CN102313533A - Method for data error analysis of on-orbit exploration of lunar laser altimeter - Google Patents

Method for data error analysis of on-orbit exploration of lunar laser altimeter Download PDF

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CN102313533A
CN102313533A CN201110213398A CN201110213398A CN102313533A CN 102313533 A CN102313533 A CN 102313533A CN 201110213398 A CN201110213398 A CN 201110213398A CN 201110213398 A CN201110213398 A CN 201110213398A CN 102313533 A CN102313533 A CN 102313533A
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zone
latitude
point
error
elevation
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CN102313533B (en
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宋爱国
王东霞
李会军
平劲松
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JIANGSU SHUANGSHUANG HI-TECH CO., LTD.
Southeast University
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Abstract

The invention discloses a method for data error analysis of an on-orbit exploration pole region of a lunar laser altimeter, and the method comprises the following steps: performing region division on lunar massive elevation data measured by the laser altimeter according to latitude; searching elevation measurement repeated point sets in all the divided regions; performing gross error elimination and calculation of residual error and standard error on the searched measurement repeated point sets; and performing contrast and analysis of error distribution characteristics on elevation data processing results in the regions in which the south latitude and the north latitude are the same. By adopting the processing method, search and data processing can be performed on measurement repeated points in the lunar elevation massive data in a faster manner, contrastive analysis can be further performed on the measurement data in the regions with the same latitude in south and north pole regions, and the distribution situation of the residual error and the standard error after the lunar elevation data error processing can be given out. Therefore, a basis is provided for further analysis of measurement error sources of the laser altimeter, and theoretical guide and reference data are provided for design of various effective loads carried by a lunar exploration satellite on precision requirements.

Description

Moon laser altimeter is in the method for rail detection data error analysis
Technical field
The present invention relates to the error processing method of a kind of moon, relate in particular to the laser altimeter that carries for CE-1 number error analysis method at the rail detection data at the rail detection data.
Background technology
On October 24th, 2007, a China's first lunar orbiting exploration satellite Chang'e I launches in Xichang Launching Site, operates on the circular polar orbit of moonscape 200 km and carries out the scientific exploration task.Satellite has carried eight kinds of scientific exploration instruments (being useful load).Obtaining whole month face 3-dimensional image figure is the primary science task of Chang'e I; The laser altimeter that carries on the satellite is an important load that realizes obtaining the moonscape 3-dimensional image; Realized sub-satellite point menology Terrain Elevation Data Acquisition, for obtaining of moonscape 3-dimensional image provides service.
Have only U.S. Clementine, Apollo15, Apollo16, Apollo17, the SELENE of Japan and " Chang'e I (CE-1) " satellite of China that moonscape was carried out laser ranging at present.But Clementine laser elevation sampled point lacks the valid data in zone more than south poles ± 75 °; And before SELENE, the high latitude area that surpasses 86 ° does not have height measured data, has only the laser acquisition data of SELENE and CE-1 to cover the face whole month.
Succeeding in sending up and moving of " Chang'e I " lunar exploration satellite is China's interior lunar space environment of the detection range earth 400,000 km scopes for the first time.Space environment will be the important place that Future in China is carried out space operation the ground-moon; And in this area of space; Exist the intense activity of cosmic rays, solar flare and CME etc., often be accompanied by the unexpected release of huge space radiation energy and high energy particle.Be operated in the above-mentioned more abominable space environment just because of " Chang'e I " lunar exploration satellite; Uncertain thermal environment, electromagnetic environment in the space environment; And the bombardment of space high energy particle and neutron irradiation; Particularly contingent at any time space electromagnetism storm etc. not only can influence the control accuracy of lunar exploration satellite, and can bring tangible measuring error to the various useful load (lunar observation instrument) of carrying on the lunar exploration satellite, reduces measuring reliability and measuring accuracy; Because the influence of a plurality of links such as instrument system noise, menology topographic relief, satellite orbit and attitude measurement contains error in the high data of the original survey of laser altimeter inevitably.Through a series of data processing, rejecting, system compensation, geometry location and the elevation that mainly comprises invalid data such as resolves at the 2B level science data that obtain possibly introduce new process errors again.The CE-1 laser altimeter is not also carried out in the error analysis of rail moon elevation detection data both at home and abroad; The particularly full polar region of the moon laser altimeter altitude figures detection of being unrealized before SELENE and CE-1; Therefore be necessary moon polar region altitude figures in the moon elevation detection data is carried out error analysis and research, for the source of further analyzing the moon two polar region errors provides certain scientific basis.
Summary of the invention
The present invention proposes the method for a kind of moon laser altimeter in the error analysis of rail detection data; This disposal route can be to measuring the processing repeat a little to search for quickly with data in the moon elevation mass data; And the measurement data to moon southern hemisphere and northern hemisphere same latitude district can compare analysis, provides the distribution situation that moon vertical error is handled back residual error and standard deviation.For the source of further analyzing the laser altimeter measuring error provides foundation.
The present invention adopts following technical scheme: a kind of moon laser altimeter comprises the steps: in the method for rail detection data error analysis
Obtain laser altimeter altitude figures file: the track of China's Chang'e I satellite is a polar circle moon track, and track is one around moon circumference.The every spot elevation data of sampling at a distance from a second of the laser altimeter that carries; The scientific exploration data of laser altimeter during the Chang'e I lunar exploration are 1400 rails altogether; Form 1400 track files, said track fileinfo comprises elevation sampling time, the moon longitude of sampled point, latitude, the altitude figures information of laser altimeter.
Step 1:From 1400 track files that moon laser altimeter records, select respectively and belong to L1 ~ h1Spot elevation data recording in the zone, L1Be regional lower boundary, L1=60+step* (i-1), unit is a latitude, and L1>=60 H1Be regional coboundary, H1=60+step*i, unit is a latitude, and H1≤90, StepFor step-length and Step=0.1, I=1,2,3 ..., 300, obtaining latitude is that 60 ° ~ 90 ° moonscapes are cut apart 300 zones of formation and corresponded respectively to the data recording of the spot elevation in 300 zones; Simultaneously,
From 1400 track files that moon laser altimeter records, select respectively and belong to L2 ~ h2Spot elevation data recording in the zone, L2Be regional lower boundary, L2=-60-step*i, unit is a latitude, and L2>=-90 H2Be regional coboundary, H2=-60-step* (i-1), unit is a latitude, and H2≤-60, StepFor step-length and Step=0.1, I=1,2,3 ..., 300, obtaining latitude is that-60 ° ~-90 ° moonscapes are cut apart 300 zones of formation and corresponded respectively to the data recording of the spot elevation in 300 zones;
Step 2:Search for duplicate measurements point in each zone one by one, the method for search duplicate measurements point is in each zone:
Step 2.1Respectively with each zone as pending zone, the order k=1,
Step 2.2Choose any spot elevation in the pending zone,
Step 2.3Find spherical distance between the selected spot elevation less than all spot elevations in 200 meters the pending zone, and with said all spot elevations and a said selected spot elevation as 1 duplicate measurements point point set
Figure 748675DEST_PATH_IMAGE001
,
Figure 821674DEST_PATH_IMAGE001
Expression the kIndividual duplicate measurements point point set is put point set with duplicate measurements again
Figure 602679DEST_PATH_IMAGE001
In spot elevation from pending zone, remove, otherwise, if in the pending zone arbitrarily the distance between the left point greater than 200 meters, simultaneously, order: current k= N, then the duplicate measurements point search finishes,
Said spherical distance
Figure 698811DEST_PATH_IMAGE002
does
Figure 472732DEST_PATH_IMAGE003
RFor with the radius of sphericity of reference ellipsoid as positive spheroid, , Be respectively 2 latitudes on the sphere;
Figure 935571DEST_PATH_IMAGE006
Be respectively on the sphere 2 longitude,
Step 2.4Order k= k + 1, return step 2.2,
Step 3: calculate each regional residual sum standard deviation one by one, the method for calculating each regional residual sum standard deviation is:
Step 3.1Calculate current each duplicate measurements point point set that is present in the zone to be calculated
Figure 450866DEST_PATH_IMAGE001
In the average of spot elevation
Figure 246259DEST_PATH_IMAGE007
And residual error
Figure 618335DEST_PATH_IMAGE008
, wherein, duplicate measurements point point set
Figure 423480DEST_PATH_IMAGE001
In the average of spot elevation
Figure 289936DEST_PATH_IMAGE009
,
Figure 192033DEST_PATH_IMAGE010
Be point set
Figure 672693DEST_PATH_IMAGE001
In jThe height value of individual point, nBe point set Total number of middle spot elevation, duplicate measurements point point set
Figure 635281DEST_PATH_IMAGE001
In the residual values of each spot elevation do
Figure 657463DEST_PATH_IMAGE011
,
Step 3.2Calculate the standard deviation in the zone to be calculated
Figure 122074DEST_PATH_IMAGE012
,
Figure 901811DEST_PATH_IMAGE013
, NRepresent regional duplicate measurements point point set sum to be calculated, mAll spot elevation sums in the zone to be calculated in the expression,
Step 3.3Residual values and standard deviation to being obtained by step 3.1, step 3.2. are carried out the rejecting of gross error, and following method is adopted in the rejecting of gross error: with residual absolute value greater than 3 times of standard deviations promptly
Figure 359337DEST_PATH_IMAGE014
Altitude figures point as the gross error point, from the zone, reject the data recording of the spot elevation corresponding, and from duplicate measurements point point set with gross error point
Figure 173709DEST_PATH_IMAGE001
The middle gross error point of rejecting returns step 3.1; If all residual absolute values are smaller or equal to 3 times of standard deviations
Figure 812151DEST_PATH_IMAGE015
Promptly , then preserve all the spot elevation residual values in current zone to be calculated and the whole regional standard difference result in zone to be calculated, and carry out the calculating of the ultimate criterion difference in final zone to be calculated,
Step 4:Altitude figures result to latitude same latitude district, north and south, moon the two poles of the earth compares, the analytical error characteristic distributions, and method is:
The regional residual error of result of calculation contrast moon south poles same latitude according to step 3 distributes, and draws each spot elevation place moon longitude of residual sum of each spot elevation in each zone, the distribution plan of latitude; Each the regional standard deviation that obtains according to step 3, and drawing area and standard deviation distribution plan.
Advantage of the present invention:
(1) the error analysis research to moon laser altimeter altitude figures is to carry out first; To the error analysis of laser altimeter detection data research, the design of the various useful load (lunar observation instrument) that can carry for the lunar exploration satellite provides theoretical direction and reference data in accuracy requirement.
(2) handle through the moonscape zoning being carried out altitude figures, can realize effectively handling fast mass data.
(3) the present invention can compare analysis to the measurement data in moon southern hemisphere and northern hemisphere same latitude district, provides the distribution situation of residual error and standard deviation after the moon altitude figures Error processing.For the source of further analyzing the laser altimeter measuring error provides foundation.
(4) pass through error result and Analysis of error source; Orbit data in conjunction with moonik; The distribution situation of spatial and temporal distributions angle inverting lunar space environment thermal environment, electromagnetic environment and the high energy particle radiation belt that also can produce from measuring error, and the probability of the incident of undergoing mutation in the environment of lunar space.
(5) can the method be used for the error analysis of the scientific exploration data of other celestial bodies.
Description of drawings
Fig. 1 moon two polar region menologies are cut apart the area schematic of formation.
The measurement that searches in selected certain zone of Fig. 2 repeats a little NIndividual point set
Figure 340401DEST_PATH_IMAGE017
Launch synoptic diagram by the distribution of region longitude.
Fig. 3 latitude area-88.0 °～-88.1 ° of longitude-residual error distribution scatter diagrams.
88.0 °～88.1 ° longitudes of Fig. 4 latitude area-residual error distribution scatter diagram.
60 °～90 ° each latitude area-standard deviation distribution plans of Fig. 5 latitude scope.
Fig. 6 latitude scope-60 °～-90 ° of each latitude area-standard deviation distribution plans.
86 °～90 ° scopes of Fig. 7 north and south latitude are the zone of totally 80 latitude areas-standard deviation distribution plan.
60 °～90 ° scopes of Fig. 8 north and south latitude are the zone of totally 600 latitude areas-standard deviation distribution plan.
Fig. 9 main flow chart.
Figure 10 calculates each regional residual error and standard deviation distribution sub-process figure.
Embodiment:
Below in conjunction with accompanying drawing the present invention is further specified:
A kind of method that is used for moon laser altimeter in the error analysis of rail detection data is characterized in that concrete steps are following:
Obtain laser altimeter altitude figures file: the track of China's Chang'e I satellite is a polar circle moon track, and track is one around moon circumference.The every spot elevation data of sampling at a distance from a second of the laser altimeter that carries; The scientific exploration data of laser altimeter during the Chang'e I lunar exploration are 1400 rails altogether; Form 1400 track files, said track fileinfo comprises elevation sampling time, the moon longitude of sampled point, latitude, the altitude figures information of laser altimeter.
Laser altimeter carries on the Chang'e I satellite; Sample track to the menology elevation also is to get back to the polar circle moon track of polar region again from the polar region, so the closer to the polar region, number of data points distributes intensive more; Measurement repeats a little many more; Low latitude district in the moon, image data point distributes sparse more, measure repeat a little few more.Repeat a little search and the scheme of altitude figures Error processing and analysis so adopt two polar region altitude figuress records to carry out each area inner measuring by the latitude zoning.
Step 1:From 1400 track files that moon laser altimeter records, select respectively and belong to L1 ~ h1Spot elevation data recording in the zone, L1Be regional lower boundary, L1=60+step* (i-1), unit is a latitude, and L1>=60 H1Be regional coboundary, H1=60+step*i, unit is a latitude, and H1≤90, StepFor step-length and Step=0.1, I=1,2,3 ..., 300, obtaining latitude is that 60 ° ~ 90 ° moonscapes are cut apart 300 zones of formation and corresponded respectively to the data recording of the spot elevation in 300 zones;
Be illustrated in figure 1 as the sectional view of moonscape Region Segmentation, 70 °～70.1 ° in the moon Northern Hemisphere latitude that indicates among the figure, 70.1 °～70.2 ° is wherein two zones in above-mentioned 300 zones.
Simultaneously, from 1400 track files that moon laser altimeter records, select respectively and belong to L2 ~ h2Spot elevation data recording in the zone, L2Be regional lower boundary, L2=-60-step*i, unit is a latitude, and L2>=-90 H2Be regional coboundary, H2=-60-step* (i-1), unit is a latitude, and H2≤-60, StepFor step-length and Step=0.1, I=1,2,3 ..., 300, obtaining latitude is that-60 ° ~-90 ° moonscapes are cut apart 300 zones of formation and corresponded respectively to the data recording of the spot elevation in 300 zones;
Be illustrated in figure 1 as the moon the Southern Hemisphere latitude-70 that indicates in the sectional view of moonscape Region Segmentation °～-70.1 ° ,-70.1 °～-70.2 ° is wherein two zones in-60 ° ~-90 ° moonscapes 300 zones cutting apart formation to latitude.
Step 2:Search for duplicate measurements point in each zone one by one, the method for search duplicate measurements point is in each zone:
Step 2.1Respectively with each zone as pending zone, the order k=1,
Step 2.2Choose any spot elevation in the pending zone,
Step 2.3Find spherical distance between the selected spot elevation less than all spot elevations in 200 meters the pending zone, and with said all spot elevations and a said selected spot elevation as 1 duplicate measurements point point set
Figure 822329DEST_PATH_IMAGE001
, Expression the kIndividual duplicate measurements point point set, for example shown in Figure 2 is that the measurement that searches in institute's favored area repeats a point set by region longitude expansion synoptic diagram.Again point set is put in duplicate measurements
Figure 632339DEST_PATH_IMAGE001
In spot elevation from pending zone, remove, otherwise, if in the pending zone arbitrarily the distance between the left point greater than 200 meters, simultaneously, order: current k= N, then the duplicate measurements point search finishes,
Said spherical distance
Figure 447980DEST_PATH_IMAGE002
does
Figure 971365DEST_PATH_IMAGE003
RFor with the radius of sphericity of reference ellipsoid as positive spheroid,
Figure 197947DEST_PATH_IMAGE004
,
Figure 252622DEST_PATH_IMAGE005
Be respectively 2 latitudes on the sphere;
Figure 793324DEST_PATH_IMAGE006
Be respectively on the sphere 2 longitude,
Step 2.4Order k= k + 1, return step 2.2,
Step 3: calculate each regional residual sum standard deviation one by one, the method for calculating each regional residual sum standard deviation is:
Step 3.1Calculate current each duplicate measurements point point set that is present in the zone to be calculated
Figure 233533DEST_PATH_IMAGE001
In the average of spot elevation
Figure 834279DEST_PATH_IMAGE007
And residual error
Figure 107741DEST_PATH_IMAGE008
, wherein, duplicate measurements point point set
Figure 514451DEST_PATH_IMAGE001
In the average of spot elevation
Figure 746849DEST_PATH_IMAGE009
,
Figure 331546DEST_PATH_IMAGE010
Be point set
Figure 344501DEST_PATH_IMAGE001
In jThe height value of individual point, nBe point set
Figure 227006DEST_PATH_IMAGE001
Total number of middle spot elevation, duplicate measurements point point set
Figure 392540DEST_PATH_IMAGE001
In the residual values of each spot elevation do
Figure 335088DEST_PATH_IMAGE011
,
Step 3.2Calculate the standard deviation in the zone to be calculated
Figure 835339DEST_PATH_IMAGE012
,
Figure 334585DEST_PATH_IMAGE013
, NRepresent regional duplicate measurements point point set sum to be calculated, mAll spot elevation sums in the zone to be calculated in the expression,
Step 3.3Residual values and standard deviation to being obtained by step 3.1, step 3.2. are carried out the rejecting of gross error.
According to orbit Design and the actual rail data of surveying, the orbit altitude of CE-1 is (200 ± 25) km scope, about 20 km of the maximum topographic relief of moonscape, so the rational distance measurement value of laser altimeter also should be within this scope., signal to noise ratio (S/N ratio) smooth owing to abnormal signal, menology noise, lunar surface accident of terrain crossed reasons such as low, and some distance measurement value reading has exceeded this scope, need weed out.The elimination of rough difference method has Lay with special criterion, Dixon criterion and Vladimir Romanovskiy criterion etc.; Because number of data points is very many; Be hundreds of or several thousand points; And lunar surface altitude figures Normal Distribution for guaranteeing safe rejecting and the high precision and the high efficiency of data, has adopted Lay to handle with special criterion here.Levin culling gross error to adopt special guidelines: the residual absolute value greater than three times the standard deviation
Figure 541575DEST_PATH_IMAGE015
is elevation data point as a gross error points removed from the regional point of gross errors and corresponding elevation point data logging, and from the repeated measurements little collection
Figure 642572DEST_PATH_IMAGE001
to exclude gross errors point, return to step 3.1; if all residuals absolute value less than or equal to 3 times the standard deviation
Figure 671141DEST_PATH_IMAGE015
is
Figure 60534DEST_PATH_IMAGE016
, then save the current zone to be calculated for all elevation points to be calculated residuals and standard deviation of the entire area of zone results the final area to be calculated and the final standard deviation is calculated,
Step 4:Altitude figures result to latitude same latitude district, north and south, moon the two poles of the earth compares, the analytical error characteristic distributions, and method is:
The regional residual error of result of calculation contrast moon south poles same latitude according to step 3 distributes, and draws each spot elevation place moon longitude distribution plan of residual sum of each spot elevation in each zone; Each the regional standard deviation that obtains according to step 3, and drawing area and standard deviation distribution plan.
Like latitude area-88.0 °～-88.1 ° of longitude-residual error distribution scatter diagram such as Fig. 3,88.0 °～88.1 ° longitude-residual error distribution scatter diagram such as Fig. 4 of latitude area.88.0 °～88.1 ° zones of latitude search to measure and repeat 649 of point set sums, and after handling through step 3, the regional standard difference is 71.21m, and the altitude figures that relates to is counted 1240; Latitude-88.0 °～-88.1 ° of zones searches to measure and repeats 895 of point set sums, and after handling through step 3, the regional standard difference is 102.17m, and it is 1778 that the altitude figures that relates to is counted.
60 °～90 ° each regional standard deviation result of calculation such as Fig. 5 and Fig. 6 of being cut apart of polar region, north and south latitude scope; Wherein in 60 °～90 ° scopes of Fig. 5 middle latitude, there are two regional standard differences obviously bigger than normal; They are 73 °～73.1 ° of latitude areas; The regional standard difference is 219.55m, 73.1 °～73.2 ° of latitude areas, and the regional standard difference is 166.93m.A regional standard difference near lunar North Pole point among Fig. 5 is often big, is clear contrast two polar region standard deviations, and this zone is not shown in the diagram, and it is 89.8 °～89.9 ° of latitude areas, and the regional standard difference is 293.00m; Have two regional standard differences obviously bigger than normal in Fig. 6 middle latitude-60 °～-90 ° of scopes, they are latitude areas-75.4 °～-75.5 °, and the regional standard difference is 186.46m; Latitude area-65.5 °～65.6 °, the regional standard difference is 185.47m, in Fig. 6 above-mentioned 2 standard deviations bigger than normal; Lunar South Pole is unusual big zone near limit two regional standard differences in addition; Poor for each regional standard of clear contrast two polar regions, this two zone is not shown in the diagram, and they are; Latitude area-89.7 °～-89.8 °, the regional standard difference is 460.89m, latitude area-89.8 °～-89.9 °, the regional standard difference is 793.59m.
And before SELENE; The high latitude area that surpasses 86 ° does not have height measured data; Have only the laser acquisition data of SELENE and CE-1 to cover the face whole month; Therefore drawn standard deviation result of calculation comparison diagram Fig. 7 that 86 °～90 ° intervals of two polar region latitudes have about 80 intervals altogether (wherein-89.7 °～-89.8 ° do not put into figure with-89.8 °～-89.9 °) specially with 89.8 °～89.9 ° three zones of latitude; Abscissa value is on the occasion of being 86 °～90 ° 40 zones that are divided into of latitude scope among the figure; Abscissa value be negative value be latitude scope-86 °～-90 ° of 40 zones that are divided into, the direction that the horizontal ordinate absolute value increases is towards the moon two extreme directions.Be that horizontal ordinate is that 40 zone is 89.9～90 ° of zones of latitude.From Fig. 7, the zone is during near moon the two poles of the earth, and the standard deviation in lunar South Pole zone is bigger than normal.
Step 3 is calculated whole 595 (600 zones altogether; Remove latitude area-89.7 °～-89.8 ° ,-89.8 °～-89.9 ° and unusual big zone of 89.8 °～89.9 ° three standard deviations of latitude area; And 89.9 °～90 ° of latitude areas with-89.9 °～-90 ° in the elevation posting field is not arranged) zone and respective standard difference be listed among Fig. 8 by the two poles of the earth areal distribution in proper order; The direction that the horizontal ordinate absolute value increases is towards the moon two extreme directions; The whole difference of two polar region standard deviations is apparent in view near the position of two polar region limits; The average difference in 298 zones that Fig. 8 middle latitude scope is 60 °～90 ° is 74.16m; The average difference in 297 zones of latitude scope-60 °～-90 ° of scopes is 83.67m, and whole latitude scope-60 °～-90 ° is that 60 °～90 ° inner region standard deviations of south latitude latitude scope are bigger than normal.
Cause 60 °～90 ° reasons that the range criterion difference is bigger than normal of polar region, moon north and south latitude; Except that the landform that will consider the moon itself changes evident characteristic; If other orbit data in conjunction with moonik; Also can study from the distribution situation of spatial and temporal distributions angle inverting lunar space environment thermal environment, electromagnetic environment and the high energy particle radiation belt of measuring error generation, and the probability of the incident of undergoing mutation in the environment of lunar space.

Claims (1)

1. a moon laser altimeter is characterized in that in the method for rail detection data error analysis concrete steps are following:
Step 1:From 1400 track files that moon laser altimeter records, select respectively and belong to L1 ~ h1Spot elevation data recording in the zone, L1Be regional lower boundary, L1=60+step* (i-1), unit is a latitude, and L1>=60 H1Be regional coboundary, H1=60+step*i, unit is a latitude, and H1≤90, StepFor step-length and Step=0.1, I=1,2,3 ..., 300, obtaining latitude is that 60 ° ~ 90 ° moonscapes are cut apart 300 zones of formation and corresponded respectively to the data recording of the spot elevation in 300 zones; Simultaneously,
From 1400 track files that moon laser altimeter records, select respectively and belong to L2 ~ h2Spot elevation data recording in the zone, L2Be regional lower boundary, L2=-60-step*i, unit is a latitude, and L2>=-90 H2Be regional coboundary, H2=-60-step* (i-1), unit is a latitude, and H2≤-60, StepFor step-length and Step=0.1, I=1,2,3 ..., 300, obtaining latitude is that-60 ° ~-90 ° moonscapes are cut apart 300 zones of formation and corresponded respectively to the data recording of the spot elevation in 300 zones;
Step 2:Search for duplicate measurements point in each zone one by one, the method for search duplicate measurements point is in each zone:
Respectively with each zone as pending zone, the order k=1,
Choose any spot elevation in the pending zone,
Find spherical distance between the selected spot elevation less than all spot elevations in 200 meters the pending zone, and with said all spot elevations and a said selected spot elevation as 1 duplicate measurements point point set
Figure 899801DEST_PATH_IMAGE001
,
Figure 374645DEST_PATH_IMAGE001
Expression the kIndividual duplicate measurements point point set is put point set with duplicate measurements again
Figure 402643DEST_PATH_IMAGE001
In spot elevation from pending zone, remove, otherwise, if in the pending zone arbitrarily the distance between the left point greater than 200 meters, simultaneously, order: current k= N, then the duplicate measurements point search finishes,
Said spherical distance does
Figure 914844DEST_PATH_IMAGE003
RFor with the radius of sphericity of reference ellipsoid as positive spheroid,
Figure 549088DEST_PATH_IMAGE004
,
Figure 928248DEST_PATH_IMAGE005
Be respectively 2 latitudes on the sphere;
Figure 292233DEST_PATH_IMAGE006
Be respectively on the sphere 2 longitude,
Order k= k+ 1, return step 2.2,
Step 3: calculate each regional residual sum standard deviation one by one, the method for calculating each regional residual sum standard deviation is:
Calculate current each duplicate measurements point point set that is present in the zone to be calculated
Figure 918387DEST_PATH_IMAGE001
In the average of spot elevation
Figure 915293DEST_PATH_IMAGE007
And residual error
Figure 95214DEST_PATH_IMAGE008
, wherein, duplicate measurements point point set
Figure 251388DEST_PATH_IMAGE001
In the average of spot elevation
Figure 110760DEST_PATH_IMAGE009
,
Figure 532645DEST_PATH_IMAGE010
Be point set
Figure 440558DEST_PATH_IMAGE001
In jThe height value of individual point, nBe point set Total number of middle spot elevation, duplicate measurements point point set
Figure 481513DEST_PATH_IMAGE001
In the residual values of each spot elevation do
Figure 390694DEST_PATH_IMAGE011
,
Calculate the standard deviation in the zone to be calculated
Figure 164615DEST_PATH_IMAGE012
,
Figure 29803DEST_PATH_IMAGE013
, NRepresent regional duplicate measurements point point set sum to be calculated, mAll spot elevation sums in the zone to be calculated in the expression,
Step 3.3Residual values and standard deviation to being obtained by step 3.1, step 3.2. are carried out the rejecting of gross error, and following method is adopted in the rejecting of gross error: with residual absolute value greater than 3 times of standard deviations Promptly
Figure 627454DEST_PATH_IMAGE015
Altitude figures point as the gross error point, from the zone, reject the data recording of the spot elevation corresponding, and from duplicate measurements point point set with gross error point
Figure 142749DEST_PATH_IMAGE001
The middle gross error point of rejecting returns step 3.1; If all residual absolute values are smaller or equal to 3 times of standard deviations
Figure 678423DEST_PATH_IMAGE014
Promptly
Figure 988181DEST_PATH_IMAGE016
, then preserve all the spot elevation residual values in current zone to be calculated and the whole regional standard difference result in zone to be calculated, and carry out the calculating of the ultimate criterion difference in final zone to be calculated,
Step 4:Altitude figures result to latitude same latitude district, north and south, moon the two poles of the earth compares, the analytical error characteristic distributions, and method is:
The regional residual error of result of calculation contrast moon south poles same latitude according to step 3 distributes, and draws each spot elevation place moon longitude of residual sum of each spot elevation in each zone, the distribution plan of latitude; Each the regional standard deviation that obtains according to step 3, and drawing area and standard deviation distribution plan.
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CN104614730A (en) * 2015-01-20 2015-05-13 中国人民解放军63920部队 Method for calibrating moon elevation model by utilizing selenographic laser reflection array coordinate
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CN114964176A (en) * 2022-04-08 2022-08-30 同济大学 Landform surveying and mapping method for permanent shadow area of moon

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