Planetary and Space Science 87 (2013) 173–182
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Planetary and Space Science
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Short Communication A new lunar global DEM derived from Chang’E-1 Laser Altimeter data based on crossover adjustment with local topographic constraint
Wenmin Hu a,b, Kaichang Di a,n, Zhaoqin Liu a, Jinsong Ping c a State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing Applications, Chinese Academy of Sciences, Beijing 100101, PR China b IOT Perception Mine Research Center, China University of Mining and Technology, Xuzhou 221008, PR China c National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, PR China article info abstract
Article history: This paper presents a crossover adjustment method with local topographic constraint and a new lunar Received 11 March 2013 global digital elevation model (DEM) derived from Chang’E-1Laser Altimeter (LAM) data based on the Received in revised form crossover adjustment. With about 9.12 million altimetric points acquired by the LAM, we derived more 23 July 2013 than 141,000 crossovers that cover the entire lunar surface after eliminating outliers of orbits and Accepted 5 August 2013 altimetric points. The global lunar surface is divided into 32 local blocks, and the least squares Available online 23 August 2013 adjustment of crossover differences is performed for each block using the local topographic constraint Keywords: information extracted from the planar areas. Smooth transitions among the neighbouring blocks are Lunar Topography ensured through sufficient overlapping areas and virtual control points from the planar areas. After the DEM crossover adjustment, root mean square (RMS) of the residuals is reduced from 149.51 m to 54.75 m after Chang’E-1 using three parameters for each profile in each block in the mid-latitude region. In polar regions, RMS is Laser Altimeter fi Crossover Analysis reduced from more than 150 m to less than 100 m after using seven parameters for each pro le. The Adjustment resulting lunar global DEM has a significantly improved quality in the local consistencies, i.e. artefacts in the original DEM are eliminated or decreased. The new lunar global DEM is also compared with the laser altimeter data from NASA's LRO mission and JAXA's KAGUYA mission. After comparison, the result shows that the DEMs are consistent and that adjustment does not deform the lunar terrain. & 2013 Elsevier Ltd. All rights reserved.
1. Introduction After the Apollo missions, the Clementine mission mapped the Moon with imaging sensor at visible and infrared wavelengths Lunar topography provides fundamental data support for lunar from February 19 to May 3 in 1994 (Nozette et al., 1994).In scientific research. Since laser altimeter was first carried on Apollo addition, Clementine obtained useful laser altimeter data from 15 and 16 to measure the Moon in 1971 and 1972 respectively 284 of its revolutions (Smith et al., 1997). Orbits were charac- (Davies et al., 1987; Kaula et al., 1973; Sjogren and Wollenhaupt, terised by repeatability in the radial position of approximately 1973), laser altimetry has been the major topographic tool to 10 m, and had a radial accuracy with respect to the lunar centre of measure the size and shape of planetary bodies in lunar and mass of approximately 70 m with the range resolution of 39.972 m planetary explorations. In the Apollo15 to 17 missions, the laser (Smith et al., 1997). altimeters acquired 7080 range measurements from these three The Clementine mission demonstrated a new, efficient diode- missions (Smith et al., 1997). Absolute radial accuracy of the Apollo pumped laser technology (McEwen and Robinson, 1997; altimetry data was about 400 m.Using the altimetry data, a lunar Neumann, 2001). Using the range measurements from laser mean radius of 1737.7 km with the centre of mass at 2.55 km altimeter, Goddard Lunar Topography Model-2 with a 72nd order away (251E) was determined (Kaula et al., 1974). Given that only a spherical harmonic expansion of lunar radii was designated, which limited region of the lunar surface was covered by these laser had an absolute vertical accuracy of about 100 m and a spatial altimeter data (Neumann, 2001), the principal objective of the resolution of 2.51 (Smith et al., 1997). Global topographic and instruments was to provide range measurements to scale images gravitational models derived from Clementine data showed an from the Apollo metric cameras for high-resolution regional maps improved picture of the shape, internal structure, and thermal (Kaula et al., 1972; Light, 1972). history of the Moon (Neumann et al., 1996; Zuber et al., 1994). Images and altimeter data were used to improve the global lunar topographic model, which resulted in the Unified Lunar Control n Corresponding author. Tel.: þ86 10 64868229; fax: þ86 10 64807987. Network2005 (Archinal et al., 2006a, 2006b).This new model E-mail address: [email protected] (K. Di). serves as a base for tying other existing imagery and for registering
0032-0633/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pss.2013.08.004 174 W. Hu et al. / Planetary and Space Science 87 (2013) 173–182 other regional or local topographic information. However, this generation of these two global lunar DEMs. A preliminary testing model has weak accuracy on the lunar farside and polar area of the crossover analysis of CE-1 LAM data was performed for the because the orbits were less well-determined over the lunar regional mapping application and co-registration with CE-1 ima- farside and only a few valid measurements covered such area. gery data (Di et al., 2012).However, the result of global adjustment From 2007 to 2009, four typical lunar missions such as China's was not better than the local one (Hu et al., 2011). In our previous Chang’E-1 (CE-1) (Ouyang et al., 2010)and Chang’E-2, JAXA's research, the global adjustment method could reduce the residuals SELenological and ENgineering Explorer (SELENE/KAGUYA) (Kato of crossover differences to a certain extent, but numerous artefacts et al., 2008), India's Chandrayaan-1(Goswami and Annadurai, still exist. Given that the crossovers locations are not distributed 2009), and NASA’s Lunar Reconnaissance Orbiter (LRO) Mission uniformly (majority are in polar regions) and orbit uncertainties (Chin et al., 2007; Zuber et al., 2010) were launched. Chang’E-1, are different at different areas, a global adjustment with the same SELENE, and LRO all carry laser altimeters, global lunar topo- correction model for all crossovers would not properly solve the graphic model is derived with the altimeter range measurements problem. that cover the global lunar surface (Araki et al., 2009; Li et al., Considering the different densities of crossovers in local areas, 2010; Ping et al., 2009; Smith et al., 2010).Chandrayaan-1 also we divide the lunar surface into small local blocks, and use a carried laser altimeter, but only preliminary results (no global method of least-squares crossover adjustment with a series of surface product) have been reported (Kamalakar et al., 2009). basis functions of time and location to reconcile the LAM data by The laser altimeter (LALT) on board SELENE is designed to minimising the crossover residuals globally. Every profile in each measure distances of the lunar surface from the altitude of 100 km block has its own parameters to solve in the adjustment. To avoid by transmitting laser pulses at 1 Hz and at a nominal range terrain deformation in the local area and ensure smooth transition resolution of 1 m (Araki et al., 2008; Tsubokawa et al., 2002). of neighbouring blocks, there is an overlapping area covering one During the one-year operation of SELENE, this mission acquired degree between adjacent blocks and local topographic information about 10.4 million points over the lunar surface. A global lunar extracted from a cluster of planar points is also used as the height topographic map with a spatial resolution finer than 0.51 was constraint. This joint processing is effective in a lunar mare, where derived from the LALT data, and the map reveals an unbiased lunar artefacts in the original DEM are distinct. The comparison results topography for scales finer than a few hundred kilometres (Araki are presented at the end with LALT and LOLA-derived DEMs before et al., 2009). The Lunar Orbiter Laser Altimeter (LOLA) instrument and after the adjustment. equipped on LRO has a five-beam laser pulse measuring type in a 50 km polar orbit, with a nominal ranging precision of 10 cm at 28 Hz, and each laser spot is about 5 m in diameter on the ground 2. CE-1 LAM data and crossover adjustment method (Vondrak et al., 2010). LOLA acquired over 3.5 billion altimeter observations (Smith et al., 2011), which provide a precise global The LAM of CE-1 fires one narrow pulse of 1064 nm wavelength lunar topographic model with less than 1 m for radial accuracy light per second to the Moon surface. A ground track consists of (Mazarico et al., 2012). 200-m-diameter footprints about 1.4 km apart along the track. Given that the wide coverage and high density of satellite Distance measuring range is about 200725 km and ranging altimetry were achieved, a crossover analysis of laser altimeter accuracy is about 5 m in the aircraft tests (Ping et al., 2009). data is used in present deep space explorations to help improve During the operation of CE-1 from November 28, 2007 to Decem- orbit determination and derive more precise DEMs. During the ber 4, 2008, the laser altimeter acquired 1397 orbital profiles with course of the Near Earth Asteroid Rendezvous laser rangefinder about 9.12 million altimetric points (Li et al., 2010). DE403 from JPL investigation of 433 Eros, over 16,000,000 altimetric points were was used as the lunar orientation model for orbit determination of acquired. Afterwards, 3,800,000 crossovers were analysed, and an CE-1 (Chen et al., 2011; Yan et al., 2010). In this paper, crossovers adjustment of four cycles per asteroid revolution reduced the root and crossover differences are calculated from these LAM data, and mean square (RMS) residuals from 82.7 m to 17.9 m after exclud- least-squares adjustment is used for the crossovers. Details of ing grossly mislocated data (Neumann, 2001; Zuber et al., 2000). crossover calculation and adjustment are given below. Crossover adjustment of Mars Orbiter Laser Altimeter data was also performed for the topographic modelling and mapping of 2.1. Crossover and crossover calculation with CE-1 LAM data Mars, with a reduction of residual for crossovers from 8.3 m to 1.82 m (Neumann, 2001). LOLA-derived crossover data in the five- An altimetric crossover is the intersecting location of two distinct beam laser pulse were adjusted and used to improve orbit knowl- ground tracks at different time t and t'.Atacrossover,theheightofthe edge and gravity field estimation, and a high-resolution global same location is given twice, generally by the observations of an lunar DEM was generated (Mazarico et al., 2010; Mazarico et al., ascending and a descending ground track. Crossover difference is the 2011; Smith et al., 2010). In the current paper, the reprocessing of deviation between the two altimeter heights at the crossover point. spacecraft trajectory increased the accuracy as a result of alti- Two crossing passes provide independent measurements at the same metric crossovers (Mazarico et al., 2012). Crossovers from LALT are location at different times. used as a constraint in orbit determination of the SELENE satellite As there are generally no direct observations at crossover locations, (Goossens et al., 2011). Fok et al. (2011) used crossover analysis to an interpolation is used to acquire these two altimeter ranges along estimate the radial differences and internal accuracy of the CE-1 their respective ground tracks by fitting a quasi-hermite spline (Akima, and SELENE lunar topographic models. 1970) with three nearest points on each side of the crossover point. In Artefacts in DEM generation with CE-1 laser altimeter (LAM) our study, more than 141,000 crossovers were extracted from 1393 data were found in the local area, especially in some planar areas, ground tracks that covered the entire lunar surface after eliminating which means that inconsistencies occur among the measurements the outliers of orbits and points. Fig. 1 displays the global distribution acquired by different passes. A global topographic model (CLTM- of crossovers on the lunar surface. The colour bar shows the S01) of the Moon was produced with more than 3 million range amplitudes of crossover differences. measurements from CE-1 LAM data (Ping et al., 2009). A global Given the rotation of the Moon, crossovers occur at all lunar DEM with 3 km spatial resolution was constructed using latitudes. Since the CE-1 probe had a polar circular orbit with an about 9.12 million measurements from the CE-1 LAM data (Li et al., inclination angle of 88.21 (Li et al., 2010), the track of sub- 2010). However, no crossover adjustments were found in the spacecraft points is basically parallel with the longitude in low W. Hu et al. / Planetary and Space Science 87 (2013) 173–182 175
Fig. 1. Global distribution of crossovers on the lunar surface.
latitudes. Therefore, crossovers are denser at high latitudes than For each profile, an unknown pj matrix is found with (nþ1) that at middle and low latitudes. coefficients. Thus, Eq. (2) has 2(nþ1) unknown coefficients to be Crossover differences are the combined results of the uncer- solved at each crossover. All crossovers lead to a very sparse tainties in altimetry, such as orbit, range, timing, or alignment. In system of equations. Given that each intersection between one the calculation of crossover differences, the interpolation of cross- track and crossing tracks can be used and the number of intersec- over locations and corresponding heights introduce several uncer- tions increases as the number of cyclic motion increases, numer- tainties. To avoid introducing more errors into the crossover ous observations can be performed to solve Eq. (2). On the other differences, we set three rules to eliminate crossovers that are hand, since the values in matrix Gi are very similar, the adjustment not suitable in the subsequent adjustment. The three rules are solution of parameters pj can be singular. We set the initial values time, slope, and amplitude checks. Time check constrains the time of pj to zero and calculate the final pj by iteration using an inverse 1 intervals of the adjacent points within the track to be small covariance matrix Cpp to constrain the iteration and thus avoid enough (o ¼3 s) so that the interpolation will be reliable. Slope singularity. The solution at the (kþ1)th iteration is obtained from check constrains the gradient between the neighbour points to be Tarantola and Valette(1982) smaller than the threshold of 601.Furthermore, crossovers with p ¼ p þðGT GþC 1Þ 1ðGT Δd C 1p Þð4Þ amplitudes larger than 300 m are not used in the adjustment. The k þ 1 k pp pp k original RMS value for all crossovers after the checks is 155.97 m, Residual Δd is calculated from Eq. (2) with pk at the kth which is consistent with the results of the accuracy assessment of iteration. With the coefficient pj, altimetric observations for each lunar topography models by Fok et al. (2011). profile can be adjusted with the same model. For each altimetric point, time parameter t or wi and location latitude parameters are 2.2. Least-squares adjustment of crossover differences substituted into Eq. (3) to obtain the adjusted value f(t). Thus, ð Þ¼ ð Þ þ ð ÞðÞ h t h t 0 f t 5 Crossover adjustment is based on the least-square method (Neumann et al., 2001) with some modifications for each block. where h(t)0 is the original altimetric value and h(t) is the corrected Let h(t) and h(t′) be the heights at the crossover. The crossover altimetric value. residual is then defined as follows: 2.3. Crossover adjustment with local topographic constraint dðt; t′Þ¼hðtÞ hðt′Þð1Þ where t and t′ are time tags of the two crossing tracks. To minimise In a lunar mare, the surface is approximately planar and the the discrepancy of the two height values, we assign each crossover artefacts are very distinct. Considering that the number of cross- two corrections, f (t) and f(t′), in the residual vector Δd. overs is limited in the low and middle latitude areas, the topographic information in the planar area is extracted as a cluster Δ ð Þ¼þ ð ; ′Þþ ð Þ ð ′Þ d t d t t f t f t of virtual control points to constrain the adjustment by the Δdðt′Þ¼ dðt; t′Þ f ðtÞþf ðt′Þð2Þ crossovers. The criteria of planar points used in this paper are: (1) the height differences with adjacent points both along-track Δd(t′) has an equal value withΔd(t) but an opposite sign. The and across-track should be smaller than 20 m, and (2) the number adjustment value at the ith crossover in the jth profile is modelled of neighbour points along track that satisfy the first condition by a time-dependent polynomial or a time-location function should be more than 15.These points provide an average height ð Þ¼ þ þ⋯þ n ¼ f t p0 p1t pnt Gipj value for the plane area and act as reference adjustment values for the correction. As a result, the correction for the original LAM or points with the parameters derived from the crossover adjustment ð Þ¼ þ þ⋯þ n 3 f t p0 p1t pn 3t will be constrained by the value of planar points to avoid þ ð Þþ ð Þþ 2ð Þ¼ ð Þ deformation; this also provides a reference for the mosaic king pn 2 sin wi pn 1 cos wi pn sin latitude Gipj 3 of adjacent blocks. Given that the acquisition of LAM points is not where t is a normalised time at the crossover and wi is the continuous because of the tracking problem and abnormal power i frequency of time variation.Gi¼[1 t…t ] is used for the low and off of the memory, no altimetry measurements were performed in i 2 mid-latitude areas.Gi¼[1 t…t sin(wi) cos(wi) sin (latitude)] and quite a few passes during the operation of CE-1 (Ping et al., 2009). T pj¼ [p0 p1… pn] is used for the polar regions. Tracking measurement and control of the satellite orbit are worse 176 W. Hu et al. / Planetary and Space Science 87 (2013) 173–182 in the lunar farside (Chen et al., 2011; Ping et al., 2009).As a result, profile based on the comparative tests with four different models some initial system errors were found in the altimetry observa- in our previous research (Hu et al., 2011). Fig. 3 shows the DEMs of tions for several tracks. In the planar area, we compare the mean the 10 km resolution (a) before and (b) after crossover adjustment. height values among adjacent tracks to detect the tracks that have An obvious improvement of DEM is observed because fewer the initial errors. These errors will be used as initial corrections for artefacts are seen in the DEM after adjustment. the crossover analysis in the local area. Fig. 2 shows the procedure Artefacts are very distinct (Fig. 4(a)) in the lunar area (01Eto for the adjustment. This joint processing with the virtual control 901 E, 01Nto601N). Fig. 4(b) shows the DEM effect after crossover points and crossovers considers the topographic information in adjustment. Crossover adjustment can reduce most of the artefacts the local area. This process was performed to make the quality of in this area. However, a few new artefacts occurred in some planar the DEM generated from the adjusted LAM data higher than the areas where no obvious artefacts were found before the proces- quality when using only crossover adjustment. sing. After the local planar points were extracted and used to constrain the adjustment, most of the remaining artefacts were reduced. Fig. 5(a) shows the distribution of 136,781 planar points located in this area with the height difference threshold set at 3. Results 20 m. Fig. 5(b) shows the DEM after the joint processing with crossovers and local topographic constraint information, which 3.1. DEM in the local area shows the disappearance of most of the artefacts, e.g., artefacts around E321, E501, and E751–901, N501–601are eliminated com- Crossover adjustment was performed for 399,629 LAM points pared with Fig. 4(b). to provide a more precise base data for the co-registration of CE-1 stereo images in a local area (01Nto601N, 501Wto01W) having 2593 crossovers, where the differences are less than 300 m after 3.2. Lunar global DEM eliminating the outliers (Di et al., 2012).RMS of the original crossover residual is 62.1 m, which is reduced to 36.8 m after We divide the global lunar surface into 32 blocks with bound- using a second-order polynomial for the adjustment of each aries at W1401, W901, W501 ,01, E501, E901,E1401,E1801and N601,
Fig. 2. Crossover adjustment with local topographic constraint information.
Fig. 3. LAM DEMs (a) before and (b) after a second-order polynomial adjustment of crossovers and (c) LOLA-derived DEM. W. Hu et al. / Planetary and Space Science 87 (2013) 173–182 177
Fig. 4. DEM in area (01Eto901E, 01Nto601N) (a) before and (b) after crossover adjustment.
Fig. 5. (a) Distribution of planar points and (b) DEM after crossover adjustment with local topographic constraint.
Table 1 Residuals of crossover differences before and after adjustment (unit: m).
Region Number of crossovers RMS Mean Median Minimum Maximum
Mid-latitude Region 24,789 Before 149.51 1.26 1.73 493.70 490.05 After 54.75 0.00 0.027 242.91 247.78
North polar region 60,832 Before 154.31 9.74 5.15 498.49 498.46 After 96.30 0.12 0.55 464.80 453.38
South polar region 55,937 Before 164.07 7.46 3.01 499.49 498.78 After 99.06 0.35 0.02 463.08 425.21
S601 and perform an adjustment for the LAM points in each block. positional accuracy is 445 m and the radial accuracy is 60 m (Li Crossover adjustments in the blocks use a series of piecewise et al., 2010). We use crossover differences to characterise the radial functions to adjust the LAM points, which is potentially more accuracy. Table 1 lists the numerical results before and after accurate than a global solution where in one set of coefficients is adjustment for the mid-latitude and polar areas. All crossover solved for each entire profile. As crossovers are sparse in low-mid residuals are reduced by the adjustments. RMS of crossover latitude area, the following simplified from of Eq. (3) is used. residuals is reduced from 149.51 m to 54.75 m after using three parameters for each profile in the areas of low and middle latitude ð Þ¼ þ þ 2 ð Þ f t p0 p1t p2t 6 regions. In the polar regions, nearly 40% of crossover residuals are where three parameters are solved for each profile. And crossovers reduced after using seven parameters for each profile. Table 2 lists are dense in polar regions, the following form of Eq. (3) is used. the statistics of the adjustments in the blocks in this paper and the results of an entire global model adjustment in our previous ð Þ¼ þ þ 2 þ 3 þ ð Þ f t p0 p1t p2t p3t p4 sin wi research (Hu et al., 2011). The result of the adjustment of blocks þ ð Þþ 2ð ÞðÞ is better than the one which used global adjustment for all the p5 cos wi p6 sin latitude 7 crossovers. As overlapping areas between two adjacent blocks where seven parameters are solved for each profile. One-degree have different parameters, the adjusted height values would not overlapping area is kept for any pair of adjacent blocks to ensure be exactly the same from adjacent blocks. To avoid the saltation smooth transition between the blocks. As most of LAM points were between blocks, the adjusted height values in the overlapping area acquired in the case of no orbit tracking data, the estimated of different blocks are also compared to determine if there is a 178 W. Hu et al. / Planetary and Space Science 87 (2013) 173–182
Table 2 block effect. Mean difference of the adjusted height values from Residuals of crossover differences with adjustments in blocks and globally for all the adjacent blocks is 7.35 m, which is much less than the cross- crossovers (unit: m). over residuals. The final adjusted height values of the points in
RMS Mean Median Minimum Maximum overlapping areas are the averages of the adjusted values from adjacent blocks. Although the crossover adjustments were per- Before adjustment 155.97 0.34 0.14 497.23 495.76 formed by blocks, this result shows that the constraints from Adjustment in blocks 83.37 0.15 0.20 390.26 375.46 the planar points are effective and that DEM is consistent globally. Global adjustment 106.39 0.20 0.14 510.53 458.17 Fig. 6 shows the DEM in the mid-latitude region (a) before
Fig. 6. Lunar DEM in the mid-latitude region (601Sto601N) (a) before and (b) after adjustment (3 km resolution, interpolated by Kriging). W. Hu et al. / Planetary and Space Science 87 (2013) 173–182 179 and (b) after our adjustment. Obvious artefacts were found in the gravity model¼SGM100i, orbit data ¼NAOJ_RISE_MAIN_ORBIT_ mare planar area (601Wto601E). Artefacts around 601Sto301Sand SGM100i_20071020_0000-20081226_0430.bsp”), and CE-1 LAM 1601Wto1201W (area enclosed in the rectangle)were significantly data. We can see that the adjustment for LAM points did not reduced. Fig. 7 and Fig. 8 show the lunar DEM (a) before and change the basic global lunar shape, which was measured by the (b) after our adjustment in the polar regions respectively. Obvious altimetry. However, there is a notable difference between the artefacts around 301Eto601Eand1201Wto1501W were reduced. average values of LAM and LALT or LOLA DEMs; this may be a systematic difference due to orbit determination. Using an iterative least square method, a triaxial ellipsoid is 3.3. Comparison with LOLA and LALT DEM adopted to fit the lunar global DEM as follows:
To assess the external accuracy of the adjustment of LAM ðx x Þ2 ðy y Þ2 ðz z Þ2 0 þ 0 þ 0 ¼ 1 ð8Þ points, comparisons of CE-1 DEM with LOLA- and LALT-derived 2 2 2 a b c DEMs are performed. Table 3 lists the statistics of the LOLA grid DEM with 128 pixels/degree of map resolution (ldem_128.img, where a, b, c are Equatorial long radius, Equatorial short radius,
Version is V1.07, 2012-03-15), LALT points (https://www.soac. and polar radius, (x0, y0, z0) are the coordinates of Center of selene.isas.jaxa.jp/archive/index.html.en, Version ID is “20101201 Figure (COF) with respect to Center if Mass (COM).Table 4 lists the
Fig. 7. Lunar DEM in the North polar region (a) before and (b) after adjustment (3 km resolution, interpolated by Kriging).
Fig. 8. Lunar DEM in the South polar region (a) before and (b) after adjustment (3 km resolution, interpolated by Kriging). 180 W. Hu et al. / Planetary and Space Science 87 (2013) 173–182
Table 3 Statistics of LOLA, LALT, and CE-1 LAM data covering the global surface (unit: m).
Number of points Average RMS Lowest point Highest point
CE-1 LAM before adjustment 8,568,555 718.68 2207.17 9251.44 10615.40 CE-1 LAM after adjustment 8,555,170 721.0660 2202.56 9251.44 10655.79 LOLA DEM 1,061,683,200 519.33 2208.07 9126.50 10766.50 LALT 10,340,710 480.01 2205.66 9064.00 10752.00
Table 4 Parameters of lunar triaxial ellipsoid obtained by Chang’E-1 LAM data before and after crossover adjustment.
a(km) b(km) c(km) x0(km) y0(km) z0(km) Ellipticity
Before 1737.7506 1737.4724 1735.8112 1.5006 0.7131 0.2659 1/965.1611 After 1737.7260 1737.4685 1735.7905 1.4652 0.6868 0.2809 1/961.7002
Table 5 Differences between CE-1 DEMs and DEM from LOLA in a local area (01Nto601N, 501Wto01W) (Resolution: 10 km).
X(m) Y(m) Z(m) X(m) Y(m) Z(m)
DEM before adjustment Average 88.2 46.2 65.4 After ICP co-registration 0 0 0 RMS 73.7 49.8 69.1 75.2 48.3 68.8
DEM after adjustment Average 88.4 46.4 65.5 After ICP co-registration 0 0 0 RMS 73.3 49.9 69.1 74.8 48.3 68.8
Table 6 Differences between CE-1 DEMs and DEM from LOLA in the Copernicus crater (8.171N to 11.231N, 21.631W to 18.571W). (Resolution: 1400 m).
X(m) Y(m) Z(m) X(m) Y(m) Z(m)
DEM before adjustment Average 448.1 172.0 164.1 After ICP co-registration 10.5 18.7 1.6 RMS 209.4 388.3 453.8 209.2 375.7 342.4
DEM after adjustment Average 94.7 43.7 83.7 After ICP co-registration 9.7 19.8 0.9 RMS 205.9 382.5 452.6 207.8 376.8 343.3 lunar parameters obtained by Chang’E-1 LAM data before and after differences with the DEM derived from LOLA. Both DEMs before our adjustment; the results show that the adjustment does not and after adjustment can reach good co-registration with the LOLA deform the global topography. Results in Table 4 are similar with DEM, this shows that the crossover adjustment does not deform the overall parameters obtained by CE-1 LAM data with different the lunar terrain. data pre-processing (Wang et al., 2010) or data selection (Ping We choose the DEM of the Copernicus crater (area enclosed in the et al., 2009). However, there may be systematic differences red rectangle in Fig. 3). Copernicus crater is a typical landmark in this between the global parameters from CE-1 LAM and KAGUYA- area; it is used to assess the adjustment for the detailed terrain. DEMs LALT (Araki et al., 2013) or LRO-LOLA(http://pds-geosciences. are resampled in 1400 m (E0.0461) resolution according to the wustl.edu/lro/lro-l-lola-3-rdr-v1/lrolol_1xxx/data/lola_shadr/lro_ altimetric point along the track and co-registered with LOLA DEM. ltm04_720_sha.tab);again, this may be attributed to differences in Table 6 lists the variation between CE-1 DEMs and DEM from LOLA in orbit determination. the Copernicus crater (8.171Nto11.231N, 21.631Wto18.571W) before To make a detailed comparison, DEM in local area is further and after ICP co-registration. The results show that both the DEMs compared to the DEM derived from LOLA, which has the highest before and after adjustment are consistent with the LOLA DEM after precision so far. A co-registration between the CE-1 DEM and LOLA co-registration, and the difference in Z direction is reduced from DEM in the local area (01Nto601N, 501Wto01W) was tested to 1.55 m to 0.91 m after co-registration, indicating that the DEM after check the terrain changes after the adjustment. The two DEMs are crossover adjustment is closer to LOLA. It should be noted that, the both resampled in 10 km resolution, and co-registered using differences of two DEMs are always statistical errors in the Z direction iterative closest point (ICP) algorithm (Besl and McKay, 1992) with the same XY grid, however, ICP is a rigid transformation which which can select the closest points as the correspondences and make an overall rotation and translation for the registration, the XY re-calculate the rotation and translation parameters between the grid are not exactly same with each other, to avoid more errors in two DEMs to achieve co-registration. Next, the differences resampling, the statistical differences of the X, Y, Z three directions are between the two DEMs in the X, Y, and Z directions are calculated. made with the closest distance. Fig. 3(b) shows the DEM, which has fewer artefacts after crossover adjustment. This DEM is closer to the DEM derived from LOLA in the same area (Fig. 3(c)).Table 5 lists the differences between CE-1 4. Conclusion and discussion DEMs and DEM from LOLA in the 01Nto601N, 501Wto01W area with a large scale (10 km, E0.331). According to the table, the A crossover adjustment method with local topographic con- DEM before and after crossover adjustment can retain similar straints is developed in this study. Based on this method, a new W. Hu et al. / Planetary and Space Science 87 (2013) 173–182 181 lunar global DEM model is derived from the CE-1 LAM data. All Chen, M., Tang, G., Cao, J., Zhang, Y., 2011. Precision orbit determination of CE-1 adjustments in the mid-latitude and polar regions can reduce the lunar satellite. Geomatics and Information Science of Wuhan University 36 (2), 212–217. residuals of crossover differences. For example, the RMS of the Chin, G., Brylow, S., Foote, M., Garvin, J., Kasper, J., Keller, J., Litvak, M., Mitrofanov, I., residuals is reduced from 149.51 m to 54.75 m in the mid-latitude Paige, D., Raney, K., 2007. Lunar Reconnaissance Orbiter overview: the instru- region after using three parameters for each profile in each block. ment suite and mission. Space Science Reviews 129 (4), 391–419. fi In the polar regions, the RMS of more than 150 m is reduced to less Davies, M.E., Colvin, T.R., Meyer, D.L., 1987. A uni ed lunar control network: the near side. Journal of Geophysical Research 92 (B13) 14177-14184. than 100 m after using seven parameters for each profile. As a Di, K., Hu, W., Liu, Y., Peng, M., 2012. Co-registration of Chang'E-1 Stereo Images and result, artefacts in the original DEM were eliminated or decreased. Laser Altimeter Data with Crossover Adjustment and Image Sensor Model fi – Thus, the resultant new lunar global DEM has significantly Re nement. Advances in Space Research 50 (2012), 1615 1628. Fok, H., Shum, C., Yi, Y., Araki, H., Ping, J., Williams, J.G., Fotopoulos, G., Noda, H., improved quality in the local consistencies than the original CE- Goossens, S., Huang, Q., 2011. Accuracy assessment of lunar topography models. 1 DEM. The results of comparison with the LOLA DEM and LALT Earth, Planets and Space 63 (1), 15–23. data show that the adjustment does not deform the lunar terrain. Goossens, S., Matsumoto, K., Rowlands, D., Lemoine, F., Noda, H., Araki, H., 2011. Orbit determination of the SELENE satellites using multi-satellite data types Crossover adjustment results show that the adjustment in the and evaluation of SELENE gravity field models. Journal of Geodesy 85 (8), blocks is much better than the global solution. Local topographic 487–504. constraints from the virtual planar points are effective in prevent- Goswami, J., Annadurai, M., 2009. Chandrayaan-1: India's first planetary science mission to the moon. Current Science 96 (4), 486–491. ing terrain deformation and ensuring the smooth transition Hu, W., Yue, Z., Di, K., 2011. Crossover analysis of Chang’E-1 laser altimeter data. among neighbouring blocks.It should be noted that the adjust- International Achieves of the Photogrammetry, Remote Sensing and Spatial ment results in the polar regions (including nearside and farside) Information Sciences, ISPRS Workshop on Geospatial Data Infrastructure: From are not as significant as the mid-latitude regions even with seven Data Acquisition and Updating to Smarter Services 38, 4/W25. Kamalakar J., Laxmi Prasad A., Bhaskar K., Selvaraj, P., Sridhar Raja, V., Goswami, A., parameters for each profile. This may be due to the relatively poor Gopinath, N., 2009. Laser Ranging Experiment Aboard Chandrayaan-1: instru- orbit determination in the farside of the lunar surface (Chen et al., mentation and preliminary results. In: Proceedings of the 40th Lunar and 2011). It is worth to note that the along- and across-track offsets of Planetary Institute Science Conference Abstracts, pp. 1487. Kato, M., Sasaki, S., Tanaka, K., Iijima, Y., Takizawa, Y., 2008. The Japanese lunar fi the pro les are not discussed in this paper and only ground mission SELENE: science goals and present status. Advances in Space Research altimetry points are used to make the crossover adjustment of 42 (2), 294–300. radial errors and DEM improvement. Crossover analysis consider- Kaula, W., Schubert, G., Lingenfelter, R., Sjogren, W., Wollenhaupt, W., 1972. Analysis and interpretation of lunar laser altimetry. In: Lunar and Planetary Science ing along- and across-track offsets and combined processing with Conference Proceedings, pp. 2189–2204. orbit tracking data will be helpful for precision orbit determina- Kaula, W., Schubert, G., Lingenfelter, R., Sjogren, W., Wollenhaupt, W., 1973. Lunar tion. This will be investigated in the future when orbit tracking topography from Apollo 15 and 16 laser altimetry. In: Proceeding of the Fourth Lunar Science Conference, pp. 2811–2819. data become publically available. More terrain undulation was also Kaula, W., Schubert, G., Lingenfelter, R., Sjogren, W., Wollenhaupt, W., 1974. Apollo found where the higher interpolation errors introduced into the laser altimetry and inferences as to lunar structure. In: Lunar and Planetary crossover differences. In future research, we will also study the Science Conference Proceedings, pp. 3049–3058. impact of terrain relief on the calculation of crossover locations Li, C., Ren, X., Liu, J., Zou, X., Mu, L., Wang, J., Shu, R., Zou, Y., Zhang, H., Lü, C., Liu, J., Zuo, W., Su, Y., Wen, W., Bian, W., Wang, M., Xu, C., Kong, D., Wang, X., Wang, F., and differences. Furthermore, we will perform more detailed Geng, L., Zhang, Z., Zheng, L., Zhu, X., Li, J., Ouyang, Z., 2010. Laser altimetry data comparisons of the available lunar global DEMs and investigate of Chang'E-1 and the global lunar DEM model. Science China Earth Sciences 53 – DEM fusion methods to improve the global DEM from multiple (11), 1582 1593. Light, D.L., 1972. Photo geodesy from Apollo. Photogrammetric Engineering 38, data sources. 574–587. Mazarico, E., Neumann, G., Rowlands, D., Smith, D., 2010. Geodetic constraints from multi-beam laser altimeter crossovers. Journal of Geodesy 84 (6), 343–354. Acknowledgements Mazarico, E., Rowlands, D., Neumann, G., Smith, D., Torrence, M., Lemoine, F., Zuber, M., 2012. Orbit determination of the Lunar Reconnaissance Orbiter. Journal of Geodesy 86 (3), 193–207. Funding of this research by the National Basic Research Mazarico, E., Rowlands, D., Neumann, G., Torrence, M., Smith, D., Zuber, M., 2011. Program of China (2012CB719902) and the National Natural Selenodesy with LRO: radio tracking and altimetric crossovers to improve orbit knowledge and gravity field estimation. In: Proceedings of the Lunar and Science Foundation of China (41171355) is acknowledged. We Planetary Institute Science Conference Abstracts, p. 2215. thank the Lunar and Deep Space Exploration Science Applications McEwen, A., Robinson, M., 1997. Mapping of the Moon by Clementine. Advances in – Center of the National Astronomical Observatories (NAOC) for Space Research 19 (10), 1523 1533. Neumann, G.A., 2001. Some aspects of processing extraterrestrial LIDAR data: providing the CE-1 LAM data. The LOLA and LALT data used in Clementine NEAR MOLA. International Archives of Photogrammetry and this research were downloaded from NASA Planetary Data System Remote Sensing 34 (3), W4. (PDS) and Japan Aerospace Exploration Agency respectively. Neumann, G.A., Rowlands, D.D., Lemoine, F.G., Smith, D.E., Zuber, M.T., 2001. Crossover analysis of Mars orbiter laser altimeter data. Journal of Geophysical Research 106 (E10) 23753-23768. References Neumann, G.A., Zuber, M.T., Smith, D.E., Lemoine, F.G., 1996. The lunar crust: global structure and signature of major basins. Journal of Geophysical Research 101 (E7) 16841-16863. Akima, H., 1970. A new method of interpolation and smooth curve fitting based on Nozette, S., Rustan, P., Pleasance, L., Kordas, J., Lewis, I., Park, H., Priest, R., Horan, D., local procedures. Journal of the ACM (JACM) 17 (4), 589–602. Regeon, P., Lichtenberg, C., 1994. The Clementine mission to the Moon: Araki, H., Noda, H., Tazawa, S., Ishihara, Y., Goossens, S., Sasaki, S., 2013. Lunar laser scientific overview. Science 266 (5192), 1835–1839. topography by LALT on board the KAGUYA lunar explorer-operational history, Ouyang, Z., Li, C., Zhou, Y., Zhang, H., Nv, C., Liu, J., Liu, J., 2010. The primary science new topographic data, peak height analysis of laser echo pulses. Advances in result from the Chang'E-1 probe. Science China Earth Sciences 40 (3), 261–280. Space Research 52 (2), 262–271. Ping, J., Huang, Q., Yan, J., Cao, J., Tang, G., Shu, R., 2009. Lunar topographic model Araki, H., Tazawa, S., Noda, H., Ishihara, Y., Goossens, S., Sasaki, S., Kawano, N., CLTM-s01 from Chang’E-1 laser altimeter. Science in China Series G: Physics, Kamiya, I., Otake, H., Oberst, J., 2009. Lunar global shape and polar topography Mechanics and Astronomy 52 (7), 1105–1114. derived from Kaguya-LALT laser altimetry. Science 323 (5916), 897–900. Sjogren, W., Wollenhaupt, W., 1973. Lunar shape via the Apollo laser altimeter. Araki, H., Tazawa, S., Noda, H., Tsubokawa, T., Kawano, N., Sasaki, S., 2008. Science 179 (4070), 275. Observation of the lunar topography by the laser altimeter LALT on board Smith, D., Zuber, M., Neumann, G., Mazarico, E., HeadIII, J., Torrence, M., 2011. Japanese lunar explorer SELENE. Advances in Space Research 42 (2), 317–322. Results from the Lunar Orbiter Laser Altimeter (LOLA): global, high-resolution Archinal, B., Rosiek, M., Kirk, R., Redding, B., 2006a. A Clementine Derived Control topographic mapping of the Moon. In: Proceedings of the 42nd Lunar and Network and Topographic Model-The Unified Lunar Control Network 2005, 26. Planetary Science Conference,# 2350, Lunar and Planet, Inst., The Woodlands, Archinal, B.A., Rosiek, M.R., Kirk, R.L., Redding, B.L., 2006b. The Unified Lunar Texas. Control Network 2005. US Geological Survey. http://pubs.usgs.gov/of/2006/ Smith, D.E., Zuber, M.T., Jackson, G.B., Cavanaugh, J.F., Neumann, G.A., Riris, H., Sun, 1367/ULCN2005-OpenFile.pdf. X., Zellar, R.S., Coltharp, C., Connelly, J., 2010. The lunar orbiter laser altimeter Besl, P.J., McKay, N.D., 1992. A method for registration of 3-D shapes. IEEE investigation on the lunar reconnaissance orbiter mission. Space Science Transactions on pattern analysis and machine intelligence, 239–256. Reviews 150 (1), 209–241. 182 W. Hu et al. / Planetary and Space Science 87 (2013) 173–182
Smith, D.E., Zuber, M.T., Neumann, G.A., Lemoine, F.G., 1997. Topography of the Yan, J., Ping, J., Li, F., Cao, J., Huang, Q., Fung, L., 2010. Chang'E-1 precision orbit Moon from the Clementine lidar. Journal of Geophysical Research 102 (E1), determination and lunar gravity field solution. Advances in Space Research 46 1591–1611. (2010), 50–57. Tarantola, A., Valette, B., 1982. Generalized nonlinear inverse problems solved using Zuber, M.T., Smith, D.E., Cheng, A.F., Garvin, J.B., Aharonson, O., Cole, T.D., Dunn, P.J., the least squares criterion. Reviews of Geophysics and Space Physics 20 (2), Guo, Y., Lemoine, F.G., Neumann, G.A., 2000. The shape of 433 Eros from the – 219 232. NEAR-Shoemaker laser rangefinder. Science 289 (5487), 2097–2101. Tsubokawa, T., Araki, H., Tazawa, S., Asari, K., Kawano, N., 2002. Development of Zuber, M.T., Smith, D.E., Lemoine, F.G., Neumann, G.A., 1994. The shape and internal laser altimeter(LALT) on board SELENE orbiter. In: Proceedings of the twenty- structure of the Moon from the Clementine mission. Science 266 (5192), third International Symposium on Space Technology and Science(Selected 1839–1843. – Papers), vol. II, pp. 1986 1991. Zuber, M.T., Smith, D.E., Zellar, R.S., Neumann, G.A., Sun, X., Katz, R.B., Kleyner, I., Wang, W., Li, F., Liu, J., Ren, X., Zhou, X., Mou, L., Yan, J., Zhou, Y., Zhang, H., Lü, C., Liu, Matuszeski, A., McGarry, J.F., Ott, M.N., 2010. The lunar reconnaissance orbiter J., Zuo, W., Su, Y., Wen, W., Bian, W., Wang, M., Li, C., Ouyang, Z., 2010. laser ranging investigation. Space Science Reviews 150 (1), 63–80. Chandrayaan ellipsoid models of the Moon based on the laser altimetry data of Chang'E-1. Science China Earth Sciences 40 (8), 1022–1030. Vondrak, R., Keller, J., Chin, G., Garvin, J., 2010. Lunar Reconnaissance Orbiter (LRO): observations for lunar exploration and science. Space Science Reviews 150 (1), 7–22.