SIRGAS Solution: ?+ distortion model INTRODUCTION INTRODUCTION. Æ distortions. due equipaments. used in. There CA7072 SAD69 SAD96

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1 FIG Working Week Integrating Integrating Generations Generations Stockholm, Stockholm, Sweden Sweden DISTORTION DISTORTION MODELING MODELING BETWEEN BETWEEN GEODETIC GEODETIC NETWORKS NETWORKS IN IN BRAZIL: BRAZIL: A -BASED APPROACH GRID A GRIDGRID-BASED APPROACH João Paulo Magna Jú Júnior Paulo de Oliveira Camargo Maurício Galo João Francisco Galera Monico C A P E S INTRODUCTION INTRODUCTION A national geodetic network is the fundamental structure for geodetic positioning and spatial data base in a country. The geodetic networks should be consistent, precise and to accomplish the tendencies and technological evolution. Following the world tendencies and the technological evolutions, the Geodetic Brazilian System (SGB) has been updated along the years. A consequence Æ the necessity of conversion approaches to change from one frame to another. The main and most recent change occurred in February 005 with the adoption of the Geocentric Reference System for the Americas (SIRGAS000) as the new official referential. 1

2 INTRODUCTION INTRODUCTION Z1 X1 Solution: Solution: Y1 X X 1 X Y = Y + Y 1 Z Z 1 Z?+ distortion model There areideal errorscase due equipaments used in In the (abstract space) surveying and adjustment methods... Æ distortions Reference Reference Frames Frames used used in in Brazil Brazil rree AAlleegg rreeggoo onnss r r ó ó CC aliz aatti io rreealiz CA CA707 SIRGAS SIRGAS DD6699 SSAA tioionnss lizaat rreeaaliz SAD69 SAD96 FIG Working Week 008 Integrating Generations

3 DISTORTION MODELING GRID-BASED APPROACH The distortion modeling approach proposed in this research is based on three phases : To compute the distortions between the frames To generate the regular grid based on the Shepard method To interpolate the distortions of the interested points 3

4 GRID-BASED APPROACH DISTORTION COMPUTATION The distortions can be defined by the differences between the known coordinates (determined in the network adjustment process) and the calculated coordinates (through the official transformation parameters) for a set of stations. GRID GENERATION SHEPARD METHOD The distortion grid generation process consists in finding the distortion values of the grid nodes, through the known distortions in the control stations. Shepard s interpolation method: variable search radius; weighting by the distance and relative position of the nearest points. 4

5 GRID GENERATION SHEPARD METHOD Selection of the interpolation points: Example: n min = 4 e n max = 7 4 r' P 1 3 r 7 8 r' 4 P 3 r GRID GENERATION SHEPARD METHOD The distance weighting 1 d 7 d s( d) = 1 4r' r' 0 r' if 0 < d 3 r' if < d r' 3 if r' < d Weight Distance 5

6 GRID GENERATION SHEPARD METHOD The directional weighting The direction weighting has the intension of representing the shadowing of the influence of a data point P by the nearest one in the same direction. t i = j D j C ' s [1 cos( D PD )] s j D j C ' i j GRID GENERATION PRECISION INDICATOR It is also important to know the precision of the interpolated points. The computation of the precision indicator is given as: wi ( wi ) P =. ( δ δ ) i n 1 6

7 DISTORTION INTERPOLATION OF THE INTERESTED POINTS For each given point is performed the bilinear interpolation to compute the distortion and the precision indicator. 7

8 EXPERIMENTS AND RESULTS To perform the experiments, 797 homologous stations in SAD96 and SIRGAS000 were made available by Brazilian Institute of Geographic and Statistic (IBGE). In this data set: 6634 stations were used in the distortions computation; 663 stations ( 10%) were used to perform the quality control (test stations). EXPERIMENTS AND RESULTS DISTORTION ANALYSIS There is a great variability in the distortion behavior along the Brazilian territory Distortion Minimum Maximum Average Standard deviation RMS Latitude (m) Longitude (m) systematic tendency - South FIG Working not systematic Week 008 behavior Integrating Generations Middle West 8

9 EXPERIMENTS AND RESULTS DISTORTION GRID The distortion modeling was carried out by a distortion grid with a spacing of 1º x 1º, covering the Brazilian territorial limits Shepard s method parameters: n min = 4 e n max = 10 Inicial radius = 60 km Distortion (m) Precision Indicator (m) Minimum Maximum Average Average Nodes number Latitude Longitude EXPERIMENTS AND RESULTS ANALYSES IN THE TEST STATIONS To check the modeling results it was computed the distortions in the test stations and performed the comparison of the computed coordinates and the known ones. 9

10 ( ) Latitude Distortions (m) Distortions (m) g ( ) Longitude These In the stations three are cases, in the the great It final can stations be verified in the majority derivated from GNSS It is improvements also graphics observed have after a not possible the The modeling does not distortion outlier improved near modeling their station values in most 550 provide and, of in improvement stations many cases tested. in the this results case. were worst ( ) Resultant Distortions (m) Distortion before Distortion after + Improvement Test stations EXPERIMENTS AND RESULTS ANALYSES IN THE STATIONS TEST Statistics for the test stations without satellite techniques Distortions Before After Average (m) Standard (m) RMS (m) Average (m) Standard (m) RMS/Improvement Number of improved stations Test stations Latitude (-66%) % Longitude (-56%) % 435 Resultant (-63%) % 10

11 FINAL CONSIDERATIONS AND CONCLUSIONS In this paper, a contribution related to the modeling distortion process was realized, considering SAD69 (realization of 1996) and SIRGAS000 reference frames The average distortion computed was of about 0.54m with a precision indicator of 0.15m The experiments using the test stations showed that the stations originated from satellites techniques do not require corrections. The good results obtained show that the approach used appears to be very promising, as well as the Shepard method looks appropriated to the grid generation 11

12 FINAL FINAL CONSIDERATIONS CONSIDERATIONS AND AND CONCLUSIONS CONCLUSIONS This is one of the 6 approaches that have been evaluated by IBGE as a new official Brazilian distortion model. ACKNOWLEDGEMENT ACKNOWLEDGEMENT C A P E S 1

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