Saied Sadeghian; Asghar Milan Lak; Hamed Ahmadi Masine; Roohollah Karimi
Abstract
Extended Abstract
Introduction
Applying GPS/IMU data in aerial triangulation has increased the strength of photogrammetric block and reduced the number of ground control pointsneededfor block adjustment. Systematic errors in data used fortriangulation reduce the accuracy of the process and make ...
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Extended Abstract
Introduction
Applying GPS/IMU data in aerial triangulation has increased the strength of photogrammetric block and reduced the number of ground control pointsneededfor block adjustment. Systematic errors in data used fortriangulation reduce the accuracy of the process and make ground control pointsnecessarydespitetheexistenceof GPS/IMU data. Therefore, reducing systematic errorsin data naturally increases the accuracy of triangulation and reduces the number of ground control points required forblock adjustment andthe number of crossstrips used to eliminate systematic errorsin GPS data.
Materials
Digital images captured by the National Cartographic Centerof Iran from an area in Fars province usingUltraCam-Xpcamera in2010 were used in the present study to investigate the roleof self-calibration parameters in the reduction of ground control points and cross strips requiredfor block adjustmentin aerial triangulation. The intended block consists of 58 images and four strips; two of which are cross strips. Control points in this block include eight horizontal control points, eight vertical control points and eight full control points. Each image has a dimension of 11310 by 17310 pixels, a pixel dimensionof 6 microns, afocal length of 10500 microns, an end lap of 70%, and a side lap of 30%. Theregion has an average elevation of 760 m. Given the focal length, flight height and pixel dimensions, ground resolution is around 12 centimeters. Each image covers anarea of 2077.2 mlength and 1357.2 mwidth on the ground.
Methodology
The present study investigates theroleof self-calibration parameters, such as elimination of systematic error in GPS/IMU data and image sensor,in increased accuracy oftriangulation, and reduced number of ground control points and cross strips required for block adjustment. To reach this aim, optimal self-calibration parameters are determined using a genetic algorithm and the identified parameters are used in the bundle block adjustment. Variance components estimation method was used to solve the problem of equationsinstability. This method not only stabilizes the equation, but also determines the optimal weight matrix during the adjustment process.
Results and Discussion
Since images at a scale of 1:2000 were used in the present study, maximum RMSE equals 60 cm and maximum residual errorsequal 1.2 m. Using additional parameters to eliminate systematic errors results in an acceptable maximum error at the control points, but absence of additional parameters results in an unacceptable maximum error at the horizontal and vertical control points even in the presence of crossstrips. In addition to the evaluation of horizontal and vertical errors at the ground control points, horizontal and vertical RMSE of the checkpointsare also used to evaluate the geometric accuracy of aerial triangulation. Again, applying additional parameters keeps the RMSE at a much lower level than the accepted limit, while absence of additional parameters results in a horizontal and verticalRMSE higher than the accepted limit even in the presence of cross strips. It should be noted that using cross strips reduces RMSE at the vertical component.
Conclusion
Results indicated that using self-calibration parameters and reducing errorsin data used for the adjustment process decreases the number of control points and cross strips required for block adjustment.Using optimal self-calibration parameters(even in the absence of control points) resultsin a maximum RMSE of 0.143 m at the checkpoints, while absence of these parameters results in a maximum RMSE error of around one meter with or without cross strips. Genetic algorithm is capable of determining optimal self-calibration parameters. It is also capable of optimizing nonlinear functions. Therefore, it is not necessary to linearize the equations before determination of self-calibration parameters, which reduces the amount of necessary calculations. Variance components estimation can also be used along with the bundle block adjustment method to stabilize the equations and determine the optimal weight matrix. As a result, it is suggested to take advantage of these three methods, i.e. block adjustment, stabilization and optimal weight matrixdetermination, simultaneously.
Roohollah Karimi; Ali Reza Azmoude Ardalan; Siavash Yousefi
Abstract
Introduction
Components of verticaldeflection, i.e., North-South component and East-West component ,are used for accurate determination of geoid or quasigeoid. Moreover, vertical deflection components area useful source for determination of variations in subsurface density and geophysical interpretations. ...
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Introduction
Components of verticaldeflection, i.e., North-South component and East-West component ,are used for accurate determination of geoid or quasigeoid. Moreover, vertical deflection components area useful source for determination of variations in subsurface density and geophysical interpretations. Generally, there are two definitions for verticaldeflection. According to Helmert definition, vertical deflection at any given pointis the angle between the actualgravity vector (actual plumb line) and a line that is normal to the reference ellipsoid(a straight line perpendicular to the surface of reference ellipsoid). Another definition of vertical deflection is proposed by Molodensky. According this definition, vertical deflection at any given point is the angle between actualgravity vector and normal gravity vector (normal plumb line). Some relations have been introduced to convert Molodensky vertical deflection to Helmert vertical deflection. Helmert vertical deflection is estimated using astrogeodetic observations (combination of astronomical and geodetic observations).
Presently, global geopotential models (GGMs) have been expanded to the degree of2190, which is equivalenttoabout 5-min spatial resolution. Vertical deflectionat any point on the Earth can be calculated using the GGM. The resulting vertical deflection is consistent with Molodensky definition.Unfortunately, accuracy of GGMs is not sufficient for estimation of verticaldeflection.In other words, since GGMs are expanded up to a limited degree due to their resolution, omission error(or truncation error) occurs in computation of the earth’s various gravity field functionals, such as the geoidal height and verticaldeflection. Combining GGM with a digital terrain model (DTM) is a method used to reduce omission error.It should be noted that DTM has a higher spatial resolution as compared to GGM.In this method, the omitted signals of GGM can be modeled using residual terrain model (RTM) derived from subtracting high resolution DTM from a reference smooth surface. The reference smooth surface is obtained from eitherapplying average operator to DTM or expanding global topography into spherical harmonics. Fortunately, DTMs with spatial resolution of 3seconds or more,and reference smooth surface based on 2190 degree spherical harmonics are publicly available.
The present study seeks to assess vertical deflectionderived from a combination of GGM and DTM in Iran. Previously, Jekeli(1999) has studied EGM96 geopotential model with the aim of computingvertical deflection in the USA. Hirt(2010) and Hirt et al. (2010a) have assessed vertical deflection in Europe and the Alps using a combination of EGM2008 and RTM models.In Iran, GO_CONS_GCF_2_TIM_R4, a GOCE-only model, and EGM2008 geopotential model have been used toobtain vertical deflection and the results have been evaluated byKiamehr and Chavoshi-Nezhad(2014).
Materials & Methods
To implement the present study,a EGM2008 model with a spatial resolution of about 5-min is selected asGGM and a SRTM model with 3-sec spatial resolution is considered as DTM. To obtain RTM, DTM2006 model based on2190 degree spherical harmonicsis selected as the reference smooth surface.To compute the residual topography effect, prism method was used in an ellipsoidalmulti-cylindrical equal-area map projection system. First, we compute vertical deflectionusing EGM2008 model. It is also calculated using a combination of EGM2008 model and RTM(EGM2008/RTM method). In the next step, vertical deflection derived from the first method (EGM2008 model) and the second one (combination of EGM2008 model and RTM) are compared with vertical deflectionderived from astrogeodetic observations in 10 available Laplace stations in Iran.
Results & Discussion
Results indicate that there is a 1.2sec difference between North-South component of vertical deflection (i.e.) obtained from EGM2008 model and astrogeodetic observations.With RTM, this will reach 1 sec, which shows a 15% improvement. Moreover, there is a5.7secdifference between East-West component of vertical deflection () obtained from EGM2008 model and astrogeodetic observations, while this value will reach 5.6sec using RTM. Improvement in East-West component () is1.4%, which is smaller than the improvement of North-South component (). Based on the computations, we found that values of and in the Laplace stations canreach 17sec (RMS=7sec) and 15sec (RMS=8sec), respectively. Therefore, it is concluded that the relative error ofNorth-South component ()computation using EGM2008/RTM method is about 6% and the relative error ofEast-West component ()computation is about 37%.
Conclusion
The present research has studied the RTM effect on the improvement of GGM used for the determination of vertical deflectionin Iran. To performthe study, EGM2008 model with around 5-min spatial resolution was selected as GGM. RTM is also derived from subtracting the DTM2006 model (based on2190 degree spherical harmonics)from the 3-sec spatial resolutionSRTM model. Numerical findings indicate that a combination of RTM and GGM can improve the results of vertical deflectioncomputation, as compared to the results obtained from GGM-only approach. The improvement in North-South component of vertical deflection () is about15%and East-West component of the vertical deflection () undergoes about 1.4% improvement. In general, EGM2008 model and its combination with RTM have been more successful in the computation of component as compared to computationin the geographical region of Iran. There is no clear explanation for this difference, but it can be due to errors in theastronomical or geodetic observations oflongitude in Laplace stations.
Naser Abdi; Ali Reza Azmoude Ardalan; Roohollah Karimi
Abstract
Extended Abstract
Precise Point Positioning (PPP) is a technique to determine the position of a single receiver using un-differenced dual-frequency code and carrier phase observations. In this technique, the precise satellite orbit and clock products obtained from the GPS reference station network ...
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Extended Abstract
Precise Point Positioning (PPP) is a technique to determine the position of a single receiver using un-differenced dual-frequency code and carrier phase observations. In this technique, the precise satellite orbit and clock products obtained from the GPS reference station network are also required. Unlike the relative positioning techniques, the network needed for PPP is not necessary to be dense, and even a sparse network with long baselines like the International GNSS Service (IGS) network can be used. The IGS collects, archives, and distributes GPS observation data sets of sufficient accuracy to satisfy the objectives of a wide range of applications and experimentation. These data sets are used by the IGS to generate the data products which are made available to interested users through the IGS website. Moreover, in contrast to the relative positioning techniques, PPP can provide a uniform accuracy throughout the world without having the reference station observations. In the last decade, PPP has been widely used for the static and kinematic applications. The use of this technique in various applications requires to know its accuracy, processing software requirements, and performing methods. The aim of this paper is to study the performance of PPP by using the static and kinematic observations in comparison with the double difference relative solutions. For this purpose, the static observations of four dual-frequency receivers within Iranian Permanent GNSS Network (IPGN), namely AHVA, SFHN, SNDJ and TORQ, and the kinematic observations of GPS receiver installed on airplane were processed in the PPP and double difference relative solutions by the Bernese GNSS software version 5.0. The Bernese GNSS Software is a scientific, high-precision, GNSS data processing software developed at the Astronomical Institute of the University of Bern (AIUB). It is, e.g., used by Center for Orbit Determination in Europe (CODE) for its international (IGS) and European activities. In the double difference relative solution, the coordinates of 10 IGS stations in ITRF2008, which have been located around Iran, have been chosen as the weighted constraints, where the accuracy of constraints for horizontal and vertical components has been taken equal to 1 mm and 2 mm, respectively. The double difference relative results are assumed as reference values for comparisons. To find the optimum time interval of PPP for obtaining the accuracy better than 10 cm in the horizontal and vertical components, the various sessions have been taken in to account. The GPS station observations of each session are separately processed by the Bernese software in the PPP mode regarding the required parameters such as solid earth tide, ocean tidal loading, windup, antenna phase center offsets and variations for satellites and receivers, and satellite Differential Code Biases (DCBs). Then, the double difference relative results as reference values are subtracted from the obtained PPP results in X, Y and Z coordinates. To show the performance of PPP in both of horizontal and vertical components, the coordinate differences from Earth Centered Earth Fixed (ECEF) reference frame are transferred to the Local Geodetic (LG) reference frame in order to provide Northing (N), Easting (E) and Up (U) coordinates. From the PPP static results, we find that the minimum required time interval of the GPS observations is one hourin order to obtain the accuracy better than 10 cm. For assessment of the PPP performance in kinematic mode, the GPS observations collected by mounted GPS receiver on airplane are processed in relative and PPP modes. The duration of these observations is about 6 hours. In the relative kinematic processing by the Bernese software, the observations of 4 GPS reference stations within IPGN and IGS precise satellite orbit and clock products are used. The outputs of this step are three coordinates of GPS antenna mounted on airplane in 30-second epochs, which are considered as reference values. Like the static mode, the reference values are subtracted from the PPP kinematic results in X, Y and Z coordinates and transferred to the LG frame. The results show that the accuracy better than 10 cm and 20 cm can be obtained using the PPP kinematic technique in the horizontal and vertical components, respectively. These accuracies are enough for many applications such as hydrography, aerial photogrammetry and navigation. As a result, this study shows that the PPP technique can be an adequate alternative for the relative techniques.