A Robust Indoor Localization Algorithm Based on Polynomial Fitting and Gaussian Mixed Model

Wireless sensor network(WSN)positioning has a good effect on indoor positioning,so it has received extensive attention in the field of positioning.Non-line-of sight(NLOS)is a primary challenge in indoor complex environment.In this paper,a robust localization algorithm based on Gaussian mixture model and fitting polynomial is proposed to solve the problem of NLOS error.Firstly,fitting polynomials are used to predict the measured values.The residuals of predicted and measured values are clustered by Gaussian mixture model(GMM).The LOS probability and NLOS probability are calculated according to the clustering centers.The measured values are filtered by Kalman filter(KF),variable parameter unscented Kalman filter(VPUKF)and variable parameter particle filter(VPPF)in turn.The distance value processed by KF and VPUKF and the distance value processed by KF,VPUKF and VPPF are combined according to probability.Finally,the maximum likelihood method is used to calculate the position coordinate estimation.Through simulation comparison,the proposed algorithm has better positioning accuracy than several comparison algorithms in this paper.And it shows strong robustness in strong NLOS environment.

The Error Compensation of Inclinometer Based on Polynomial Fitting

In order to reduce the influence of nonlinear characteristic and temperature on the measuring accuracy of inclinometer, the application of polynomial fitting principle to compensate the measuring error of inclinometer is studied. According to the analysis of the experimental data of inclinometer, a polynomial model of the nonlinear error and the measured value is constructed, and then the relation between the coefficient of the polynomial model and the temperature is obtained by fitting, and finally the function of the measurement error of inclinometer on the measured inclination and temperature is obtained. The results show that this method is feasible and effective, which can not only reduce the influence of temperature, but also correct its nonlinear error.

Adaptive Order Polynomial Fitting for Pulmonary Nodule Segmentation in Chest Radiograph

Segmentation of pulmonary nodules in chest radiographs is a particularly challenging task due to heavy noise and superposition of ribs,vessels,and other complicated anatomical structures in lung field. In this paper,an adaptive order polynomial fitting based raycasting algorithm is proposed for pulmonary nodule segmentation in chest radiographs. Instead of detecting nodule edge points directly,the nodule intensity profiles are first fitted by using the polynomials with adaptively determined orders. Then,the edge positions are identified through analyzing the local minimum of the fitted curves.The performance of the proposed algorithm was evaluated over an image database with 148 nodule cases in chest radiographs that were collected from a variety of digital radiograph modalities. The preliminary results show the proposed algorithm can obtain a high rate of successful segmentations.

Predicting of Land Surface Temperature Distribution in Freetown City, Sierra Leone by Using Polynomial Curve Fitting Model

Global warming has attracted much concern about the worldwide organization, civil society groups, researchers, and so forth because the worldwide surface temperature has been expanding. This investigation intends to assess and compare the ability of a combination of land cover indices to predict the future distribution of land surface temperatures in Freetown using the Polynomial model analysis. Landsat satellite images of 1988, 1998, 2000, 2010, and 2018 of the Freetown Metropolitan zone were utilized for analysis. The investigation had adopted two land covers indices, Modification of normalized difference water index and Urban Index (UI) (e.g., MNDWI and UI) and applied a multi regression equation for forecasting the future LST. The stimulation results propose that the development will be accompanied by surface temperature increases, especially in Freetown’s western urban area. The temperature prevailing in the west of the metropolitan area may increase in the city somewhere in the range from 1988 to 2018. Additionally, the results of the LST prediction show that the model is perfect. Our discoveries can be represented as a helpful device for policymakers and community awareness by giving a scientific basis for sustainable urban planning and management.

Constrained polynomial fit-based k-domain interpolation in swept-source optical coherence tomography

We propose a k-domain spline interpolation method with constrained polynomial fit based on spectral phase in swept-source optical coherence tomography(SS-OCT).A Mach-Zehnder interferometer(MZI)unit is connected to.the swept-source of the SS-OCT system to generate calibration signal in sync with the fetching of interference spectra.The spectral phase of the calibration signal is extracted by Hilbert transformation.The fitted phase-time relationship is obtained by polynomial fitting with the constraint of passing through the central spectral phase.The fitting curve is then adopted for k-domain uniform interpolation based on evenly spaced phase.In comparison with conventional k-domain spline interpolation,the proposed method leads to improved axial resolution and peak response of the axial point spread function(PSF)of the SS-OCT system.Enhanced performance resulting from the proposed method is further verified by OCT imaging of a home-constructed microspheres-agar sample and a fresh lemon.Besides SS-OCT,the proposed method is believed to be applicable to spectral domain OCT as well.

Improved Baseline Correction Method Based on Polynomial Fitting for Raman Spectroscopy

Raman spectrum, as a kind of scattering spectrum, has been widely used in many fields because it can characterize the special properties of materials. However, Raman signal is so weak that the noise distorts the real signals seriously. Polynomial fitting has been proved to be the most convenient and simplest method for baseline correction. It is hard to choose the order of polynomial because it may be so high that Runge phenomenon appears or so low that inaccuracy fitting happens. This paper proposes an improved approach for baseline correction, namely the piecewise polynomial fitting （PPF）. The spectral data are segmented, and then the proper orders are fitted, respectively. The iterative optimization method is used to eliminate discontinuities between piecewise points. The experimental results demonstrate that this approach improves the fitting accuracy.

A New Pre-alignment Approach Based on Four-Quadrant-Photo-Detector for IC Mask

In this paper, a new pre-alignment approach based on Four-Quadrant-Photo-Detector （FQPD） for IC mask is presented. The voltage outputs from FQPDs are the functions of alignment mark＇s position offsets with respect to FQPDs. The functions are obtained with least squares error （LSE）-based polynomial fitting after the normalization of experimental data. As the acquired functions are not monotonic about their variables, the alignment mark＇s position offset cannot be given by direct inverse operation on the obtained functions. However, the piecewise polynomial fitting gives the inverse function, with which the alignment mark＇s position offset can be predicted according to the voltage outputs of FQPDs. On the basis of prediction, a pre-alignment control strategy is proposed. The feasibility and robustness of the pre-alignment approach is shown by experiments. Furthermore, the results demonstrate that the maximum error of mask＇s position offset in the X- and Y- directions is less than 15μm after coarse pre-alignment. Keywords： Four-Quadrant-Photo-Detector （FQPD）, pre-alignment, IC mask, polynomial fitting

A global solution for robust parameter design of aeronautical electrical apparatus based on interactions analysis and polynomial fitting

Robust Parameter Design(RPD) has been widely applied for improving quality and reliability of products.One of the key drawbacks of applying RPD using Taguchi method is that the stable factors may not be independent of the adjustment factors, resulting in unsatisfactory design.Moreover, the Taguchi method cannot guarantee global optimality since the levels set in the experiment are usually discrete to ensure orthogonal design.In this paper, robust solutions of the stable factors are obtained via a nonlinear model based on polynomial fitting;while the adjustment factors are obtained via interactions analysis so that they are independent of the stable factors.In particular, the values of the adjustment factors are determined by output offset compensation so as to achieve robustness of the design scheme.An example on the design of an aeronautical electrical apparatus is presented to illustrate the procedure.The results show that the proposed method can take full advantage of the nonlinearity in the response and achieve the desired outcome.

Human motion prediction using optimized sliding window polynomial fitting and recursive least squares

Human motion prediction is a critical issue in human-robot collaboration(HRC)tasks.In order to reduce the local error caused by the limitation of the capture range and sampling frequency of the depth sensor,a hybrid human motion prediction algorithm,optimized sliding window polynomial fitting and recursive least squares(OSWPF-RLS)was proposed.The OSWPF-RLS algorithm uses the human body joint data obtained under the HRC task as input,and uses recursive least squares(RLS)to predict the human movement trajectories within the time window.Then,the optimized sliding window polynomial fitting(OSWPF)is used to calculate the multi-step prediction value,and the increment of multi-step prediction value was appropriately constrained.Experimental results show that compared with the existing benchmark algorithms,the OSWPF-RLS algorithm improved the multi-step prediction accuracy of human motion and enhanced the ability to respond to different human movements.

Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging

X-ray diffraction sorbing low-Z sample. How enhanced imaging （DEI） is applied to extract phase information from to inspect internal structures of weakly abraw images measured in different positions of rocking curve is the key problem of DEI. In this paper, we present an effective extraction method called polynomial curve fitting method, in order to extract accurate information angular in a fast speed. It is compared with the existing methods such as multiple-images statistical method and Gaussian curve fitting method. The experiments results on a plastic cylinder and a black ant at the Beijing Synchrotron Radiation Facility prove that the polynomial curve fitting method can obtain most approximate refraction-angle values and its computation speed is 10 times faster than the Gaussian curve fitting method.

Assessment of Wind Power Potential at Eastern-Jerusalem, Palestine

Due to the energy demand and lack of supplied energy of Palestinian cities, wind resource assessment is important and necessary. The objective of the work is to analyze the wind speed data characteristics and wind power potential at eastern Jerusalem that are collected at 10 m above ground level from 2008 to 2018. The variations of monthly, seasonal, and annual wind speed are analyzed, and the measured maximum, minimum, and mean values are presented in this study. Wind speed characteristics have been analyzed by the well-known Weibull distribution function, and used to evaluate the wind power of the proposed site. Moreover, the relationship between wind power and mean wind speed is fitted by a second-order polynomial. The shape parameter moderate values showed that wind speed was relatively steady at the site. The highest average maximum value was found to be 5.7 m/s in June-2008, whereas the mean maximum values ranged from 5.4 m/s in June to 3.8 m/s in November. The highest mean power value was found to be 31.66 w/m2 in July with a maximum value of 23.18 w/m2 in 2013. R2 of the polynomial fit provides values of 95% for monthly mean and 96% for annual mean.

Trends in gravity changes from 2009 to 2013 derived from ground-based gravimetry and GRACE data in North China

North China is a key region for studying geophysical progress. In this study, ground-based and Gravity Recovery and Climate Experiment（GRACE） gravity data from 2009 to 2013 are used to calculate the gravity change rate（GCR） using the polynomial fitting method. In general, the study area was divided into the Shanxi rift, Jing-Jin-Ji（Beijing-Tianjin-Hebei Province）, and Bohai Bay Basin（BBB） regions. Results of the distribution of the GCR determined from ground-based gravimetry show that the GCR appears to be ＂negativepositive-negative＂ from west to east, which indicates that different geophysical mechanisms are involved in the tectonic activities of these regions. However, GRACE solutions are conducted over a larger spatial scale and are able to show a difference between southern and northern areas and a mass redistribution of land water storage.

Biomimetic Experimental Research on Hexapod Robot's Locomotion Planning

To provide hexapod robots with strategies of locomotion planning, observation experiments were operated on a kind of ant with the use of high speed digital photography and computer assistant analysis. Through digitalization of original analog video, locomotion characters of ants were obtained, the biomimetic foundation was laid for polynomial trajectory planning of multi-legged robots, which was deduced with mathematics method. In addition, five rules were concluded, which apply to hexapod robots marching locomotion planning. The first one is the fundamental strategy of multi-legged robots＇ leg trajectory planning. The second one helps to enhance the static and dynamic stability of multi-legged robots. The third one can improve the validity and feasibility of legs＇ falling points. The last two give criterions of multi-legged robots＇ toe trajectory figures and practical recommendatory constraints. These five rules give a good method for marching locomotion planning of multi-legged robots, and can be expended to turning planning and any other special locomotion.

A Method of Time-Varying Rayleigh Channel Tracking in MIMO Radio System

A method of MIMO channel tracking based on Kalman filter and MMSE-DFE is proposed. The Kalman filter tracks the time-varying channel by using the MMSE-DFE decision and the MMSE-DFE conducts the next decision by using the channel estimates produced by the Kalman filter. Polynomial fitting is used to bridge the gap between the channel estimates produced by the Kalman filter and those needed for the DFE decision. Computer simulation demonstrates that this method can track the MIMO time-varying channel effectively.

A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson’s approach. Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory.

Cubic polynomial curve-guided method for isochromatic determination in three-fringe photoelasticity

A method for isochromatic determination in three-fringe photoelasticity is presented. It combines the phaseshifting method with cubic polynomial curve-fitting technology to eliminate the errors caused by color repetition.We perform a demonstration of the method on a circular disc subjected to compressive loading and an injectionmolded cover with residual stresses. The test results compare well with the theoretical results.

Extension of continuous scanning laser Doppler vibrometry measurement for complex structures with curved surfaces

The continuous Scanning Laser Doppler Vibrometry(SLDV)developed on the base of the galvanometer scanner system has made it possible to quickly obtain the full field vibration responses within a rectangular area of the structure.In this paper,an arbitrary continuous scanning path generating method for Continuous Scanning Laser Doppler Vibometry(CSLDV)is further put forward in order to allow the CSLDV suitable for testing structures featured by complex shapes not just for regular areas.In the first step,the relationship between position of laser spot and the driving voltages of galvanometer scanner system has been described by a mathematical modeling.Then,a novel arbitrary scanning path generating strategy based on CSLDV is presented by deforming a normalization rectangular scanning path to an arbitrary continuous scanning path.The mapping relation between the normalization rectangular scanning path and arbitrary continuous scanning path is established using the reference points.In the second step,a compressor blade with curved surface was taken as an example for modal test using the proposed method.At the same time,a validated experiment was performed in SLDV.The results show the mode shapes derived from the extended CSLDV are in agreement with those from SLDV and the Modal Assurance Criterion(MAC)between the two are all greater than 0.96.They also demonstrate the feasibility and effectiveness of the proposed method for CSLDV test and show strong potential on further practical engineering applications.

Pretreating near infrared spectra with fractional order Savitzky–Golay differentiation(FOSGD)

With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation（IOSGD）,FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.

Efficient background removal based on two-dimensional notch filtering for polarization interference imaging spectrometers

A background removal method based on two-dimensional notch filtering in the frequency domain for polarization interference imaging spectrometers（PIISs） is implemented. According to the relationship between the spatial domain and the frequency domain, the notch filter is designed with several parameters of PIISs, and the interferogram without a background is obtained. Both the simulated and the experimental results demonstrate that the background removal method is feasible and robust with a high processing speed. In addition, this method can reduce the noise level of the reconstructed spectrum, and it is insusceptible to a complicated background, compared with the polynomial fitting and empirical mode decomposition（EMD） methods.

Numerical Discretization-Based Kernel Type Estimation Methods for Ordinary Differential Equation Models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation（ODE） models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method（kernel smoothing or local polynomial fitting） in the first stage, and a numerical discretization method（Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method） in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.