CN102645229A - Spaceborne laser altimeter in-orbit moon elevation detection uncertainty evaluation method - Google Patents

Abstract

The invention discloses a spaceborne laser altimeter in-orbit moon elevation detection uncertainty evaluation method which comprises the following steps of: screening an area of which the terrain change is flat from a laser altimeter moon surface elevation detection full-moon area; eliminating a pseudo elevation and calculating the area elevation mean value and the standard deviation in the screened area; analyzing various uncertainty influence factors influencing the elevation detection and the distribution density; and carrying out laser altimeter in-orbit moon elevation detection uncertainty evaluation in combination with the various influence factors and by utilizing the ''Monte Carlo Method for Evaluation of Measurement Uncertainty''specification and giving the elevation results. The method has the advantage that the elevation detection uncertainty can be given to the spaceborne laser altimeter in-orbit moon surface terrain elevation detection according to the selected area to provide a basis for further analyzing the source of laser altimeter measurement error and provide a reference and a basis for making a high-precision moon digital elevation map.

Description

The satellite borne laser altitude gauge is surveyed the uncertainty evaluation method at rail moon elevation

Technical field

The present invention relates to a kind of method that is used for the satellite borne laser altitude gauge in rail moon elevation detection uncertainty evaluation, relate in particular to the laser altimeter that carries for CE-1 number is surveyed uncertainty evaluation at rail moon elevation method.

Background technology

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, and reduce measuring reliability and measuring accuracy, therefore be necessary the moon exploration data are carried out error analysis and uncertainty research.

In view of the importance of moonik detection data error analysis, domestic and international all kinds of space flight units are all studied correlation technique.Beijing space travel control center has researched and developed Real-time Error analytic system software, fully utilizes all kinds of measurement data caculation orbit, has realized the accurate observing and controlling to " Chang'e I " lunar exploration satellite.Chinese Academy of Sciences's Shanghai Observatory etc. utilizes the method for analogue simulation that the error source that influences the moonik orbit determination accuracy is analyzed, high spot reviews priori orbit error and the observational data type etc. of lunar gravity field error, observed quantity precision, initial time to the influence of lunar orbiter orbit determination accuracy.How these researchs mainly utilize various measurement data, the flight track of moonik are controlled and are supported, and for the error and the reutilization technology thereof that exist in rail measurement data itself, do not carry out system as yet and further investigate.Units such as Southeast China University, Hefei robotization research institute, University Of Tianjin have carried out number of research projects to the analysis of measurement errors in fields such as civilian industry instrument and navigation and the modeling and the theory of uncertainty.At present, the uncertainty problem is the focus of data processing and error analysis area research, and American National quantitative study institute (NIST) and European standard metering association (EUROMET) have all proposed multiple uncertainty computing method and recommended standard respectively.

Laser altimeter is one of scientific exploration instrument of carrying of China's Chang'e I, The present invention be directed to laser altimeter and the menology landform altitude is surveyed is carried out uncertainty evaluation.

Error analysis and uncertain evaluation to moon laser altimeter detection data; For making high precision moon digital elevation figure certain reference frame is provided; Accurately locate for the mankind explore the understanding moon, realize the more scientific research of the moon is reached the development and use to moon resource.

Summary of the invention

The present invention proposes a kind of satellite borne laser altitude gauge that is used for and survey the uncertainty evaluation method at rail moon elevation, it is to filter out landform in the laser altimeter moonscape elevation detection ball zone whole month to change smooth zone; In the zone that filters out, carry out the calculating of the rejecting of pseudo-elevation, regional elevation average and standard deviation; The various uncertain influence factor of analyzing influence elevation; Utilize " Monte Carlo method evaluation uncertainty of measurement " standard to carry out laser altimeter in conjunction with each influence factor and survey uncertainty evaluation, and provide evaluation result at the rail elevation.This method can be surveyed by institute's favored area at rail topography of lunar surface elevation the satellite borne laser altitude gauge and provide elevation detection uncertainty; For the source of further analyzing the laser altimeter measuring error provides foundation; For what make high precision moon digital elevation figure reference and foundation be provided, the design of the various useful load of carrying for the lunar exploration satellite provides theoretical direction and reference data in accuracy requirement.

The present invention adopts following technical scheme:

A kind of method that is used for the satellite borne laser altitude gauge in rail moon elevation detection uncertainty evaluation comprises the steps:

Data of the present invention take from laser altimeter that China's Chang'e I satellite carries at rail elevation detection data, the track of China's Chang'e I satellite is a polar circle moon track, 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, and elevation information covers the ball whole month.Said track fileinfo comprises elevation sampling time, the moon longitude of sampled point, latitude, the altitude figures information of laser altimeter.

Step 1: from laser altimeter ball whole month elevation search coverage, select topography of lunar surface and change smooth zone;

Step 2: in the zone of selecting, carry out the calculating of the rejecting of pseudo-elevation, regional elevation average and standard deviation, concrete grammar is:

Step 2.1 is calculated each point menology landform altitude value average

in institute's favored area

N is that all elevations are counted in institute's favored area;

Step 2.2 is calculated each spot elevation residual values v in institute's favored area _i,

$v_i=h_i-\stackrel{\‾}{h}$

Step 2.3 is calculated institute's favored area elevation standard deviation

$\mathrm{\σ}=\sqrt{\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{v_i}^2}$

The result that step 2.4 is calculated by step 2.1,22,2.3 carries out the rejecting of pseudo-elevation, and method is: with residual absolute value greater than 3 times of standard deviations promptly | v _i| the measurement of higher degree point of＞3 σ is rejected from institute's favored area as pseudo-spot elevation.If there is not the elevation residual error point that satisfies this condition; Then preserving the height value of all current measurement of higher degree points (preserves the elevation average and the regional elevation standard deviation sigma of institute's favored area of current calculating, changes step 3; Otherwise repeating step 2.1,2.1,2.3 calculates average, residual error, and the standard deviation of residue spot elevation in institute's favored area, and repeating step 2.4 once more, carry out the rejecting of pseudo-elevation in the residue spot elevation in institute's favored area.

Step 3: analyze the uncertainty factor source of enumerating measurement of higher degree value, mainly consist of the following components: the error X that measurement of higher degree repeatability causes ₁, probability distribution density is obeyed expectation

The normal distribution of standard deviation sigma, wherein

With standard deviation sigma all for remove the regional elevation average that obtains behind the pseudo-elevation by step 2.4

And standard deviation sigma; Laser altimeter range error X ₂, 3 times of standard deviations are less than 5m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the normal distribution of 5/3m; Laser altimeter installs and measures error X ₃Be 1m, probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 1m; The measurement of higher degree error X that laser measurement of round trip time error is introduced ₄, 1 times of standard deviation equals 1m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 1m; The measurement of higher degree error X that attitude of satellite measuring error is introduced ₅, standard deviation is 1m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 1m; The vertical error X that the orbit measurement error is introduced ₆, be 60m by the data standard difference of no observing and controlling segmental arc, probability density distribution is 0 according to obeying expectation, standard deviation is the normal distribution of 60m; The measurement of higher degree error X that the laser light spot causes ₇, 3 standard deviations are 5m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 5/3m.

Step 4 utilizes Monte Carlo method to carry out laser altimeter moon measurement of higher degree assessment on uncertainty.

In Evaluation of uncertainty of measurement, adopting Monte Carlo method (Monte Carlo method MCM), is a kind of numerical method that realizes the distribution propagation through repeated sampling.MCM is through the PDF discrete sampling to input quantity Xi; Propagate the distribution of input quantity by measurement model; Calculate the discrete sampling value of the PDF that obtains output quantity, and then directly obtain best estimate, the standard uncertainty of output quantity and comprise the interval by the Discrete Distribution numerical value of output quantity.Concrete grammar is:

Step 4.1 with the various uncertain source of the measurement of higher degree in the step 3 as input quantity; The favored area elevation H of institute is as output quantity; Set up satellite borne laser altitude gauge moon measurement of higher degree uncertainty mathematical model, the relation between the favored area elevation H of institute and each input quantity is:

H＝X ₁+X ₂+X ₃+X ₄+X ₅+X ₆+X ₇

Step 4.2 is selected the big or small M of Monte Carlo experiment sample size,

Choose reasonable Monte Carlo experiment number of times is the big or small M of sample size, the number of times of measurement model calculating just.

Step 4.3 is from input quantity X _iProbability density function (PDF) in extract M sample value x _Ir, i=1,2 ... 7, r=1,2 ..., M is to each sample vector (x _1r, x _2r..., x _7r), calculate the model value h of corresponding H;

Step 4.4 is pressed the ordering of strictly increasing order with these M model value, and the model value of these orderings obtains the discrete representation G of the PDF of output quantity H;

Step 4.5 G calculated by the estimated value of H

, and h is the standard uncertainty

$\tilde{h}=\frac{1}{M}\underset{r=1}{\overset{M}{\mathrm{\Σ}}}{h}_r$

$u\left(\tilde{h}\right)=\sqrt{\frac{1}{M-1}\underset{r=1}{\overset{M}{\mathrm{\Σ}}}{(h_r-\tilde{h})}^2}$

Step 4.6 is calculated by G and is comprised interval [h at given H when comprising Probability p _(low), h _(high)]

If pM is an integer, establish q=pM, otherwise the value of getting q is the integral part of pM+1/2.If (M-q)/the 2nd, integer is got r=(M-q)/2; Otherwise, get the integral part that r equals (M-q+1)/2, can get probability symmetry 100p% and comprise interval [h _(r), h _(r+q)]

Advantage of the present invention:

(1) the satellite borne laser altitude gauge being surveyed the uncertainty evaluation method at rail moon elevation is to carry out first; Laser altimeter moon elevation is surveyed uncertainty evaluation research, and 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) through selecting the smooth moon sea region of topography of lunar surface to handle, can reduce the menology landform to greatest extent and change influence, improve result's accuracy result.

(3) to laser altimeter moon exploration uncertainty constituent analysis and evaluation; For making high precision moon digital elevation figure certain reference frame is provided; Accurately locate for the mankind explore the understanding moon, realize the more scientific research of the moon is reached the development and use to moon resource.

(4) can the method be used for the uncertainty evaluation of the scientific exploration data of other celestial bodies.

Description of drawings

The position view in Fig. 1 zone 1.

The position view in Fig. 2 zone 2.

Fig. 3 zone 1 original altitude figures distribution plan.

Fig. 4 zone 1 remove behind the pseudo-elevation the spot elevation distribution plan.

Fig. 5 zone 2 original altitude figures distribution plans.

Fig. 6 zone 2 remove behind the pseudo-elevation the spot elevation distribution plan.

Fig. 7 zone 1 is by M=10 that MCM provided ⁶Individual model value histogram frequency distribution diagram.

Fig. 8 zone 2 is by M=10 that MCM provided ⁶Individual model value histogram frequency distribution diagram.

Fig. 9 main flow chart.

Figure 10 Monte Carlo evaluation process sub-process figure.

Embodiment:

Below in conjunction with accompanying drawing the present invention is further specified:

A kind of satellite borne laser altitude gauge that is used for is surveyed the uncertainty evaluation method at rail moon elevation, it is characterized in that concrete steps are following:

Obtain the laser altimeter altitude figures: 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 laser altimeter ball whole month elevation search coverage, select topography of lunar surface and change smooth zone;

The landform of lunar surface mainly contains: crater, lunar maria, month land and mountain range, rays, valley, wherein lunar maria is the shade on the finding of naked eye lunar surface, is actually the wide Plain on the lunar surface.Fixed lunar maria has 22, and the overwhelming majority is distributed near side of the moon, and the lunar maria area in the front is slightly larger than 50%.Wherein maximum Oceanus procellarum, about 5,000,000 square kilometres of the area of crying.About 900,000 square kilometres of Mare Imbrium area.About 260,000 square kilometres of Mare Tranquillitatis area of lunar surface central authorities.In addition, bigger also have Chenghai, Mare Foecunditatis, Mare Crisium, sea of clouds etc.Because a month sea region is actually llanura, can reduce the landform variation influence that detection brings to the menology landform altitude to greatest extent so select the laser altimeter altitude figures of month sea region to study uncertainty.Therefore from different moon sea region the altitude figures in the zone of selection relatively flat as process object.From Oceanus procellarum and Chenghai, select two zones among the present invention and carry out the elevation uncertainty evaluation.

Zone 1 is as shown in Figure 1, is the comparatively smooth rectangular area of in Chenghai, selecting through repeatedly testing of physical features, about 310,000 km of the Chenghai total area ², be one of lunar maria bigger on the moon, be positioned near side of the moon, the sea is quite smooth, and the sea is approximately than low about 1700 meters of the average level of the moon.Zone 1 area is 10193.233kn ², be positioned at 24.961 °～28.032 ° in moon latitude, 13.853 °～17.482 ° of longitudes.

Zone 2 is as shown in Figure 2, is the comparatively smooth rectangular area of in Oceanus procellarum, selecting through repeatedly testing of physical features, about 4,000,000 kn of the Oceanus procellarum total area ², be the maximum lunar maria of the moon, be positioned at the moon the Western Hemisphere, towards the west side of earth one side, be the wide grey Plain of a slice.Zone 2 area 13121.106km ², be positioned at 18.277 °～22.029 ° in moon latitude, longitude-60.732 °～-56.858 °.

Step 2: in the zone of selecting, carry out the calculating of the rejecting of pseudo-elevation, regional elevation average and standard deviation, concrete grammar is:

Step 2.1 is calculated each point menology landform altitude value average

in institute's favored area

N is that all elevations are counted in institute's favored area;

Step 2.2 is calculated each spot elevation residual values v in institute's favored area _i,

$v_i=h_i-\stackrel{\‾}{h}$

Step 2.3 is calculated institute's favored area elevation standard deviation

$\mathrm{\&sigma;}=\sqrt{\frac{1}{N-1}\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="N\; v\; i"\; filenames="HDA0000151049860000032.png,HDA0000151049860000041.png"\; state="\{\{state\}\}">N</figure-callout>}}{\mathrm{\&Sigma;}}}{v_i}^{}{{}_{}}^2}$

The result that step 2.4 is calculated by step 2.1,22,2.3 carries out the rejecting of pseudo-elevation, and method is: with residual absolute value greater than 3 times of standard deviations promptly | v _i| the measurement of higher degree point of＞3 σ is rejected from institute's favored area as pseudo-spot elevation.If there is not the elevation residual error point that satisfies this condition; Then preserving the height value of all current measurement of higher degree points (preserves the elevation average

and the regional elevation standard deviation sigma of institute's favored area of current calculating, changes step 3; Otherwise repeating step 2.1,2.1,2.3 calculates average, residual error, and the standard deviation of residue spot elevation in institute's favored area, and repeating step 2.4 once more, carry out the rejecting of pseudo-elevation in the residue spot elevation in institute's favored area.

Zone 1 original elevation N=1519 that counts; Behind the pseudo-spot elevation of step 2 removal; The residue elevation N=1511 that counts, the elevation average

and the regional elevation standard deviation sigma=52.62m in the zone behind the pseudo-elevation of removal that must cross by step 2.4.Altitude figures distribution plan 3 before and after 1 lunar surface pseudo-elevation in zone is rejected is with shown in Figure 4.

Zone 2 original elevations N=1907 that counts; Behind the pseudo-spot elevation of step 2 removal; The residue elevation N=1903 that counts, the elevation average

and the regional elevation standard deviation sigma=39.54m in the zone behind the pseudo-elevation of removal that must cross by step 2.4.Altitude figures distribution plan 5 before and after 2 lunar surfaces pseudo-elevation in zone is rejected is with shown in Figure 6.

Step 3: analyze the uncertainty factor source of enumerating measurement of higher degree value, mainly consist of the following components: the error X that measurement of higher degree repeatability causes ₁, probability distribution density is obeyed expectation The normal distribution of standard deviation sigma, wherein

With standard deviation sigma all for remove the regional elevation average that obtains behind the pseudo-elevation by step 2.4

And standard deviation sigma; Laser altimeter range error X ₂, 3 times of standard deviations are less than 5m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the normal distribution of 5/3m; Laser altimeter installs and measures error X ₃Be 1m, probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 1m; The measurement of higher degree error X that laser measurement of round trip time error is introduced ₄, 1 times of standard deviation equals 1m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 1m; The measurement of higher degree error X that attitude of satellite measuring error is introduced ₅, standard deviation is 1m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 1m; The vertical error X that the orbit measurement error is introduced ₆, be 60m by the data standard difference of no observing and controlling segmental arc, probability density distribution is 0 according to obeying expectation, standard deviation is the normal distribution of 60m; The measurement of higher degree error X7 that the laser light spot causes, 3 standard deviations are 5m, and probability density distribution is 0 according to obeying expectation, and standard deviation is the even distribution of 5/3m.

Step 4 utilizes Monte Carlo method to carry out laser altimeter moon measurement of higher degree assessment on uncertainty.

In Evaluation of uncertainty of measurement, adopting Monte Carlo method (Monte Carlo method MCM), is a kind of numerical method that realizes the distribution propagation through repeated sampling.MCM is through the PDF discrete sampling to input quantity Xi; Propagate the distribution of input quantity by measurement model; Calculate the discrete sampling value of the PDF that obtains output quantity, and then directly obtain best estimate, the standard uncertainty of output quantity and comprise the interval by the Discrete Distribution numerical value of output quantity.Concrete grammar is:

Step 4.1 with the various uncertain source of the measurement of higher degree in the step 3 as input quantity; The favored area elevation H of institute is as output quantity; Set up satellite borne laser altitude gauge moon measurement of higher degree uncertainty mathematical model, the relation between the favored area elevation H of institute and each input quantity is:

H＝X ₁+X ₂+X ₃+X ₄+X ₅+X ₆+X ₇

Step 4.2 is selected the big or small M of Monte Carlo experiment sample size,

Choose reasonable Monte Carlo experiment number of times is the big or small M of sample size, the number of times of measurement model calculating just, and among the present invention, M=10 ⁶

Step 4.3 is from input quantity X _iProbability density function (PDF) in extract M sample value x _Ir, i=1,2 ... 7, r=1,2 ..., M is to each sample vector (x _1r, x _2r..., x _7r), calculate the model value h of corresponding H;

Zone 1:

X ₁＝-2702.0+randn(1，1000000)*52.62

X ₂＝randn(1，1000000)*(5/3)

X ₃＝rand(1，1000000)

X ₄＝rand(1，1000000)

X ₅＝rand(1，1000000)

X ₆＝randn(1，1000000)*60

X ₇＝rand(1，1000000)*(5/3)

H＝X ₁+X ₂+X ₃+X ₄+X ₅+X ₆+X ₇

Zone 2:

X ₁＝-2302.6+randn(1，1000000)*39.54

X ₂＝randn(1，1000000)*(5/3)

X ₃＝rand(1，1000000)

X ₄＝rand(1，1000000)

X ₅＝rand(1，1000000)

X ₆＝randn(1，1000000)*60

X ₇＝rand(1，1000000)*(5/3)

H＝X ₁+X ₂+X ₃+X ₄+X ₅+X ₆+X ₇

Step 4.4 is pressed the ordering of strictly increasing order with these M model value, and the model value of these orderings obtains the discrete representation G of the PDF of output quantity H;

Step 4.5 G calculated by the estimated value of H

, and h is the standard uncertainty

Step 4.3 and Step 4.4 by the calculated estimates obtained H

, and h is the standard uncertainty

$\tilde{h}=\frac{1}{M}\underset{r=1}{\overset{M}{\mathrm{\&Sigma;}}}{h}_r$

$u\left(\tilde{h}\right)=\sqrt{\frac{1}{M-1}\underset{r=1}{\overset{M}{\mathrm{\&Sigma;}}}{(h_r-\tilde{h})}^2}$

Zone 1 H elevation estimate standard uncertainty

Region 2 the estimated value of the elevation H

standard uncertainty

Step 4.6 is calculated by G and is comprised interval [h at given H when comprising Probability p _(low), h _(high)]

If pM is an integer, establish q=pM, otherwise the value of getting q is the integral part of pM+1/2.If (M-q)/the 2nd, integer is got r=(M-q)/2; Otherwise, get the integral part that r equals (M-q+1)/2, can get probability symmetry 100p% and comprise interval [h _(r), h _(r+q)]

Comprise Probability p among the present invention and get 95%, calculate through step 4.6:

Zone 1 is at given Probability p=95% o'clock of comprising, the comprising of H interval be [2856.3m ,-2543.5m];

Zone 2 is at given Probability p=95% o'clock of comprising, the comprising of H interval be [2441.3m ,-5129.7m];

Fig. 7 has provided zone 1 by M=10 that MCM provided ⁶Individual model value histogram frequency distribution diagram comprises probability 95% and is comprising interval end points shown in perpendicular line among Fig. 7.

Fig. 8 has provided zone 2 by M=10 that MCM provided ⁶Individual model value histogram frequency distribution diagram comprises probability 95% and is comprising interval end points shown in perpendicular line among Fig. 8.

Utilize " Monte Carlo method evaluation uncertainty of measurement " standard (MCM) to carry out the uncertainty evaluation of laser altimeter among the present invention in rail detection altitude figures; With according to the evaluation of " measuring uncertain evaluation and expression " standard (GUM) as a comparison; Shown in table 1 and table 2; The evaluation result of the two kinds of methods in two zones is consistent, and the standard uncertainty of MCM method is slightly less than normal.

Two kinds of evaluation results in table 1 zone 1

Zone 1	?MCM	GUM
			Standard uncertainty u (h)	?79.76m	79.83m
The interval that comprises that comprises probability 95%	?[-2856.30m，-2543.50m]	[-2866.66m，-2542.34m]

Two kinds of evaluation results in table 2 zone 2

Zone 2	MCM	GUM
			Standard uncertainty u (h)	71.82m	71.89m
The interval that comprises that comprises probability 95%	[-2441.3m，-2159.3m]	[-2446.38m，-2158.82m]

Claims (1)

1. a satellite borne laser altitude gauge is surveyed the uncertainty evaluation method at rail moon elevation, it is characterized in that concrete steps are following:

Step 1: from laser altimeter ball whole month elevation search coverage, select topography of lunar surface and change smooth zone;

Step 2: in the zone of selecting, carry out the calculating of the rejecting of pseudo-elevation, regional elevation average and standard deviation, concrete grammar is:

Step 2.1 is calculated each point menology landform altitude value average

in institute's favored area

N is that all elevations are counted in institute's favored area;

Step 2.2 is calculated each spot elevation residual values v in institute's favored area _i,

$v_i=h_i-\stackrel{\&OverBar;}{h}$

Step 2.3 is calculated institute's favored area elevation standard deviation

$\mathrm{\&sigma;}=\sqrt{\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{v_i}^2}$

The result that step 2.4 is calculated by step 2.1,22,2.3 carries out the rejecting of pseudo-elevation, and method is: with residual absolute value greater than 3 times of standard deviations promptly | v _i| the measurement of higher degree point of＞3 σ is rejected from institute's favored area as pseudo-spot elevation.If there is not the elevation residual error point that satisfies this condition; Then preserving the height value of all current measurement of higher degree points (preserves the elevation average

and the regional elevation standard deviation sigma of institute's favored area of current calculating, changes step 3; Otherwise repeating step 2.1,2.1,2.3 calculates average, residual error, and the standard deviation of residue spot elevation in institute's favored area, and repeating step 2.4 once more, carry out the rejecting of pseudo-elevation in the residue spot elevation in institute's favored area,

Step 3: laser altimeter moon elevation is surveyed uncertainty factor source analysis

Satellite borne laser altitude gauge moon elevation is surveyed uncertainty factor source mainly by following several parts: the measuring error X that measurement of higher degree repeatability causes ₁, probability distribution density is obeyed expectation

The normal distribution of standard deviation sigma, wherein

With standard deviation sigma all for remove the regional elevation average that obtains behind the pseudo-elevation by step 2.4

And standard deviation sigma; Laser altimeter range error X ₂, probability density distribution is according to Normal Distribution; Laser altimeter installs and measures error X ₃, probability density distribution distributes according to obeying evenly; The measurement of higher degree error X that laser measurement of round trip time error is introduced ₄, probability density distribution distributes according to obeying evenly; The measurement of higher degree error X that attitude of satellite measuring error is introduced ₅, probability density distribution distributes according to obeying evenly; The vertical error X that the orbit measurement error is introduced ₆, probability density distribution is according to Normal Distribution; The measurement of higher degree error X that the laser light spot causes ₇, probability density distribution distributes according to obeying evenly,

Step 4 utilizes Monte Carlo method to carry out laser altimeter moon measurement of higher degree assessment on uncertainty.Concrete grammar is:

Step 4.1 with the various uncertain source of the measurement of higher degree in the step 3 as input quantity; The favored area elevation H of institute is as output quantity; Set up satellite borne laser altitude gauge moon measurement of higher degree uncertainty mathematical model, the relation between the favored area elevation H of institute and each input quantity is:

H＝X ₁+X ₂+X ₃+X ₄+X ₅+X ₆+X ₇

Step 4.2 is selected the big or small M of Monte Carlo experiment sample size,

Step 4.3 is from input quantity X _iProbability density function (Probability density function PDF) in extract M sample value x _Ir, i=1,2 ... 7, r=1,2 ..., M is to each sample vector (x _1r, x _2r..., x _7r), calculate the model value h of corresponding H,

Step 4.4 is pressed the ordering of strictly increasing order with these M model value, and the model value of these orderings obtains the discrete representation G of the PDF of output quantity H,

Step 4.5 G calculated by the estimated value of H

, and h is the standard uncertainty

Step 4.6 is calculated by G and is comprised interval [h at given H when comprising Probability p _Low, h _High].

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