July 31, 2008
Image Navigation for the FY2 Geosynchronous Meteorological Satellite
By Lu, Feng Zhang, Xiaohu; Xu, Jianmin
ABSTRACT An automatic image navigation algorithm for Feng Yun 2 (FY2) spin-stabilized geosynchronous meteorological satellites was determined at the National Satellite Meteorological Center (NSMC) of the China Meteorological Administration (CMA). This paper derives the parameters and coordinate systems used in FY2 image navigation, with an emphasis on attitude and misalignment parameters. The solution to the navigation model does not depend on any landmark matching.The time series dataset of the satellite orientation with respect to the center line of the earth's disk contains information on the two components of the attitude (orientation of the satellite spin axis) and the roll component of the misalignment. With this information, the two attitude components can be solved simultaneously, expressed as declination and right ascension (with diurnal variation in the fixed earth coordinate system) and the roll component of the misalignment (with no diurnal variation).
In each spin cycle, the satellite views the sun and earth. The position of the sun is detected and used to align earth observation pixels in the scan line together with an angle subtended at the satellite by the sun and earth (beta). With satellite position and attitude known, the beta angle can be calculated and predicted with sufficient accuracy. Next, the image is assembled. Prediction of the beta angle takes an important role in the image formation process, as imperfect beta angle prediction may cause east-west shift and image deformation. In the image registration process of FY2, both the east-west shift and the image deformation are compensated for.
The above-mentioned solution to the navigation model requires accurate knowledge of astronomical parameters and coordinate systems. The orbital, attitude, misalignment, and beta angle parameters are produced automatically and routinely without any manual operation. Image navigation accuracy for the FY2 geosynchronous meteorological satellite approaches 5 km at the subsatellite point (SSP).
(ProQuest: ... denotes formulae omitted.)
Image navigation is an essential and fundamental component in data processing of geosynchronous meteorological satellites. Currently, image animation is broadly used in daily weather forecasts and public services. Smooth animation is meaningful not only for forecasters to diagnose the weather, but also for the public to understand weather systems. Image navigation performance affects all services provided by geosynchronous meteorological satellites, including their data and products. Small errors in navigational parameters may cause significant shifts in image animation. Products derived with a series of images such as atmospheric motion vector and cloud classification are especially sensitive to image navigation accuracy. Furthermore, navigation parameters of geosynchronous meteorological satellites need to be predicted before observation is performed, since those parameters are used to supervise the observation process. Highaccuracy image navigation parameters are essential for smooth operation of the whole satellite system. In summary, stable and accurate image navigation is one of the most important quality indicators for geosynchronous meteorological satellites.
The geosynchronous satellite observes the earth pixel by pixel. The observation pixels are pieced together to form images. Based on the definition by Kamel (1996), image registration refers to the process of keeping any pixel within an image pointed to its nominal1 earth location within a specified accuracy; image navigation is the process of determining the location of any pixel within an image in terms of earth latitude and longitude. Therefore, image registration is a measure of pointing stability, while image navigation is a measure of absolute pointing accuracy. Since it is impossible to completely separate the image registration and navigation processes, this paper also refers to the related image registration process.
In the past, various efforts have been made to find mathematical solutions to the image navigation of spinstabilized geosynchronous meteorological satellites. Those efforts include the establishment of basic mathematical formulas, the determination of the direction the satellite is pointing relative to the earth, and the improvement of image grids.
Hambrick and Phillips (1980, hereafter HP80) derived a general solution of image navigation based on mathematical formulations where they defined attitude and misalignment parameters. Observation pointing vectors as known quantities are used to determine the attitude and roll misalignment parameters. Thus, the observation pixel positions can then be transferred from image (line-element) coordinates into geometric (latitude-longitude) coordinates. HP80 did put forward a succinct and effective mathematical solution to geosynchronous meteorological satellite image navigation, resulting in a classical study of image navigation of geosynchronous meteorological satellites.
The pointing of the satellite toward earth is essential for remote earth sensing. For spin-stabilized geosynchronous meteorological satellites, the pointing is maintained by the opening time of the radiometer during a spin cycle. During each spin cycle, the satellite views both the sun and earth. Since the sun sensor provides a highly accurate sun position, it is used along with the angle between the sun and earth (beta) to control the opening time of the radiometer. Knowledge of the beta angle is important during the image assembly process. The Man Computer Interactive Data Access System (McIDAS) navigation manual of the Space Science and Engineering Center (SSEC) put forward an algorithm to calculate the beta angle based on statistics (Space Science and Engineering Center 1986). Landmark column count locations at different times are used to make the statistical calculations and corrections.
Although geosynchronous meteorological satellites are expected to be stationary relative to earth, in reality, their positions keeps changing; this in turn causes changes in the captured images. There are two major methods for image grids to refer to political and geographic boundaries: to match grids for individual observations accurately, or to provide images with nominal image grids. Kigawa (1991) provided a good way to match grids to individual observations. He presented programs for Geostationary Meteorological Satellite (GMS) images to transfer observed pixel positions between image (line-element) coordinates and geometric (latitude-longitude) coordinates. When navigation parameters are accurately derived, these programs perform accurately. Also, the near-real-time rectification and dissemination process is used for Meteosat satellites from the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT; Adamson et al. 1988; Agrotis 1988; Doolittle et al. 1973; Wolff 1985). Rectification and dissemination starts immediately after the beginning of image acquisition. By measuring raw observation images, navigation parameters and the deformation matrix are determined. Remapping is then performed, and nominal images are obtained (Bos et al. 1990).
Because of a variety of reasons, users of geosynchronous meteorological satellites are puzzled by image navigation errors shown as imperfect matches between images and grids, or as shifts in image animation. At the initial stage of Feng Yun 2 (FY2) operation- FY2 is the Chinese series of geosynchronous meteorological satellites-those errors have negatively affected its application. This paper thoroughly reviews the algorithm used and the data produced by the satellite. Two main areas with the potential to improve image navigation include the mathematical formulation solution and the process of pointing the satellite toward the earth.
Over the past 2 decades, our knowledge and ability to obtain mathematical solutions in astronomical surveying has greatly improved, and new and more accurate standards for time and coordinate systems have been issued. With this improved knowledge and standards, coordinate systems are better defined. Careful analysis of the behavior of FY2 raw image animations has indicated that the time series of observation vectors pointing to the earth disk center can be used as representative input parameters for the solution of navigational equations (Xu et al. 2002). This approach is successful in practice for FY2, where image navigation in the south-north direction has been improved.
Determination of the direction from the satellite to earth's center is the key for geosynchronous meteorological satellite remote sensing. In FY2 observation, the geometric formulation solution of the beta angle is derived. Important beta angle parameters that previously had to be obtained by statistics can now be accurately calculated. With the geometric formulation solution of the beta angle, the accuracy of determining the direction from the satellite to earth is greatly improved. After the pointing direction has been calculated accurately, small shifts in the east-west direction are further analyzed. The irregular bias of the actual earth disk center column count from predictions may be explained by inaccurate satellite position prediction, and be compensated for as pitch misalignment in the navigation formulation. This paper introduces the improvements realized at the National Satellite Meteorological Center (NSMC) that result in a fully automatic image navigation procedure for FY2. The structure of this paper is as follows: after the introduction, section 2 briefly introduces the observation procedure of the FY2 meteorological satellite, with particular attention to the software approach to image registration. section 3 examines the time series of the earth disk center line count, its relationship with the basic image navigation formulation, and its use as a known quality of the formulation. section 4 describes formulation in the east-west direction and the related image registration components. Geometric formulation of the beta angle is discussed with the associated column count and deformation of the image. Section 5 illustrates the solution process of the formulations, and section 6 shows the navigation results along with the actual parameters calculated in June 2006. Section 7 is a summary discussion of algorithm performance and characteristics. Actual data from the FY2C operation show high-quality image navigation for FY2 meteorological satellites.
2. Image registration procedure of FY2 meteorological satellites
Until now, four FY2 satellites have been launched, termed FY2A, B, C, and D. At present, FY2C and FY2D are both in operation, located at 105[degrees] and 86.5[degrees]E, respectively. The expected lifetime for FY2 satellites is 3 yr. After FY2D, four more FY2 satellites are planned in order to continue these services up to the year 2015. The FY2 satellites are spin stabilized, and the primary observational instrument of FY2 satellites is a Multichannel Visible and Infrared Spin Scan Radiometer (MCVISSR) with one visible (VIS) channel and four infrared (IR) channels. Specifications of FY2 satellites and MCVISSR have been previously described (National Satellite Meteorological Center 2004, 2006).
a. Image registration procedure of FY2 satellites
FY2 meteorological satellites acquire observation images through cooperative work of space and ground segments. The coherent observation technique was first developed and used in the U.S. Geostationary Operational Environmental Satellite (GOES; Whitney et al.; Bristor 1975) based on a hardware approach. For FY2, this is mainly realized through a software approach (Fan et al. 1998). The software approach is beneficial to the compensation jobs in image registration, and is very helpful in improving image navigation quality.
Figure 1 explains how individual scan lines are registered with software at ground segments to form images. Figure 1a is a diagram of the spin plane of the satellite, while Fig. 1b illustrates the process of the registration of individual scan lines. The upper part of Fig. 1b hints that in each spin cycle the satellite views the sun and earth as expressed in Fig. 1a; earth and sun acquisition time as well as observation data are transmitted to the ground segment. The middle part of Fig. 1b shows how the ground segment recovers a precise sun pulse. The bottom part of Fig. 1b shows that with accurate sun pulse measurements and knowledge of beta, the individual scan lines can be aligned.
To observe earth, it is essential to maintain the pointing direction of the radiometer toward earth. For spin geosynchronous satellites, this is performed by controlling the opening time of the radiometer. In geosynchronous orbit, the viewing angle of the earth's disk is approximately 17.4[degrees] x 17.4[degrees], so the observation scope is designed as 20[degrees] x 20[degrees]. While the satellite spins and faces earth, the MCVISSR opens. The raw data gained are sent in real time to a ground segment where they are pieced together to form images. The image signal is stretched to the remaining 340[degrees], where MCVISSR faces space, and relayed to the utilization stations in another cycle. Figure 1a expresses this process. After a scan line is obtained in a cycle, MCVISSR moves one step downward and prepares for the next scan cycle. The observation process for a full disk image takes 25 min and is composed of 2500 scan cycles.
The MCVISSR opens while the MCVISSR faces the earth. This process is controlled by a clock on board the satellite. To compensate for the revolution of the satellite around earth, after a number (70.4) of cycles, the opening of the MCVISSR comes forward for a short time period (292.57 [mu]s; see the upper part of Fig. 1b). This measure ensures that the earth's disk is fully viewed on each scan line each day, and also helps to inform the ground segment of the MCVISSR opening time on the satellite. Based on this time, individual scan lines are aligned to form images. The transmission of this time from satellite to ground is jointly realized by two data channels.
Accurate transmission of the MCVISSR opening time to the ground segment is the key for image registration. The MCVISSR opening time is controlled by a sun sensor installed on the side face of the satellite column. When the sun sensor senses the sun, a sun pulse signal is triggered with an accuracy of 0.2-[mu]rad, equivalent to 0.1 visible pixels. The sun pulse should be transmitted to the ground segment with sufficient accuracy for image registration. A double channel transmission is designed. The sun pulse received at the ground segment in the narrowband channel is not sufficiently accurate for imaging, and the wide band MCVISSR data channel helps to accurately recover the sun pulse at the ground segment. As mentioned previously, the MCVISSR only opens at one of the discrete instants after the sun pulse arrives. By overlay of the narrowband sun pulse with a series of discrete moments (integer times of 292.57 [mu]s) ahead of the MCVISSR opening time, a high-accuracy sun pulse is recovered at the ground segment (see middle part of Fig. 1b).
Based on an accurate sun position and beta angle prediction, individual scan lines are aligned, resampled, and registered at the ground segment, and observation images are assembled (see the bottom part of Fig. 1b). The accurate prediction of beta is a precondition of image registration. The influence of the beta angle on image registration and navigation will be further described in sections 4 and 5.
b. Influence of spin variation and eclipse
The scan process moves the scan mirror within the satellite, hence changing the mass distribution within the rotating body, which has a significant impact on the spin period. The result is that the top or bottom parts of images are scanned under faster spin rates, while the middle part is scanned slower. MCVISSR samples all scan lines at an identical time interval. In ground segments, raw observation oversampled with identical time intervals is converted into identical angular intervals, removing the impact of spin rate change. Spin periods are gained based on differences between the arrival times of successive scan lines.
During spring and autumn eclipse periods, the earth's shadow falls on the satellite around midnight. The longest duration of the earth's shadow may last for 72 min. In the earth's shadow, the satellite cools down, the spin rate increases, and the sun sail is unable to obtain energy. Thus, image acquisitions are suspended during this period, and they are restarted about 1 h after the satellite steps out of the earth's shadow, at which time the spin rate recovers.
3. Image navigation model
a. Time series of the earth disk center line count
Viewed from a spin geosynchronous satellite, the earth's disk location passes through a diurnal cycle. This phenomenon is schematically illustrated in Fig. 2, which presents FY2 observation geometry. In an ideal situation, the spin axis of the satellite should be parallel to the earth's axis of rotation. In practice, this ideal is not achieved. As shown in Fig. 2, at 0600 (1800) UTC, the satellite looks up (down) at earth, and the earth's disk is in the downward (upward) side of the image. Around these two moments, the earth's disk center is displaced mostly in the north-south direction on the images, and the images experience only a small amount of turning in a day. At 0000 (1200) UTC, the earth's disk is minimally displaced, but the scan lines deflect the greatest amount, and the turnings of the images become the largest in a single day. At 0000 (1200) UTC, the satellite views earth with its spin axis turning clockwise (anticlockwise), while the image turns anticlockwise (clockwise). The phenomena described above reflect the impact of the satellite attitude on the imaging process, and can be detected easily by image animation. When the image origins are placed at the first line and column of the image animation, the earth's disk shifts in the north-south direction one cycle each day. When the image origins are placed at the earth disk center and made into an image animation, the earth's disk swings clockwise and anticlockwise one cycle each day.
To express the phenomena mentioned above, a time series of earth disk center line counts (namely, the north-south movement of the earth's disk in the image) on 7-9 June 2006 is shown in Fig. 3. The movement appears as a simple sinusoidal function with a cycle of 366.25/365.25 days. In Fig. 3b, the sinusoidal function is simulated with previous data from 7 to 8 June 2006 (black dots) and extended to 9 June 2006 (hollow dots). The good overlap of the hollow dots on the extension part of the sinusoidal curve shows that the earth disk center line count is predictable. The formulation to describe the above-mentioned phenomena will follow, but the parameters and coordinate systems necessary for the formulation are first described.
b. Navigation parameters and coordinate systems
HP80 mentioned 13 parameters to describe geometric orbit and attitude for spin geosynchronous meteorological satellites: 6 orbital parameters [Montenbruck and Gill (2000)]; inclination, right ascension of the ascending node, semimajor axis, eccentricity, argument of perigee, mean anomaly at epoch), 3 attitude parameters (declination and right ascension of the spin axis, spin angular velocity), 3 misalignment parameters (roll, pitch, yaw), and 1 beta angle parameter. Table 1 defines the satellite and MCVISSR coordinate systems for FY2 satellites, and vectors related to defining the satellite coordinate system (S^sub X^, S^sub Y^, S^sub Z^) are also expressed in Fig. 4. The unit vectors (i^sub S^, j^sub S^, k^sub S^) of (S^sub X^, S^sub Y^, S^sub Z^) define the satellite coordinate system. Figure 5 illustrates misalignment. Figure 5a shows the difference of actual MCVISSR assembling status from the ideal. In manufacturing, the principle axis of the satellite column body should be the free axis with the maximum spin angular momentum, and the 1250th scan line of the MCVISSR should scan out a plane. In practice, this ideal status is seldom satisfied. Because of misalignment, the 1250th line normally scans out a cone, as shown in Fig. 5b. Misalignment is very small in magnitude, but due to the distance of the satellite from earth, the misalignment has a significant impact on image navigation. Figure 3a shows that the central line of the sinusoidal function is at 1245.2, which is somewhat deviated from the image center at 1250. This is due to the effect of misalignment. In HP80, the definition of attitude and misalignment components was not nominal, but this paper adopts nominal expression. Table 2 shows the differences in the expressions for attitude and misalignment components between Hambrick's and nominal expressions.
c. Formulation for spin axis orientation and roll misalignment
Observation vectors can be measured on the observation images (see Fig. 4). The observation vector (the vector from the satellite toward the observation objective) in the satellite coordinate systems can be measured as
In (1), R and M are observation and misalignment matrices, respectively (HP80):
In (2), Q is the step angle between observation lines, J is the line count counted from the top end of the image downward, 1250 is the central line count of the image (J^sub C^ = 1250), P is the scan angle between observation pixels, I is the column count counted from the left end of the image rightward, and 1145 is the central column count of the image (I^sub C^ = 1145). If there is no misalignment, the image center C is identical to O.
Multiply S with S^sub Y^, and assume that the earth disk center column count has been accurately measured on the image plane as shown in Fig. 4. Under this assumption, the pitch misalignment does not exist, I^sub C^ = I, zeta = 0;
S . S^sub Y^ = -sin[Q(J^sub C^ - J) + rho]. (4)
Angle Q(J^sub C^ - J) in Eq. (4) is expressed in Fig. 4 as theta. Considering -sin[Q(J^sub C^ - J) + rho] = cos[pi/2 + Q(J^sub C^ - J) + rho] and defining an angle phi = pi/2 + Q(J^sub C^ - J), (4) is written as
S^sub E^ . S^sub Y^ = cos(phi + rho). (5)
Equation (5) with 0 pitch misalignment was originally expressed by HP80.
The action of p misalignment in Eq. (4) is also illustrated in Fig. 5c. In Fig. 5c, rho is an angle from k^sub S^ turning to k^sub V^ around i^sub S^. If the 1250th scan cones toward the north (south) side of the actual scan plane, the roll misalignment is defined as positive (negative), and the earth's disk is in the south (north) side of the image. Since images are taken when the MCVISSR faces earth, the impact of roll misalignment on the imaging process does not experience diurnal variation.
Vector S is a known quantity, and should be expressed in an inertial coordinate system. Otherwise, the solution S^sub Y^ in Eqs. (4) or (5) cannot be achieved. The orientations of the satellite spin axis and earth rotation axis are only conservative in inertial coordinate systems. In this paper, the J2000 coordinate system (J2000) is adopted as the inertial coordinate system, as described in Harris et al. (1996).
d. Formulation for pitch misalignment
Pitch misalignment can be formulated with a similar approach. The observation vector is expressed as Eq. (1). Vector S^sub Y^ x S is perpendicular to either vector S^sub Y^ or S. If it is perpendicular to S^sub Y^, it is in the spin plane of the satellite; if it is perpendicular to S, then the angle between vectors S and S^sub Z^ is equivalent to the angle between vectors S^sub Y^ x S and S^sub X^:
Scalar quantity S^sub Y^ x S . S^sub X^ measures the angle between vectors S^sub Y^ x S and S^sub X^, which is equivalent to the angle between S and S^sub Z^. This scalar quantity is the cosine of the earth disk shifting angle in the east-west direction projected on the satellite spin plane due to misalignment:
In (7), Q(J^sub C^ - J), P(I - I^sub C^), rho, and zeta are all small quantities, and the double sine of any of them can be ignored. Equation (7) can then be written as
In Eq. (8), cos[Q(J^sub C^ - J) + p] is a projection factor from the scan line passing through the earth's center to the scan line on the spin plane. Both theta = Q(J^sub C^ - J) and rho are shown in Fig. 4. Equation (8) shows that if the earth's disk center is placed at the central column of the image, namely I = I^sub C^, the actual earth's disk center shifts in the east-west direction to cos(rho) cos(zeta), which is caused by zeta and rho. Here, cos(rho) is a projection factor. In Fig. 5d, zeta misalignment is schematically illustrated. For a spin geosynchronous meteorological satellite, zeta misalignment may be explained by inaccurate beta prediction. This will be further discussed in section 4.
The remaining misalignment component is yaw (eta). As shown in Fig. 5e, eta misalignment causes turning around k^sub S^. It does not have a major influence on image navigation. This may also be noticed in the spread expression of the observation vector in satellite coordinate system (1), in which eta does not exist.
4. Determination of the pointing of the satellite to earth
Spin geosynchronous meteorological satellites use the sun to control the pointing of the radiometer to earth, and to align scan lines together with the beta angle. Figure 6 is a scheme diagram of the beta angle geometric formulation. In Fig. 6a, S^sub Y^ is the spin axis of the satellite, S^sub Earth^ is the vector pointing from the satellite to the earth's center, and S^sub Sun^ is the vector pointing from the satellite to the sun. Here, we define the following three planes: the S plane consists of the spin axis and the sun, the E plane is defined by the spin axis and the earth, and the P plane passes through the satellite and is perpendicular to the satellite spin axis. Notice that S^sub Y^ x S^sub Sun^ and S^sub Y^ x S^sub Earth^ are perpendicular to the vectors S^sub Sun^ and S^sub Earth^ projected at the satellite spin plane, respectively. The beta angle can be written as
beta = cos^sup -1^[(S^sub Y^ x S^sub Sun^) . (S^sub Y^ x S^sub Earth^)]. (9)
Here, beta is a significant parameter for observation by spin- stabilized geosynchronous meteorological satellites. In Eq. (9), vectors S^sub Sun^ and S^sub Earth^ are related to satellite position and S^sub Y^ to attitude. When the satellite position and attitude are well predicted, beta can be calculated. The value thresholds of beta are from 2pi to 0. At a time near local midnight, when the sun, earth, and spin axis of the satellite share a common plane, beta is given a value of 2pi. The value of beta decreases monotonously until a time near the next local midnight when it approaches 0, as shown in Figs. 6b,c. With the addition of Eq. (9), the navigation model becomes complete, and a fully automatic solution of the equations is realized for FY2.
For FY2 meteorological satellites, the sun is sensed by a sun sensor installed on the side face of the satellite column body at an angle from the MCVISSR. Because of the deviation of the sun sensor from the MCVISSR (earth sensor), the alternation of the beta value thresholds appears around 0120 UTC for FY2C, rather than around the local midnight. For simplicity, this paper ignores this difference, assuming that the alternation of the beta value thresholds appears around local midnight.
To have an earth image fully viewed and well registered, the value of beta must be accurately predicted. If the value of beta is incorrect, then the earth's disk is shifted in an east-west direction, and if the trend of beta over time is deviated from the actual trend, the earth image is skewed. Figure 7 shows skew images caused by incorrect beta prediction. Figure 7a is a normal image with correct beta prediction; the image does not show any deformation. Figures 7b,c are the same images with positive and negative dbeta/dt biases added, which show tremendous image deformation although the absolute value of the added dbeta/dt is only 1.69596e-005. The FY2C image scan process is performed from north to south, with southern scan lines taken later. With a positive (negative) dbeta/dt bias added, the initiating point of resampling shifts westward (eastward) with time; this effect makes the earth's disk skew eastward (westward) toward the south in the image as shown in Fig. 7b (7c). Those phenomena are also explained in the bottom part of Fig. 1b.
5. Solution process of FY2 image navigation model
a. Implementation procedures for the solution of the FY2 image navigation model
Implementation procedures for the solution of the FY2 image navigation model are outlined in Fig. 8. The two basic image navigation equations are (4) and (9), expressed in sections 3 and 4, respectively. Equation (4) is used for diagnosis of attitude and roll misalignment in the previous day. Equation (9) is used for prediction of the beta angle on the subsequent day. The solution to Eq. (4) and prediction with Eq. (9) are performed once a day around the time when the beta angle approaches the minimum. The predicted parameters are used on the successive day for image acquisition and registration. For Eq. (4), S and Q(J^sub C^ - J) are known quantities. Those quantities are sampled for each full disk image from the previous day. Normally, FY2 satellites take 28 full disk images in a day, 24 hourly plus 4 extra images for atmospheric motion vector derivation. Three ranging stations at Beijing, Urumqi, and Melbourne measure the distances from the stations to the satellite 8 times a day. With distance data, orbital parameters are diagnosed and future satellite positions are predicted. Considering the asymmetric mass distribution of earth, solar radiation pressure, and the gravitational effects of the sun and moon, the accuracy of satellite position diagnosis and prediction is less than 100 m. With satellite position prediction, S is obtained, and it is expressed in J2000. The earth's center line count (J) is measured by an earth edge detection procedure that will be further explained in section 5b. Both S^sub Y^ and rho are well-conserved quantities, so the mean values from the previous day may be used directly in the successive day as prediction values.
While Eq. (4) is solved with observation data from the previous day as known quantities, Eq. (9) is solved with prediction data from the successive day as known quantities. Of the known quantities for Eq. (9), S^sub Y^ is obtained from Eq. (4), while vectors S^sub Sun^ and S^sub Earth^ are determined by the position predictions of the sun, earth, and satellite for the successive day. Sun position is based on Jet Propulsion Laboratory (JPL) planetary and lunar ephemerides DE200, downloaded from their Web site (http:// ssd.jpl.nasa.gov/?planet_eph_export). Predictions of the beta angle at 5-min intervals are transmitted to the Beijing ground station of FY2 and stored in the computer of the Image Acquisition System (IAS), where they are interpolated and used in the resampling of individual scan lines to assemble images.
Normally, for individual observations in a day, the actual column counts deviate from the prediction by a magnitude of less than 1 IR pixel. To further reduce the bias of actual column counts from predicted values, compensation is made in the image registration processing stage based on historical statistics for the time of the day. As a result, the earth disk center column count bias is further reduced and the deformation of the image is minimized. This compensation is performed before the stretched data are broadcasted. In the document block of the FY2 data stream, zeta is hidden and given a value of 0.
After navigation parameters are derived, the algorithm presented by Kigawa (1991) is used to transfer observation pixel counts to latitude-longitude positions. Parameters used by Kigawa are in earth- fixed coordinates, so before using those programs, coordinates must be transferred from inertial to earth fixed.
b. Earth edge detection procedure
The earth disk center line count J is a key element for the solution of Eq. (4) and J is acquired automatically by an earth edge detection procedure. Full disk images of the IR channel are used to detect the earth's edge with the dynamic threshold method, and then to obtain the earth's center line and column counts. It is difficult to find a unique threshold in an image to distinguish earth from outer space, since there are clouds inside the earth's disk and scatter radiation outside the earth's disk. Because of scatter radiation, radiance measurements in some places out of earth's disk are even higher than inside the earth's disk where dense cumulonimbus (Cb) clouds exist. Fortunately for FY2 satellites, high and dense Cb clouds are normally at equatorial latitudes, while relatively high scatter radiance is mainly distributed to the northwest of the earth's disk. Thus, FY2 images are divided into five zones: arctic, midlatitudes of the Northern Hemisphere, equatorial latitudes, and midlatitudes of the Southern Hemisphere and Antarctic. For each zone, thresholds to distinguish earth and outer space on the images are separately obtained by statistics. Earth's edges along the scan lines are detected with dynamic thresholds in different zones.
Midpoints are obtained between the two earth edges in the vertical and horizontal directions of the image. Two linear equations are derived to simulate these midpoints, and individual midpoints are eliminated that deviate from the simulations by more than 0.5 pixels. The cross point of the two simulation equations is assigned as the earth's disk center, and the line and column counts of the earth's disk center are then obtained. After quality control, the simulation equation in the vertical direction contains more samples than in the horizontal direction. Hence, the accuracy of the vertical simulation is better than the horizontal, which results in the earth disk center column count being of better quality than the line counts.
The line counts of the earth's disk center throughout a day are simulated again with a sinusoidal function as expressed in section 3a and Fig. 3. Individual earth disk observations where the actual central line count deviates from the simulation by more than 0.5 pixels are eliminated. The earth disk center line counts that pass quality control are added to the solution of the image navigation Eqs. (4). Normally, out of 28 earth disk observations on a given day, 25 may pass quality control.
c. Compensation of the earth disk center column count
FY2 beta angle prediction performance is acceptable, with accuracy within less than one IR pixel. Scan lines in the observation images are aligned based on the accurate sun pulse time recovered at the ground segment and the beta angle prediction, as described in section 2a. For individual scan lines, and also for the entire earth's disks, central column counts of earth's disk centers in the images are expected at 1145. Figure 9 shows a time series of the actual earth disk center column counts in FY2C images, where Fig. 9a represents 7 and 8 June 2006, and Fig. 9b represents the whole month of June 2006. In Fig. 9, the ordinale is time (units: UTC hours for Fig. 9a, days for Fig. 9b) downward positive, and the abscissa is the actual earth disk center column count. The scale of the abscissa is 0.1 IR pixels, and all earth disk center column counts in Fig. 9a are within 1 IR pixel, from 1136 to 1136.8.
The difference of the actual earth disk center column count from expected values may be expressed as pitch (zeta) misalignment, as described in section 3d. Pitch misalignment may actually be due to inaccurate positioning of sun and earth sensors on the satellite, difference of the principal axis from the actual spin axis of the satellite, or errors in beta angle prediction. It is expected that the long time mean value of the differences is due to the former two factors, and the diurnal variation is due to the latter one.
For the FY2C meteorological satellite, image observation parameters are predicted once every 24 h at 0120 UTC and used for the successive 24 h. In Fig. 9a, from 0200 to 1400 UTC, the early half-day of the parameter prediction period, the earth disk center column counts are around 1136.1 or 1136.2 pixels with only small deviations. From 1500 to 0100 UTC, the later half-day of the parameter prediction period, the earth disk center column counts deviate more, from 1136.1 to 1136.8 pixels. Figure 9b shows data for the whole month of June 2006. The time series of the column counts have the same diurnal variation pattern as seen over the whole month. It is expected that the earth disk center column count deviation is mainly caused by incorrect a angle prediction, which is due to inaccurate satellite position prediction. For the later half- day of the parameter prediction period, the actual satellite position deviates more from the predicted position, thus the earth's disk deviates more in the east-west direction in the image.
Although the earth disk center column count predictions are all within one IR pixel, attempts are still made to reduce the error by compensation with a previous mean bias for the time of day. The compensations are performed automatically in the image registration stage of the data processing while individual scan lines are resampled.
d. Influence of ground segment performance and maneuvers to image navigation and the solution
Since the solution of the FY2 image navigation model uses orbital and attitudinal parameters from the previous day, stable operation of the whole satellite system is essential for high-quality image navigation. In the early stages of FY2 operation, poor image navigation appeared very frequently because of a variety of difficulties in the ground segment. Many cases of inaccurate image navigation were caused by inappropriate operation on the previous day, such as straight shooting sunlight, ranging failure, bad image quality, database trouble, etc. The operation quality has been improved by making every effort to diagnose and isolate the problems, find the reasons causing them, eliminate the trouble, and deduce similar troubles.
On the other hand, the satellite needs to make maneuver operations after some period of time. After these operations, the orbital and attitude parameters change, and it takes about 24-36 h to acquire the new values. During this short period, image navigation quality unavoidably degrades. The following measures have been adopted to reduce the extent of the degradation:
1) For FY2, the subsatellite position should be maintained around its nominal +-0.5[degrees]; spin axis orientation should be maintained +-0.5[degrees] around the negative perpendicular to the satellite orbital plane. If it is expected that one of the orbital or attitude parameters will not be exceeded prior to the next maneuver, then this parameter does not have to be adjusted in the present maneuver operation. 2) In the case that only orbital parameters are adjusted, the original orbital parameters are used until 12 h after the maneuver operation; 12 h later, orbital parameters are calculated repeatedly, and new orbital parameters are compared with the previous ones to enable a choice. Since the attitude parameters are not adjusted, they remain applicable after the maneuver operation.
3) In the case that only attitude parameters are adjusted, the objective attitude parameters are used until 18 h after the maneuver operation; 18 h later, attitude parameters are calculated repeatedly and new attitude parameters are compared with the previous ones to enable a decision. Since orbital parameters are not adjusted, they remain applicable after the maneuver operation.
4) In the case that both orbital and attitude parameters are adjusted, objective orbital and attitude parameters are used; 12 (18) hours later, orbital (attitude) parameters are calculated repeatedly and new parameters are compared with the previous ones to enable a decision.
5) From 24 to 36 h after the maneuver operation, the navigation processing procedure recovers. Up to 24-36 h after maneuver operations, a manual image navigation operation is performed to reduce the extent of quality degradation.
6) To reduce the maneuver operation frequency, overadjustments to orbital and attitude parameters in maneuver operations are usually adopted.
6. Image navigation results
This algorithm was put into operation in January 2001 and has run for more than 6 yr. Over this time, the algorithm, software, and hardware have been developed to fit with each other. As a result, FY2 image navigation performance has improved in both stability and accuracy. In this section, the FY2C image navigation parameters in June 2006 are shown along with sample images overlaid with coastlines and other geographical symbols to illustrate the results of these solutions. The FY2C attitude and misalignment parameters listed in section 3b, except for the inactive eta misalignment, are given for the whole month of June 2006 along with the relevant statistics. All actual parameters in this paper were obtained during the real-time operation of FY2 satellites, and no alterations were made to the data for publication.
Figure 10 shows components of the spin axis on J2000 in June 2006 in order to represent attitude parameters. Figure 10 shows three components of directional cosine on the ordinale versus the date on the abscissa. Figure 11 shows the trajectory of the FY2C spin axis projected in the O-X-Y plane of J2000 in June 2006. The spin axis projection trajectory drawn in Fig. 11 shows the daily mean values, calculated hourly. The date is labeled at the two ends of the trajectory. FY2 is a spin-stabilized satellite, and because of the moment of force caused by sunlight, the spin axis of the satellite experiences precession and mutation, which are clearly shown in Fig. 11.
Figure 12 shows a time series of the earth disk center bias of FY2C in June 2006 caused by the related misalignment components. Figures 12a,b show the northsouth and east-west biases caused by roll and pitch misalignments, respectively. The ordinale of Fig. 12 shows the unit IR pixels and microradians. For IR channels of the FY2 meteorological satellite, a one-pixel bias on the image is associated with a 140-[mu]radian misalignment angle. In principle, misalignment parameters should remain unchanged between the two maneuver operations, as stated in section 3c. Actually, misalignment parameters absorb any deficiencies in the navigation model and may change with time. Time series of the misalignment parameters and the associated earth disk center position throughout the day appear in specific patterns. Figure 9a shows the time series of the earth disk center column count on two successive days. The east-west shifts of the earth disk center column count are mainly caused by inaccurate beta angle prediction explained as pitch misalignment. Before real- time images are broadcasted, misalignments are compensated during image registration based on the historical statistics.
Figure 13 shows a histogram of the earth disk center bias (deviation of forecasted values from the diagnosed values) in June 2006. Seven-hundred and ninety samples were involved in this statistical analysis. Figure 13a shows the bias in the north-south direction alone. The mean bias and standard deviation of the earth disk center line counts in June 2006 were 0.016 and 0.410, respectively. Figure 13b shows the east-west direction alone. The mean bias and standard deviation of the earth disk center column counts in June 2006 are 0.002 and 0.201 pixels, respectively. These statistics show that FY2C image navigation accuracy reaches 1 IR pixel (5 km) at subsatellite point (SSP).
Histogram statistics in Fig. 13 show that image navigation quality is worse in the north-south direction than in the east-west direction. This is mainly due to the following:
1) The known quantities input into the image navigation model are distributed over a 24-h period. Thus, attitude and rho-misalignment parameters obtained by the solution of the image navigation model are 24-h mean values. For the spin satellite, while there is a minor change in attitude over time, it is well maintained over a time period of 1-2 days. As a result of the pressure of sunlight on the satellite, which is not restricted to the center of mass of the satellite, the spin axis experiences precession and nutation (Sorensen 1997). Therefore, the instantaneous attitude deviates somewhat from the mean, which is the major source of error.
2) As illustrated in section 5b, the earth disk center line count is less accurate compared to the column.
3) Earth is surrounded by atmosphere. High-latitude atmosphere is thinner in the winter hemisphere than in the summer. Thus, the earth disk center obtained by edge detections involves the effect of atmospheric thickness, and tends to deflect toward the summer hemisphere side. During the spring or autumn, this deflection changes relatively faster with time, requiring adjustments in the north-south direction.
Figure 14 shows observation images overlaid with latitude- longitude grids, coastlines, and other geographical symbols. The images in Fig. 14 are all visible images at 0456 UTC 8 June 2006 from FY2C. The resolution for the visible channel is 4 times better than the IR channel. Coastlines overlaid on the images are predicted ones. Figure 14a is a full disk image, while the other images are local section images with raw visible resolution. To show detail, the image pixel size in the local section images is zoomed to 10 times larger than the geographical symbol size. These images clearly show a good overlap between images and grids.
7. Summary discussion and algorithm features
This paper introduces the image navigation algorithm for FY2 meteorological satellites. The major features of the algorithm include the geometric formulas for calculation of the beta angle, the adoption of earth center line counts as one of the known quantities, the adoption of J2000 as the inertial coordinate system, compensations with historical error statistics, and the stable operation of the system.
For spin-stabilized satellites like FY2, the pointing of the satellite toward earth relies heavily on the beta angle. During the observation process, the beta angle is used not only to make the radiometer open together with the sun pulse, but also to align the scan lines. Accurate beta angle prediction helps not only in determining the earth disk center column counts in the east-west direction, but also in reducing image deformation. FY2 accurately calculates and predicts the beta angles with a geometric formulation, which is an important feature of the algorithm.
In the north-south direction, earth disk center line counts are used as one of the known input qualities of HP80's formulation to measure the angles between the spin axis and observation vectors, and are sampled once an hour. Considering the revolution of satellites around the earth, the known quantities are homogenously distributed in space. With a dynamic earth edge detection procedure, the earth disk center line counts can be accurately calculated. The good performance of the navigation model solution is also due to the input of known qualities with homogenous distribution and high quality. The adoption of the earth disk center line counts as one of the input quantities allows for this high level of success.
In the earth-fixed coordinate systems, attitude parameters are not conserved over time. Therefore, image navigation equations must be solved in inertial coordination systems. The adoption of J2000 as an inertial coordinate system ensures the stable solution of the navigation equations. All coordinate conversions are carefully programmed to ensure their accuracy.
In this algorithm, the east-west biases of the earth disk center column count are compensated for during the image registration stage based on historical statistics. This measure further improves image navigation in the east-west direction.
Since observation parameters from the previous day are used to derive parameters to control observations on the successive day, the stable operation of the entire satellite system is essential for high-quality image navigation. Thus, every effort has been made to improve operation stability, and as a result, FY2 has achieved a 5- km-level image at SSP.
Acknowledgments. This research was supported by Grant 40275007 from the National Natural Science Foundation of China and Grant 863- 2003AA133050 from the Ministry of Science and Technology of China.
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Department of Atmospheric Science, School of Physics, Peking University, and National Satellite Meteorological Center,
China Meteorological Administration, Beijing, China
XIAOHU ZHANG AND JIANMIN Xu
National Satellite Meteorological Center, China Meteorological Administration, Beijing, China
(Manuscript received 5 January 2007, in final form 4 December 2007)
Corresponding author address: Jianmin Xu, No. 46, Zhong Guan Cun South Street, Beijing 100081, China.
E-mail: [email protected]
Copyright American Meteorological Society Jul 2008
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