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Yicheng Jiang, Zhuoqun Wang, "Analysis for Resolution of Bistatic SAR Configuration with Geosynchronous Transmitter and UAV Receiver", International Journal of Antennas and Propagation, vol. 2013, Article ID 237463, 10 pages, 2013. https://doi.org/10.1155/2013/237463
Analysis for Resolution of Bistatic SAR Configuration with Geosynchronous Transmitter and UAV Receiver
Bistatical SAR with geosynchronous illuminator and unmanned aerial vehicle receiver (GEO-UAV BiSAR) has significant potential advantages in the field of continuous local observation under a dangerous environment within nearly 24 h. Due to the extreme platform velocity differences, the ellipse orbital movement of GEOSAR makes this BiSAR configuration not like the conventional spaceborne BiSAR. In this paper, based on the orbital kinetic characteristic of GEOSAR, we theoretically analyze the variations of bistatic configuration effect on common azimuth coverage and coherent accumulated time. In addition, two-dimension the resolution is deduced by geometrical configuration on the basis of gradient method. The simulations show that the appropriate selection of initial bistatic configuration can restrain from the appearance of the dead zone in common coverage. And the image results are obtained by frequency domain RD based on Method of Series Reversion (MSR). It is shown that GEO-UAV BiSAR has the high resolution ability.
Spaceborne synthetic aperture radar (SAR) has been applied to the wide fields such as landform measurement, ocean observation, earthquake monitor, and digital elevation model (DEM) . For decades, lots of low-orbit (LEO) satellite emitted have high-resolution capability. However, beam irradiation extent of LEO is limited in dozens of kilometers near the nadir, and the revisit time is much longer. To this aspect, geosynchronous SAR (GEOSAR) can overcome the shortcomings aforementioned [2–4].
Geosynchronous orbits have the unique characteristic that their orbital period is nearly 24 h. It makes GEOSAR suitable for the continuous imaging on the specific partial region within 24 h . And the ground coverage provided by a GEOSAR can be nearly one third of the globe for a highly inclined orbit, and it can be as small as few hundred kilometers for a SAR placed in a slightly inclined orbit .
Nevertheless, it requires a larger antenna to overcome the energy attenuation of the ionosphere and stratosphere [7–9]. There exists difficulties to hardware realization. In addition, imaging accumulation time, which reaches a few hours, makes the imaging quality quite easier to be affected by unstable factors in larger ground coverage. To solve these problems, the literature  derives a space-based radar surveillance concept employing geosynchronous illumination and bistatic reception on either unmanned aerial vehicles (UAVs) or LEO. Due to the wide beam coverage of GEOSAR, it is easy to realize distributed imaging configuration with illuminator GEOSAR and multiple receivers (aircraft, UAV, LEO, and MEO satellites). Not only the wide imaging area is achieved, but also the requirements for the transmitted power and antenna size are reduced [11, 12].
In particular, bistatic geometrical configuration of GEOSAR illuminator and UAVSAR receiver (GEO-UAV BiSAR) may realize local observation in a dangerous environment. However, since the orbital characteristics of GEOSAR, we need to control the attitude of UAVSAR in the ground station for high resolution. Hence, it is different from other configurations, for example, GEO illumination and LEO receiver; GEO illumination and airborne receiver.
A key factor in determining the performance of GEO-UAV BiSAR systems is the two-dimensional resolution, but performance analysis of BiSAR characterized for any configuration is usually complex. The literature  describes comprehensive knowledge regarding the resolution of BiSAR with geostationary illuminator and UAV receiver, which can be obtained from the gradient method in terms of time delay and the Doppler shift [14, 15]. Yet, it does not consider the variation of geometrical configuration as a function of time effect on resolution. In this case, the geostationary orbit is just a special one of geosynchronous orbit, and it ignores orbital motion and earth rotation effect on GEOSAR velocity, when orbit inclination is not equal to zero.
Before the imaging study for GEO-UAV BiSAR, its two-dimensional spectrum is demanded to discuss. Currently, the traditional method has two kinds, Loffeld’s bistatic formula (LBF) [16, 17] and Method of Series Reversion (MSR) [18, 19]. The former mainly applies the Taylor expansion on phase histories of transmitter and receiver individually. The latter considers a power series method to count the stationary point of bistatic phase histories, and its accuracy is scalable in a sense. To this end, MSR is more applicable to the imaging study of GEO-UAV BiSAR.
This paper is organized as follows. It begins with a description of GEOSAR ground track in local ground coordinate system. Section 3 discusses the relative movement of two platforms effect on common coverage and coherent accumulated time owing to the extreme platform velocity differences. In Section 4, the formulas of two-dimensional resolution are deduced from the geometrical relationship of GEOSAR and UAVSAR based on gradient method. In Section 5, we analyze GEO-UAV BiSAR configuration influences on range and azimuth resolution by simulations. And proper initial selecting configuration can avoid the appearance of dead zone in the swath. Then, the imaging results by frequency domain RD method based on MSR are presented and analyzed.
2. Analyses to Movement Model of GEOSAR
2.1. Movement Track of GEOSAR
Suppose that GEOSAR runs on the ellipse orbit and the earth is uniform sphere, orbital inclination is , right ascension of ascending node is , and argument of perigee is . The satellite position equation can be expressed in earth fixed coordinate system: where is the center time point of time range, is the earth rotation angular velocity and is the geocenter distance of the satellite.
In the time range foregoing, the velocity of GEOSAR related to the earth is given by where is a semimajor axis, is a gravitation constant, is the earth radius, and is a GEOSAR distance of ground.
Thus, when , GEOSAR is the stationary state and GEO-UAV BiSAR images in the local area near the equator. With the increase of , goes up gradually, and the variation of latitude is in “Figure 8” imaging area. For maximum irradiation of Chinese territory, we choose . Based on GEOSAR basic parameters (see Table 1), the ground track of GEOSAR () is shown in Figure 1.
Due to higher altitude of GEOSAR , the rate at which the spacecraft moves along its orbital path is unequal to the rate at which the footprint of the antenna beam moves along the surface of the earth: .
2.2. GEOSAR Velocity in Local Ground Coordinate System
In general, GEOSAR is described in earth-fixed coordinate system as well as UAVSAR in local ground coordinate system. We will convert GEOSAR into the local ground coordinate system in which the original point O represents the intersection between the satellite line of sight and the ground, the Ox-axis corresponds with track direction of GEOSAR, the Oz-axis corresponds with the connection between satellite and subpoint, and the Oy-axis is determined according to the right-hand rule (see Figure 2).
GEOSAR runs around the earth within a periodical time, . In , the range (Oy-axis) and the azimuth (Ox-axis) acceleration of GEOSAR ground track is shown in Figure 3.
(a) Range acceleration
(b) Azimuth acceleration
The trend of range acceleration is similar to a cosine curve whose period is . The peak value is , and the valley value is . Furthermore, the trend of azimuth acceleration is similar to a sine curve whose period is . The maximum is , and the minimum is .
The range coverage of GEOSAR ground track and the azimuth coverage where and are the range and azimuth bandwidth of GEOSAR separately; is an incidence angle, is a squint angle, when range acceleration reaches peak, the surface coverage will deviate from the Ox-axis for ( represents common irradiation time, of two platforms; the limited time length is calculated by the formula ). Besides, for the azimuth acceleration is much smaller, the ground track velocity of GEOSAR is considered uniform motion as in the condition of .
3. Coherent Integration Time and Azimuth Common Coverage
Based on the theoretical research of resolution , the coherent integration time and azimuth common coverage influence azimuth resolution capability of GEO-UAV BiSAR.
Coherent integration time and azimuth coverage are relative to GEOSAR azimuth coverage , UAVSAR azimuth coverage , and antenna footprint velocity of two platforms. Movement of GEOSAR is described as the uniform motion in under the aforementioned study. While UAV is difficult to control motion stability in aerodynamic interference (roll angle, pitch angle, and heading angle of UAVSAR are variable). In this case, the accurate calculation is very troubling. To simplify calculation, we consider that roll angle, pitch angle and heading angle of UAVSAR are all constants, and UAV is a uniform motion in a straight line, . Therefore, the antenna footprint velocity ratio can be shown as where is the azimuth unit vector.(1) If , GEOSAR is the stationary station.(2) If , UAV flies the same direction with transmitter. When , otherwise .(3) If , UAV flies the opposite direction with transmitter.
Assume that footprint middle points of GEOSAR and UAVSAR are given by and , respectively, on the Ox-axis in Figure 2. Left and right edges of GEOSAR is and ; and . If two platforms intersect at , and ; if they intersect at , and . Then, .
For the subsequent simulation data show (see Tables 1 and 2), we primarily discuss and in the case of . When , , while and achieve the maximum. Suppose that represents the distance between the corresponding right edge points of the transmitter and the receiver in the Ox-axis. The change trend of is with the relative movement of two platforms (see Figure 2). Thus, by (23) and (24) in the Appendix is calculated. Besides, the common irradiation time of two platforms is .
Taking into account the difference value of , we count and , respectively (see the Appendix), when . While in the case that , and are constants, is inversely proportional to if ( if ). And the maximum depends on the synthetic aperture time of receiver. If the coherent accumulated time is less than the maximum , the imaging quality is fuzzy in the zone which is known as “dead zone1”. Conversely, it is called as “clear zone”.
4. Resolution of GEO-UAV BiSAR
GEO-UAV BiSAR geometry in local ground coordinate system is shown in Figure 4. The center of the scene is O point, GEOSAR locates ; UAVSAR locates . The time-domain matched filter is constructed by forming an instantaneous slant range to a point target referred to as the range equation where
Note that depends on the angular rate of two platforms. For and , UAVSAR dominates :
The maximum delay time for movement in the ground plane is along the projection of into xOy plane, . Similarly, the maximum change in the Doppler frequency moves along the projection of into xOy plane, . Thus, the range resolution and the azimuth resolution are given by
BiSAR resolution has the properties of time varying and spatial varying. On the basis of the GEO-UAV BiSAR geometry, (8) is redescribed as where is the illuminator out-of-plane angle (with respect to the receiver and centered in the origin), is the angle between the Ox-axis and the projection of UAVSAR position into xOy plane, and is determined by .
The range resolution mainly depends on through (9). It attains the maximum for and the minimum values for . In other words, the gradient of time delay has no component onto xOy plane for , GEO-UAV BiSAR construction has the worst range resolution.
The azimuth resolution is relative to coherent accumulated time and the attitude change of UAV. With the shorter coherent accumulated time , the imaging quality of GEO-UAV BiSAR will decline gradually (dead zone1). Whereas, the azimuth resolution can further simplify as in the clear zone. When reaches an enough value, is the maximum for . And the gradient of the Doppler shift is the smallest component onto xOy plane.
For aforesaid reasons, the proper selection of original UAVSAR attitudes, and , can make GEO-UAV BiSAR exhibit high resolution. To achieve this aim in clear zone, we will avoid the appearance of the worst construction in mutual movement process of transmitter and receiver. (Worst construction illuminates the area called dead zone2.)
In a periodical time of GEOSAR, the relative movement of GEOSAR and UAVSAR works in finite time (the local ground coordinate system is different for varying). Suppose that the original value of (corresponding ) is in CCI with regard to good imaging quality. For the sake of platform velocity differences, the variation range of , is still in CCI:
where is related to the velocity ratio of the two platforms, . Considering , is given by where is the GEOSAR subpoint. And (11) can be further simplified as Since
where is expressed as
When , is the same to (14). However, GEOSAR runs on a circle orbit if . Under this circumstance, is meaningless for . Hence, the range resolution is given by
5. Simulation Analysis
In order to study the resolution of GEO-UAV BiSAR, we discuss the influence of coherent accumulated time and attitude change of UAV on the two-dimensional resolution. And the imaged results are disposed through using frequency domain RD method based on MSR.
5.1. Effect of Coherent Accumulated Time on Azimuth Resolution
Within a periodical time of GEOSAR, the velocity is a variable. The bistatic configuration changes with the different time instant selected (origin O is different with a function in local ground coordinate system). According to the parameters of GEOSAR and UAVSAR (see Tables 1 and 2), we can gain . In the condition of and , the azimuth coverage and the coherent accumulated time are calculated through (23) and (24) in the appendix. GEOSAR beam surface velocity, clear-zone, dead zone1, and coherent accumulated time for are shown in Table 3.
Simulations that demonstrate the azimuth coverage of GEO-UAV BiSAR are inversely proportional to. At a constant , the size of dead zone1 shows a decrease with going up. The change of follows the squint angle of receiver that varies owing to the orbital movement of GEOSAR.
Taking as an example, the influence of coherent accumulated time on azimuth resolution is drawn in Figure 5. In the clear zone, the azimuth resolution will achieve 0.99 m, while the azimuth resolution capability reduces with coherent accumulated time dropping gradually in the dead zone1.
(a) Coherent accumulated time
(b) Azimuth resolution
5.2. Effect of the Initial Attitudes for Two Platforms on Resolution
Based on resolution analysis in Section 4, the appropriate attitude control of UAVSAR enables to avoid the appearance dead zone2 in the clear zone. As far as of range and the Doppler resolution are concerned, Figure 6 shows their variations as two functions of and for GEO-UAV BiSAR ().
(a) Range resolution
(b) Azimuth resolution
has a great effect on the range resolution, to which is meaningless. If and , BiSAR has higher resolution and . If , BiSAR resolution is much lower and . When , it is the worst condition that gradient of time delay is equal to zero such that the range resolution reaches the maximum value (see Figure 6(a)).
For the azimuth resolution, both and have certain mount of influences. If , the azimuth resolution of GEO-UAV BiSAR is lower than 1.4 m (critical value of resolution). And if , the azimuth resolution is still impacted by (see Figure 6(b)).
To assure the high resolution of range and azimuth, the range value of is drawn in Figure 7. A unit circle represents the position projection of transmitter and receiver in xOy plane. If , GEO-UAV BiSAR configuration can show high-resolution ability in the content of 2 and area 3, whereas we need to avoid that appears in area 1 and area 3 if .
With the mutual movement of two platforms (, and is time varying), the variational range of is different in the periodical time of GEOSAR. To avoid the appearance of the dead zone2 in the clear zone, we demand to meet (10). The variational range of in the whole period of GEOSAR is shown in Figure 8. And obtains the maximum when . Hence, the proper extent of initial UAV attitude can be written as
Based on the aforementioned condition, we select and . Figure 9 shows the range and azimuth resolution distributions of GEO-UAV BiSAR in xOy plane (). It is worth noting that the coherent accumulated time (2.71 s in Table 3) is considered for all point target in the bistatic scene area. The bistatic scene dimensions are 400 m in range and 244 m in azimuth. And the range resolutions from 1.07 m to 1.14 m are expected along with azimuth resolutions ranging from 0.99 m to 1.00 m. These values are deduced by (8) and (9). Thus, GEO-UAV BiSAR is suitable to the image in the local area.
(a) Range resolution (m)
(b) Azimuth resolution (m)
5.3. Frequency Domain RD Based on MSR
To evaluate the resolution of GEO-UAV BiSAR, we will focus on an image with a frequency-domain SAR processor. The corresponding processing approach has been developed based on MSR by means of the four-level Taylor expansion [18, 19]. RD method in frequency domain is performed by four steps, that is, range compression, secondary range compression, range cell migration, and azimuth compression.
If the attitude parameters of UAVSAR are and , the impulse response output at the scene center target () is drawn in Figure 10. The corresponding measured −3 dB resolutions are 1.08 m and 1.08 m, respectively, in comparison to the theoretical values of 1.08 m and 0.99 m (in Figure 9). It can be seen that the resolution has range and azimuth broadening of about 0.3% and 9%.
(a) Range impulse response output
(b) Azimuth impulse response output
Bistatic geometrical configuration using GEOSAR as a transmitter and UAVSAR as a receiver is analyzed. From a theoretical level, firstly, the variation of bistatic geometrical configuration which has influence on azimuth common coverage and coherent accumulated time is studied according to the ellipse orbital movement of GEOSAR; then, the gradient method based on GEO-UAV SAR configuration (GEOSAR exhibits the characteristics of high altitude and periodical motion) is proposed to deduce two-dimensional resolution.
Simulations illustrate that the resolution is accurately obtained from the geometrical simplification of gradient method which consists of two impact factors on the coherent accumulated time and the UAV attitude. The azimuth resolution capacity of GEO-UAV BiSAR shows a gradual decrease with coherent accumulated time reducing the relative motion of two platforms. Moreover, the proper initial selection of UAV attitude can avoid the appearance of dead zone in the swath. Such theoretical analysis, along with simulation results, further demonstrates the potential performance of GEO-UAV BiSAR that is mainly affected by the UAV attitude design when GEOSAR follows the orbital operation. Besides, the feasibility of GEO-UAV BiSAR configuration for high resolution imaging in the local field is verified.
The foregoing works in this paper inspire us to research on the existing bistatic particularities. However, the effect of nonstationary movement related to phase center for GEOSAR and UAVSAR, which reduce the two-dimensional resolution, is ignored in this paper. In this case, the further experiments based on the nonstationary will be developed, and the resolution will be analyzed.
See Table 4.
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Copyright © 2013 Yicheng Jiang and Zhuoqun Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.