REPLACEMENT SENSOR MODEL (RSM) PERFORMANCE ... - asprs

REPLACEMENT SENSOR MODEL (RSM) PERFORMANCE FOR TRIANGULATION
AND GEOPOSITIONING
ABSTRACT
Charles R. Taylor, Sr. Principal Engineer
John T. Dolloff, Technical Director
Michelle M. Iiyama, Sr. Principal Engineer
BAE Systems
10920 Technology Pl.
MZ62ENG
San Diego, CA, 92127
charles.taylor@baesystems.com
john.dolloff@baesystems.com
michelle.iiyama@baesystems.com
The Replacement Sensor Model (RSM) allows the functionality of many diverse sensor models to be captured in a
single generic model. The RSM concept is for the replacement support data to be generated from the original sensor
models and their image support data “up-stream” of the user community. Geopositioning performance studies of
RSM compare the absolute and relative geolocations and error estimates (accuracy predictions) for objects or
“targets” extracted from images using original sensor models with those extracted using RSM with the same image
measurements. Triangulation performance studies of RSM compare the absolute and relative geolocations and error
estimates of tie points that participate in triangulations. In these studies, two triangulations are performed – one
based on the original sensor models and their image support data, and another based on the RSM sensor models and
their image support data. The most recent RSM triangulation and geopositioning performance results are presented
in this paper, incorporating the latest enhancements in RSM adjustability and error modeling. The results show that
the RSM performance is virtually equivalent to the original sensor model performance.
INTRODUCTION
A complete geopositioning sensor model includes (as a minimum) the projective model algorithms to compute
the image coordinates for any ground location in the field of view, an error model that describes the predicted
accuracy of the projective model, and an adjustment model consistent with the error model to allow the projective
model and error model to be improved by triangulation with other images and ground control. One of us (JTD)
began to develop the Replacement Sensor Model as a generic mathematical model that has all of these capabilities
and is capable of reproducing these functions with high fidelity for virtually any rigorous or physical sensor model.
The theoretical development culminated in a Manual of Photogrammetry article (Dolloff, 2004) which outlines both
the generic mathematical model and the algorithms for fitting them to existing sensor models.
A Replacement Sensor Model Support Data (RSMSD) format was developed (Dolloff and Taylor, 2004) and
then extended (Dolloff and Taylor, 2006). The first software development kit (RSM 1.0) implementing Dolloff's
algorithms to generate and exploit RSMSD was released in 2004. A companion paper to this one (Dolloff et. al.
2008) gives an extended overview of RSM including the integration status of the software.
Performance studies of RSM have been conducted since its inception with favorable results, beginning with
simulations and continuing with studies of various real sensors. One RSM performance study of note used large
angular field-of-view aerial frame images (Taylor et. al., 2006). In this study it was found that the RSM projective
model and error model performed virtually the same as a rigorous model for geopositioning and triangulation with
the images under study. Projective model fitting errors were under 0.001 pixel, and error estimates and triangulation
adjustments agreed with the rigorous frame sensor model to within 0.1 m in ground space.
This paper gives new RSM performance study results from the latest software release (RSM 2.2). RSM
performance with commercial satellite imagery is addressed. After a brief description of the RSM support data
generation process, we will describe the results of the projective model generation, adjustable parameter selection,
and error covariance mapping for the QuickBird and WorldView images under study. We will then describe RSM
geopositioning and triangulation performance studies using QuickBird and WorldView.
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Portland, Oregon April 28 - May 2, 2008

RSM SUPPORT DATA GENERATION
RSM Generator Introduction
As described in the companion paper, the RSM Generator module is a software development kit that can be
integrated into any application. The application provides the original, rigorous sensor model to the RSM Generator
through a standard Application Program Interface (API) and the RSM Generator uses it to create the RSMSD. In
these studies, RSM Generator 2.2 was integrated into BAE Systems rapid prototyping environment, in which many
commercial sensor models are available via BAE Systems Socet Set® software libraries. * No modifications to the
RSM 2.2 code were needed to accomplish these new studies.
The rapid prototyping environment used in the RSM performance studies also contains BAE Systems Multi-
Image Geopositioning (MIG) service, which performs monoscopic, stereoscopic, and multi-image target extraction
and triangulation with sensor models and Digital Elevation Models (DEMs). In order for the MIG service to use the
RSMSD, RSM Exploiter 2.2 is also integrated into the environment. The RSM Exploiter parses the RSMSD and
delivers sensor model functionality through the same API that is used for the original, rigorous sensor model. Thus,
in addition to testing the RSM performance, the studies also demonstrate the capability of the RSMSD format to
communicate all of the information needed to exploit RSM.
The RSM Generator begins its processing by obtaining the original sensor type from the sensor model and
looking up any fitting strategies that have been configured for that type. If there are none, then it uses the
configured default strategies. Each strategy has an associated priority order, and if the first strategy results in a fit
that doesn't meet the criteria, then the next strategy is tried. Typically one of the first strategies selected meets the fit
criteria, but if necessary the RSM Generator will try all of the sensor-specific strategies followed by all of the
default strategies until it finds a fit that meets the criteria. If all of the strategies are exhausted, then the RSM
Generator will return the best fit and alert the calling application that the criteria were not met.
The strategy-driven logic of the RSM Generator is diagrammed in Figure 1. The same logic is used in both
major operations of the RSM Generator: projective model fitting, and adjustable parameter selection/error
covariance mapping.
Start
Save
No
No
Usable?
Yes
Best
so far?
Yes
No
Get next
strategy?
Fit using strategy
Compute metrics
Pass?
Yes
Return
this fit
Yes
Figure 1. RSM Generator logic.
No more
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Portland, Oregon ♦ April 28 - May 2, 2008
Return best
saved fit
(if any)
The sensor-specific and default strategies are configurable in each RSM Generator installation. On initial
installation, the sensor-specific strategies are those that have been identified by BAE Systems in previous
performance studies as having the best performance. In addition, the default strategies have been researched
carefully, such that on initial installation the default strategies alone give good performance for every sensor that has
been studied by BAE Systems. This gives the integrator confidence that the RSM Generator is likely to perform
well even for a new sensor type that has not participated in previous performance studies.
* Socet Set is a registered trademark of BAE Systems.

For the commercial satellite study being reported in the paper, the first tests were conducted without any sensorspecific
strategies for QuickBird or WorldView. Following the procedures outlined in the RSM Generator Users
Manual, the RSM generation metrics were reviewed for the first few images, and sensor-specific strategies that are
minor departures from the defaults were created in order to arrive immediately at the best strategy. This
configuration process required only a short time, and did not require any software modifications. Once complete,
the configuration was used successfully for all of the images.
Projective Model Fitting
The primary elements of a projective model fitting strategy are whether to use rational polynomials for the
ground-to-image function, and if so then how many sections will be used to cover the image, and which terms
(coefficients) will be used in the numerator and denominator for the row and column functions, and whether to use
an interpolating grid, either by itself or as a correction to the rational polynomials. Along with those primary
elements, the strategy also specifies what ground coordinate system is to be used for the polynomials and/or grid,
and how the fitting is to be done.
The projective model fitting accuracy is evaluated by the RSM Generator as part of the fitting process. Since
the fitting process typically uses the original sensor model ground-to-image function output on a regular 3dimensional
grid, the evaluation is usually done by calling the original sensor model ground-to-image function at an
additional 1000 points generated randomly in the image domain and height range of interest. It is these randomly
selected evaluation points whose statistics will be considered below.
A test set of 58 QuickBird 2 images and 4 WorldView 1 images were used to test the RSM Generator. The
images were made available as Basic Products with rigorous sensor model support data. BAE Systems Socet Set
was used to import the support data into the testbed, and Socet Set libraries provided the rigorous sensor model
functionality in the testbed.
Past testing with line-scanning sensors indicated that a polynomial with a correction grid would be a good
choice for the RSM projective model for these sensors, and a few quick experiments confirmed this and provided a
specific strategy. The coordinate system used is a rectangular system with the Z-axis along a nominal line of sight
and the X-axis nominally aligned with the scan direction. The baseline polynomial is the same for both image row
and image column. It has a numerator with terms up to fifth order in X and Y, and up to third order in Z, with cross
terms up to a maximum combined order of 5. It has a denominator with terms of first order only (no cross terms).
The same strategy is used for both QuickBird and WorldView with one exception. It was found that in order to
keep the maximum RSM fitting error below 0.05 pixel required a finer grid-spacing in the X-direction for
WorldView.
The projective model fitting is summarized in Table 1. The "typical RMS fit error" is the mean of the RMS
combined fit errors for all images. The "maximum fit error" is the largest combined (row and column) residual error
for any point in any image. The "maximum grid spacing" is a strategy parameter such that the actual grid spacing is
smaller in every image. The "typical grid spacing" is the mean for all of the images. The support data size per
image is displayed as a range from the smallest to the largest.
Table 1. Projective model statistics for QuickBird and WorldView
RSM projective model fitting statistic QuickBird WorldView
Number of images 58 4
Number of image rows 25956 - 37120 57344 - 79872
Number of image columns 27552 35840
Typical RMS fit error 0.002 pixel 0.001 pixel
Maximum fit error 0.040 pixel 0.049 pixel
Maximum/Typical grid spacing-row direction 400 m / 250 m 100 m / 60 m
Maximum/Typical grid spacing--column 2000 m / 1300 m 2000 m / 1100 m
direction
Grid spacing--LOS direction 1000 m 1000 m
Original support data size 0.41 - 1.22 Mbyte 0.51 - 0.57 Mbyte
RSM support data size 0.06 - 0.12 Mbyte 0.87 - 1.11 Mbyte
The average time required to generate the RSM support data in these experiments was about 1.7 s per image for
QuickBird and 12 s per image for WorldView, and the time also includes adjustable parameter selection and error
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covariance mapping (see the following section). These times are for a single Pentium processor running at 1.86
GHz. No effort has been made to optimize the time performance of the RSM Generator, which tends to be limited
by the time for the original sensor model projective model calls for the fitting and evaluation points. In addition to
the ground-to-image calls needed to populate the interpolating grid, the 110 coefficients of the baseline polynomial
(55 for row and 55 for column) are calculated by calling the original sensor model image-to-ground function at 1000
fitting points, and the original sensor model image-to-ground function is also called at the 1000 randomly generated
evaluation points.
The polynomial for the baseline projective model is in a single section covering the entire image. The RSM
Generator automatically divides the interpolating grid into sections as needed in order to be represented within the
RSMSD format. For QuickBird a single section was used, and for WorldView about 32 sections were used for each
image.
It is a simple matter to configure the RSM Generator for alternative projective model strategies, make the fits,
and generate the metrics for comparison. A few of these are shown in Table 2 below. The cubic rational
polynomial is the most commonly used replacement sensor model. The table shows that its typical RMS error is
about one pixel, and the maximum error is nearly three pixels. The baseline rational polynomial when used without
the interpolating grid does only slightly better. The last two lines of the table make use of the RSM capability of
sectioning the image for the purposes of fitting the projective model. In each case, the images were sectioned into
32 sections in the row direction and 8 sections in the column direction, for a total of 256 sections. The sectioned
polynomials give fits that are much better than a single section for these images, but not nearly as good as the singlesection
polynomial with the interpolating grid. Note also that the 256-section polynomial fits take about three times
longer than the baseline projective model to generate.
Table 2. Alternative projective models and metrics for WorldView
RSM adjustable parameter set Typical RMS fit error Maximum fit error
Baseline (rational polynomial with
interpolation grid)
0.001 pixel 0.049 pixel
1-section cubic rational polynomial 0.915 2.617
1-section baseline polynomial 0.880 2.564
256-section cubic rational polynomial 0.076 0.317
256-section baseline polynomial 0.059 0.286
In summary, the RSM projective model fit is excellent for all of the images studied. The traditional
replacement model, the cubic rational polynomial, is not able to attain subpixel projective model accuracy for these
line scanning sensors, but RSM does so through the use of the interpolation grid, while keeping the support data size
and time-to-fit within acceptable limits.
Adjustable Parameter Selection and Error Covariance Mapping
Adjustable parameter selection and error covariance mapping are done if the original sensor model has
adjustable parameters with an associated error covariance that is available through the sensor model API. If the
original sensor model does not have adjustable parameters with an associated error covariance, then these are not
supported in the RSM Generator and Exploiter for that sensor, and only the projective model is supported. The
RSM adjustable parameters and their associated error covariance are distinct from the parameters of the RSM
projective model. The adjustable parameters are chosen and the original sensor model error covariance is mapped to
these parameters such that the RSM performance is a good match to the original sensor model performance for
adjustment and error propagation.
As with the projective model fitting, the RSM Generator begins the adjustable parameter selection process by
obtaining the original sensor type from the sensor model and looking up any strategies that have been configured for
that type. If there are none, then it uses the configured default strategies.
The primary choice to be made in choosing the RSM adjustable parameters is whether the adjustments should
be applied prior to the RSM ground-to-image projection ("ground-space adjustment") or after ("image-space
adjustment"). Past experiments have shown that ground-space adjustment is best for frame sensors and image-space
adjustment is best for line scanning sensors. (For other sensors such as SAR there is little difference between
ground-space and image-space adjustment choices.)
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Another choice to be made is which specific ground- or image-space adjustment parameters are to be
considered, and whether the best linear combinations of the parameters are to be used or whether the parameters are
to be used without being combined. The former is recommended by the RSM development team, and it requires the
updated RSMSD format.
When the choice is made to use the best linear combinations of the RSM adjustable parameters, the RSM
Generator performs a principal components analysis of the RSM adjustable parameter error covariance, and selects
enough of the resulting eigenvectors to match the original sensor model performance faithfully. The error
covariance condition number is also computed and used as a criterion in the selection process. (The condition
number computation insures that the RSM adjustable error covariance is a legitimate positive-definite matrix and
gives confidence that the adjustment and error propagations that use it will be numerically stable.) Since the RSM
adjustable parameter error covariance is diagonal when expressed in terms of the principal components, it results in
very stable performance in adjustment.
Note that the "choices" above are made when the RSM Generator is configured. In normal operation, the
adjustable parameter selection and covariance mapping (and indeed all of the steps of the RSMSD generation) are
done automatically by the RSM Generator, with no operator interaction required.
The error covariance mapping is done as described in the Manual of Photogrammetry article referenced in the
introduction. This process requires the original sensor model, from which the RSM Generator obtains the adjustable
parameters and their error covariance. The a priori QuickBird adjustable parameter error covariance used was the
default covariance coded in Socet Set. Since the Socet Set WorldView sensor model was coded prior to the
calibration of the WorldView sensor, the coded defaults were not used. An a priori error covariance consistent with
the WorldView specification was used instead.
A few quick experiments with QuickBird and WorldView confirmed our earlier findings that image-space
adjustable parameters perform well for line-scanning sensors. The image-space adjustable parameters are two
correction polynomials, one for image row (line) and one for image column (sample), that are applied after the
projective model computations in the ground-to-image function as explained in the companion paper. We chose to
allow linear combinations of image space corrections as a function of the image-aligned rectangular coordinates,
with terms up to third order in X and Y and up to first order in Z, with cross-terms up to a maximum combined order
of 3. This is a total of 32 terms, from which the RSM Generator chooses the best linear combinations. Since the
number of original sensor model adjustable parameters is 6, the number of combinations must also be 6 or less, and
6 were used.
The adjustable parameter selection and covariance mapping metrics are summarized in Table 3. The
normalized frobenius norm of the residual adjustable parameter error covariance projected to image space is a
covariance mapping metric that can be regarded as a fractional error in the process. The maximum for either image
type is much less than 0.01, and the smaller the normalized frobenius norm the better the covariance mapping. The
condition numbers of the error covariances are shown as well. The smaller the condition number the more stable the
error covariance is likely to be in adjustment and error propagation computations.
Table 3. Adjustable parameter selection and error covariance mapping statistics for QuickBird and WorldView
RSM projective model fitting statistic QuickBird WorldView
Typical normalized frobenius norm 0.0016 0.000783
Maximum normalized frobenius norm 0.0039 0.000836
Typical condition number 3.5e+4 4.0e+6
Maximum condition number 1.11e+6 1.14e+7
It is instructive to compare the metrics of the adjustable parameter selection and error covariance mapping
process with those of other potential RSM adjustable parameter sets. This comparison can be seen in Table 4 for the
WorldView test images and three variations on the adjustable parameter set. With six ground-space adjustable
parameters, a set that typically works well for frame images, the normalized frobenius norm is about three times
larger than for the baseline set, which is still good, but the condition number is up to two orders of magnitude larger,
so that solutions are not as stable. The 6-parameter image-space adjustment that is linear in image coordinates is a
set sometimes used with RPC replacement models, despite the fact that the NITF TREs aren't capable of
transmitting the error covariance. Its normalized frobenius norm is about four times larger than for the baseline set
and the condition number is up to an order of magnitude larger. The 2-parameter image space offsets have a much
lower fidelity with a normalized frobenius norm over ten times larger than for the baseline set. The condition
number is of course much smaller than for the baseline case since there are only two parameters.
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Table 4. Alternative adjustable parameter selection and error covariance mapping statistics for WorldView
RSM adjustable parameter set Maximum normalized Maximum
frobenius norm condition number
Baseline (6 linear combinations of imagespace
adjustments as a function of imagealigned
ground coordinates)
0.000826 1.14e+7
6-parameter ground-space offset and rotation 0.002570 1.52e+9
6-parameter image-space adjustment linear in
image coordinates
0.003024 3.46e+8
2-parameter image-space offsets 0.010016 1.01
The adjustable parameter selection and covariance mapping results show that the RSM Generator has arrived at
a superior adjustable parameter set for these test images, and it has done so automatically given the original sensor
models and the RSM Generator configuration.
RSM GEOPOSITIONING PERFORMANCE STUDIES WITH QUICKBIRD
The geopositioning performance studies conducted with QuickBird test images were of the type outlined in
Figure 2, termed the "replace/extract" scenario.
Original
support
data
Extract
Generate RSM
Extract
ASPRS 2008 Annual Conference
Portland, Oregon ♦ April 28 - May 2, 2008
Compare:
absolute and
relative point
positions,
absolute and
relative error
estimates
Figure 2. "Replace/Extract" RSM geopositioning performance test procedure.
The rigorous "original" sensor model is provided to the testbed by the Socet Set libraries. Prior to testing, the
images have been imported with Socet Set, so the "original support data" consists of Socet Set support files.
The "extract" operation is done with BAE Systems Multiple-Image Geopositioning (MIG) service. It consists
of a simultaneous least squares solution for the point positions given their measurements in all images. In the case
of extraction from a single image, Digital Terrain Elevation Database (DTED) is used to establish the point heights.
The sources of error in MIG error propagation are image measurement errors (estimated at 2 pixels 1-sigma), sensor
model adjustable parameter errors, and DTED errors.
The RSM support data generation is done with the RSM Generator, and the sensor model used in the RSM
extraction is provided by the RSM support data and the RSM Exploiter. The RSM extraction is done with the same
MIG service used for the original sensor model extraction. The same image measurements and uncertainty are used
as for the original sensor model extraction. The sensor model adjustable parameters for the RSM extraction are the
ones selected by the RSM Generator and communicated via the RSM support data.
The first test set for RSM geopositioning tests with QuickBird consists of a pair of overlapping images acquired
on different passes. The first image has an off-nadir angle of 8 degrees and the second has an off-nadir angle of 29
degrees. The stereo convergence angle is 24 degrees. The ground sample distances (GSDs) are 0.6 m to 0.7 m
(measured normal to the nominal line of sight). The horizontal CE for the QuickBird images is 23 m at nadir, and
somewhat larger off-nadir. (The confidence level for all absolute and relative CE and LE metrics in this paper is 90
% and is computed from the appropriate a posteriori ground point error covariance matrix.) Two corresponding
points were measured in each of these two images, and geopositioning was performed for each image with DTED,

and for the stereo pair. The original sensor model results and the RSM results are tabulated in Table 5 (absolute
geopositioning) and Table 6 (relative geopositioning).
The first two columns of Table 5 identify the images and point used for the row. The third and fourth columns
are the horizontal CE for geopositioning with the original sensor model and with RSM. In every case these are in
extremely good agreement. Note that for single-image geopositioning the CE is larger for the second point than the
first, because the off-nadir angle is greater, and therefore the DTED vertical error affects it to a greater degree.
The fifth and sixth columns of Table 5 are the vertical LE using the original sensor model and RSM. For
single-image geopositioning, the LE is strictly determined by the DTED accuracy, so it is not surprising that the
original sensor model and RSM are in good agreement, but the agreement is excellent for stereo geopositioning as
well. (The LE is larger for stereo geopositioning than for mono, because the convergence angle is not very
favorable, and the DTED was not used to assist the stereo geopositioning for these tests.)
The seventh column of Table 5 is the difference in the horizontal position for RSM geopositioning as compared
to the original sensor model geopositioning. The largest difference in the table is 0.074 m, which is an insignificant
fraction of the horizontal uncertainty of 26.239 m for the same point. The last column of Table 5 is the difference in
the vertical position for the RSM geopositioning as compared to the original sensor model geopositioning. Only the
last two rows are significant (because DTED is the only source of vertical information for the single-image cases),
and these are in extremely good agreement.
Table 5. Absolute geopositioning results for 2 QuickBird images
Image(s) Point Original RSM Original RSM Horiz. Pos. Vert. Pos.
CE (m) CE (m) LE (m) LE (m) diff. (m) diff. (m)
1 1 24.550 24.556 18.001 18.001 0.001 0.000
1 2 25.055 25.062 18.000 18.000 0.000 0.000
2 1 31.361 31.309 18.001 18.001 0.004 0.000
2 2 31.942 31.884 18.002 18.002 0.006 0.000
1 and 2 1 26.239 26.233 63.901 63.779 0.074 -0.028
1 and 2 2 26.562 26.558 65.256 65.136 0.067 -0.084
It is not enough to assess the RSM performance with absolute geopositioning results. Sensor models are also
used to compute point-to-point distances, angles, and so forth, which requires high-fidelity relative geopositioning.
The relative geopositioning results in Table 6 below show that RSM has excellent performance for these purposes
just as it has for absolute geopositioning. The first two columns identify the images and points used for the row.
The third and fourth columns are the relative CE for the point pair, computed with the original sensor model and
RSM. Note that CErel is larger for the second image, because the off-nadir angle is greater and the random DTED
error has a greater horizontal effect.
The fifth and sixth columns of Table 6 are the relative LE for original sensor model and RSM geopositioning,
respectively. The results are identical for single-image geopositioning, due to the use of the same DEM, and the
result is in excellent agreement for stereo geopositioning.
The seventh column of Table 6 is the relative horizontal position difference, that is, the difference in the
horizontal distance from the two geopositioning solutions. The small differences are negligible in comparison with
the horizontal error estimates.
The last column of Table 6 is the relative vertical position difference, that is, the difference in the height of the
second point relative to the first as computed using RSM as compared with the original sensor model. Only the last
entry is significant due to use of the same DEM for single-image geopositioning, and the difference of 0.056 m is
tiny in comparison with the relative LE of 10.096 m.
Table 6. Relative geopositioning results for 2 QuickBird images
Image(s) Points Original RSM Original RSM Rel. Horiz. Rel. Vert.
CErel (m) CErel (m) LErel (m) LErel (m) Pos. diff. (m) Pos. diff. (m)
1 1-2 5.504 5.505 25.457 25.457 0.001 0.000
2 1-2 15.447 15.448 25.458 25.458 0.002 0.000
Stereo 1-2 4.112 4.113 10.096 10.097 0.008 0.056
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A more challenging extraction test case was established as follows. In one of the QuickBird image sets there
are 56 images in 7 strips of 8 images each. The overlap of two of the strips is at the reasonably favorable
convergence angle of 30 degrees. Along the overlap many tie points have been measured. The extraction test below
is a 10-point simultaneous extraction that uses 4 adjacent images on the strip. The results of this test are
summarized in Table 7 and Table 8.
Table 7. Absolute geopositioning statistics for simultaneous extraction of 10 points from four QuickBird images
Statistic Original RSM Original RSM Horiz. Pos. Vert. Pos.
CE (m) CE (m) LE (m) LE (m) diff. (m) diff. (m)
RMS 24.711 24.715 53.956 53.962 0.037 0.118
Max 35.695 35.696 76.020 75.965 0.065 0.269
Table 8. Relative geopositioning statistics for simultaneous extraction of 10 points from four QuickBird images
Statistic Original RSM Original RSM Horiz. Rel. Vert. Rel.
CErel (m) CErel (m) LErel (m) LErel (m) Pos. diff. (m) Pos. diff. (m)
RMS 31.002 31.001 67.648 67.639 0.053 0.166
Max 50.384 50.365 108.224 108.126 0.115 0.380
The results in Table 7 and Table 8 show that even in a more complex multi-image target extraction the RSM
performance is a very good approximation to that of the original sensor model. The error estimates (absolute and
relative CE and LE) are virtually indistinguishable, with differences between the two less than 0.1 percent. In terms
of the computed absolute point positions, the largest difference was 0.065 m in horizontal position for one of the
points, which was much less than one percent of CE. Similarly, the largest difference in relative positions was 0.38
m which was much less than one percent of the relative LE.
The excellent agreement in QuickBird target extraction results for RSM as compared with the original rigorous
sensor model are typical of what has been seen for other sensors in other studies. We next consider the WorldView
sensor, and additional scenarios that showcase additional capabilities of RSM.
GEOPOSITIONING PERFORMANCE STUDIES WITH WORLDVIEW
The test procedure of Figure 2 is just the first of four tests of increasing complexity that were performed with
two overlapping WorldView images. The second of these, termed the "triangulate/replace/extract" test is shown in
Figure 3. The procedure is for the sensor models to be triangulated with ground control and tie points before being
used for extraction and RSM generation. The adjusted sensor models and the full a posteriori joint error covariance
(a 12x12 matrix) of the adjustable parameters for the two images are provided to both the MIG tool for the rigorous
sensor model target extraction and the RSM Generator. The RSM support data contain the full joint error
covariance of the RSM adjustable parameters, and this is used in the MIG for the RSM sensor model target
extraction.
Original
support
data
Triangulate
Extract
Generate RSM
Extract
ASPRS 2008 Annual Conference
Portland, Oregon ♦ April 28 - May 2, 2008
Compare:
absolute and
relative point
positions,
absolute and
relative error
estimates
Figure 3. "Triangulate/Replace/Extract" RSM geopositioning performance test procedure.

In the two test procedures already described, the RSM adjustable parameters are not actually adjusted, they are
just a vehicle for the error propagation. In the third and fourth scenarios they are adjusted. The "triangulate/replace"
scenario is shown in Figure 4. The performance is measured for the tie points that participate in the triangulation:
their geolocations and error estimates are expected to be nearly the same after triangulation if RSM is successful.
Original
support
data
Triangulate
Generate RSM
Triangulate
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Portland, Oregon ♦ April 28 - May 2, 2008
Compare:
absolute and
relative tie
point
positions,
absolute and
relative error
estimates
Figure 4. "Replace/Triangulate" RSM geopositioning performance test procedure.
The "replace/triangulate/extract" scenario of Figure 5 is the most challenging end-to-end RSM performance test.
Not only must the RSM triangulation and subsequent extraction give results close to those of the original sensor
model triangulation and subsequent extraction, but the RSMSD must be generated once prior to the triangulation and
then updated prior to the extraction. Note that in the second call to the RSM Generator, it is the RSM sensor model
that is input and not the original sensor model. The projective model fit and the adjustable parameter selection/error
covariance mapping are not repeated, but rather the parameter adjustments and a posteriori error covariance are
placed in the appropriate support data extensions and these are used to supplement the RSMSD already present.
Original
support
data
Triangulate
Generate RSM
Triangulate
Extract
Generate
adjusted
RSM Extract
Compare:
absolute and
relative point
positions,
absolute and
relative error
estimates
Figure 5. "Replace/Triangulate/Extract" RSM geopositioning performance test procedure.
The replace/triangulate/extract tests showcase an RSM capability that is not present with many original sensor
models in use: a support data format that is able to capture parameter adjustments and the associated full error
covariance. The ability to do this, for any sensor, should serve as motivation to integrate RSM into exploitation
systems.
The WorldView performance test results for absolute geopositioning are shown in Table 9 for all four scenarios.
The relative geopositioning results are shown in Table 10. The first two columns of each table identify the scenario
and the statistic under consideration. The third and fourth columns give the CE (or CErel) for the original sensor
model and RSM test, respectively. The fifth and sixth columns give the LE (or LErel) for the original sensor model
and RSM. The last two columns give the absolute (or relative) horizontal and vertical position differences.
For all except the replace/triangulate scenario, the statistics are over the four points used for target extraction.
For the replace/triangulate scenario, the statistics are over the nine tie points used in the triangulation. The image
measurement errors are estimated at one pixel (one-sigma) for all of the points.

The same four ground control and nine tie points are used in the triangulation in the three scenarios that include
triangulation.
The off-nadir look angles for the images are about 37 degrees and 25 degrees. The stereo convergence angle for
the two images is about 31 degrees. The GSDs are 0.55m to 0.62 m (measured normal to the line of sight). The
replace/extract absolute CE statistics are around 5.1 m, within the specification of 6.5 m and the range of 4.0-5.5 m
stated as a typical horizontal accuracy for WorldView images (at nadir, apart from terrain effects). The other
scenarios, which include triangulation with control, have CE within the 2 m stated for WorldView images with
control. Note that the ground control point accuracy has been estimated at one-meter (one-standard-deviation along
all three axes), which is easily obtainable with GPS surveying. Prior to triangulation the errors between the ground
control points are assumed to be uncorrelated.
For all of the scenarios, the RSM performance is excellent in all respects, for both absolute and relative
geopositioning. For absolute geopositioning, the statistics are over the four extracted points (9 tie points for the
replace/triangulate scenario). For relative geopositioning, the statistics are over the six possible pairs of extracted
points (36 tie point pairs for the replace/triangulate scenario). The largest differences in error estimates (absolute or
relative CE or LE) for any of the tests is under 0.01 m. The largest solution differences (absolute or relative
horizontal or vertical position) are about 0.04 m for the replace/triangulate scenario, where these differences are an
insignificant 2 % or less of the corresponding error estimate.
Table 9. Absolute geopositioning results for 2 WorldView images
Scenario Statistic Original RSM Original RSM Horiz. Pos. Vert. Pos.
CE (m) CE (m) LE (m) LE (m) diff. (m) diff. (m)
Replace/Extract RMS 5.076 5.077 8.287 8.287 0.014 0.030
Max 5.136 5.136 8.307 8.313 0.014 0.030
Triangulate/ RMS 1.845 1.845 2.668 2.668 0.002 0.001
Replace/Extract Max 1.860 1.860 2.677 2.678 0.002 0.002
Replace/
RMS 1.846 1.846 2.687 2.686 0.011 0.016
Triangulate Max 1.889 1.888 2.733 2.731 0.024 0.038
Replace/
RMS 1.845 1.845 2.668 2.668 0.004 0.005
Triangulate/Extract Max 1.860 1.860 2.677 2.677 0.005 0.007
Table 10. Relative geopositioning results for 2 WorldView images
Scenario Statistic Original
CErel (m)
RSM
CErel (m)
Original
LErel (m)
RSM
LErel (m)
ASPRS 2008 Annual Conference
Portland, Oregon ♦ April 28 - May 2, 2008
Horiz. Rel.
Pos. diff. (m)
Vert. Rel.
Pos. diff.
(m)
Replace/Extract RMS 1.981 1.981 3.227 3.227 0.001 0.000
Max 1.991 1.991 3.240 3.240 0.001 0.001
Triangulate/ RMS 1.979 1.979 3.227 3.227 0.001 0.000
Replace/Extract Max 1.991 1.991 3.240 3.239 0.001 0.001
Replace/
RMS 1.982 1.982 3.252 3.252 0.013 0.019
Triangulate Max 2.025 2.025 3.299 3.299 0.027 0.043
Replace/
RMS 1.979 1.979 3.227 3.227 0.003 0.004
Triangulate/Extract Max 1.991 1.991 3.240 3.239 0.004 0.005
Excellent RSM performance for triangulation and geopositioning has been seen in all of the WorldView
scenarios in this section. These studies have been done with one stereo pair. Photogrammetric triangulations often
involve many images, but all of the complexity of the problem is already present with two images, multiple tie
points, and multiple ground control points, and these are very large images.
CONCLUSION
The tests conducted for this study show excellent agreement in triangulation and geopositioning between RSM
and the rigorous commercial satellite sensor models they replace. Not only is the RSM projective model a very

good fit to the original, but the error estimates are very close, and the models perform virtually the same with
triangulation adjustments.
These results supplement earlier studies that demonstrated equally good performance for other types of
imagery. In all of these studies, both the original and the RSM sensor models were used in the testbed to show the
performance match. With each successful study, there is added confidence that a lean exploitation system with a
single sensor model, RSM alone, is viable.
The viability of the RSMSD format has received additional confirmation, since the testbed used it in every test
to transmit the support data from the RSM Generator to the RSM Exploiter. The maturity of the RSM software
development kits (Generator and Exploiter) has also received confirmation, since no modifications were made in the
course of the study.
The way forward for RSM is clear: RSMSD should now be generated and included in image products along
with rigorous sensor model support data, to enable performance testing by the wider community, and the
development of leaner, more robust and less expensive RSM-only exploitation systems.
ACKNOWLEDGEMENTS
We would like to thank Walter Scott and Milan Karspak of Digital Globe, Ed Mikhail of Purdue University, and
Fidel Paderes, Reuben Settergren, Kevin Allen, Karen Diener, Randy Burt, Brian Highland, and Shannon McDonald
of BAE Systems for their contributions to the RSM performance studies.
REFERENCES
Dolloff, J.T., 2004. Replacement Sensor Models, Chapter 11.3, Manual of Photogrammetry, 5th Edition,
J. C. McGlone, Editor, ASPRS, pp. 887-943.
Dolloff, J.T. and C.R. Taylor, 2004. Replacement Sensor Model Tagged Record Extensions Specification for NITF
2.1,
http://www.gwg.nga.mil/ntb/coordinationitems/RSM%20TRE%20Appendix%20A_July_23_04.pdf.
Dolloff, J.T. and C.R. Taylor, 2006. Proposed Updates to RSM TREs (Updates to the Replacement Sensor Model
Tagged Record Extensions Specification for NITF 2.1,
http://www.socetgxp.com/docs/products/special/pp_rsm_treupdates.pdf
Dolloff, J.T., M.M. Iiyama, and C.R. Taylor, 2008. The Replacement Sensor Model (RSM): Overview, Status, and
Performance Summary, ASPRS 2008 Annual Conference, April 28 - May 2, 2008 (forthcoming).
Taylor, C.R., J.T. Dolloff, M.M. Iiyama, and E.M. Mikhail, 2006. RSM Extraction and Adjustment of Large Field
of View Frame Imagery, http://www.socetgxp.com/docs/products/special/pp_rsm_largeformatframe.pdf.
ASPRS 2008 Annual Conference
Portland, Oregon ♦ April 28 - May 2, 2008