Gayana 68(2): 373-380, 2004

ABSOLUTE CALIBRATION OF THE ERS-2 SCATTEROMETER IN GYRO-LESS MODE USING TRANSPONDERS

Nicolas Manise, Xavier Neyt & Marc Acheroy

Royal Military Academy, Brussels, Belgium nmanise@elec.rma.ac.be

ABSTRACT

The scatterometer on-board ERS-2, earth-observation satellite developed by the European Space Agency, is an active real aperture radar instrument designed to measure the backscatter coefficient ⁰ from the earth. Its main utility is to measure physical parameters such as wind speeds and directions over the sea surface. Due to malfunctions of the on-board gyroscopes and even though a new attitude and orbit control system is used, the yaw-orientation of the spacecraft still exhibits random variations from the nominal attitude. This unpredictable attitude requires re-developing the calibration chain of the scatterometer instrument. Distributed targets, such as the rain forest, are used to perform a relative calibration while transponders situated at known locations in Spain permit an absolute calibration of the instrument.

The scope is to expose the obtained results and the improvements brought by the new chain regarding the absolute calibration. An analysis of the received echo with a sub-pixel resolution (better than the nominal resolution) allows getting accurate transponder localization. The localization error is used to determine, among other quantities, the antenna mounting angles errors. Since the signal emitted by the transponders is calibrated, radiometric calibration is also possible, including determination of a large set of parameters such as the absolute gain of each antenna. The raw data quality (such as DC offsets, gain imbalance, phase imbalance) and the spatial resolution are also computed.

Keywords: Scatterometer, calibration, transponder

INTRODUCTION

The Scatterometer instrument on board the ERS-2 satellite is a three antennae side looking active microwave sensor (C-Band). The three antennae mounted on the top of the satellite provide backscattering measurements in three look directions with respect to the satellite velocity, 45° foreward (fore-beam), sideways (mid-beam) and 45° backwards (aft-beam) of the Earth surface [4].

Due to successive losses of the gyroscopes, new Attitude and Orbit Control Systems have been adopted from the beginning of February 2000 to eventually lead to a gyro-less mode in January 2001. Nevertheless, the yaw orientation still exhibits random variations [7].

As the previous calibration chain [4] assumes that the satellite attitude is nominal, this calibration chain has to be redeveloped to take into account the attitude uncertainty.

The following sections expose the methods and results of the absolute calibration. The Impulse Response Function (IRF), the spatial resolution, the transponder localization (and associated antennae pointing errors), the calibrated gain constants, the azimuth antenna patterns and the calibration pulse I/Q characterization will successively be explained.

OPERATION MODE

The calibration takes place in the following way. Every time the satellite over flies the transponders situated in Spain, the wind scatterometer is configured in calibration mode, and RF pulses are transmitted to the transponders by the Fore, Mid and Aft antennae (F-M-A) during periods of 120, 40 and 120 seconds, respectively.

The transponder units amplify the received pulses by around 80 dB and uplink the amplified pulses to the satellite with a frequency shift of 540 kHz. This added frequency shift permits to easily filter out clutter echo signal components. Therefore, the echo only contains the signal sent back by the transponders and some thermal noise. The transponders are seen as punctual spots in the echo.

The transponders record the transponder gain and the received powers and frequencies [2].

The spacecraft passes over the transponders and records useful calibration data approximately once every three days (best case). During these three days, the attitude of the satellite changes significantly. Therefore, the computed parameters provide the attitude of the satellite only at punctual times.

VALIDATION AND RESULTS

Introduction

The validation and the results have been performed using two sets of data corresponding to two different piloting modes of the satellite. The first dataset was acquired before January 2000. The three on-board gyroscopes were operational and the attitude of the satellite has therefore been considered as nominal (Yaw-Steering Mode ­ YSM). As the previous calibration chain of the scatterometer instrument (Calproc) worked on the basis that the attitude of the satellite was nominal, the validation of the new chain will be made with the YSM data.

The second dataset was acquired after January 2001. All gyroscopes were out of order or very noisy and the satellite started to work in Zero-Gyro Mode (ZGM) [7].

Instrument Impulse Response function (IRF)

Figure 1 shows the IRF of the instrument. An along-track and across-track cuts are shown. The bright spots on the right of Figure 1 represent the IRF.

Figure 1: IRF ­ On the left an along-track cut, in the middle an across-track cut and on the right a 2D representation of the echo. Each line represents one beam.

Spatial resolution

The spatial resolution is defined by the width of the IRF where it reaches 50% of its peak value. This applies to across track and along track. The azimuth spatial resolution is governed by the projection of the azimuth antenna pattern on ground. Similarly, the across-track resolution depends on the length of the emitted pulse projected on ground and on the pass-band of the system [5]. As can be seen in Figure 2, the across-track resolution of the Mid-beam is lower. This is due to the fact that the emitted pulse length is shorter.

Figure 2: Spatial Resolution ­ In black (stars), the Fore-beam, in red (diamonds), the Mid-beam and in blue (+), the Aft-beam. Left: resolution in azimuth as a function of the range of the target (YSM). Right: resolution across-track as a function of the range of the target (ZGM).

Transponder Localization error

The three transponders are situated in the south of Spain (Figure 3). A sub-pixel resolution (better than the nominal resolution) is required to localize the maximum of energy in the echo data. The method consists in defining a sub-region around the peak echo energy and to compute iso-energy lines on the IRF. Averaging the points situated on these isolines

Figure 3: Transponder localization ­ The red stars show the transponders. The blue, green and black colors represent respectively the fore, mid and aft beams. The red line is the satellite track (ascending in this example).

provides the Center of Gravity (CoG) of the IRF as shown in Figure 4 where the green star shows the CoG, the red star shows the point of maximum energy and the blue star, the transponder localization. The +'s represent the data actually measured by the satellite and the dotted lines indicate the across-track direction.

Figure 4: CoG ­ The green star is the CoG, the blue star shows the transponder localization and the red star shows the point of maximum energy.

The localization error is defined as the distance between the CoG and the transponder. In YSM, this distance is small as Figures 4 and 5 show. This localization error can be translated into two pointing errors (roll and yaw angles) for each beam as the right graph of Figure 5 shows (YSM).

Figure 5: Localization error YSM ­ Distance in km from the real transponder and the CoG of the echo peak (left) and antennae pointing errors (right).

In Figure 6, the localization error in ZGM is shown for the Fore-beam. At the beginning of the ZGM (beginning of 2001), results show a strongly degraded attitude of the satellite (error of more than 30 km). On the right of figure 6, the corresponding antenna pointing errors are shown.

Figure 6: Localization error ZGM (Fore-beam) ­ Distance in km between the real transponder and the CoG of the echo peak (left) and antennae pointing errors (right).

Calibrated gain constant

The power received by the transponder is defined by the (one-way) radar equation:

(1)

where P_t is the power received by the transponder, P_i is the power emitted by the satellite, G_q(q) is the gain in elevation, G_f(f) is the gain in azimuth, s is the Radar Cross Section of the transponder and R is the distance between the satellite and the transponder.

The same equation can be written for the power received by the satellite:

(2)

where P_r is the power received by the satellite, ERF is called the External Rescale Factor (gathers all constants) used to convert the "counts" to power unit. The parameter of interest in equation (2) is K called the gain constant: the ideal value of K is 1 (0dB).

The gain constants computed in YSM (Figure 8) show a very good match with the results of Calproc (Figure 7). The measurements are performed at fixed incidence angle. Points corresponding to same incidence angles are averaged together then linked together (lines in Figure 8). A small offset depending on the beam and on the transponder considered has been detected.

Figure 7: Gain constants- Left: Calproc gain constants (Fore-beam). Middle: Calproc gain constants (Mid-beam). Right: Calproc gain constants (Aft-beam).

Figure 8: Gain constants- Left: Tosca gain constants in YSM (Black: Fore-beam; Red: Mid-beam; Blue: Aft-beam). Right: Tosca gain constants in ZGM

The calibrated gain does roughly not depend on the incidence angle in YSM and ZGM. In ZGM, the values are concentrated around 0 dB but are more "noisy" than in YSM (where the gain is constant within 0.5 dB [2]). A possible explanation for this is that the signal spectrum is shifted due to imperfect on-board Doppler frequency compensation since the yaw angle is not nominal. The on-board low pass filter attenuates the signal [4].

Antenna pattern in azimuth

Each time the satellite over flies the calibration area, the transponders record the signal that they receive and retransmit. As these transponders follow the satellite track, the recorded signal directly provides the antenna patterns in azimuth as Figure 9 shows. A comparison with the theoretical antenna diagram shows that the measured diagram is very close to the theoretical one.

Figure 9: Antenna pattern in azimuth ­ Comparison between the theoretical azimuth antenna gain (black) and the normalized power (red) recorded by the transponder. This graph corresponds to the Aft-beam of a pass acquired in April 1999.

Calibration I/Q characterization

The on-board ADC converts the pulses into an in-phase and in-quadrature digitized signals. Determining the I/Q parameters is relatively simple if the phase of the signal is uniformly distributed over 2p. The assumption of uniform phase distribution is well founded for the target signal but is questionable for the calibration signal (unknown phase). In the following, the calibration I/Q characterization uses the internal calibration pulses from passes over the transponders where the calibration pulses amplitude is constant during the pass [2].

In the ideal case, the pulses are distributed around a circle. Due to the imperfections of the receiving chains, pulses are more likely distributed around an ellipse (Figure 10).

Figure 10: I/Q characterization ­ Bx controls the horizontal offset of the ellipse, By, the vertical offset, q, the shape ("flatness") and e, the tilt. is the signal amplitude, Gx and Gy are the I/Q gains and a is the tilt angle

defined by

where

The I/Q characterization consists in determining the DC offsets (B_x and B_y), the gain imbalance (q) and the phase imbalance (e) of the I/Q receiver channels. In Figure 10, B_x controls the horizontal offset of the ellipse, B_y, the vertical offset, q, the shape ("flatness") and , the tilt.

A practical procedure is to fit in the least-square sense an ellipse through the whole set of data points as figure 11 shows. The function (of the four parameters) to minimize is a measure of the deviation between the data points and the ellipse. The minimization method is the Taylor Differential-Correction. The initial estimates of the parameters are set to zero, then improved iteratively until convergence. The initial estimates are assumed to be close to the final ones (small I/Q parameters) [6].

Figure 11: I/Q characterization ­ The black ellipse is the reference (circle). The red stars are the calibration pulses and the red line is the fitted ellipse on those points. The figure on the left corresponds to a Fore-beam while the figure on the right corresponds to a Mid-beam (less samples during the pass over the transponders than the Fore and Aft-beams).

The aim of the I/Q parameters computation is to correct the signal for the receiving chains imperfections. To validate the parameters estimation and the efficiency of the correction, the first step consists in computing the I/Q parameters using not-corrected data. Then, these parameters are used to correct the I and Q channels of the calibration pulses. Finally, the I/Q parameters are re-computed using the corrected data. Results are shown in Table 1. After correction, the parameters are very small which means that the calibration pulses are distributed around a circle. Therefore, the parameters estimation and the correction method are validated.

Conclusions

The previous calibration chain assumed that the satellite attitude was nominal. Since the on-board gyroscopes were declared out of order, the chain was no longer able to compute the calibration parameters. Therefore, a new calibration chain has been developed in order to take into account uncertainties in the attitude of the satellite.

The new chain has been validated comparing the results while the satellite was working in YSM. Analysis of the results in degraded mode (ZGM) has been performed and the attitude of the satellite has been deduced.

In particular, the localization error of the transponders has been translated into two antenna angle errors (Roll and Yaw). This can be used to determine the attitude of the spacecraft. The calibrated gain does

ACKNOWLEGMENTS

This work was performed under European Space Agency (ESA) contracts. We would like to thank the ESA for the use of data and the provision of industry-confidential information ([1] and [3]). This work would not have been possible without the help of Pascal Lecomte and Raffaele Crapolicchio from the European Space Agency/ESRIN.

References

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H. Eichenherr, U. Kummer, & P. Hans, Apr. 1989, Study of product quality assurance and long-loop sensor performance analysis methods for ERS-1 AMI scatterometer. Technical report ESA Contract No. 7684/88/HGE-I, Study note Workpackage 200 and 300, Issue 3. [3]

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