Positional Error Model of Line Segments with Modeling and Measuring Errors Using Brownian Bridge

Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science.There are not only the measuring errors of the endpoints but also the modeling errors between the line segments and the actual geographical features.This paper presents a Brownian bridge error model for line segments combining both the modeling and measuring errors.First,the Brownian bridge is used to establish the position distribution of the actual geographic feature represented by the line segment.Second,an error propagation model with the constraints of the measuring error distribution of the endpoints is proposed.Third,a comprehensive error band of the line segment is constructed,wherein both the modeling and measuring errors are contained.The proposed error model can be used to evaluate line segments’overall accuracy and trustability influenced by modeling and measuring errors,and provides a comprehensive quality indicator for the geospatial data.

Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement.We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control(CNC)machine tools.This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method.We consider a three-axis gantry-type CNC machine tool,and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain.The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle.A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg-Marquardt nonlinear least squares method,and the geometric error is solved using Taylor’s first-order linearization iteration.The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer.For a volume of 800 mm×1000 mm×350 mm,the maximum differences of the linear,angular,and spatial position errors were 2.0μm,2.7μrad,and 12.0μm,respectively,which verifies the accuracy of the proposed algorithm.This research proposes a modeling method for the precise measurement of errors in machine tools,and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

A Combined Antenna Array Deployment with High Positioning Accuracy and Low Angular Measurement Error

In this paper,an antenna array composed of circular array and orthogonal linear array is proposed by using the design of long and short baseline“orthogonal linear array”and the circular array ambiguity resolution design of multi-group baseline clustering.The effectiveness of the antenna array in this paper is verified by sufficient simulation and experiment.After the system deviation correction work,it is found that in the L/S/C/X frequency bands,the ambiguity resolution probability is high,and the phase difference system error between each channel is basically the same.The angle measurement error is less than 0.5°,and the positioning error is less than 2.5 km.Notably,as the center frequency increases,calibration consistency improves,and the calibration frequency points become applicable over a wider frequency range.At a center frequency of 11.5 GHz,the calibration frequency point bandwidth extends to 1200 MHz.This combined antenna array deployment holds significant promise for a wide range of applications in contemporary wireless communication systems.

System error iterative identification for underwater positioning based on spectral clustering

The observation error model of the underwater acous-tic positioning system is an important factor to influence the positioning accuracy of the underwater target.For the position inconsistency error caused by considering the underwater tar-get as a mass point,as well as the observation system error,the traditional error model best estimation trajectory(EMBET)with little observed data and too many parameters can lead to the ill-condition of the parameter model.In this paper,a multi-station fusion system error model based on the optimal polynomial con-straint is constructed,and the corresponding observation sys-tem error identification based on improved spectral clustering is designed.Firstly,the reduced parameter unified modeling for the underwater target position parameters and the system error is achieved through the polynomial optimization.Then a multi-sta-tion non-oriented graph network is established,which can address the problem of the inaccurate identification for the sys-tem errors.Moreover,the similarity matrix of the spectral cluster-ing is improved,and the iterative identification for the system errors based on the improved spectral clustering is proposed.Finally,the comprehensive measured data of long baseline lake test and sea test show that the proposed method can accu-rately identify the system errors,and moreover can improve the positioning accuracy for the underwater target positioning.

A New Approach to Simulate Positional Error of Line Segment in GIS

To determine the distribution of positional error of a line segment, Monte Carlo approach is applied to simulate the probability density function of a line segment with the assumption that the error of endpoints in a line segment follows a two-dimensional normal distribution. For such purpose, a stochastic generator used for uncertain endpoints with the two-dimensional normal distribution is presented. This forms the basis of the generation of random line segment for the simulation of the error model of a whole line segment. The error models cover the cases where two endpoints are either independent or dependent to each other, also including a special case that the distance between two random endpoints in a line segment is close enough.

POSITIONAL ERROR CURVES BAND OF A PLANAR LINE SEGMENT WITHIN GISs

In this paper, the positional error curve of point features was extended to an error curves band of line segment features. Firstly, the constitution and shape of the error curves band were analyzed. On this basis, the general boundary curve formula of that band was derived. Secondly, the visualizing error curves bands were realized through three exam- ples. Finally,area index has been examined by comparing numerical results from error curves band and error ellipes band.

Multi-Branch Fault Line Location Method Based on Time Difference Matrix Fitting

The distribution network exhibits complex structural characteristics,which makes fault localization a challenging task.Especially when a branch of the multi-branch distribution network fails,the traditional multi-branch fault location algorithm makes it difficult to meet the demands of high-precision fault localization in the multi-branch distribution network system.In this paper,the multi-branch mainline is decomposed into single branch lines,transforming the complex multi-branch fault location problem into a double-ended fault location problem.Based on the different transmission characteristics of the fault-traveling wave in fault lines and non-fault lines,the endpoint reference time difference matrix S and the fault time difference matrix G were established.The time variation rule of the fault-traveling wave arriving at each endpoint before and after a fault was comprehensively utilized.To realize the fault segment location,the least square method was introduced.It was used to find the first-order fitting relation that satisfies the matching relationship between the corresponding row vector and the first-order function in the two matrices,to realize the fault segment location.Then,the time difference matrix is used to determine the traveling wave velocity,which,combined with the double-ended traveling wave location,enables accurate fault location.

Novel camera calibration method based on invariance of collinear points and pole-polar constraint

To address the eccentric error of circular marks in camera calibration,a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper.Firstly,the centers of the ellipses are extracted,and the real concentric circle center projection equation is established by exploiting the cross ratio invariance of the collinear points.Subsequently,since the infinite lines passing through the centers of the marks are parallel,the other center projection coordinates are expressed as the solution problem of linear equations.The problem of projection deviation caused by using the center of the ellipse as the real circle center projection is addressed,and the results are utilized as the true image points to achieve the high precision camera calibration.As demonstrated by the simulations and practical experiments,the proposed method performs a better location and calibration performance by achieving the actual center projection of circular marks.The relevant results confirm the precision and robustness of the proposed approach.

Calculation and correction of magnetic object positioning error caused by magnetic field gradient tensor measurement

Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object（2.44 Am^2@1 kHz） can be increased from（0.45 m, 0.75 m）,（0？, 25？） to（0.30 m, 0.80 m）,（0？,80？）, respectively.

Effect of the firing position on aiming error and probability of hit

Sources of dispersions that contribute to delivery error and reduce the soldier performance in terms of hit probability are numerous.In order to improve the warfighter performance,the source of the errors contributing to the inaccuracy and dispersion of the weapon systems must be understood.They include ammunition dispersion error,gun dispersion,aerodynamic jump and the aiming error.The aiming error or gun pointing error is defined as the angle between the gun muzzle at the instant the trigger is pulled and the line of fire that corresponds to the intendent aim point.This is a round-to-round error.In weapons systems that include the rifle,the ammunition,a sight and a gunner,the aiming error was shown to be the single most important source of dispersion for the regular infantryman.In other words,for the general purpose rifle weapon system,the weak link is often the human.In order to verify and quantify this assertion,an experimental investigation was carried out to determine the aiming error associated with general purpose rifle fired by infantryman.The aiming error was evaluated for various firing positions and scenarios using infantryman for ranges varying between 100 m and 500 m.The results show that the aiming error is the main contributor to dispersion for the general purpose rifle fired by a non-specialized infantryman.The aiming error induced dispersion for unstressed and rested gunners is shown to be at best equivalent to that of the weapon fired from a bench rest by a marksman.Crown Copyright(?) 2019 Production and hosting by Elsevier B.V.on behalf of China Ordnance Society.

Motor Imagery and Error Related Potential Induced Position Control of a Robotic Arm

The paper introduces an electroencephalography(EEG) driven online position control scheme for a robot arm by utilizing motor imagery to activate and error related potential(ErrP) to stop the movement of the individual links, following a fixed(pre-defined) order of link selection. The right(left)hand motor imagery is used to turn a link clockwise(counterclockwise) and foot imagery is used to move a link forward. The occurrence of ErrP here indicates that the link under motion crosses the visually fixed target position, which usually is a plane/line/point depending on the desired transition of the link across 3D planes/around 2D lines/along 2D lines respectively. The imagined task about individual link's movement is decoded by a classifier into three possible class labels: clockwise, counterclockwise and no movement in case of rotational movements and forward, backward and no movement in case of translational movements. One additional classifier is required to detect the occurrence of the ErrP signal, elicited due to visually inspired positional link error with reference to a geometrically selected target position. Wavelet coefficients and adaptive autoregressive parameters are extracted as features for motor imagery and ErrP signals respectively. Support vector machine classifiers are used to decode motor imagination and ErrP with high classification accuracy above 80%. The average time taken by the proposed scheme to decode and execute control intentions for the complete movement of three links of a robot is approximately33 seconds. The steady-state error and peak overshoot of the proposed controller are experimentally obtained as 1.1% and4.6% respectively.

Kinematic Geometry for the Saddle Line Fitting of Planar Discrete Positions

The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curve needs to minimize the maximum fitting error to acquire the dimension of a planar binary P-R link. Based on the saddle point programming, the fitting straight line is determined to the planar discrete point-path traced by the point of the rigid body in planar motion. The property and evolution of the defined saddle line error can be revealed from three given separate points. A quartic algebraic equation relating the fitting error and the coordinates is derived, which agrees with the classical theory. The effect of the fourth point is discussed in three cases through the constraint equations. The multi-position saddle line error is obtained by combination and comparison from the saddle point programming. Several examples are presented to illustrate the solution process for the saddle line error of the moving plane. The saddle line error surface and the contour map presented to show the variations of the fitting error in the fixed frame. The discrete kinematic geometry is then set up to disclose the relations of the separate positions of the rigid body, the location of the tracing point on the moving body, and the position and orientation of the saddle line to the point-path. This paper presents a new analytic geometry method for saddle line fitting and provides a theoretical foundation for position synthesis.

Using self-location to calibrate the errors of observer positions for source localization

The uncertainty of observers＇ positions can lead to significantly degrading in source localization accuracy. This pa-per proposes a method of using self-location for calibrating the positions of observer stations in source localization to reduce the errors of the observer positions and improve the accuracy of the source localization. The relative distance measurements of the two coordinative observers are used for the linear minimum mean square error （LMMSE） estimator. The results of computer si-mulations prove the feasibility and effectiveness of the proposed method. With the general estimation errors of observers＇ positions, the MSE of the source localization with self-location calibration, which is significantly lower than that without self-location calibra-tion, is approximating to the Cramer-Rao lower bound （CRLB）.

Influence of positioning errors of optical shaping components for single emitter laser diode on beam shaping effects

Beam shaping is required for semiconductor lasers to achieve high optical fiber coupling efficiency in many applications.But the positioning errors on optics may reduce beam shaping effects,and then lead to low optical fiber coupling efficiency.In this work,the positioning errors models for the single emitter laser diode beam shaping system are established.Moreover,the relationships between the errors and the beam shaping effect of each shapers are analysed.Subsequently,the relationship between the errors and the optical fiber coupling efficiency is analysed.The result shows that position errors in the Z axis direction on the fast axis collimator have the greatest influence on the shaping effect,followed by the position errors in the Z axis direction on the converging lens,which should be strictly suppressed in actual operation.Besides,the position errors have a significant influence on the optical fiber coupling efficiency and need to be avoided.

Effects of laser beam divergence angle on airborne LIDAR positioning errors

The influence of laser beam divergence angle on the positioning accuracy of scanning airborne light detection and ranging （LIDAR） is analyzed and simulated. Based on the data process and positioning principle of airborne LIDAR, the errors from pulse broadening induced by laser beam di vergence angle are modeled and qualitatively analyzed for different terrain surfaces. Simulated results of positioning errors and suggestions to reduce them are given for the flat surface, the downhill of slope surface, and the uphill surface.

Cone beam computed tomography-guided differences among registration methods for lung cancer and the effects of tumor position,treatment model,and tumor size on positioning errors

Objective To explore the differences in three different registration methods of cone beam computed tomography(CBCT)-guided down-regulated intense radiation therapy for lung cancer as well as the effects of tumor location,treatment mode,and tumor size on registration.Methods This retrospective analysis included 80 lung cancer patients undergoing radiotherapy in our hospital from November 2017 to October 2019 and compared automatic bone registration,automatic grayscale(t+r)registration,and automatic grayscale(t)positioning error on the X-,Y-,and Z-axes under three types of registration methods.The patients were also grouped according to tumor position,treatment mode,and tumor size to compare positioning errors.Results On the X-,Y-,and Z-axes,automatic grayscale(t+r)and automatic grayscale(t)registration showed a better trend.Analysis of the different treatment modes showed differences in the three registration methods;however,these were not statistically significant.Analysis according to tumor sizes showed significant differences between the three registration methods(P<0.05).Analysis according to tumor positions showed differences in the X-and Y-axes that were not significant(P>0.05),while the autopsy registration in the Z-axis showed the largest difference in the mediastinal and hilar lymph nodes(P<0.05).Conclusion The treatment mode was not the main factor affecting registration error in lung cancer.Three registration methods are available for tumors in the upper and lower lungs measuring<3 cm;among these,automatic gray registration is recommended,while any gray registration method is recommended for tumors located in the mediastinal hilar site measuring<3 cm and in the upper and lower lungs≥3 cm.

Error Analysis on the Positioning Accuracy of a Pneumatic Vibration Isolator

A method of error analysis on the positioning accuracy of a pneumatic vibration isolator was proposed.First,the necessity of positioning accuracy was studied,in addition to the key factors associated with positioning accuracy.These analyses indicated that the positioning accuracy of the pneumatic vibration isolator was mainly attributed to the position error of the push button and the gap between the spindle and valve stem.Second,the error model of the positioning accuracy of the pneumatic vibration isolator was established through geometric simplification and geometric calculation.There are different methods used to calculate the position error of the push button for the different valves.Finally,an example analysis evaluating the impact of a specific two-position three-way valve on the positioning accuracy was given by means of error distribution.Experimental results validated the accuracy of the error model and the example analysis.This error model can be used to guide the structural parameter optimization design according to the requirements for positioning accuracy.

Endemic error correction model and quantitative analysis of precise point positioning

To identify the endemic error of the precise point positioning which cannot be weakened or eliminated in precise point positioning (PPP) zero-difference model, the 24 h observation data acquired from CHAN station on Oct 31st, 2010, were adopted for analyses, different correction models of various errors were discussed and their influences on traditional zero-difference model were analyzed. The results show that the errors cannot be ignored. They must be corrected with suitable models and estimated with auxiliary parameters. The influence magnitudes of all errors are defined, and the results have guiding significance to improve the accuracy of precise point positioning zero-difference model.

Partition of Forecast Error into Positional and Structural Components

Weather manifests in spatiotemporally coherent structures.Weather forecasts hence are affected by both positional and structural or amplitude errors.This has been long recognized by practicing forecasters(cf.,e.g.,Tropical Cyclone track and intensity errors).Despite the emergence in recent decades of various objective methods for the diagnosis of positional forecast errors,most routine verification or statistical post-processing methods implicitly assume that forecasts have no positional error.The Forecast Error Decomposition(FED)method proposed in this study uses the Field Alignment technique which aligns a gridded forecast with its verifying analysis field.The total error is then partitioned into three orthogonal components:(a)large scale positional,(b)large scale structural,and(c)small scale error variance.The use of FED is demonstrated over a month-long MSLP data set.As expected,positional errors are often characterized by dipole patterns related to the displacement of features,while structural errors appear with single extrema,indicative of magnitude problems.The most important result of this study is that over the test period,more than 50%of the total mean sea level pressure forecast error variance is associated with large scale positional error.The importance of positional error in forecasts of other variables and over different time periods remain to be explored.

Relationship of Milk Line Position with Grain Weight and Mechanized Harvest of Summer Corn

To investigate the relationship of milk line position with grain weight and mechanized harvest of summer corn in Huang-Huai-Hai Region, 8 varieties （A, B, C, D, E, F, G, H） with large planting areas were selected to measure the grain filling rate, 100-grain weight, water content and milk line position, and the correlation was analyzed. Results showed that when the milk line position was 90%, the grain filling of all the 8 varieties finished and 100-grain weight reached the highest value, which was 43.02 g. The grain filling time was in positive correlation with 100-grain weight. However, when the milk line position completely disappeared, the 100-grain weight was reduced by 8.66% at most. There was no significant difference during the periods of grain weight rising, but in the periods of grain weight falling, the traits of D, E, H were significantly different with the other varieties, and water loss rate of C and A showed significant difference with the other six varieties. The water content of grain was negatively correlated with milk line position. When the milk line percentage was 90% , the grain water content was less than 30% . The key factor influencing the mechanized harvest of summer corn is harvesting time, rather than the varieties. Moreover, milk-line position of 90% is the best time for harvest; if the harvest is too late, the yield will be reduced with varying degrees.