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.

LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

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.

Fitting method of pseudo-polynomial for solving nonlinear parametric adjustment

The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [

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.

Complex derivatives valuation: applying the Least-Squares Monte Carlo Simulation Method with several polynomial basis

Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.

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.

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

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.

A CONCISE M-METRIC LEAST SQUARE FORMULA FOR POLYNOMIAL ANALOGY

An M-metric least square method for polynomial analogy is presented. The relative normal eqUation is of diagonal form, such that the concise solution formula is explicit, and it is suitable to Parallel computation. On the other hand, by error analysis of a typical example, we can see that the presented method is reliable.

A dynamic coefficient polynomial predistorter based on direct learning architecture

A dynamic coefficient polynomial predistorter based on direct learning architecture is proposed.Compared to the existing polynomial predistorter,on the one hand,the proposed predistorter based on thedirect learning architecture is more robust to initial conditions of the tap coefficients than that based on in-direct learning architecture;on the other hand,by using two polynomial coefficient combinations,differ-ent polynomial coefficient combination can be selected when the input signal amplitude changes,whicheffectively decreases the estimate error.This paper introduces the direct learning architecture and givesthe dynamic coefficient polynomial expression.A simplified nonlinear recursive least-squares(RLS)algo-rithm for polynomial coefficient estimation is also derived in detail.Computer simulations show that theproposed predistorter can attain 31 dB,28dB and 40dB spectrum suppression gain when our method is ap-plied to the traveling wave tube amplifier(TWTA),solid state power amplifier(SSPA)and polynomialpower amplifier(PA)model,respectively.

光强非线性响应下的光致热弹光谱光强修正

提出了基于光强非线性响应的光致热弹光谱光强修正方法,实现了激光光强的准确修正。控制DFB激光器工作于波长调制模式,设置激光调制频率为16369.75 Hz,通过光纤放大器增强其出射光强非线性项的幅值,光束经多次反射池后汇聚于石英音叉根部激发光热信号,采用数字锁相放大器解调得到对应的谐波信号,通过多项式拟合谐波信号背景,反演得到与浓度及光强分别对应的谐波信号。实验结果表明,当光强从22.03 mW变化至3.16 mW,谐波信号背景幅值与光强具有良好的线性关系,线性相关系数大于0.998,归一化后的谐波信号幅值波动小于0.37%。针对甲烷测量,系统在较大的浓度范围内具有良好的线性响应,谐波信号信噪比表明系统的最低检测限达0.22×10-6。该研究为光致热弹光谱的光强修正提供了一种新的方法,可有效提高LITES系统在长期测量应用中的稳定性。

纯铝、铁与钛薄板各向异性比较

为了明晰晶体结构对金属薄板塑性各向异性(r值)的影响,以3种典型晶体结构的高纯金属材料1A99纯铝、YT01纯铁和TA1纯钛为研究对象,采用数字图像相关技术并结合三阶多项式拟合法探究其r值演化规律。结果表明,在各向异性方面,纯铝与取样方向相关,这是取样方向与主滑移系之间的关系所致;而纯钛为各向同性,这仅与密排六方结构有关;而纯铁介于两者之间没有明显规律,这不仅与取样方向有关,还与BCC结构有关。在r值方面,纯铝不同方向的r值均小于1,而纯铁的r值稍大于1,纯钛的r值均大于1.68。说明在抗减薄能力上纯钛>纯铁>纯铝,这与晶体结构相一致。同时在取样90°时三者均有较优的抗减薄能力,这与取样方向偏离主滑移系最远有关。最后,在r值演化方面,纯铝在3个方向上差异巨大,而纯铁均先增大后减小,纯钛除取样0°几乎不变外均先减小后增大,这些复杂的现象可能与择优取向组织的体积分数和织构演化有关。

基于小扰动频率量测数据的电网节点惯量分布评估方法

惯量在电力系统抵抗扰动中起到关键作用。随着新能源渗透率的提升,电力系统中低惯量与惯量时空分布不均的特征日益凸显,准确评估电网节点惯量分布具有重要意义。为此,文中提出一种基于小扰动频率量测数据的节点惯量分布评估方法。首先,分析了频率与惯量的数学耦合机理,揭示了新型电力系统惯量分布特征。然后,根据单次小扰动下的频率量测数据与系统电源参数,分别提出了考虑各节点频率相较于系统中心频率变化水平偏差的节点等效惯量定义方法,以及基于自适应阶数多项式拟合的节点频率变化率计算方法,两层方法相结合即可计算出单次小扰动下的节点等效惯量。进一步,鉴于单次小扰动下求出的节点等效惯量具有一定的随机误差,提出考虑多次扰动事件评估结果的动态聚合策略,形成适用于新型电力系统的节点等效惯量分布评估方法。最后,分别以IEEE 39节点系统、中国某省级电网为例验证了所提方法的有效性。结果表明,所提方法所需数据量少,仅需各节点同步相量测量单元采集的频率量测数据即可实现对电网惯量分布的有效评估,评估结果准确性高且时效性强。

发泡聚乙烯最大加速度-静应力曲线快速获取方法研究

目的研究快速、准确预测最大加速度-静应力曲线的方法。方法首先利用落锤冲击试验机获取了5个不同高度下,5种不同厚度的发泡聚乙烯的最大加速度-静应力曲线。在此基础上,分析对比文中3种不同的改进拟合法与已有的动应力与动能量多项式拟合法的区别。结果研究发现,当不区分高度的情况下,以最大加速度因子为函数值,以跌落高度、衬垫厚度、静应力为变量进行拟合时,其代表预测精度R^(2)的平均为0.835,相比动应力与动能量多项式拟合法的0.2996要高。但曲线右侧的预测精度偏低。引入以静应力为变量的多项式作为修正因子后,R^(2)的平均值为0.934。预测精度有所提高,右侧的预测偏差减小,但仍存在。在区分高度的情况下,以带有修正因子的公式进行预测时,R^(2)的平均值为0.984,曲线向右侧预测偏差逐渐增大的现象明显改善。结论区分高度情况下,利用带修正因子的预测公式可以快速且较准确地预测最大加速度-静应力曲线,可以为冲击防护设计及相关软件的开发提供一定的帮助。

利用前视和测高声呐的UUV地形跟踪动态路径生成方法

保持对海底地形的定高跟踪航行是无人水下航行器(UUV)执行海洋勘测和水下目标搜索任务时常采用的一种运动形式,其核心是UUV如何对未知起伏的海底地形进行实时探测,并基于探测信息在线、动态地生成跟踪路径,以实现对地形的定高跟踪航行,同时避免与地形发生碰撞。针对上述问题,提出了一种基于前视声呐探测地形信息、基于多项式拟合动态生成跟踪路径的方法。首先,UUV利用前视声呐对海底地形进行实时探测,对获得的地形探测数据进行仿射处理后,得到具有离散特性的定高仿射数据。然后,采用基于最小二乘准则的三次多项式方法对仿射数据进行拟合,生成基于多项式函数描述的UUV地形跟踪航行路径。最后,设计了一种包含声呐探测、数据仿射、路径生成和跟踪控制的动态执行框架,实现UUV的实时地形跟踪航行任务。文中所提出的跟踪路径生成和动态执行框架通过对典型的海底“上坡”地形和“山地”地形跟踪的仿真验证,证明了其有效性和可行性。

改进的局部最值分段多项式拟合算法精确校正拉曼光谱基线

基线校正作为拉曼光谱预处理极为关键的步骤之一,对进一步拉曼光谱数据分析和实现拉曼成像等有重要意义。目前,最常用的基线校正算法基于多项式拟合,由于其采用手动或半手动的形式,因此依赖人工经验,对用户的专业性要求较高,处理过程繁琐,处理结果差异较大。同时,在使用过程中,多项式阶数及移动分段窗口难以选择确定,因此处理的结果常出现欠拟合或过拟合现象。针对传统多项式拟合算法的此类局限性,改进了局部最值分段多项式拟合(NPPF)算法用于精确校正拉曼光谱基线。首先采用了改进的基于分段的局部最值算法,选取光谱中最宽峰底部轮廓的近似横向宽度作为背景点窗口宽度,依次选取窗口内的最小两个值作为需要拟合的背景基线点,避免直接比较或者人工选取导致的背景点选取困难,实现更准确地选取每个背景轮廓基线点。然后通过每个窗口三次拟合迭代覆盖的方式,得到三个拟合曲线函数,选取窗口内每个点对应三个曲线函数值,分别计算与前一拟合值的差值绝对值,取绝对值最小的曲线函数值作为此点拟合曲线值,从而较好地避免了传统分段多项式拟合(PPF)算法中的欠拟合和过拟合现象,同时也确定了拟合过程中的阶数和分段窗口。模拟了两种不同背景类型的拉曼光谱,将NPPF与PPF算法分别对两种模拟光谱进行处理比较,发现NPPF处理结果均方根误差(RMSE)小,证实NPPF较于PPF的优越性。最后,对实际样品(烯啶虫胺、罗丹明6G)的拉曼光谱进行了NPPF和PPF对比处理,发现NPPF的拟合基线较为准确,证实该算法NPPF在拉曼光谱基线校正预处理中具有广泛的实际应用价值和前景。

改进的多项式曲线拟合轨迹预测算法

针对传统多项式曲线拟合轨迹预测算法对复杂多变的轨迹预测准确率不高问题,提出改进的多项式曲线拟合轨迹预测算法。首先,获得轨迹的曲率、挠率阈值;然后,通过该阈值识别预测误差可能较大的轨迹部位,并采用插值滚动预测算法进行预测;最后,采用双误差预测值更新算法,对预测值进行更新。仿真结果表明,相较于传统多项式曲线拟合轨迹预测算法,所提算法的平均位移误差(average displacement error,ADE)下降了42.77%,最终位移误差(final displacement error,FDE)下降了36.62%,从而验证了所提算法的可行性和有效性。