governing equations is implemented by the least-squares method. The equal-order moving least-squares (MLS) approximation is employed. Gauss quadrature is used in the background cells constructed by the quadtree algorithm and the boundary conditions are enforced by the penalty method. The matrix-free element-by-element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. A numerical example with analytical solution for the Stokes problem is devised to analyze the error estimates of the LSMFM. Also, cavity-driven flow for the Stokes problem and the flow past a circular cylinder at low Reynolds numbers for the steady incompressible viscous flow are solved. Through the comparisons of the LSMFMÕs results with other experimental and numerical results, the numerical features of the presented LSMFM are investigated and discussed.

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

Statistical Pronouncements IV JMASM is an independent print and electronic journal (http://tbf.coe.wayne.edu/jmasm) designed to provide an outlet for the scholarly works of applied nonparametric or parametric statisticians, data analysts, researchers, classical or modern psychometricians, quantitative or qualitative evaluators, and methodologists. Work appearing in Regular Articles, Brief Reports, and Early Scholars are externally peer reviewed, with input from the Editorial Board; in Statistical Software Applications and Review and JMASM Algorithms and Code are internally reviewed by the Editorial Board. Three areas are appropriate for JMASM: (1) development or study of new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computerintensive Monte Carlo, bootstrap, jackknife, or resampling methods, (2) development or study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms, pseudo-random number generators, simulation techniques, and self-contained executable code to carry out new or interesting statistical methods. Problems may arise from applied statistics and data analysis; experimental and nonexperimental research design; psychometry, testing, and measurement; and quantitative or qualitative evaluation. They should relate to the social and behavioral sciences, especially education and psychology.

Significant gravity changes observed around the Mayon Volcano (Philippines) between 1992 and 1994 at 26 stations are interpreted in terms of an increase of mass and pressure changes at several point sources modelled using a fast inversion process. This inversion approach attempts to fit gravity and elevation changes by combining a random search for the positions of the sources and a linear least-squares fit for the incremental mass, pressure and possible common regional values for gravity or elevation changes. Some stabilizer terms are included in the misfit function. Models with one and two sources were tested against the observed changes at Mayon. Models with only one-source give a best fit for a shallow source with a positive mass increment, horizontally displaced far from the summit. The study using two sources gives a best fit that is similar to the one-source model, but in addition indicates anomalous behavior at stations in the SW. Neglecting the stations located southward from a local fracture, the bestfitting model suggests one central positive mass change source, which is likely to be an intrusion of about 0.5 MU with a depth of about 5 km beneath the volcano. Standard deviation for the residuals ranges from 7-8 lGal for one-source models to 6-7 lGal for models with two sources. Both of the cases are below the error value of 9.4 lGal estimated for the gravity data, so that it is not possible to discriminate between both possible interpretations without additional information.

The study shows that leaf area index (LAI), leaf chlorophyll content (LCC) and canopy chlorophyll content (CCC) can be mapped in a heterogeneous Mediterranean grassland from canopy spectral reflectance measurements. Canopy spectral measurements were made in the field using a GER 3700 spectroradiometer, along with concomitant in situ measurements of LAI and LCC. We tested the utility of univariate techniques involving narrow band vegetation indices and the red edge inflection point, as well as multivariate calibration techniques, including stepwise multiple linear regression and partial least squares regression. Among the various investigated models, CCC was estimated with the highest accuracy (R 2 cv = 0.74, nRMSE cv = 0.35). All methods failed to estimate LCC (R 2 cv ≤ 0.40), while LAI was estimated with intermediate accuracy (R 2 cv values ranged from 0.49 to 0.69). Compared with narrow band indices and red edge inflection point, stepwise multiple linear regression generally improved the estimation of LAI. The estimations were further improved when partial least squares regression was used. When a subset of wavelengths was analyzed, it was found that partial least squares regression had reduced the error in the retrieved parameters. The results of the study highlight the significance of multivariate techniques, such as partial least squares regression, rather than univariate methods such as vegetation indices in estimating heterogeneous grass canopy characteristics.

A traveltime inversion technique is applied to model the upper ∼40 m of the subsurface of a glaciated shield rock area in order to calculate static corrections for a multi-azimuth multi-depth walk-away vertical seismic profile and a surface seismic reflection profile. First break information from a seismic refraction survey is used in conjunction with a ray-tracing program and an iterative damped least-squares inversion algorithm to create a two-dimensional model of the subsurface. The layout of the seismic survey required crooked seismic lines and substantial gaps in the source and receiver coverage to be accounted for. Additionally, there is substantial topographical variation and a complex geology consisting of glaciofluvial sediment and glacial till overlying a crystalline bedrock. The resolution and reliability of the models is measured through a parameter perturbation technique, normalized χ2 values, root means square traveltime residuals and comparison to known geology.

We propose a new robust estimator of the regression function in a nonparametric regression model. Empirical evidence suggests that the proposed estimator performs better (in an averaged squared error sense) than the popular local least squares estimator for non normal error distributions. The proposed estimator has the same asymptotic properties as all classical estimators.

A geophysical survey including electrical resistivity tomography (ERT) and seismic refraction tomography (SRT) was carried out to study a landslide site in the Altındağ district of İzmir city, western Turkey. In the city, landslide is one of the causes of natural hazard, and one of the most important landslide sites is located in the Altındağ district. The ERT studies were performed along four profiles over the landslide body in the directions of N-S and E-W. A Wenner-Schlumberger configuration was used during the resistivity measurements. The SRT survey was carried out using vertical geophones along a profile coincident with one of N-S trending resistivity profiles. Both the resistivity and the seismic data sets were processed by least-squares inversion techniques. In the first-arrival traveltime inversion of the surface refraction data, a method which is not based on ray tracing was used. Instead, the method used the functional description of traveltimes to generate the Jacobian and this matrix was calculated by using a finite-difference approximation based on the perturbation of the cell slownesses. Traveltime calculations were performed by an eikonal solver. Each technique produced useful results on the internal structure of the landslide, physical properties of the landslide material and sliding surface geometry. The landslide material was characterized by low resistivity and low seismic velocity. The resistivity results also indicated the zones associated with the high water and clay contents within the landslide mass. A layer of consolidated clastic rocks was considered to be the landslide bedrock, and it was represented by relatively high (moderate) resistivity and high velocity. Integrated interpretation of the resistivity and the seismic refraction data along one of N-S trending profiles helped us identify the geometry of the failure surface and the changes in the thickness of the landslide material. An undulating sliding surface is present along that profile and the landslide material gets thicker in the middle and the northern parts (the toe area) of the profile. Moreover, the water content is thought to have a key role in the mass movement in the landslide site.

For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori knowledge of matrix structure. In particular, we consider linearly structured matrices, such as Hankel and Toeplitz, as well as positive semidefinite matrices. The performance of the algorithm, referred to as alternating least-squares (ALS), is evaluated by simulations and compared to the Cramér-Rao bounds.

The study introduces an efficient methodology to perform the transformations between station coordinate and velocity
solutions where either minimum or redundant datum constraints have been imposed employing the estimated state vector
and the covariance matrix thereof. The analytical methodology presented herein facilitates the datum alignment of largenetwork
solutions, especially for the GNSS technique. The computational complexity reduction is achieved by avoiding the
expensive normal equation system reconstruction and the subsequent inversion thereof, which is the current norm, in favor
of an elegant approach involving the inversion of an up to 14-order matrix. All information parsed in our algorithm is readily
available in the widely used space geodetic solution files following the Solution Independent Exchange (SINEX) format. Our
transformation approach is evaluated in two globally distributed GNSS-derived solutions and one terrestrial reference frame
with a spatial concentration in South America. The results prove the equivalence of the current and proposed algorithm and
that our approach is at least an order of magnitude faster. In addition, we test the Fast Constraints Transformation (FCT)
through simulated networks, with a size of up to 5000 stations. The FCT presented here accelerates the transformation by
almost 140 times compared to the commonly used strategy.

The lack of publicly accessible datasets with a reliable ground truth has prevented in the past a fair and coherent comparison of different methods proposed in the mobile robot Simultaneous Localization and Mapping (SLAM) literature. Providing such a ground truth becomes specially challenging in the case of visual SLAM, where the world model is 3-dimensional and the robot path is 6-dimensional. This work addresses both the practical and theoretical issues found while building a collection of six outdoor datasets. It is discussed how to estimate the 6-d vehicle path from readings of a set of three Real Time Kinematics (RTK) GPS receivers, as well as the associated uncertainty bounds that can be employed to evaluate the performance of SLAM methods. The vehicle was also equipped with several laser scanners, from which reference point clouds are built as a testbed for other algorithms such as segmentation or surface fitting. All the datasets, calibration information and associated software tools are available for download http://babel.isa.uma.es/mrpt/papers/dataset2009/.

Sensor fusion of a MEMS IMU with a magnetometer is a popular system design, because such 9-DoF (degrees of freedom) systems are capable of achieving drift-free 3D orientation tracking. However, these systems are often vulnerable to ambient magnetic distortions and lack useful position information; in the absence of external position aiding (e.g. satellite/ultra-wideband positioning systems) the dead-reckoned position accuracy from a 9-DoF MEMS IMU deteriorates rapidly due to unmodelled errors. Positioning information is valuable in many satellite-denied geomatics applications (e.g. indoor navigation, location-based services, etc.). This paper proposes an improved 9-DoF IMU indoor pose tracking method using batch optimization. By adopting a robust in-situ user self-calibration approach to model the systematic errors of the accelerometer, gyroscope, and magnetometer simultaneously in a tightly-coupled post-processed least-squares framework, the accuracy of the estimated trajectory from a 9-DoF MEMS IMU can be improved. Through a combination of relative magnetic measurement updates and a robust weight function, the method is able to tolerate a high level of magnetic distortions. The proposed auto-calibration method was tested in-use under various heterogeneous magnetic field conditions to mimic a person walking with the sensor in their pocket, a person checking their phone, and a person walking with a smartwatch. In these experiments, the presented algorithm improved the in-situ dead-reckoning orientation accuracy by 79.8 – 89.5% and the dead-reckoned positioning accuracy by 72.9 – 92.8%, thus reducing the relative positioning error from metre-level to decimetre-level after ten seconds of integration, without making assumptions about the user's dynamics.

Position information is often one of the key requirements for a wireless sensor network (WSN) to function as intended. Due to drawbacks in using GPS or having to manually setting sensor positions, extracting the position information by means of the network itself has been extensively studied in the literature. In this approach, it is commonly assumed that there are a few sensor nodes with known positions, called reference nodes, and some type of measurements are taken between different nodes.

Illegal pumping from underground reservoirs is approached as an inverse problem. The procedure seeks among a set of suspected potential areas the ones from which water is effectively pumped out (or in) and at what rate does this take place? Influence coefficient and finite element are combined in order to simulate the aquifer response to hypothetical pumping scenarios. Then the