A NEW AND EFFICIENT METHOD FOR THE GENERATION OF A GROUND CONTROL NETWORK WITH A LARGE AREA OF COVERAGE

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1 A NEW AND EFFICIENT METHOD FOR THE GENERATION OF A GROUND CONTROL NETWORK WITH A LARGE AREA OF COVERAGE John Dolloff, Technical Director Michelle Iiyama, Sr. Principal Engineer Reuben Settergren, Sr. Principal Engineer BAE Systems Network Solutions 192 Technology Pl San Diego, CA john.dolloff@baesystems.com michelle.iiyama@baesystems.com reuben.settergren@baesystems.com ABSTRACT This paper presents a new and efficient method for the generation of a ground control network that is both accurate and consistent (high relative accuracy) across its entire area of coverage, which can range from a few kilometers squared to the size of countries and conceivably continents. Due to its unique generation process and data content (the 3D locations of the ground control points, their multi-point error covariance, image patches, and ancillary metadata), the network is termed the Metric Information Network (MIN). The MIN is generated and maintained using only the standard inputs and outputs from a series of individual image block adjustments (triangulations) in conjunction with a fusion algorithm. The fusion of information from a new image block adjustment with the current MIN improves the accuracy of all ground control points already in the network and allows for the addition of new points in an optimal and theoretically correct manner. Furthermore, this approach is capable of ingesting and exploiting externally surveyed points, with the fusion of new image block adjustments propagating the surveyed points information (accuracy) to the other points in the network. A hypothetical MIN implementation: Use a series of image block adjustments of commercial satellite imagery, along with a sparse set of surveyed ground control points to generate a MIN, and in turn use it to provide control and check points for future image block adjustments, exploitation products, or quality assurance. This paper also presents quantitative MIN performance results related to this scenario. INTRODUCTION Commercial satellite image products require the use of photo-identifiable ground control during their generation or subsequent refinement in order to achieve high accuracy on the order of a few meters. However, the availability of ground control points is problematic, particularly since image products can vary greatly in terms of location and area of coverage. A recently published paper (Dolloff and Iiyama, 27) describes a new, innovative, and efficient method to generate and maintain a ground control network using the standard inputs and outputs of a series of individual image block adjustments (aka triangulations). Collectively, this network and generation technique is termed a Metric Information Network (MIN); where both the size of the network and the imagery used for its generation can vary greatly, depending on the application. This paper presents an overview of the MIN directed at an audience familiar with photogrammetry, including image block adjustment (see (Mikhail et. al., 21) and (Dolloff, 24)); as well as an application of the MIN to the control of commercial satellite imagery and its products. A specific MIN corresponds to a particular area of interest, such as a city, country, or conceivably a continent. Its generation uses a series of partially overlapping image block adjustments that eventually cover the area of interest (see Figure 1), in conjunction with a parallel fusion algorithm that combines information between image blocks without placing any new requirements on the image block adjustments themselves. Thus, although the MIN is generated sequentially one block at a time, its resulting ground control points are equivalent to the adjusted tie points in a (hypothetical) simultaneous multi-image block adjustment involving all image blocks processed up to that point. However, the sequential MIN approach is faster, more practical than the simultaneous multi-image block adjustment approach, and throughout its generation process and maintenance, the MIN is available as a source of

2 ground control points to any application. (Note that ground control points can also be used as check points for product Quality Assurance.) Furthermore, it is a far more timely solution in that a simultaneous multi-image block adjustment must wait for the availability of all image blocks before proceeding. With the sequential MIN approach, information in all the corresponding imagery and its support data is transferred to the ground control points, continuously improving their accuracy as new (real-time or legacy) image blocks are processed. New image block adjustments also supply new ground control points to the MIN in the form of new adjusted tie points. As an option, any available external ground control (e.g., photo- identifiable GPS surveyed ground points) can also be added to the MIN at any time. Subsequent image block adjustments transfer their accuracy to the other ground control points, making them even more accurate. Area Of Interest In general, image blocks can be of any size and orientation, contain any number of images, and can correspond to any mix of commercial sensors. However, in this paper we further assume that image blocks are made up of partially overlapping stereo pairs Image block n of commercial satellite imagery the baseline case where a stereo pair can Image block n + 1 correspond to either a deliberate stereo collect, or stereo by opportunity. If instead, image blocks were made up of partially overlapping monoscopic images, i.e., monoscopic image blocks, more blocks would be required with greater overlap between them in order to get comparable results. Figure 1. Image blocks covering an area of interest (interim results). The actual data corresponding to a MIN is contained in a MIN Repository. The MIN data consists of the 3D locations of all ground control points, their full multi-ground point error covariance, image patches corresponding to the ground control points to aid in their subsequent measurement in new images, and ancillary meta-data. The multi-ground point error covariance characterizes the absolute accuracy of each ground point and the relative accuracy between each ground point pair, and is essential for the proper weighting of the ground control points by an arbitrary application as well as for rigorous error propagation. Fusion Overview the Stage 1 Adjustment and Stage 2 Update in the Sequential MIN Approach The information in a new image block is fused with the current MIN as illustrated in Figure 2. The process contains two stages, an image block adjustment (Stage 1), followed by the update of all ground control points already in the MIN (Stage 2). All that is required is access to the current MIN Repository, and access to the standard inputs and outputs of an image block adjustment that has full functionality. Appendix A presents further details regarding the inputs, outputs, and functionality of a fully-functional image block adjustment. Such an adjustment includes the ability to weight (constrain) a priori ground control point locations with their corresponding full a priori error covariance. Stage 1 of the process performs a standard image block adjustment using both tie and control points. The latter are any (a priori) control points X1 and their error covariance P11 currently available in the MIN Repository that can be measured in the block s images. After the image block adjustment is complete, the adjusted image support data is saved in the usual fashion, and the adjusted (a posteriori) X1 and its error covariance are output and made available to the Stage 2 update module, i.e. X1+ and P11+ are output from Stage 1 and made available to Stage 2. The remaining (a priori) control points X2 in the MIN Repository, their error covariance P22, and their crosscovariance with X1, P21, are then updated by the Stage 2 module to become X2+, P22+, and P21+, respectively, using the following equations: X2+ = X2 + ( P21 )( P11 ) -1 ( X1+ X1 ) P22+ = P22 ( P21 )( P11 ) -1 ( P11 P11+ )( P11 ) -1 ( P12 ) P21+ = P21 ( P21 )( P11 ) -1 ( P11 P11+ ) This Stage 2 update completes the fusion of information between the current image block and the current MIN. It transfers the information in the adjusted control points X1+ to the other control points X2 in the MIN via the correlation between X2 and X1, which was induced by the previous Stage 1 image block adjustments, and is

3 represented by P21. (Note that ( P11 ) -1 represents the matrix inverse of P11.) Image support data & measurements Z Adjusted image support data Image Block Adjustment (Stage 1) Relevant control points X1, P11 All control pts X1, X2 P11, P12, P22 X1+, P11+ Adjusted control pts (including tie point solutions) MIN Repository MIN Update (Stage 2) Updated control pts X1+, X2+ P11+, P12+, P22+ Figure 2. Fusion of a new image block with the MIN. The a posteriori X1+ and X2+ and their corresponding error covariance then replace their a priori counterparts in the MIN Repository. In addition, although not explicitly depicted in Figure 2, the adjusted tie points from the Stage 1 image block adjustment (or selectable subset), are also placed in the MIN Repository as new ground control points, i.e., they augment X1+. Their corresponding error covariance and appropriate cross-covariance also augment P11+, P12+ and its transpose P21+, see (Dolloff and Iiyama, 27) for details, including a derivation of the above equations and a proof that the sequential MIN approach corresponds to an optimal estimator. Note that the image measurements Z that drive the Stage 1 adjustment are not referenced by the Stage 2 update, and that no changes are required to the standard image block adjustment module exercised in Stage 1 in order to exercise the Stage 2 module. In addition, the Stage 1 adjustment automatically generates adjusted image support data that is consistent with the entire MIN following the Stage 2 update. As a result, the adjusted image support data for the current block reflects the relevant information in all ground control points in the current MIN, and correspondingly, all previous image blocks. Also, note that if X1 contains n1 3D ground points, it is a 3n1x1 vector and P11 is a 3n1x3n1 matrix; if X2 contains n2 3D ground points, it is a 3n2x1 vector, P22 is a 3n2x3n2 matrix, and P21 is a 3n2x3n1 matrix and its transpose P12 is a 3n1x3n2 matrix. Also, for most image blocks, n1<<n2. Roadmap The remainder of this paper illustrates MIN performance starting with the application of the MIN to simulated commercial satellite imagery, which is followed by an example that includes a sparse set of simulated external ground control points. With the use of simulated data, ground truth is known and corresponding errors computed. Following the simulated examples is an application of the MIN to actual commercial satellite imagery, and since ground truth is unavailable, various internal metrics are computed, including predicted accuracy and actual interblock shear. Finally, MIN throughput and storage requirements are examined and compared to a corresponding (hypothetical) simultaneous multi-block adjustment, which is then followed by a summary and references. MIN METRIC PERFORMANCE BASED ON SIMULTAED DATA: NO EXTERNAL CONTROL A MIN prototype and simulation capability to supply inputs and assess MIN performance was developed using MATLAB. Image measurements, image support data, and ground truth were simulated, including corresponding random errors that were generated using Gaussian distributions in statistical conformance with their specified a priori error covariances. The particular scenario presented in this section reflects both a limited number of image blocks and a limited number of images per block in order to facilitate the scenario s description and to best illustrate how the MIN works.

4 Experiment Set-up As shown in Figure 3, there are 8 image blocks with one or two stereo image pairs per block and a total of 62 2-ray tie points and 49 4-ray tie points. Other scenarios and experiments have also been performed involving hundreds of images with similar MIN performance to that presented later in this section. GP1 6 x 14 Block 7 GP13 Block 1 4 GP7 Block 6 GP68 GP8 1 Stereo model in Block 1 2 Block 5 Y GP3 Block GP55 Block 4 GP84-8 GP19 Block 3 GP59 GP11 Block X x 1 4 Figure 3. The 8 image block layout. The specific number of images and corresponding (orbital) passes per block are presented in Table 1. Note that images from the same pass are always grouped in the same image block so that image support data (errors) are uncorrelated between image blocks, as is required for an optimal solution discussed in (Dolloff and Iiyama, 27). The a priori error covariance for the image support Table 1. Images per block and associated orbital pass data adjustable parameters is characterized in Table 2 by the standard deviation of error (sigma) and temporal correlation time constant (T) for each of 9 adjustable parameters per image corresponding to a Block # # of images per block Pass # Seconds between images of stereo pair Seconds between stereo pairs Notes Same pass stereo Same pass stereo & 4 64 >72 Same pass stereo Same pass stereo & >72 Same pass stereo & 9 >72 Stereo by opportunity Same pass stereo & 7 >72 Stereo by opportunity generic commercial push-broom sensor. Image size and ground sample distance (GSD) are also specified in the table; in addition, for all images, the standard deviation of image measurement error was.5 pixel for both the line and sample components, the sensor height was approximately 2 nautical miles, focal length was 3 meters, scan rate was 348 lines/sec, and typical stereo convergence angles and image elevation angles were 5 degrees and 6 degrees, respectively. Note that the characteristics presented in the various tables are not meant to correspond to any specific commercial sensor. They are very general and vary from block to block, thus helping to illustrate the flexibility of the MIN approach. Also, both the simulated and actual a priori image support data for commercial satellite imagery is reasonably accurate to begin with and does not require resection.

5 Table 2. Image size, GSD, and image support data a priori error covariance data per block Sensor Parameters Format (Units) Blocks 1-3, 5, 7-8 Block 4 Block 6 Image size line x sample 25k x 25k 25k x 25k 5k x 25k GSD m In-track sigma (m) / T (sec) 6 / 2 12 / 2 6 / 2 Position Cross-track sigma (m) / T (sec) 8 / 3 16 / 3 8 / 3 Radial sigma (m) / T (sec) 4 / 1 8 / 1 4 / 1 Alpha sigma (urad) / T (sec) 15 / 2 3 / 2 15 / 2 Attitude Beta sigma (urad) / T (sec) 15 / 15 3 / / 15 Kappa sigma (urad) / T (sec) 15 / 3 3 / 3 15 / 3 Focal length sigma (mm) / T (sec) 1 / 5 1 / 5 1 / 5 Attitude Alpha sigma (urad/sec) / T (sec) 1 / 2 1 / 2 1 / 2 rate Beta sigma (urad/sec) / T (sec) 1 / 2 1 / 2 1 / 2 Experiment Results The experiment started with an empty MIN, and processed the eight image blocks sequentially from block 1 to block 8 for convenience. Furthermore, for each block, a Stage 1 image block adjustment was immediately followed by a Stage 2 MIN update. Since the MIN was empty at the start, the block 1 Stage 1 image block adjustment used no ground control points, and after Stage 1 completed, its Stage 2 update simply consisted of placing the 15 adjusted tie points (from Stage 1) into the MIN Repository as ground control. Following this, the block 2 Stage 1 image block adjustment was then performed. Of the 15 ground control points added to the MIN Repository from block 1, 5 overlapped block 2 and were used as ground control points in block 2 s Stage 1 image block adjustment along with 1 new tie points. After the Stage 1 adjustment was completed, Stage 2 updated the MIN Repository by replacing the 5 ground control points that were used in Stage 1 with their adjusted counterparts, updated the 1 remaining ground control points already in the MIN Repository via the update equations presented earlier, and also added the 1 adjusted new tie points from Stage 1. This general process continued for the remaining six image blocks. (Note that, although not mentioned explicitly in the above, the appropriate multi-ground point error covariance was also used and/or updated along with the corresponding set of ground points.) Table 3 presents the predicted accuracies of the various ground points in the MIN Repository by their general location (column) and by the sequential step (row) in the MIN process. ( Bi represents image bock number i ; and no adj corresponds to a stereo extraction using unadjusted image support data.) The predicted accuracies are the average CE and LE taken over the appropriate points in the MIN Repository. CE is defined as.9p horizontal error and LE is defined as.9p vertical error and computed from each point s 3x3 error covariance in the MIN Repository. Note the general improvement in predicted accuracy as more blocks are processed due to the fusion of information between blocks and the varying image geometry across blocks. Table 3. CE/LE predicted ground control point accuracy (m) by block location and by block adjustment number B1 B2 B3 B4 B5 B6 B7 B8 no adj 23 / / / / / / / / 25 B1 adj 23 / 13 B2 adj 16.1 / / 1.2 B3 adj 12.1 / / / 7.7 B4 adj 12.1 / / / / 25 B5 adj 12.1 / / / / / 1.1 B6 adj 12.1 / / / / / / 11.3 B7 adj 11.1 / / / / / / / 6.9 B8 adj 1.7 / / / / / / / / 7.3 The above table illustrates a reduction in CE/LE by more than 5% by processing 8 relatively small and partially overlapping image blocks, with the typical CE/LE for ground control points in the MIN Repository being about 9/7 meters after the last block is processed. In a typical implementation with real commercial imagery the

6 improved CE/LE is even smaller due to more imagery and GSDs closer to 1 meter than the 2.5 meters simulated. One final comment regarding the above table concerns the relative size between CE and LE for stereo extraction ( no adj ), i.e., notice that CE is larger than LE for all blocks except blocks 6 and 8. This is due to the high temporal correlation corresponding to same pass images and adjustable parameters with relatively large time constants. (If an adjustable parameter has a time constant equal to T seconds, the correlation of error in the parameter s value between one image and another image acquired dt seconds later on the same orbital pass equals exp(-dt/t).) Non-same pass images that form a stereo pair ( stereo by opportunity ) have uncorrelated errors and a larger LE than CE. Figure 4 plots actual horizontal error (absolute value) relative to ground truth along with the CE accuracy predictions for all 111 ground points in the final MIN Repository. Figure 5 does the same thing for vertical error and LE. The solution errors are consistent with the accuracy predictions, as expected for an optimal estimator. 15 CE and Horizontal with respect to Truth 15 LE and Vertical with respect to Truth LE Vert Err CE Horiz Err Figure 4. MIN horizontal error and CE (meters). Figure 5. MIN vertical error and LE (meters). To further illustrate that the MIN sequential approach corresponds to an optimal estimator, the final MIN Repository was compared to the adjusted tie point solutions of all ground points in a simultaneous, multi-image block adjustment involving all 8 blocks. Figure 6 presents the difference in the horizontal solution between the two approaches, and also the CE from each approach. Figure 7 presents the same thing but for vertical error. (Ground point numbering on the x-axis is different for these figures than for the previous two figures.) As seen in the figures, CE and LE accuracy predictions are identical and the horizontal and vertical locations virtually identical between the two approaches. (A typical one meter absolute difference in location is negligible when compared to an approximate 1 meter CE or LE and also when the relatively large 2.5 meter GSD is taken into consideration.) 15 Simultaneous Soln CE, MIN CE and their Horizontal Difference 15 Simultaneous Soln LE, MIN LE and their Vertical Difference Sim CE MIN CE Horiz Diff Sim LE MIN LE Vert Diff Figure 6. Horizontal solution differences (meters) between MIN and simultaneous approaches. Figure 7. Vertical solution differences (meters) between MIN and simultaneous approaches. Finally, the MIN approach also improves the relative accuracy between image blocks, which is important for consistent image products over the area of interest. Table 4 presents relative CE and relative LE accuracy predictions for a typical pair of ground control points in the final MIN Repository, where each point is in a different image block. Relative CE is defined as.9p relative horizontal error, and LE is defined as.9p relative vertical error. As seen in the table, improvements are greatest for blocks closest together. Both relative CE and relative LE are computed from the 6x6 error covariance from the final MIN Repository corresponding to the estimated location

7 of both ground points. Note the significant improvement in relative CE and relative LE with the MIN approach as Table 4. CE/LE predicted relative accuracy (meters) compared to stereo extraction with unadjusted by pair location and adjustment approach support data ( no adj ), which in this scenario is also approximately the same as results from an B1 & B2 B1 & B7 B1 & B5 individual image block adjustment without the CErel / LErel CErel / LErel CErel / LErel benefit of the MIN. No Adj 32.2 / / / 18.2 Min Soln 3.9 / / / 1. MIN METRIC PERORMANCE BASED ON SIMULATED DATA: SPARSE EXTERNAL CONTROL As mentioned earlier, the MIN can also include externally generated ground control points (e.g., GPS surveyed points). They are simply inserted into the MIN Repository at any time with the appropriate error covariance and related data. Their use can improve the accuracy of all other ground control points in the MIN Repository, as illustrated in this section of the paper. 6 x 14 Block Block 7 Block 6 Experiment Set-up This experiment was set-up exactly as the previous experiment, but with 4 of the tie points replaced with external 3D ground control points (see Figure 8). These 4 points have a priori error covariance corresponding to CE/LE accuracies of 1/1 meter, and their errors are uncorrelated between points. The errors in their a priori positions were simulated consistent with their a priori error covariance. Y Block 5-8 Block 3 Block 4 Block 2 Block X x 1 4 Figure 8. 4 external ground control points (in pink). Experiment Results Table 5 presents the predicted accuracies of ground control points in the MIN Repository by block location and as a function of block adjustment number. It is comparable to Table 3 of the previous experiment which did not include use of external ground control points. The use of sparse external control made a significant improvement in predicted accuracies. Even though there was only one external ground point in each of 4 blocks and none in the other four, the sequential MIN process propagated their information to all other ground control points in the MIN Repository. The use of sparse external control is a viable and cost effective method for commercial satellite imagery applications when used in conjunction with the MIN which acts as an information multiplier. Furthermore, in an actual application, results would improve over those indicated in Table 5 due to more images and smaller GSDs.

8 Table 5. CE/LE predicted ground control point accuracy (meters) by block location and by block adjustment number using sparse external control B1 B2 B3 B4 B5 B6 B7 B8 No adj 23 / / / / / / / / 25 B1 adj 22.5 / 13 B2 adj 9.3 / / 5.3 B3 adj 4.1 / / / 5.1 B4 adj 4.1 / / / / 7.9 B5 adj 4.1 / / / / / 6.2 B6 adj 4.1 / / / / / / 9.5 B7 adj 4 / / / / / / / 5.3 B8 adj 3.8 / / / / / / / / 5.7 Figures 9 and 1 present ground control point location errors and accuracy predictions for all points in the final MIN Repository. Note, the solution errors are consistent with their accuracy predictions. Figures 11 and 12 present the difference in ground point locations between the sequential MIN approach and a simultaneous image block adjustment of all 8 image blocks and all ground points. The MIN approach provides virtually identical results. 8 CE and Horizontal with respect to Truth 8 LE and Vertical with respect to Truth CE Horiz Err LE Vert Err Figure 9. MIN horizontal error and CE (meters) using sparse external control. Figure 1. MIN vertical error and LE (meters) using sparse external control Simultaneous Soln CE, MIN CE and their Horizontal Difference Sim CE MIN CE Horiz Diff Simultaneous Soln LE, MIN LE and their Vertical Difference Sim LE MIN LE Vert Diff Figure 11. Horizontal solution differences (meters) between MIN and simultaneous approaches using sparse external control. Figure 12. Vertical solution differences (meters) between MIN and simultaneous approach using sparse external control.

9 MIN METRIC PERFORMANCE BASED ON IKONOS IMAGERY The MIN concept was also evaluated using actual commercial satellite imagery. A MIN prototype was utilized, based on C++, XML for the MIN Repository, Perl for experiment control, and GXP s Socet Set image block adjustment (triangulation) module for Stage 1 adjustments. Experiment Set-up A set of 1 partially overlapping stereo pairs of IKONOS imagery was utilized with a GSD of one meter. Their footprints are presented in Figure 13 and are in the general vicinity of Cape Town, South Africa. The IKONOS sensor model and image support data corresponds to adjustable RPC, with m Pair 5 Pair 1 Pair 6 Pair 2 Pair 3 Pair 7 Pair 8 Table 6. Stereo pair image block relationship and other data Pair Conv Image Off Num Nadir Lines Samples GMT Time : : : : : : : : : : : : : : : : : : : :42 Pair 4 Pair 9 Pair 1 Figure 13. IKONOS image footprints for 1 stereo pairs. adjustable parameters per image a bias and two rate corrections for each image coordinate (Grodecki and Dial, 23). The a priori image support data was unadjusted. We wish to thank GeoEye and Gene Dial for supplying this high-precision imagery (small GSD) and permission for its use in this experiment. To ensure that accuracy predictions for ground control points in the MIN Repository were conservative for this particular experiment, the a priori error covariance for image support data adjustable parameters were set to conservative values. E.g., the adjustable parameter standard deviations were set to 1 pixels for the bias, and 5 ppm for the rates. Furthermore, images on different orbital passes were modeled as uncorrelated, while same pass images were modeled with.5 (5%) correlation between errors between the same adjustable parameters. The 1 image pairs were grouped into 8 image blocks, color coded in Table 6. This particular assignment basically corresponds to time of image acquisition, with same-pass images assigned to the same block. Note that any other assignment that assigned images from the same pass to the same block could have been made as well. E.g., pairs 1-4 could have been assigned to one block and pairs 5-1 to another block without changing results. Table 6 also presents image size, imaging geometry, and other related data.

10 Experiment Results As in the simulated experiment, the 8 image blocks were processed sequentially from block 1 to block 8 with the MIN approach (results are process-order independent). For each block, a Stage 1 image block adjustment was followed by a Stage 2 MIN update. As a result, without external ground control, a total of 94 (27 2-ray, 43 4-ray, 22 6-ray, and 2 8-ray) ground control points were generated and placed in the MIN Repository. In addition, for comparison purposes, two more approaches were analyzed: one in which each block was adjusted independently without use of a MIN ( No MIN ), and the other a simultaneous multi-image block adjustment ( Simul ). Table 7 presents these results comparing the CE and LE predicted accuracies and solution differences relative to the simultaneous approach, and the average and maximum statistics computed over all points in all blocks. Note: the MIN results are from the final MIN Repository; and for brevity, interim results between blocks are not presented. Table 7. Ground point comparison between the No MIN, MIN, and Simultaneous approaches CE9(m) LE9(m) Horiz dist (m) Vert dist (m) Case Avg Max Avg Max Avg Max Avg Max Case 1 (No MIN) Case 2 (MIN) Case 3 (Simul) With the MIN approach, CE/LE was reduced by over 6% relative to the independent block adjustment approach due to the fusion of information from the 8 small image blocks. In addition, the MIN approach and simultaneous approach gave virtually identical results, although if more and/or larger image blocks were involved the sequential MIN approach would also be more timely and more practical. Furthermore, the CE/LE values corresponding to the MIN approach would become even smaller given any combination of the following: improved imaging geometry (relative to some of the Cape Town stereo pairs), more images, sparse external ground control, or less conservative a priori image support data uncertainty. For instance, if the adjustable RPC bias uncertainty is reduced from 1 to 6 pixels, one sigma, and same-pass images are modeled as uncorrelated, CE and LE are reduced to approximately 3.5 meters. In addition, if three times the amount of uncorrelated imagery were available over the area, we estimate that the 3.5 meters would be reduced by a factor of square-root-of 3, yielding a CE and LE of approximately 2. meters. Similarly, availability of sparse external ground control would reduce this to approximately 1. meter, the assumed accuracy of the external control. Since no ground truth was available for this particular experiment, actual ground control point location errors could not be assessed; rather, inter-block shear results were assessed for all three approaches. Because shear is computed by taking the 3D location difference between stereo extractions of common ground points in overlapping stereo pairs, adjusted image support data is required for its computation. However, since the MIN was not near steady state for this area of interest (it was initially generated using these 8 image blocks), the adjusted image support data generated for the first few blocks did not nearly reflect the same amount of information as in the adjusted image support data for the other blocks. Therefore, after the final MIN Repository was generated with the MIN approach, each a priori image block was then readjusted individually (independently) using the overlapping ground control points from the MIN Repository as control. (The a priori image support data was also de-weighted by multiplying its a priori covariance matrix by a factor of 9.) In the following results, this technique is termed MIN++ and was implemented prior to computing shear for the MIN approach. Figures 14 and 15 compare inter-block shear between the three approaches: independent block adjustments ( Indep aka No MIN ), MIN ( MIN++ ), and simultaneous (Simul ). Note the MIN and simultaneous results are virtually identical and are clearly superior to the independent block adjustment approach. If the corresponding MIN Repository were used to control commercial image products, these products would be consistent, i.e., would have small intra-product and inter-product shear, indicative of high relative accuracy.

11 Probability.6.4 Probability.6.4 Simul. Simul..2 Indep..2 Indep. MIN++ MIN Horiz. Shear (m) Vert. Shear (m) Figure 14. Horizontal shear (meters) probability distribution function. Figure 15. Vertical shear (meters) probability distribution function. MIN THROUGHPUT AND STORAGE REQUIREMENTS The sequential MIN approach for the generation of a ground control network requires significantly less throughput than a corresponding simultaneous multi-image block adjustment. Figure 16 presents approximate operation counts as a function of the total number of images covering the area of interest, assuming 9 adjustable parameters per image, 1 stereo pairs per image block, and 5 ground control points per stereo pair are inserted into the MIN Repository. A square grid of partially overlapping image blocks is assumed over the area of interest. Also, note that a total of 4 images over the area of interest corresponds to the generation of 1 3D ground control points. Four cases are represented: (1) simultaneous multi-image block adjustment with standard bandwidth reduction for solution of the normal equations ( ), (2) simultaneous multi-image block adjustment with custom solution of the tri-diagonal normal equations ( ), (3) total MIN throughput (sum of all Stage 1 and Stage 2 processing over all image blocks) (+), and (4) average MIN throughput for one image block ( ) number of operations number of images Figure 16. Throughput versus total number of images in area of interest.

12 To put the operation counts presented in Figure 16 into perspective, let us assume that computations are exercised on a computer with a single 12 Mhz CPU and enough internal memory such that memory is not a factor, and an individual operation corresponds to a double precision multiply. Thus, assuming a total of 4 images are used, processing time corresponds to approximately 4 minutes ( ), 14 hours (+), 28 hours ( ), and 2 days ( ). With the MIN approach, processing is done one image block at a time throughout the entire time period in which image blocks are received. The average processing time for one of these blocks is only 4 minutes. Some noteworthy observations: Notice that the operation count for total MIN throughput (+) begins to approach that of the fastest simultaneous multi-image block adjustment ( ) as the total number of images increase due to the realistic assumption that a large simultaneous multi-image block adjustment can only compute (a posteriori) error covariance diagonal blocks (i.e., no error cross-covariance blocks between images, etc., are computed), while the MIN Stage 1 adjustment computes the full error covariance corresponding to all adjustable parameters for the image block, and the Stage 2 adjustment computes/updates the full error covariance for all ground control points in the MIN Repository. Also, MIN storage requirements are dominated by the full ground point error covariance in the MIN Repository. For double precision representation of an error covariance corresponding to 1 3D ground control points, storage requirements correspond to approximately 3.6 gigabytes, a small amount of storage for today s COTS computers. See (Dolloff and Iiyama, 27) for a more detailed discussion of MIN throughput and storage requirements, as well as practical approximations under research which minimize both MIN throughput and storage requirements for a MIN Repository much greater than 1 points. SUMMARY The MIN is a self-bootstrapping, continuously improving, network of ground control points, and includes a rigorous, flexible, and efficient method for their generation using the standard inputs and outputs of individual image block adjustments. The MIN can easily contain up to 1 3D points, and significantly more if practical approximations are employed. The ground control points are both accurate and consistent over the area of interest, which can range in size from that of a city, to a country, and conceivably a continent. For large sets of imagery covering the area of interest,, the MIN approach is significantly faster and much more practical than a simultaneous multi-image block adjustment, while giving virtually identical ground point solution results. In addition, as new blocks of imagery become available, the MIN is updated sequentially making it continuously available with the latest information. MIN performance was demonstrated using both simulated and actual commercial satellite imagery; as well as the benefits of optional external ground control with the MIN serving as an information multiplier. Based on an extrapolation of these results, we estimate that a network of ground control points with approximate two meter.9p accuracy is readily achievable with the MIN approach, given a reasonable amount of overlapping high-precision commercial satellite imagery over the area of interest. However, if a sparse set of external (surveyed) ground control points is also inserted into this MIN during its generation, one meter accuracy for the entire network should be also achievable. Thus, control of various image products using a MIN generated from a series of commercial satellite image blocks (large or small) should make these products both highly accurate and consistent in a cost effective manner. APPENDIX A The image block adjustment module used in Stage 1 is assumed to have full functionality. It performs a weighted least-squares estimate with a priori data, and corresponds to a Best Linear Unbiased Estimator. The equations for solution are linearized about the a priori estimates and iterated although for today s high-resolution commercial satellite imagery, few if any iterations are required for re-linearization due to image support data adjustment and are primarily for re-linearization due to ground location adjustment, convergence detection, and measurement editing, when necessary. The image block adjustment adjusts the a priori estimates of image support data (e.g., sensor position, attitude, etc.), tie point locations, and ground control point locations. The a priori estimates for each of these groups of adjustable parameters are weighted (constrained) by their corresponding a priori error covariance. For both the image support data and ground control point groups, their error covariance may be full include cross-blocks (aka cross-covariance or correlations) between adjustable parameters when applicable (see (Dolloff, 24)). For

13 example, if there were two 3D ground control points, their 6x6 a priori error covariance matrix may have non-zero off-diagonal elements, i.e., the matrix may not simply be diagonal or block diagonal. The a priori ground control point locations would be weighted by the inverse of this matrix. (Recall that the error covariance of the n1x1 vector X1 is the n1xn1 matrix E{(eX1)(eX1_tr)}, where e denotes the vector s mean-zero (unbiased) error relative to truth, tr vector transpose, and E expected value. Similarly, the error cross-covariance between vectors X1 and X2 is the n1xn2 matrix E{(eX1)(eX2_tr)}, where X2 has dimension n2x1.) The a priori estimates and error covariance are inputs to the image block adjustment module. However, a priori tie point locations and error covariance are usually set internally, the latter to a diagonal matrix with very large default values. After the adjustment is complete, the adjusted image support data parameters, adjusted tie point locations, and adjusted ground control point locations are output from the image block adjustment module, along with their a posteriori error covariance. The MIN requires the adjusted locations and the full a posteriori error covariance for the group of ground points to be inserted into the MIN Repository. (As an example, GXP s Socet Set triangulation module has full functionality, including the ability to output any combination of a posteriori error covariance blocks and cross-blocks for any specifiable set of adjustable parameters that are solved for.) REFERENCES Dolloff, J., 24. Replacement Sensor Models, Chapter 11.3, Manual of Photogrammetry, 5th Edition., J. C. McGlone editor. ASPRS, pp Dolloff, J., and M. Iiyama, 27. Fusion of image block adjustments for the generation of a ground control network, Proceeding from the Information Fusion, 27 1 th International Conference, July 9-12, Grodecki, J., and G. Dial, 23. Block adjustment of high-resolution satellite images described by rational polynomials, Photogrammetric Engineering & Remote Sensing, Vol. 69 No. 1, pp Mikhail, E., J. Bethel, and C. McGlone, 21. Introduction to Modern Photogrammetry, John Wiley & Sons.