ELSEVIER

Wide-Area Terrain Surveying with Interferometric SAR

Lawrence P. Orwig, * Alan D. Aronoff,” Paul M. Ibsen,* Harold D. Maney, * James D. O’Brien, * and Hugh D. Halt, Jr. *

F or many applications, extraction of useful data from synthetic aperture radar (SAR) or other sensor imagery of the Earth’s surface can be expedited by encoding terrain relief cues within the image. Shadowing may provide quuli- tat& cues, but the most accurate relief inf&nution rezults

from direct measurement of terrain ekvation on a pixel-by- pixel basis. Airborne inte&rometric SAR (IFSAR) o#ers a method fat- the generation of digital elevation maps (DEMs) which has recently come of age technologicaUy. B&re semiuutomuted 1FSARE (IFSAR elevation) mapping becomes comwcially prackal, cmerns in the areas of accuracy, reproducibility, throughput, and cost must be addressed. This article consia!ers these issues in the context of a study which was conducted with a production military SAR sys- tem flowlz in an experimental 1FSARE mode. Example IFS- ARE imagery from an associated Army/ARPA mapping program is presented and analyzed for detail. Geoposition- ing accuracy and reproducibility are discussed; one stan- dard was a set of high accuracy, high resolution DEMs which were produced from optical photo stereo pairs and controlled by a GPS-based ground survey. Computer throughput requirements are assessed from the standpoint of near real-time processing and low cost.

INTRODUCTION

Where mapping and identification of wide-area surface features is a goal, synthetic aperture radar (SAR) imagery has been an informative technique for a number of years, with application throughout the geological and environmental sciences. Digital interferometric SAR el- evation processing (Zebker and Goldstein, 1986) or

*Westinghouse Norden Systems, Norwalk, Connecticut

Address correspondence to Lawrence P. Orwig, Westinghouse Norden Systems, 10 Norden Place, P.O. Box 5300, MS. E012, Nor- walk, CT 06856-5300.

Received 6 April 1994; revised 7 January 1995.

REMOTE SENS. ENVIRON. 53:97-108 (1995) OElsevier Science Inc., 1995 655 Avenue of the Americas, New York, NY 10010

IFSARE, has origins in optical processing (Graham, 1974) and lunar radar astronomy (Zisk, 1972). It extracts geopositioning information in three dimensions for ev- ery pixel in the raw SAR image. This information can be used both to remove image distortions due to terrain elevation, and to encode the elevation directly in the SAR image in various ways ranging from false color to stereo pair imagery. Properly presented, such elevation cues augment the reflectance and texture cues that are naturally present in the SAR image; this expedites the identification of landforms, natural features, and cultural artifacts ranging from orchards and fields to buildings and utility rights-of-way.

One may also derive slope information from IFS- ARE data. Such information might be used to compen- sate for the effect of incidence angle on terrain reflectiv- ity in open areas, to improve assessment of soil moisture content and organic layer thickness (Fatland and Free- man, 1992); in forested terrain, it may become a key input in scattering models which rely on the trunk- ground interaction to estimate woody biomass and the moisture content of the soil and vegetation (van Zyl, 1993).

This article discusses the use of a production mili- tary SAR system in an experimental IFSARE mode to generate height-encoded SAR imagery in stripmap form. The second and third sections briefly review the mathe- matical basis of IFSARE processing and describe the SAR system which was employed in the study. A sum- mary of the test sites and the ground control survey and reference DEMs appears in the fourth section. The fifth section presents several processing examples from the standpoints of 1) identification of terrain and cultural features and 2) elevation and XY-placement reproduc- ibility across multiple passes by the same area. The sixth

0034-4257 t 95 !$9.50 SSDI 0034-4257(95)00045-3

98 Orwig et al.

section considers computer processing requirements and evaluates tlie future prospects for near real-time IFSARE processing of this nature, at an accessible cost.

cir = boresight LOS,

ij h3 = baseline = H (4)

BACKGROUND

IFSARE processing computes the interferogram of two complex SAR images which are formed at apertures separated by a suitable vertical baseline. Terrain ground range, azimuth, and elevation may then be extracted from the slant range, doppler, and interferometric phase differences v, at each pixel (Zebker and Goldstein, 1986; Madsen et al., 1993).

The degree to which the azimuth of a given range- doppler cell is coupled to elevation depends on the squint angle v/s. Purely broadside to the velocity vector (v, = 90”) the coupling vanishes, and it is linear in small doppler displacements away from broadside. This is the usual imaging geometry. However, our radar is nose- mounted and, although fully gimbaled, cannot be turned broadside. It is typically operated at 30” < v/s < 60”. At such squints the coupling is strong and distortions in the raw ground map are severe when there is terrain relief. For this reason, careful motion compensation of antenna attitude as well as platform translation is re- quired simply to achieve fidelity in the usual two dimen- sions, not just to compute good elevations.

The extraction process allows various approxima- tions, but in all cases the underlying relation is between (p and the round trip optical path length difference At that caused it:

ciz = 63 x cil.

We take B from the upper aperture to the lower, so that (& points to the left when viewed from in front of the faceplate. Now consider a point P at slant range R,, which is found from boresight by small sequential rotations 6 (about the as-axis) and E (about the resulting az-axis). In a broadside system, &and E are relative angles in doppler and elevation. We find

? = (cos & cos 6, cos & sin S, sin E), (5)

bp = g* B sin E, C

(6)

AH = ? . & = R, (sin & sins + cos & cos E cos 6), (7)

where AH is the height difference between the radar and the ground point, t& a downward pointing unit vector, and 0, the boresight look angle. [Equation (7) assumes a flat earth and no refraction.] If the velocity vector 3 is horizontal, then for right-side imaging

2 = v (~0s v/s sin eB, - sin v/s, - cos y/s cos 0~). (8)

In the broadside case (8) becomes 3 = ~(0, - 1, 0), caus- ing the doppler equation to take a simple form:

fD = $. p

,@ c0s.s sin6 C

(broadside).

For general v8, G retains all three components so that (l) (9) b ecomes a quadratic expression for cos 6, which also

depends on 8,. Nonetheless, Eqs. (6), (7), and (9) to-

(2) gether solve the three-dimensional geopositioning prob- lem for horizontal G. Accuracy is limited by errors in bp due to factors such as noise, volumetric scattering in

(3) forested areas, and multipath due to the presence of

where f is the radar frequency, co the speed of light in vacua, Ar, the slant razge difference, c the local speed of light at the radar, B the baseline vector, and P the unit line of sight vector. In applying (l), it is normally correct to ignore the slight bending and divergence of the two paths. A form such as (2) then holds; here it is written for the case where transmission is from one aperture with concurrent reception on two. However, with our imaging geometry it is common for refractive bending to amount to 1 mrad or more, making ground points appear higher than they are; this effect should be considered when applying Eq. (3).

Below, we work in antenna faceplate coordinates where the unit vectors are in the directions:

artificial structures or terrain slope changes. In practice, the formulation must also address time-varying velocity that is not horizontal, earth curvature, refraction, and (when not broadside), a range-bin-dependent horizontal range slip rate.

The interferometric phase (p is found only within a multiple of 2a; this ambiguity changes quite rapidly with range even for level ground because the SAR (imaging) plane is depressed. A general mechanism for phase unwrapping which has met with some success is described by Madsen et al. (1993) and Madsen and Zebker (1992). A simpler approach which was adequate for the terrain we imaged is discussed in Orwig et al. (1994) 1 g a on with further considerations about the motion compensation and geocoding.

Terrain Surveying with lnterjimm&ic SAR 99

THE EXPERIMENTAL SYSTEM

The Radar

We collected data using an experimental modification of the Norden Systems APG76 multimode radar, mounted in the modified nose of a Gulfstream II aircraft. The APG-76 is a Ku-band, flat plate, multiaperture array antenna. In its normal configuration, its single large “sum channel” port is centered above a horizontal row of three smaller interferometer ports. Transmission is through the sum channel, which can receive as a unit or as an elevation monopulse interferometer. It is the primary aperture used for SAR image formation. The three lower ports are receive only; they are normally used for motion detection and measurement. The pro- duction hardware supports range resolutions of 3 m, 9 m, and 18 m in the sum channel but only 9 m and 18 m in the interferometer. Polarization is W. In normal operation, the system generates single-look SAR imagery in real time at the operator’s console on a 512 x 512 pixel display; this imagery is saved in VHS format. For most experiments, range compressed complex I I Q data are collected from a small set of range gates from all four channels on an Ampex DCRSi recorder, along with navigational and various test data, for later ground processing. Nonproduction, uncompressed modes also exist.

Although the antenna was designed for a tactical mili- tary mission, not for IFSARE, the production APG-76 is fully gimbaled and so can function as an IFSARE device in either of two ways:

?? by interfering the sum channel image with the center interferometer channel image, after gain normaliza- tion;

?? by rolling the antenna 90” about its boresight axis to align the interferometer ports vertically (making the polarization HH).

Both methods were applied early in the present study to establish the baseline IFSARE capabilities of the radar. However, hardware and software changes were then installed to obtain better resolution and wider ground coverage. These changes increased the number of re- corded range gates to more than 1700 on two channels, and switched the incoming signal in the center interfer- ometer port through the sum channel hardware. In this “Ping Pang” mode the antenna received alternately on the sum and center ports with a 50 MHz bandwidth, sidestepping the 16.7 MHz IF bandwidth of the interfer- ometer channels. With a transmit PRF of about 2 kHz through the sum channel, the effective receive PRF was 1 kHz at each port. This mode supported 3 m x 3 m IFSARE processing with an area coverage rate near 50 km2 I min, and was used for most of the data collection during the study.

Physical characteristics of the radar, when operated for IFSARE as described above, are summarized in

TabZe 1. Norden IFSARE Radar Parameters

IFSARE Mode Rolled 90” Ping Pong

Frequency Effective average power Channels Effective PRF Limiting bandwidth Elevation beamwidth Azimuth beamwidth Polarization Scale factor

K. band 500 w Up, down 1.6-1.8 kHz 16.7 MHz 2.2” 3.8” HH 148

K. band 300 w Sum, center 1.04 kHz 50 MHz 7.5” 2.2” vv 113

Table 1. Typical imaging geometries fall in the range listed in Table 2.

Navigation System

The APG-76 radar data processor normally maintains knowledge of the radar state by applying a complex blending algorithm to navigation data coming from three sources with different response characteristics: A Litton LN39 inertial navigation unit (INU), a Litton LR86 inertial measuring unit (IMU) with a nominal attitude accuracy of 1.7 mrad RMS in each axis, and a precision velocity update (PVU) estimated by tracking the doppler centroid through the horizontal interferometer chan- nels. This system fulfills its design function, which is to maintain focus in the real-time SAR imagery during moderate aircraft maneuvers. However, it relies heavily on the PVU input, which is not operable during IFSARE data collection either because the antenna is rolled, or because (in Ping Pong mode) the relevant data channels cannot be collected. The remaining INU + IMU combi- nation suffices for single-look focussing if the platform motion is benign (as in the present study), but suffers from enough drift to impair multiple-look image ortho- rectification and the absolute positioning of the map itself,

For the data runs reported here, the blended INU + IMU data were augmented by differential Global Positioning System (DGPS) technology. Two Trimble Pathfinder DGPS receivers were employed, one on the aircraft and the other at a surveyed base station. Filtered DGPS data were used on the ground to adjust the INU position data and to estimate a mean velocity correction. Late in this study, the INU was replaced by a Honeywell H764G INS I GPS, which blends inertial data with global positioning system (GPS) data. Baseline comparison stud- ies were conducted with it at that time; however, the

Table 2. Typical Imaging Geometries (Ping Pong Mode)

Squint angle Altitude Center range Illuminated swath width Look angle at center range

45” 6-8 km 17-24 km 5-7 km 65-75”

100 orfdgetal.

images shown in this article were created with the LN39.

EXPERIMENTAL TEST SITES AND GROUND CONTROL

Most of the study was conducted at one of two sites:

?? Kongscut Mountain area, near Glastonbury, Connect- icut,

?? Aberdeen, Maryland area, including portions of Aber- deen Proving Grounds.

The Kongscut site was selected for its varied topography, for its proximity to our normal flight operations, and for the fact that large portions of it were readily accessible to a survey team. The Aberdeen site was selected for its flatness and for its status as a standard under the control of the sponsor. Both sites were nonideal from the standpoint of baseline testing an IFSARE system, because of their high proportion of tree-covered terrain. The tree heights are not included in the reference DEMS, and volumetric scattering in the trees can be expected to add to the measured height standard devia- tion.

General Description of Sites The Kongscut site is a 30 km2 area with about 210 m of topographic relief. It is littered with hills, having slopes of up to 40% (22”) and of varying orientations. The site is dominated by these hills which are covered with mostly deciduous trees with heights of lo-20 m. The only truly flat areas are the nonreflective surfaces of a small reservoir, lakes, and ponds. However, several gently sloping areas have been partially cleared for farming, orchards, a golf course, single-family dwellings, and a quarrying operation (gravel pits). Other cultural features include several minor roadways and streets, two 12-15 m wide clearcut swaths for (buried) natural gas pipeline rights-of-way, and two 55-60 m wide clear- cuts for electric power transmission lines. There is also a dense 300 m x 120 m stand of conifers of fairly uniform height (- 13 m) on nearly level ground, commercially planted and later abandoned. We imaged the Kongscut site both in winter conditions (leaf off) and in midspring (leaf on).

The Aberdeen site is a 60 km2 area adjoining Chesa- peake Bay. Most of this area is nearly flat and within 5-20 m of sea level. With the exception of one comer of the site, “topographic relief” is provided more by trees and buildings than by the terrain. The area is perhaps 40% open farmland, grass, or marshland. Cul- tural features include an airfield, several large-footprint commercial buildings, a major railroad and a business route highway as well as pockets of small commercial and residential structures. We imaged. the Aberdeen site in mid-spring (leaf on).

Ground Control Points and Reference DEMs For the Kongscut site, a network of 22 surveyed control points was established by Measurement Science, Inc. (MSI, Englewood, Colorado) satisfying first-order stan- dards in all station pairings. The network included 18 new points surveyed by MS1 using GPS techniques, three National Geodetic Reference System (NGRS) con- trol points, and one Connecticut Department of Trans- portation control point. Vexcel Corporation (Boulder, Colorado) used this network in conjunction with stan- dard stereophotogrammetric techniques to create high accuracy orthorectified DEMs of six 1 km2 ground patches within the surveyed region. The required aerial photography was performed in leaf-off conditions so that ground level elevations could be determined. The resulting DEMs were on a 2 m grid and had an estimated RMS height error of less than 0.3 m. Additional details on the construction of these DEMs are given in O’Brien et al. (1994).

For Aberdeen, the U.S. Army/Topographic Engi- neering Center (TEC) provided precision DEMs of sev- eral small patches within the imaged area. These DEMs were presented on 4 m or 10 m postings. Also, TEC provided the surveyed locations of 15 ground control points used in the development of the Aberdeen DEMs.

In addition to the high accuracy reference DEMs, we also used lower resolution DEMs which covered the 7.5-min United States Geological Survey (USGS) quadrangle maps of the test sites. These USGS DEMs were on a 30 m grid with maximum RMS height error of 15 m. Due to their limited accuracy and map scale, the USGS DEMs were employed mainly to check for wide area map tilts and vertical scale errors.

EXAMPLE PROCESSING RESULTS

In the false color imagery, eight colors were selected to give good visual color separation. In addition, color saturation was modulated (eight grey levels) by the radar backscatter coefficient. Color spacing is 25 ft (7.6 m) on the Aberdeen image (Fig. 1) and 50 ft (15.2 m) on the Kongscut image (Fig. 2).

The test sites were imaged from a stabilized squint angle near 45’. Look angles at center swath of 75’ and 64’ were used, creating range swath widths of 5-7 km with a center range of 17-24 km. Images are presented with the radar illumination from the left except as noted below. Typically there are 12 overlaid looks at each pixel.

Identification of Terrain and Cultural Features

Aberdeen, Marybd Figure 1 is an approximately 5.3 x 3.6 km section of a composite of three larger overlapping stripmaps, the full image being too large to show on a single page with

Terrain Sumeying with lntetjkrometric SAR 101

Figure 1. Section of IFSARE DEM of Aberdeen, MD.

Figure 2. Section of IFSARE DEM of Kongscut Mountain, CT.

102 Orwig et al.

a reasonable scale. The elevation color coding helps the eye rapidly sort the image features by height, aug- menting grey level texture cues to help form a compre- hensive interpretation of the scene. Thus, the smooth- textured areas in blue, green, and gray are grass, marsh, and agricultural fields. The darkest smooth areas are standing water (as at E), asphalt pavement (as at G), or radar shadow. Among the rough-textured areas, the scrub and smaller trees range through grey and yellow while the taller trees stand out in orange tones; this interpretation can be verified by checking the shadow lengths of isolated trees or at tree lines.

Some of the larger cultural features include: A) a business route highway, U.S. 40; B) an Amtrak railroad line with five tracks; C) a signal track spur line; D) single family residences; E) a golf course with the fair- ways (often lined with small trees) less reflective than the surrounding rough; F) a control building and airport pavement structures at Phillips Field; G) a 10-12-m- high Pier 1 Imports warehouse; H) a cold storage ware- house of similar height; and I) a 70 m high water tower (white dot directly beneath the label). Substructure within the two warehouse images is also of note. Both show a rooftop matrix of skylights (the radar imaging the metal frames of the skylights) on a relatively nonre- flective background, and a row of air conditioning units parallel to the long axis of each roof. One end of the cold storage warehouse appears as a highly reflective square. This end was the same height as the rest of the building; the radar saw differences in construction materials due perhaps to the refrigeration requirements of this warehouse. The Pier 1 warehouse is bordered on its two long sides by dark (recently paved) asphalt parking strips. The outer edge of the lower strip is lined with trucks. The upper strip shows a number of large railway shipping containers adjacent to the Amtrak line and near the loading docks.

Kongscut Mountain, Connecticut Figure 2 is taken from a single IFSARE stripmap of the central part of the Kongscut site. The upper diagonal swath edge parallels the along-track direction (left-to- right), revealing the 45” squint. The image has dimen- sions 7.4 x 5.3 km. The elevation contours were taken at 50 ft intervals to prevent wraparound and to minimize ambiguity for this presentation, albeit with some loss of height detail. The data were collected under winter conditions, so that all open areas were frozen and snow- covered. This condition includes the various bodies of “water,” which thus were as reflective as the agricultural fields.

Natural features of the topography (with elevations) include: A) the two peaks of Kongscut Mountain (210- 240 m); B) the double peak of Minnechaug Mountain (240-250 m); C) John Tom Hill (270 m); and D) Dia- mond Lake (210 m). These areas are all heavily treed,

Figure 3. Kongscut Mountain site detail: Diamond Lake (upper) and Eastbury area (lower).

although at the scale of this map most of the texture is suppressed.

This area has not seen much commercial develop- ment, so its cultural features are of a different sort from those near Aberdeen: E) Buckingham Reservoir (135 m); F) a power transmission line clear-cut swath (55- 110 m); G) a gas pipeline right of way; and H) open pits at a quarry (155-165 m). Some residential develop- ment is apparent. Smooth-textured, open areas not cov- ered by the foregoing are mostly agricultural fields with rolling or sloping contours.

The high areas on Kongscut and Minnechaug are both in the range of 210-250 m elevation as compared to adjoining low regions of 100-120 m. The highest terrain elevation on the map is 270 m near John Tom Hill. The presence of - 15 m trees in all these high areas make the IFSARE elevations somewhat higher than would otherwise be found.

Figure 3 shows two enlarged 2.2 x 1.5 km sections of the Kongscut site. Features of the upper image, from the Diamond Lake area, include: an orchard at the left end of the lake, bisected by a service road and flanked

Terrain Surveying with lnterfermetric SAR 103

Table 3. Example Map Scale Accuracy: Nine Parameter Model and Scatter Plot Regression Slope, 85 Tie Points

Mean (A) Std Dev (A) Mean (B) Std Dev (B) Units

YZ tilt angle u + 9.8 1.5 +6.5 1.3 mrads (XZ)l tilt angle 9 -1.6 1.1 -2.4 0.9 mrads (XY)” rotation K - 45.76 0.12 - 45.76 0.10 degrees X scale 0.9981 0.0029 0.9980 0.0023 m/m Y scale 0.9995 0.0024 0.9994 0.0019 m/m Z scale 0.7866 0.0038 0.8985 0.0033 m/m Z regression 0.9701 n/a 1.0124 n/a m/m

on the left by a gas pipeline right-of-way; a row of greenhouses at lower center; cleared areas at the right are open fields (lower) and a quarry (above). The lower image of Eastbury shows residential areas, a pipeline right-of-way entering at the left upper edge and cutting across to the right, and numerous roads. All forested terrain in these pictures is steeply rolling hillside.

Geolocation and Elevation Scale Accuracy

The most detailed accuracy analysis was performed on the Kongscut site because its greater topographic relief provided a more stressful test of the algorithms than did the Aberdeen site.

To estimate scale and tilt errors in the IFSARE maps of the Kongscut site while registering them to the reference DEMs in orientation and position, Vexcel computed nine-parameter least-square fits (translation, rotation, and scale) between IFSARE imagery and the references. As many as 97 tie points were used. Vexcel also made scatter plots of IFSARE elevation versus reference elevation and fit a regression line to these data. The slope of the regression line was a separate measure of vertical scale accuracy.

The references for this exercise were the high reso- lution stereooptical maps and associated orthorectified DEMs constructed by Vexcel. Features selected as tie points had to be identifiable on both the reference and the IFSARE maps. We placed corner reflectors at a number of surveyed locations. Four to eight reflectors were visible in any given strip map; these were locahz- able on both maps to within f 1 pixel. It was not possible to make an exact point-to-point correspondence of other features on the optical and SAR images. Vexcel estimated a 5-10 m (2-3 pixel) RMS uncertainty in matching tie points on the two maps.

Table 3 illustrates the general finding that the mean X and Y scale errors are similar to or smaller than the error standard deviation, reflecting the uncertainty in point matching+ The table presents data for two cases: A) heights smoothed in a 5 x 5 pixel neighborhood (15 x 15 m) and B) heights smoothed in a 21 x 21 pixel neighborhood (63 m x 63 m). The X and Y scales are not sensitive to the smoothing. In this table, “perfect” results for the three scale factors would be 1.0. The

scale errors for case B) of 0.002 and 0.0006 in X and Y amount to relative position errors of 3.3 pixels and 1.8 pixels between opposite edges of the map. The la uncertainties in these errors are 3.8 pixels and 5.7 pixels, respectively.

The Euler rotation angles o and V, correspond to tilts in range and cross range, while K approximates the radar bearing when the tilts are small. These tilts do not represent map tilt errors directly, because the locally tangential coordinate frame of the Vexcel reference DEMs differed slightly from the WGS-84 system used to compute IFSARE map heights. However, statistical errors in the tilts obtained by the nine-parameter fit influence the reported Z scale.

The tilts are very sensitive to the height smoothing, as seen in the table, and to the choice of tie points as well. This sensitivity is reflected in the reported Z scale, which is also highly variable. The errors in these values are excessive. They imply systematic relative height errors of 25-50 m at the extremes of the 230 m vertical excursion of the map. However, such errors are inconsis- tent with the scatter plot regression analysis, and were not found when map tilts were removed by hand during the reproducibility tests (cf. subsection after next). The large variation in the tilts reported by the nine-parameter fit suggest that the problem may lie with the noise in the IFSARE height data (which is about 8% RMS of the total spread in heights of the tie points) and the lack of a sensor error model in the fitting mechanism.

The scatter plot regression line slope gives more encouraging estimates of the map Z scale. They amount to relative height errors of - 7 m and + 3 m between the low and high points of the map, for cases A) and B). These values are below the unsmoothed system height accuracy expected for ground clutter [ll-I2 m (O’Brien et al, 1994)]. Because they bracket the zero- error case, they suggest that the Z-scale error is hidden in the height measurement noise. One requires terrain relief greater than the 230 m found at Kongscut, to isolate the scale error.

Vexcel interpreted the disagreement between the regression and the nine-parameter fit to imply that the IFSARE height error had a dependence on platform position, either along or across track. The fit would be

104 orwigf3td.

sensitive to such a dependence while the scatter plot regression would not (Karspeck and Stotz, 1993). This interpretation may have been correct, as IFSARE DEMs at Aberdeen and reproducibility studies at Kongscut later uncovered a 0.5 mrad RMS attitude instability in the radar. It manifested as discontinuities of the order of 5-10 m in the mean elevation difference between overlapping looks, as a function of along track position and at time intervals consistent with the system’s atti- tude calibration cycle.

Geolocation Reproducibility We augmented the results of the nine-parameter fit by performing a reproducibility test, That is, we overlaid strip maps made of the same area but from different radar bearings. To reduce hard disk storage require- ments for the many map arrays that were involved in the alignment, overlay, analysis, and display processes, array sizes were reduced by resealing the map pixels from 3 m x 3 m to 5 m x 5 m using local intensity and height averaging.

The overlay should emphasize geopositioning er- rors. For example, for right-side imaging at a squint angle of 45”, a positive height error leads to positive ground range and cross range positioning errors in the geocoding algorithm. If a given area is imaged twice from opposite bearings and the height errors are similar each time (as would be the case for a systematic vertical scale factor error) then these positioning errors will be in opposite directions in the two images, causing an elevation-dependent image doubling. For our imaging geometry, the expected doubling would be about 2 pixels each in ground range and cross range per 10 m of elevation error. Figure 4 illustrates the correct shift, showing the same hillside west of Buckingham reservoir before (upper) and aft er (1 ower) the geopositioning algo- rithm. The difference in the angle made by the power line clear cut as it comes down the hill shows the elevation dependence of the repositioning. Also note that the tall power line support structures in the left part of the swath have shifted relative to the lower trees marking the swath edges. This map section has a vertical relief of about 100 m.

The overlay was done without applying the results of the nine parameter fit. Instead, we used a semiblind overlay process which relied on a single tie point from each map. This tie point was a surveyed comer reflector, which could dilfer from map to map, and which provided a position reference for the map in WGS-84 coordinates. A second reflector was used, in conjunction with the tie point, to define the map orientation empirically; however, this reflector was not used as a positional tie point between the two maps or to adjust the map scale. We rotated one map according to the relative orientation of the two maps, and then overlaid the maps based on the relative tie point coordinates.

Figure 4. Hillside: raw IFSAR image (upper) and after geopositioning (lower).

In fact, we overlaid three stripmaps of the Kongscut area taken at radar bearings of 135”, 315”, and 45”. The first two strips, made on eastbound and westbound data legs, tested the image doubling as described above. The eastbound strip was imaged from almost twice the depression angle of the other two strips (25.3” versus 14.5” and 13.9”, at center range), greatly strengthening the elevation dependence of the ground range of a given slant range cell. The third strip, made on a northbound data leg, was included to help validate proper control of the map scale in X (cross-line-of-sight) and Y (ground range). The east and westbound strips were overlaid at their nominal map scale, without adjustment. The northbound Y scale agreed with the east- and westbound X scale, but the northbound X scale required an 0.4% adjustment to overlay the east- and westbound Y cor- rectly. This anomalously large error is the same order of size as the INU velocity accuracy, and may indicate that a poor value was used for the DGPS-based adjust- ment (cf. the earlier subsection, Navigation System).

A 2.3 km x 3.3 km portion of the overlay is shown in Figure 5, demonstrating the accuracy of the geoposi- tioning. All but the upper right corner of this composite

Terrain Surveying with lnterferometrk SAR 105

Figure 5. Section of IFSARE 3-way overlay of Kongscut Mountain. CT.

is in at least two strips; about 65% is in all three. Visual inspection of the overlay on a workstation reveals no cases of pixel doubling when areas containing comer reflectors and subpixel natural features are expanded so that individual pixels can be identified. Plots of intensity versus X or Y, taken on cuts through comer reflectors and small bright objects, show some peaks broadened relative to single look imagery, but never split in X or Y. Most of that broadening is present already in the individual 3-m strips (i.e., prior to resealing and overlay). The broadening is in doppler only and may be due to squint-related, e-dependent p&metric distortions in the single-look data. These errors show up when over- lapping looks are added to form a stripmap prior to geopositioning. We infer that end-to-end relative map distortions are no more than one 5-m pixel in either dimension. Finer resolution is required to determine the map errors more precisely.

or of another IFSARE DEM, provide accuracy and reproducibility checks on the IFSARE maps. Since the IFSARE DEMs include the effects of vegetative and artificial ground cover while the reference DEMs do not, these difference DEMs can provide revealing infor- mation about the reliability of the radar results. Vexcel performed the former test, using as reference the high accuracy DEMs which they constructed for a number of 1 km2 patches in the Kongscut area. We performed the latter test, differencing eastbound and westbound strips of that area; these strips were imaged on different flights and from different look angles.

Vexcel first adjusted the IFSARE DEM according to their nine-parameter fit, then took the pixel-by-pixel difference of this result with their high accuracy patches. These patches contained a total of 587,196 3 m x 3 m pixels. A histogram workup was then performed on each difference patch, excluding pixels that were nonreflec- tive or in radar shadow. Vexcel also sorted statistics by terrain type, classified as open, deciduous, coniferous, or other. The open areas consistently had mean IFSARE elevation bias errors of - 3 m to - 4 m, while the forested areas showed IFSARE bias errors of + 3 m to + 5 m (deciduous) and + 6 m to + 7 m (coniferous). The

relative bias offset between open and forested terrain is thus about + 6 m to + 11 m, which can reasonably be explained as due to the heights of the trees, allowing for some penetration and volume scattering.

Height error standard deviations depended on how many pixels of marginal grey level Vexcel excluded. Using approximately the 80% brightest pixels (472,745) Vexcel found la height errors of 9.3 m, 10.5 m, and 10.1 m in open, deciduous and coniferous areas. If the next-brightest 6% were included (508,180 total), the errors were 13.0 m in all three terrain types. These results are generally consistent with the 11-12 m system error budget for 3 m x 3 m pixels,

Our difference DEMs used the westbound strip as the reference map and the east- and northbound strips as the test maps. We aligned the maps (5 m x 5 m pixels) with the same tie point and orientation reference comer reflectors that were used for the intensity map overlay for the XY scale test. In keeping with our minimalist approach to map adjustments, we removed map tilts and an elevation bias for each strip by demanding agreement of the IFSARE maps with USGS DEMs (plus an offset of 20 m for tree heights’) at three small ground patches: the Minnechaug Mountain southwest peak, the Kongscut Mountain west peak, and a high area along the ridge east of Diamond Lake. Because these patches had similar elevations but were widely spaced in X and

Elevation Reproducibility Height difference maps, made by subtracting the heights of an IFSARE DEM from those of a reference DEM

’ This work was done before Vexcel reported the empirical elevation bias errors. Our use of a 20 m bias for trees does not affect the tilt removal process or the IFSARE diffreence maps, because the three ground patches had similar terrain cover.

106 Or-wig et al.

Tabb 4. Corrective Map Tilts and Scales Required for Kongscut DEM Overlays

Map Westbound Eastbound Northbound

X tilt (mrad) + 2.2 +2.9 -13.0 Y tilt (mrad) + 0.5 +4.1 -0.7 X scale 1.000 1.000 0.996 Y scale 1.000 1 .ooo 1.000 Z scale 1.000 1.000 1.000

Y, the required adjustments were determined mainly by X and Y map tilts and relatively little by the Z scale error (which we did not try to correct). Table 4 lists all tilts and scales which were applied. Except for the X tilt on the anomalous northbound run, which required I3 mrad, tilts were in the range 0.5-4.1 mrad.

The adjusted maps were aligned and differenced pixel for pixel. Statistics were computed for the largest patches that avoided significant areas of radar shadow or open water. These areas contained a mixture of the other terrain cover types, with deciduous cover being the most common followed by open terrain and then coniferous forest. The east-west difference histogram contained 635,874 pixels and had a la height variation of 7.2 m. The north-west histogram contained 285,549 pixels and had a la error of 7.1 m. This result is consistent with the 7-8 m error predicted by the system error budget for 5 m x 5 m pixels.

COMPUTER PROCESSING REQUIREMENTS

Although airborne IFSARE was applied to topographic mapping 20 years ago using optical processing methods (Graham, 1974), it has taken recent computer technol- ogy to bring the field toward maturity. It is still an expensive undertaking. The nature of the input data (real time rates on the order of 100 Mbits Is) and output (high resolution imagery at 5 Mpixels I min, if real time) has so far made IFSARE mainly a cause for special projects with data from a relatively few hours of flying being pruned, processed, and digested over a period of weeks to months. But ARPA is driving the industry toward real time surveillance applications with data rates more than an order of magnitude faster (Allen, 1993). This will help commercial-scale application of IFSARE to become widely feasible, as the technology becomes inexpensive enough to be accessible to a variety of potential users, and swift enough to provide results for large areas of the ground while the data are still fresh.

During the course of this study we evaluated IFS- ARE processing from the standpoint of present and future viability as a practical, near real time system. Our main criteria for “practical” were size and cost: small enough to use on a modest-sized airplane or in an enclosed work area, and in the price range below $l.OM. Our working definition of “near real time” was

one-sixth of literal real time, allowing generation of a test strip in flight or turnaround of a 3 h data run within 24 h. We also decided to exclude massively parallel systems (regardless of cost) on the grounds that their architecture is not the most appropriate for the IFSARE problem.

Our IFSARE development system code was written entirely in a high level language (C), and was not de- signed for optimum execution speed. We will use it as a conservative basis for discussion. A typical strip of the sort generated in the IFSARE study represented 30 s worth of flight data and required about 6 h of CPU time on a Convex C-210 mini-supercomputer with 256 MBytes of RAM. This time is slower than our criterion by a factor of 120.

The C-210 is theoretically a 50 Mflop I s peak com- puter, with a LINPACK Benchmark result of 17 Mflop I s and a hand-optimized best result of 44 Mflop I s in the Dongarra listings (Dongarra, 1994). These figures, however, are for the C-210 running primarily as a vector processor, and most of the IFSARE development code did not vectorize well as written. We estimated that the code was getting about 5-6 Mflop Is. In that case we would need 600-720 Mflopls performance to satisfy the -near real time” criterion.

To test the development code on more modern superscalar hardware, we ported it to an Intel Paragon XP I S with 32 nodes, using up to 16. (Equivalent pro- cessing power in the form of the nonexpandable XP I E-16N listed at $0.55M with minimum RAM-256 MBytes-in late 1993.) Running with a single node, we found execution times similar to those on the Convex. This result may be expected from Dongarra’s listing for the Paragon’s performance: 10 Mflop / s (LINPACK), 34 Mflop I s (best effort), and 50 Mflop I s (theoretical peak) (Dongarra, 1994), which are similar to the figures cited above for the vectorizing C-210. With minor code changes to parallelize a major processing loop, we achieved a factor of 8 speedup on 16 nodes, putting performance of this system at about 44 Mflop Is with the IFSARE code.

This is still too slow by a factor of around 15. One may suppose that with a serious but not staggering effort to tune the code for parallel scalar processing one could gain a factor of 2, to 88 Milopls or so. This seems conservative; it is perhaps 38% of what one might extrapolate for an XP I S-16’s ‘best effort” in a future Dongarra listing, based on the corresponding numbers for the Intel iPSC/Delta. It leaves a factor of 7.5 to find in hardware. Let us look then for projected hard- ware with theoretical peak speeds of around 6 Gflop I S, or about 7.5 times the XP / s-16’s nominal 800 Flop / s at double precision. These speeds are possible now on a handful of supercomputers, and are comparable to those expected of the Touchstone (militarized Paragon in a g-card box) (Keller, 1993), which Grumman hopes to

Terrain Surveying with lnte7ferometric SAR 107

fly on the Joint-STARS by the end of 1994. But such machines exceed our cost constraint.

The Intel “P-X” is the successor to the i860 proces- sor (which is used in the Paragon), beginning in late 1994 or early 1995 (Ecklund, 1993). This processor should achieve a x 4 speedup in 64-bit flops versus the i860, via a faster clock (doubled to 100 MHz) and improved superscalar floating point due to greater data width (doubled to 64 bits), bringing a 16-node Paragon- like system to 3.2 Gflopls. ARPA is funding Intel to develop a 1000 Gflop I s device. Intel has indicated that the number of nodes will be between lo3 and 104; these will use first the “P-X’ processor, and later the faster “P-Y” (Ecklund, 1993). One might predict that in the interest of minimizing complexity to keep pricing com- petitive ($30-50 M), Intel will aim at l-2K nodes. That would mean performance on the order of 0.5-1.0 Gflopis per node with the technology supporting a price around $O.O3M per node. Therefore, when the processor technology migrates to the commercial sector (as early as 1996 or 1997) a I2-node device with a theoretical 6 Gflop I s peak could be priced near $0.4M. Adding enough memory to deal with IFSARE problems should still leave the system within our budget criterion, provided that memory for these processors becomes available in quantity with prodding from market forces.

While the above scenario is mildly speculative, Sili- con Graphics took the concrete step of announcing price lists as early as January 1993 for its Power Challenge L and XL machines, which are due out by mid-1994. Using the TFP processor (a follow-on to the R4400), the 18-headed, shared memory box at the high end is described as delivering 5.4 Gflop Is peak. With 0.5 GByte RAM and 2.4 GByte disk, this machine lists below our $l.OM cutoff, and is nominally very close to the performance we specified.

In summary, the price/performance ratio is contin- uing to drop and it is possibly only a matter of 2 or 3 years before large scale, fast response IFSARE applica- tions become widely affordable.

SUMMARY

We have described the use of a production multimode radar system, with small changes, for medium resolution topographic mapping. With attention to detail in the motion compensation and geopositioning, it was possi- ble to generate strips 6 km long with sufficient geometric fidelity to permit overlay and mosaicking, and with sufficient resolution to reveal substantial surface detail. Color coding the terrain relief promoted rapid visual sorting of image features. Map scale errors were esti- mated at 0.2%, 0.06%, and - 1.2% to +3.0% in X, Y, and Z, respectively, but there were uncertainties in these values due to tiepoint matching difficulties and

height measurement noise. In reproducibility tests, X and Y errors appeared to be smaller than 5 m both locally (due to geocoding errors) and globally (due to scale errors). Height error relative to precision stereo- optic DEMs had a standard deviation of 11-12 m for 3-m pixels. Relative height reproducibility error was about 7 m for 5-m pixels. Both of these values were consistent with the system error budget. As potent new computer technology becomes more al-fordable, IFS- ARE processing will offer a means of rapid generation of wide-area digital terrain elevation maps with numerous commercial uses.

This work was supported in part by the Advanced Research Projects Agency for the U.S. Army Topographic Engineering Center under Contract DACA76-92-C-0028.

REFERENCES

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Ecklund, D. (1993), Untitled presentation at Fourth Annual Embedded High Performance Computing Symposium, Honeywell Space Systems, Clearwater, FL, 15-16 De- cember.

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