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.

Seismic noise attenuation using nonstationary polynomial fitting

We propose a novel method for seismic noise attenuation by applying nonstationary polynomial fitting （NPF）, which can estimate coherent components with amplitude variation along the event. The NPF with time-varying coefficients can adaptively estimate the coherent components. The smoothness of the polynomial coefficients is controlled by shaping regularization. The signal is coherent along the offset axis in a common midpoint （CMP） gather after normal moveout （NMO）. We use NPF to estimate the effective signal and thereby to attenuate the random noise. For radial events-like noise such as ground roll, we first employ a radial trace （RT） transform to transform the data to the time-velocity domain. Then the NPF is used to estimate coherent noise in the RT domain. Finally, the coherent noise is adaptively subtracted from the noisy dataset. The proposed method can effectively estimate coherent noise with amplitude variations along the event and there is no need to propose that noise amplitude is constant. Results of synthetic and field data examples show that, compared with conventional methods such as stationary polynomial fitting and low cut filters, the proposed method can effectively suppress seismic noise and preserve the signals.

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.

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.

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 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.

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.

A New Method for Deriving High-Vertical-Resolution Wind Vector Data from the L-Band Radar Sounding System in China

High-vertical-resolution radiosonde wind data are highly valuable for describing the dynamics of the meso-and microscale atmosphere. However, the current algorithm used in China's L-band radar sounding system for calculating highvertical-resolution wind vectors excessively smooths the data, resulting in significant underestimation of the calculated kinetic energy of gravity waves compared to similar products from other countries, which greatly limits the effective utilization of the data. To address this issue, this study proposes a novel method to calculate high-vertical-resolution wind vectors that utilizes the elevation angle, azimuth angle, and slant range from L-band radar. In order to obtain wind data with a stable quality, a two-step automatic quality control procedure, including the RMSE-F(root-mean-square error F) test and elemental consistency test are first applied to the slant range data, to eliminate continuous erroneous data caused by unstable signals or radar malfunctions. Then, a wind calculation scheme based on a sliding second-order polynomial fitting is utilized to derive the high-vertical-resolution radiosonde wind vectors. The evaluation results demonstrate that the wind data obtained through the proposed method show a high level of consistency with the high-resolution wind data observed using the Vaisala Global Positioning System and the data observed by the new Beidou Navigation Sounding System. The calculation of the kinetic energy of gravity waves in the recalculated wind data also reaches a level comparable to the Vaisala observations.

A linear crack length measurement method for railway bridges based on calibration points fitting

For the linear crack skeleton of railway bridges with irregular strike,it is difficult to accurately express the crack contour feature by using a single smoothing fitting algorithm.In order to improve the measurement accuracy,a polynomial curve fitting was proposed,which used the calibration point of crack contour as the boundary point,and then put them all together to produce a continuous contour curve to achieve the crack length measurement.The method was tested by measuring the linar cracks with different shapes.It is shown that this proposed algorithm can not only solve the jagged problem generated in the crack skeleton extraction process,but also improve the crack length measurement accuracy.The relative deviation is less than 0.15,and the measurement accuracy is over 98.05%,which provides a more effective means for the crack length measurement in railway bridges.

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.

Seismic dip estimation based on the twodimensional Hilbert transform and its application in random noise attenuation

In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.

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

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.

A rate control approach to distributed source coding for interferential multispectral image compression

Distributed source coding （DSC） is applied to interferential multispectral image compression owing to strong correlation among the image frames. Many DSC systems in the literature use feedback channel （FC） to control rate at the decoder, which limits the application of DSC. Upon an analysis of the image data, a rate control approach is proposed to avoid FC. Low-complexity motion compensation is applied first to estimate side information at the encoder. Using a polynomial fitting method, a new mathematical model is then derived to estimate rate based on the correlation between the source and side information. The experimental results show that our estimated rate is a good approximation to the actual rate required by FC while incurring a little bit-rate overhead. Our compression scheme performs comparable with the FC based DSC system and outperforms JPEG2000 significantly.

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.

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.

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.

Estimation of Winds at Different Isobaric Levels Based on the Observed Winds at 850 hPa Level Using Double Fourier Series

A technique based on the double Fourier series is developed to estimate the winds at different isobaric levels forthe limited area domain, 35°E to 140°E and 30°S to 40°N, using the observed winds at 850 hPa lcvcl for the month ofJune. For this purpose the wind field at a level under consideration is taken in the ratio form with that of 850 hPa level and the coefficients of the double Fouricr series are computed. These coefficients are subsequently used to computethe winds which are compared with the actual winds. The results of the double Fourier series technique are comparedwith those of the polynomial surface fitting method developed by Bavadekar and Khaladkar (1 992). The technique isalso applied for the daily wind data of 11. June, 1979 and the validation of the technique is tested for a few radiosondestations of india. The computed winds for these radiosonde stations arc quite close to observed winds.