Image Navigation for the FY2 Geosynchronous Meteorological

Image Navigation for the FY2 Geosynchronous Meteorological Satellite

FENG LU

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)

ABSTRACT

An automatic image navigation algorithm for Feng Yun 2 (FY2) spin-stabilized geosynchronous meteo-rological satellites was determined at the National Satellite Meteorological Center (NSMC) of the ChinaMeteorological Administration (CMA). This paper derives the parameters and coordinate systems used inFY2 image navigation, with an emphasis on attitude and misalignment parameters. The solution to thenavigation 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 diskcontains information on the two components of the attitude (orientation of the satellite spin axis) and theroll component of the misalignment. With this information, the two attitude components can be solvedsimultaneously, expressed as declination and right ascension (with diurnal variation in the fixed earthcoordinate 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 toalign earth observation pixels in the scan line together with an angle subtended at the satellite by the sunand earth (�). With satellite position and attitude known, the � angle can be calculated and predicted withsufficient accuracy. Next, the image is assembled. Prediction of the � angle takes an important role in theimage formation process, as imperfect � 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 compen-sated for.

The above-mentioned solution to the navigation model requires accurate knowledge of astronomicalparameters and coordinate systems. The orbital, attitude, misalignment, and � angle parameters are pro-duced automatically and routinely without any manual operation. Image navigation accuracy for the FY2geosynchronous meteorological satellite approaches 5 km at the subsatellite point (SSP).

1. Introduction

Image navigation is an essential and fundamentalcomponent in data processing of geosynchronous me-teorological satellites. Currently, image animation isbroadly used in daily weather forecasts and public ser-vices. Smooth animation is meaningful not only forforecasters to diagnose the weather, but also for thepublic to understand weather systems. Image naviga-tion performance affects all services provided by geo-synchronous meteorological satellites, including theirdata and products. Small errors in navigational param-

eters may cause significant shifts in image animation.Products derived with a series of images such as atmo-spheric motion vector and cloud classification are espe-cially sensitive to image navigation accuracy. Further-more, navigation parameters of geosynchronous me-teorological satellites need to be predicted beforeobservation is performed, since those parameters areused to supervise the observation process. High-accuracy image navigation parameters are essential forsmooth operation of the whole satellite system. In sum-mary, stable and accurate image navigation is one of themost important quality indicators for geosynchronousmeteorological satellites.

The geosynchronous satellite observes the earth pixelby pixel. The observation pixels are pieced together toform images. Based on the definition by Kamel (1996),

Corresponding author address: Jianmin Xu, No. 46, ZhongGuan Cun South Street, Beijing 100081, China.E-mail: [email protected]

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DOI: 10.1175/2007JTECHA964.1

© 2008 American Meteorological Society

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image registration refers to the process of keeping anypixel within an image pointed to its nominal1 earth lo-cation within a specified accuracy; image navigation isthe process of determining the location of any pixelwithin an image in terms of earth latitude and longi-tude. Therefore, image registration is a measure ofpointing stability, while image navigation is a measureof absolute pointing accuracy. Since it is impossible tocompletely separate the image registration and naviga-tion processes, this paper also refers to the related im-age registration process.

In the past, various efforts have been made to findmathematical solutions to the image navigation of spin-stabilized geosynchronous meteorological satellites.Those efforts include the establishment of basic math-ematical formulas, the determination of the directionthe satellite is pointing relative to the earth, and theimprovement of image grids.

Hambrick and Phillips (1980, hereafter HP80) de-rived a general solution of image navigation based onmathematical formulations where they defined attitudeand misalignment parameters. Observation pointingvectors as known quantities are used to determine theattitude and roll misalignment parameters. Thus, theobservation pixel positions can then be transferredfrom image (line–element) coordinates into geometric(latitude–longitude) coordinates. HP80 did put forwarda succinct and effective mathematical solution to geo-synchronous meteorological satellite image navigation,resulting in a classical study of image navigation of geo-synchronous meteorological satellites.

The pointing of the satellite toward earth is essentialfor remote earth sensing. For spin-stabilized geosyn-chronous meteorological satellites, the pointing ismaintained by the opening time of the radiometer dur-ing a spin cycle. During each spin cycle, the satelliteviews both the sun and earth. Since the sun sensor pro-vides a highly accurate sun position, it is used alongwith the angle between the sun and earth (�) to controlthe opening time of the radiometer. Knowledge of the� angle is important during the image assembly process.The Man Computer Interactive Data Access System(McIDAS) navigation manual of the Space Science andEngineering Center (SSEC) put forward an algorithmto calculate the � angle based on statistics (Space Sci-ence and Engineering Center 1986). Landmark columncount locations at different times are used to make thestatistical calculations and corrections.

Although geosynchronous meteorological satellitesare expected to be stationary relative to earth, in real-ity, their positions keeps changing; this in turn causeschanges in the captured images. There are two majormethods for image grids to refer to political and geo-graphic boundaries: to match grids for individual ob-servations accurately, or to provide images with nomi-nal image grids. Kigawa (1991) provided a good way tomatch grids to individual observations. He presentedprograms for Geostationary Meteorological Satellite(GMS) images to transfer observed pixel positions be-tween image (line–element) coordinates and geometric(latitude–longitude) coordinates. When navigation pa-rameters are accurately derived, these programs per-form accurately. Also, the near-real-time rectificationand dissemination process is used for Meteosat satel-lites from the European Organisation for the Exploita-tion of Meteorological Satellites (EUMETSAT; Adam-son et al. 1988; Agrotis 1988; Doolittle et al. 1973; Wolff1985). Rectification and dissemination starts immedi-ately after the beginning of image acquisition. By mea-suring raw observation images, navigation parametersand the deformation matrix are determined. Remap-ping is then performed, and nominal images are ob-tained (Bos et al. 1990).

Because of a variety of reasons, users of geosynchro-nous meteorological satellites are puzzled by imagenavigation errors shown as imperfect matches betweenimages and grids, or as shifts in image animation. At theinitial stage of Feng Yun 2 (FY2) operation—FY2 is theChinese series of geosynchronous meteorological satel-lites—those errors have negatively affected its applica-tion. This paper thoroughly reviews the algorithm usedand the data produced by the satellite. Two main areaswith the potential to improve image navigation includethe mathematical formulation solution and the processof pointing the satellite toward the earth.

Over the past 2 decades, our knowledge and abilityto obtain mathematical solutions in astronomical sur-veying has greatly improved, and new and more accu-rate standards for time and coordinate systems havebeen issued. With this improved knowledge and stan-dards, coordinate systems are better defined. Carefulanalysis of the behavior of FY2 raw image animationshas indicated that the time series of observation vectorspointing to the earth disk center can be used as repre-sentative input parameters for the solution of naviga-tional equations (Xu et al. 2002). This approach is suc-cessful in practice for FY2, where image navigation inthe south–north direction has been improved.

Determination of the direction from the satellite toearth’s center is the key for geosynchronous meteoro-

1 For FY2, since images are assembled with the satellite at itsviewing location, the word nominal in this sentence is not appli-cable.

1150 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 25


logical satellite remote sensing. In FY2 observation, thegeometric formulation solution of the � angle is de-rived. Important � angle parameters that previouslyhad to be obtained by statistics can now be accuratelycalculated. With the geometric formulation solution ofthe � angle, the accuracy of determining the directionfrom the satellite to earth is greatly improved. After thepointing direction has been calculated accurately, smallshifts in the east–west direction are further analyzed.The irregular bias of the actual earth disk center col-umn count from predictions may be explained by inac-curate satellite position prediction, and be compen-sated for as pitch misalignment in the navigation for-mulation.

This paper introduces the improvements realized atthe National Satellite Meteorological Center (NSMC)that result in a fully automatic image navigation proce-dure for FY2. The structure of this paper is as follows:after the introduction, section 2 briefly introduces theobservation procedure of the FY2 meteorological sat-ellite, with particular attention to the software ap-proach to image registration. Section 3 examines thetime series of the earth disk center line count, its rela-tionship with the basic image navigation formulation,and its use as a known quality of the formulation. Sec-tion 4 describes formulation in the east–west directionand the related image registration components. Geo-metric formulation of the � angle is discussed with theassociated column count and deformation of the image.Section 5 illustrates the solution process of the formu-lations, and section 6 shows the navigation results alongwith the actual parameters calculated in June 2006. Sec-tion 7 is a summary discussion of algorithm perfor-mance and characteristics. Actual data from the FY2Coperation show high-quality image navigation for FY2meteorological satellites.

2. Image registration procedure of FY2meteorological satellites

Until now, four FY2 satellites have been launched,termed FY2A, B, C, and D. At present, FY2C andFY2D are both in operation, located at 105° and 86.5°E,respectively. The expected lifetime for FY2 satellites is3 yr. After FY2D, four more FY2 satellites are plannedin order to continue these services up to the year 2015.The FY2 satellites are spin stabilized, and the primaryobservational instrument of FY2 satellites is a Multi-channel Visible and Infrared Spin Scan Radiometer(MCVISSR) with one visible (VIS) channel and fourinfrared (IR) channels. Specifications of FY2 satellitesand MCVISSR have been previously described (Na-tional Satellite Meteorological Center 2004, 2006).

a. Image registration procedure of FY2 satellites

FY2 meteorological satellites acquire observationimages through cooperative work of space and groundsegments. The coherent observation technique was firstdeveloped and used in the U.S. Geostationary Opera-tional 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 tothe compensation jobs in image registration, and is veryhelpful in improving image navigation quality.

Figure 1 explains how individual scan lines are reg-istered with software at ground segments to form im-ages. Figure 1a is a diagram of the spin plane of thesatellite, while Fig. 1b illustrates the process of the reg-istration of individual scan lines. The upper part of Fig.1b hints that in each spin cycle the satellite views thesun and earth as expressed in Fig. 1a; earth and sunacquisition time as well as observation data are trans-mitted to the ground segment. The middle part of Fig.1b shows how the ground segment recovers a precisesun pulse. The bottom part of Fig. 1b shows that withaccurate sun pulse measurements and knowledge of �,the individual scan lines can be aligned.

To observe earth, it is essential to maintain the point-ing direction of the radiometer toward earth. For spingeosynchronous satellites, this is performed by control-ling the opening time of the radiometer. In geosynchro-nous orbit, the viewing angle of the earth’s disk is ap-proximately 17.4° � 17.4°, so the observation scope isdesigned as 20° � 20°. While the satellite spins andfaces earth, the MCVISSR opens. The raw data gainedare sent in real time to a ground segment where theyare pieced together to form images. The image signal isstretched to the remaining 340°, where MCVISSR facesspace, and relayed to the utilization stations in anothercycle. Figure 1a expresses this process. After a scan lineis obtained in a cycle, MCVISSR moves one step down-ward and prepares for the next scan cycle. The obser-vation process for a full disk image takes 25 min and iscomposed of 2500 scan cycles.

The MCVISSR opens while the MCVISSR faces theearth. This process is controlled by a clock on board thesatellite. To compensate for the revolution of the sat-ellite around earth, after a number (70.4) of cycles, theopening of the MCVISSR comes forward for a shorttime period (292.57 �s; see the upper part of Fig. 1b).This measure ensures that the earth’s disk is fullyviewed on each scan line each day, and also helps toinform the ground segment of the MCVISSR openingtime on the satellite. Based on this time, individual scanlines are aligned to form images. The transmission of

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this time from satellite to ground is jointly realized bytwo data channels.

Accurate transmission of the MCVISSR openingtime to the ground segment is the key for image regis-tration. The MCVISSR opening time is controlledby a sun sensor installed on the side face of the satel-lite column. When the sun sensor senses the sun, asun pulse signal is triggered with an accuracy of 0.2-

�rad, equivalent to 0.1 visible pixels. The sun pulseshould be transmitted to the ground segment with suf-ficient accuracy for image registration. A double chan-nel transmission is designed. The sun pulse received atthe ground segment in the narrowband channel is notsufficiently accurate for imaging, and the wide bandMCVISSR data channel helps to accurately recoverthe sun pulse at the ground segment. As mentioned

FIG. 1. The process of registering individual scan lines with the software. (a) The spin plane of the satellite. (b) The process ofaligning individual scan lines in ground segments to form images.



previously, the MCVISSR only opens at one of thediscrete instants after the sun pulse arrives. By overlayof the narrowband sun pulse with a series of discretemoments (integer times of 292.57 �s) ahead of theMCVISSR opening time, a high-accuracy sun pulse isrecovered at the ground segment (see middle part ofFig. 1b).

Based on an accurate sun position and � angle pre-diction, individual scan lines are aligned, resampled,and registered at the ground segment, and observationimages are assembled (see the bottom part of Fig. 1b).The accurate prediction of � is a precondition of imageregistration. The influence of the � angle on image reg-istration and navigation will be further described in sec-tions 4 and 5.

b. Influence of spin variation and eclipse

The scan process moves the scan mirror within thesatellite, hence changing the mass distribution withinthe rotating body, which has a significant impact on thespin period. The result is that the top or bottom parts ofimages are scanned under faster spin rates, while themiddle part is scanned slower. MCVISSR samples allscan lines at an identical time interval. In ground seg-ments, raw observation oversampled with identicaltime intervals is converted into identical angular inter-vals, removing the impact of spin rate change. Spin pe-riods are gained based on differences between the ar-rival times of successive scan lines.

During spring and autumn eclipse periods, theearth’s shadow falls on the satellite around midnight.The longest duration of the earth’s shadow may last for72 min. In the earth’s shadow, the satellite cools down,the spin rate increases, and the sun sail is unable toobtain energy. Thus, image acquisitions are suspendedduring this period, and they are restarted about 1 hafter the satellite steps out of the earth’s shadow, atwhich 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, theearth’s disk location passes through a diurnal cycle.This phenomenon is schematically illustrated in Fig. 2,which presents FY2 observation geometry. In an idealsituation, the spin axis of the satellite should be parallelto the earth’s axis of rotation. In practice, this ideal isnot achieved. As shown in Fig. 2, at 0600 (1800) UTC,the satellite looks up (down) at earth, and the earth’sdisk is in the downward (upward) side of the image.Around these two moments, the earth’s disk center isdisplaced mostly in the north–south direction on the

images, and the images experience only a small amountof turning in a day. At 0000 (1200) UTC, the earth’sdisk is minimally displaced, but the scan lines deflectthe greatest amount, and the turnings of the imagesbecome the largest in a single day. At 0000 (1200) UTC,the satellite views earth with its spin axis turning clock-wise (anticlockwise), while the image turns anticlock-wise (clockwise). The phenomena described above re-flect the impact of the satellite attitude on the imagingprocess, and can be detected easily by image animation.When the image origins are placed at the first line andcolumn of the image animation, the earth’s disk shifts inthe north–south direction one cycle each day. When theimage origins are placed at the earth disk center andmade into an image animation, the earth’s disk swingsclockwise and anticlockwise one cycle each day.

To express the phenomena mentioned above, a timeseries of earth disk center line counts (namely, thenorth–south movement of the earth’s disk in the image)on 7–9 June 2006 is shown in Fig. 3. The movementappears as a simple sinusoidal function with a cycle of366.25/365.25 days. In Fig. 3b, the sinusoidal function issimulated 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 extensionpart of the sinusoidal curve shows that the earth diskcenter line count is predictable. The formulation to de-scribe the above-mentioned phenomena will follow, butthe parameters and coordinate systems necessary forthe formulation are first described.

b. Navigation parameters and coordinate systems

HP80 mentioned 13 parameters to describe geomet-ric orbit and attitude for spin geosynchronous meteo-

FIG. 2. FY2 observation geometry. Here, N is the Arctic, E isthe earth’s center, and S is the Antarctic. The line linking theArctic and Antarctic is the earth’s rotation axis. The spin axis ofthe satellite is also shown.

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rological satellites: 6 orbital parameters [Montenbruckand Gill (2000)]; inclination, right ascension of the as-cending node, semimajor axis, eccentricity, argument ofperigee, mean anomaly at epoch), 3 attitude parameters(declination and right ascension of the spin axis, spinangular velocity), 3 misalignment parameters (roll,pitch, yaw), and 1 � angle parameter.

Table 1 defines the satellite and MCVISSR coordi-nate systems for FY2 satellites, and vectors related todefining the satellite coordinate system (SX, SY, SZ) arealso expressed in Fig. 4. The unit vectors (iS, jS, kS) of(SX, SY, SZ) define the satellite coordinate system. Fig-ure 5 illustrates misalignment. Figure 5a shows the dif-ference of actual MCVISSR assembling status from theideal. In manufacturing, the principle axis of the satel-lite column body should be the free axis with the maxi-mum spin angular momentum, and the 1250th scan lineof the MCVISSR should scan out a plane. In practice,this ideal status is seldom satisfied. Because of misalign-ment, the 1250th line normally scans out a cone, asshown in Fig. 5b. Misalignment is very small in magni-tude, but due to the distance of the satellite from earth,the misalignment has a significant impact on imagenavigation. Figure 3a shows that the central line of the

sinusoidal function is at 1245.2, which is somewhat de-viated from the image center at 1250. This is due to theeffect of misalignment. In HP80, the definition of atti-tude and misalignment components was not nominal,but this paper adopts nominal expression. Table 2shows the differences in the expressions for attitudeand misalignment components between Hambrick’sand nominal expressions.

c. Formulation for spin axis orientation and rollmisalignment

Observation vectors can be measured on the obser-vation images (see Fig. 4). The observation vector (thevector from the satellite toward the observation objec-tive) in the satellite coordinate systems can be mea-sured as

S � �SX

SY

SZ

� � RM�0

0

1� . �1�

In (1), R and M are observation and misalignment ma-trices, respectively (HP80):

R � �1 0 0

0 cosQ�JC � J � � sinQ�JC � J �

0 sinQ�JC � J � cosQ�JC � J ��

cosP�I � IC� 0 � sinP�I � IC�

0 1 0

sinP�I � IC� 0 cosP�I � IC�� 2�

M � �1 0 0

0 cos� � sin�

0 sin� cos��

cos� 0 � sin�

0 1 0

sin� 0 cos��

cos� � sin� 0

sin� cos� 0

0 0 1� . �3�

FIG. 3. (a) Time series of the earth disk center line count from 7–8 Jun 2006. (b) Simulation and extension from7–9 Jun 2006 of the earth disk center line count. The ordinate is the earth disk center line count (increasingdownward); the abscissa is the time in unit hours (UTC) or days. Black dots represent the previous earth diskcenter line counts for 7–8 Jun 2006 on which the simulation and extension are based; the curve is the simulationand extension of earth disk center line counts; the hollow dots are future observations of earth disk center linecounts for 9 Jun 2006, which are independent from the extension part of the curve.



In (2), Q is the step angle between observation lines, Jis the line count counted from the top end of the imagedownward, 1250 is the central line count of the image(J

C� 1250), P is the scan angle between observation

pixels, I is the column count counted from the left endof the image rightward, and 1145 is the central columncount of the image (IC � 1145). If there is no misalign-ment, the image center C is identical to O.

Multiply S with SY, and assume that the earth diskcenter column count has been accurately measuredon the image plane as shown in Fig. 4. Under this as-sumption, the pitch misalignment does not exist, IC � I,� � 0;

S � SY � �sinQ�JC � J� ��. �4�

Angle Q(JC � J) in Eq. (4) is expressed in Fig. 4 as

�. Considering �sin[Q(JC

� J) ] � cos[� /2 Q(JC

� J) ] and defining an angle � � �/2 Q(JC � J),(4) is written as

SE � SY � cos�� . �5�

Equation (5) with 0 pitch misalignment was originallyexpressed by HP80.

The action of misalignment in Eq. (4) is also illus-trated in Fig. 5c. In Fig. 5c, is an angle from kS turningto kV around iS. If the 1250th scan cones toward thenorth (south) side of the actual scan plane, the rollmisalignment is defined as positive (negative), and theearth’s disk is in the south (north) side of the image.Since images are taken when the MCVISSR facesearth, the impact of roll misalignment on the imagingprocess does not experience diurnal variation.

FIG. 4. The satellite coordinate system (after HP80). Here, E is the earth center and S is the satellite;SY� is along the spin axis of the satellite, and the SZX plane is the spin plane of the satellite. Earth centerE and the satellite spin axis make up the SYE plane. The SYE plane crosses the satellite spin plane(SZX) to form the axis. Normally, the axis does not extend toward the earth center; it is in the planedefined by the earth center and the satellite spin axis SY

�. The SX� axis is defined by SY

� � SZ� � SX

� . Takea point O along the line extended from the vector SZ

�. Make a plane IMAGE O, which is perpendicularto SZ�. Earth is projected on the IMAGE plane to form the observation image. On the projected plane

IMAGE, the earth center E is at F. The 1250 scan line crosses the central column of the plane IMAGEat C, which is the center of the observation image.

TABLE 1. Definition of FY2 satellite and MCVISSR coordinate systems. Definitions of the unit vectors of the coordinate systemsand the converse matrices are also explained in section 3c and in Figs. 4 and 5.

Coordinates Vector expression ModulusUnit vectors in thecoordinate system

MCVISSR coordinate system

V � �VX

VY

VZ� � R�

0

0

1�

|V| � �|VX| 2 |VY| 2 |VZ| 2 �iV �VX

|V| , jV �VY

|V| , kV �VZ

|V| �

Satellite coordinate system

S � �SX

SY

SZ� � RM�

0

0

1�

|S| � �|SX| 2 |SY| 2 |SZ| 2 �iS �SX

|S| , jS �SY

|S| , kS �SZ

|S| �

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Vector S is a known quantity, and should be ex-pressed in an inertial coordinate system. Otherwise, thesolution SY in Eqs. (4) or (5) cannot be achieved. Theorientations of the satellite spin axis and earth rotationaxis are only conservative in inertial coordinate sys-tems. In this paper, the J2000 coordinate system (J2000)is adopted as the inertial coordinate system, as de-scribed in Harris et al. (1996).

d. Formulation for pitch misalignmentPitch misalignment can be formulated with a similar

approach. The observation vector is expressed as Eq.(1). Vector SY � S is perpendicular to either vector SY

or S. If it is perpendicular to SY, it is in the spin planeof the satellite; if it is perpendicular to S, then the anglebetween vectors S and SZ is equivalent to the anglebetween vectors SY � S and SX :

SY � S � ��cosQ�JC � J � sinP�I � IC� sin�

�sinQ�JC � J � sin� cos�

cosQ�JC � J � cosP�I � IC� cos� cos��

0�

� �cosP�I � IC� sin�

�sinP�I � IC� cos� cos� . �6�

FIG. 5. Schematic diagrams demonstrating misalignment. (a) Difference of the actual MCVISSR from the ideal. (b) The impact ofroll misalignment on the imaging process. (c) Misalignment of component . (d) Misalignment of component �. (e) Misalignment ofcomponent �.



Scalar quantity SY � S • SX measures the angle betweenvectors SY � S and SX, which is equivalent to the anglebetween S and SZ. This scalar quantity is the cosine ofthe earth disk shifting angle in the east–west directionprojected on the satellite spin plane due to misalign-ment:

SY � S � SX � SY � S � �1

0

0�

� �cosQ�JC � J � sinP�I � IC� sin�

�sinQ�JC � J � sin� cos�

cosQ�JC � J � cosP�I � IC� cos� cos�.

�7�

In (7), Q(JC � J), P(I � IC), , and � are all smallquantities, and the double sine of any of them can beignored. Equation (7) can then be written as

SY � S � SX � cosQ�JC � J � cosP�I � IC� cos� cos�

� cosQ�JC � J � �� cosP�I � IC� ��. �8�

In Eq. (8), cos[Q(JC � J) ] is a projection factorfrom the scan line passing through the earth’s center tothe scan line on the spin plane. Both � � Q(JC � J) and

are shown in Fig. 4. Equation (8) shows that if theearth’s disk center is placed at the central column of theimage, namely I � IC, the actual earth’s disk centershifts in the east–west direction to cos( ) cos(�), whichis caused by � and . Here, cos( ) is a projection factor.In Fig. 5d, � misalignment is schematically illustrated.For a spin geosynchronous meteorological satellite, �misalignment may be explained by inaccurate � predic-tion. This will be further discussed in section 4.

The remaining misalignment component is yaw (�).As shown in Fig. 5e, � misalignment causes turningaround kS. It does not have a major influence on imagenavigation. This may also be noticed in the spread ex-pression of the observation vector in satellite coordi-nate system (1), in which � does not exist.

4. Determination of the pointing of the satellite toearth

Spin geosynchronous meteorological satellites usethe sun to control the pointing of the radiometer toearth, and to align scan lines together with the � angle.Figure 6 is a scheme diagram of the � angle geometricformulation. In Fig. 6a, SY is the spin axis of the satel-lite, SEarth is the vector pointing from the satellite to

FIG. 6. A schematic diagram illustrating the � angle. (a) 3D view. (b) Plane view after local midnight. (c) Plane view after localnoon.

TABLE 2. Differences between Hambrick’s and nominal expressions for attitude and misalignment components.

Nominal expression formisalignment angle

Nominal expression formisalignment component

Direction with positivenominal misalignmentangle or component

Earth disk centerdisplacement or total

skew effect withpositive misalignment

Hambrick’s expressionfor misalignment angle

Roll( ) Cos( ) Around X from Y to Z South –Pitch (��)Pitch(�) Cos (�) Around Y from Z to X West –Yaw (��)Yaw(�) Cos(�) Around Z from X to Y Anticlockwise skew Roll ( )

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the earth’s center, and SSun is the vector pointingfrom the satellite to the sun. Here, we define the fol-lowing three planes: the S plane consists of the spinaxis and the sun, the E plane is defined by the spinaxis and the earth, and the P plane passes through thesatellite and is perpendicular to the satellite spinaxis. Notice that SY � SSun and SY � SEarth are perpen-dicular to the vectors SSun and SEarth projected at thesatellite spin plane, respectively. The � angle can bewritten as

� � cos�1�SY � SSun� � �SY � SEarth��. �9�

Here, � is a significant parameter for observation byspin-stabilized geosynchronous meteorological satel-lites. In Eq. (9), vectors SSun and SEarth are related tosatellite position and SY to attitude. When the satelliteposition and attitude are well predicted, � can be cal-culated. The value thresholds of � are from 2� to 0. Ata time near local midnight, when the sun, earth, andspin axis of the satellite share a common plane, � isgiven a value of 2�. The value of � decreases monoto-nously until a time near the next local midnight when itapproaches 0, as shown in Figs. 6b,c. With the additionof Eq. (9), the navigation model becomes complete,and a fully automatic solution of the equations is real-ized for FY2.

For FY2 meteorological satellites, the sun is sensedby a sun sensor installed on the side face of the satellitecolumn body at an angle from the MCVISSR. Becauseof the deviation of the sun sensor from the MCVISSR(earth sensor), the alternation of the � value thresholdsappears around 0120 UTC for FY2C, rather thanaround the local midnight. For simplicity, this paperignores this difference, assuming that the alternation ofthe � value thresholds appears around local midnight.

To have an earth image fully viewed and well regis-tered, the value of � must be accurately predicted. If

the value of � is incorrect, then the earth’s disk isshifted in an east–west direction, and if the trend of �over time is deviated from the actual trend, the earthimage is skewed. Figure 7 shows skew images caused byincorrect � prediction. Figure 7a is a normal image withcorrect � prediction; the image does not show any de-formation. Figures 7b,c are the same images with posi-tive and negative d�/dt biases added, which show tre-mendous image deformation although the absolutevalue of the added d�/dt is only 1.69596e-005. TheFY2C image scan process is performed from north tosouth, with southern scan lines taken later. With a posi-tive (negative) d�/dt bias added, the initiating point ofresampling shifts westward (eastward) with time; thiseffect 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 bottompart of Fig. 1b.

5. Solution process of FY2 image navigationmodel

a. Implementation procedures for the solution ofthe FY2 image navigation model

Implementation procedures for the solution of theFY2 image navigation model are outlined in Fig. 8. Thetwo 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 inthe previous day. Equation (9) is used for prediction ofthe � angle on the subsequent day. The solution to Eq.(4) and prediction with Eq. (9) are performed once aday around the time when the � angle approaches theminimum. The predicted parameters are used on thesuccessive day for image acquisition and registration.

For Eq. (4), S and Q(JC � J) are known quantities.Those quantities are sampled for each full disk image

FIG. 7. Influence of � prediction on the observation. (a) A normal full disk image with correct � prediction. A full disk image with(b) positive and (c) negative d� /dt error added.



from the previous day. Normally, FY2 satellites take 28full disk images in a day, 24 hourly plus 4 extra imagesfor atmospheric motion vector derivation. Three rang-ing stations at Beijing, Urumqi, and Melbourne mea-sure the distances from the stations to the satellite 8times a day. With distance data, orbital parameters arediagnosed and future satellite positions are predicted.Considering the asymmetric mass distribution of earth,solar radiation pressure, and the gravitational effects ofthe sun and moon, the accuracy of satellite positiondiagnosis and prediction is less than 100 m. With satel-lite position prediction, S is obtained, and it is ex-pressed in J2000. The earth’s center line count (J) ismeasured by an earth edge detection procedure thatwill be further explained in section 5b. Both SY and are well-conserved quantities, so the mean values fromthe previous day may be used directly in the successiveday as prediction values.

While Eq. (4) is solved with observation data fromthe previous day as known quantities, Eq. (9) is solvedwith prediction data from the successive day as knownquantities. Of the known quantities for Eq. (9), SY isobtained from Eq. (4), while vectors SSun and SEarth are

determined by the position predictions of the sun,earth, and satellite for the successive day. Sun positionis based on Jet Propulsion Laboratory (JPL) planetaryand lunar ephemerides DE200, downloaded from theirWeb site (http://ssd.jpl.nasa.gov/?planet_eph_export).Predictions of the � angle at 5-min intervals are trans-mitted to the Beijing ground station of FY2 and storedin the computer of the Image Acquisition System(IAS), where they are interpolated and used in the re-sampling of individual scan lines to assemble images.

Normally, for individual observations in a day, theactual column counts deviate from the prediction by amagnitude of less than 1 IR pixel. To further reduce thebias of actual column counts from predicted values,compensation is made in the image registration pro-cessing stage based on historical statistics for the timeof the day. As a result, the earth disk center columncount bias is further reduced and the deformation ofthe image is minimized. This compensation is per-formed before the stretched data are broadcasted. Inthe document block of the FY2 data stream, � is hiddenand given a value of 0.

After navigation parameters are derived, the algo-

FIG. 8. Implementation procedures for the solution of the FY2 image navigation model.

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rithm presented by Kigawa (1991) is used to transferobservation pixel counts to latitude–longitude posi-tions. Parameters used by Kigawa are in earth-fixedcoordinates, so before using those programs, coordi-nates must be transferred from inertial to earth fixed.

b. Earth edge detection procedure

The earth disk center line count J is a key element forthe solution of Eq. (4) and J is acquired automaticallyby an earth edge detection procedure. Full disk imagesof the IR channel are used to detect the earth’s edgewith the dynamic threshold method, and then to obtainthe earth’s center line and column counts. It is difficultto find a unique threshold in an image to distinguishearth from outer space, since there are clouds inside theearth’s disk and scatter radiation outside the earth’sdisk. Because of scatter radiation, radiance measure-ments in some places out of earth’s disk are even higherthan inside the earth’s disk where dense cumulonimbus(Cb) clouds exist. Fortunately for FY2 satellites, highand dense Cb clouds are normally at equatorial lati-tudes, while relatively high scatter radiance is mainlydistributed to the northwest of the earth’s disk. Thus,FY2 images are divided into five zones: arctic, midlati-tudes of the Northern Hemisphere, equatorial latitudes,and midlatitudes of the Southern Hemisphere and Ant-arctic. For each zone, thresholds to distinguish earthand outer space on the images are separately obtainedby statistics. Earth’s edges along the scan lines are de-tected with dynamic thresholds in different zones.

Midpoints are obtained between the two earth edgesin the vertical and horizontal directions of the image.Two linear equations are derived to simulate these mid-points, and individual midpoints are eliminated that de-viate from the simulations by more than 0.5 pixels. Thecross point of the two simulation equations is assignedas the earth’s disk center, and the line and column

counts of the earth’s disk center are then obtained. Af-ter quality control, the simulation equation in the ver-tical direction contains more samples than in the hori-zontal direction. Hence, the accuracy of the verticalsimulation is better than the horizontal, which results inthe earth disk center column count being of better qual-ity than the line counts.

The line counts of the earth’s disk center throughouta day are simulated again with a sinusoidal function asexpressed in section 3a and Fig. 3. Individual earth diskobservations where the actual central line count devi-ates from the simulation by more than 0.5 pixels areeliminated. The earth disk center line counts that passquality control are added to the solution of the imagenavigation Eqs. (4). Normally, out of 28 earth disk ob-servations on a given day, 25 may pass quality control.

c. Compensation of the earth disk center columncount

FY2 � angle prediction performance is acceptable,with accuracy within less than one IR pixel. Scan linesin the observation images are aligned based on the ac-curate sun pulse time recovered at the ground segmentand the � angle prediction, as described in section 2a.For individual scan lines, and also for the entire earth’sdisks, central column counts of earth’s disk centers inthe images are expected at 1145. Figure 9 shows a timeseries of the actual earth disk center column counts inFY2C images, where Fig. 9a represents 7 and 8 June2006, and Fig. 9b represents the whole month of June2006. In Fig. 9, the ordinate is time (units: UTC hoursfor Fig. 9a, days for Fig. 9b) downward positive, and theabscissa is the actual earth disk center column count.The scale of the abscissa is 0.1 IR pixels, and all earthdisk center column counts in Fig. 9a are within 1 IRpixel, from 1136 to 1136.8.

The difference of the actual earth disk center column

FIG. 9. Time series of the actual earth disk center column counts for FY2C (a) 7–8 Jun 2006 and (b) Jun 2006.



count from expected values may be expressed as pitch(�) misalignment, as described in section 3d. Pitch mis-alignment may actually be due to inaccurate positioningof sun and earth sensors on the satellite, difference ofthe principal axis from the actual spin axis of the satel-lite, or errors in � angle prediction. It is expected thatthe long time mean value of the differences is due to theformer two factors, and the diurnal variation is due tothe latter one.

For the FY2C meteorological satellite, image obser-vation parameters are predicted once every 24 h at 0120UTC and used for the successive 24 h. In Fig. 9a, from0200 to 1400 UTC, the early half-day of the parameterprediction period, the earth disk center column countsare around 1136.1 or 1136.2 pixels with only small de-viations. From 1500 to 0100 UTC, the later half-day ofthe parameter prediction period, the earth disk centercolumn counts deviate more, from 1136.1 to 1136.8 pix-els. Figure 9b shows data for the whole month of June2006. The time series of the column counts have thesame diurnal variation pattern as seen over the wholemonth. It is expected that the earth disk center columncount deviation is mainly caused by incorrect � angleprediction, which is due to inaccurate satellite positionprediction. For the later half-day of the parameter pre-diction period, the actual satellite position deviatesmore from the predicted position, thus the earth’s diskdeviates more in the east–west direction in the image.

Although the earth disk center column count predic-tions are all within one IR pixel, attempts are still madeto reduce the error by compensation with a previousmean bias for the time of day. The compensations areperformed automatically in the image registration stageof the data processing while individual scan lines areresampled.

d. Influence of ground segment performance andmaneuvers to image navigation and the solution

Since the solution of the FY2 image navigationmodel uses orbital and attitudinal parameters from theprevious day, stable operation of the whole satellitesystem is essential for high-quality image navigation. Inthe early stages of FY2 operation, poor image naviga-tion appeared very frequently because of a variety ofdifficulties in the ground segment. Many cases of inac-curate image navigation were caused by inappropriateoperation on the previous day, such as straight shootingsunlight, ranging failure, bad image quality, databasetrouble, etc. The operation quality has been improvedby making every effort to diagnose and isolate theproblems, find the reasons causing them, eliminate thetrouble, and deduce similar troubles.

On the other hand, the satellite needs to make ma-neuver operations after some period of time. Afterthese operations, the orbital and attitude parameterschange, and it takes about 24–36 h to acquire the newvalues. During this short period, image navigation qual-ity unavoidably degrades. The following measures havebeen adopted to reduce the extent of the degradation:

1) For FY2, the subsatellite position should be main-tained around its nominal �0.5°; spin axis orienta-tion should be maintained �0.5° around the nega-tive perpendicular to the satellite orbital plane. If itis expected that one of the orbital or attitude pa-rameters will not be exceeded prior to the next ma-neuver, then this parameter does not have to beadjusted in the present maneuver operation.

2) In the case that only orbital parameters are ad-justed, the original orbital parameters are used until12 h after the maneuver operation; 12 h later, orbitalparameters are calculated repeatedly, and new or-bital parameters are compared with the previousones to enable a choice. Since the attitude param-eters are not adjusted, they remain applicable afterthe maneuver operation.

3) In the case that only attitude parameters are ad-justed, the objective attitude parameters are useduntil 18 h after the maneuver operation; 18 h later,attitude parameters are calculated repeatedly andnew attitude parameters are compared with the pre-vious ones to enable a decision. Since orbital param-eters are not adjusted, they remain applicable afterthe maneuver operation.

4) In the case that both orbital and attitude parametersare adjusted, objective orbital and attitude param-eters are used; 12 (18) hours later, orbital (attitude)parameters are calculated repeatedly and new pa-rameters are compared with the previous ones toenable a decision.

5) From 24 to 36 h after the maneuver operation, thenavigation processing procedure recovers. Up to 24–36 h after maneuver operations, a manual imagenavigation operation is performed to reduce the ex-tent of quality degradation.

6) To reduce the maneuver operation frequency, over-adjustments to orbital and attitude parameters inmaneuver operations are usually adopted.

6. Image navigation results

This algorithm was put into operation in January2001 and has run for more than 6 yr. Over this time, thealgorithm, software, and hardware have been devel-oped to fit with each other. As a result, FY2 image

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navigation performance has improved in both stabilityand accuracy. In this section, the FY2C image naviga-tion parameters in June 2006 are shown along withsample images overlaid with coastlines and other geo-graphical symbols to illustrate the results of these solu-tions. The FY2C attitude and misalignment parameterslisted in section 3b, except for the inactive � misalign-ment, are given for the whole month of June 2006 alongwith the relevant statistics. All actual parameters in thispaper were obtained during the real-time operation ofFY2 satellites, and no alterations were made to the datafor publication.

Figure 10 shows components of the spin axis on J2000in June 2006 in order to represent attitude parameters.Figure 10 shows three components of directional cosineon the ordinate versus the date on the abscissa. Figure11 shows the trajectory of the FY2C spin axis projected

in the O–X–Y plane of J2000 in June 2006. The spin axisprojection trajectory drawn in Fig. 11 shows the dailymean values, calculated hourly. The date is labeled atthe two ends of the trajectory. FY2 is a spin-stabilizedsatellite, and because of the moment of force causedby sunlight, the spin axis of the satellite experiencesprecession and mutation, which are clearly shown inFig. 11.

Figure 12 shows a time series of the earth disk centerbias of FY2C in June 2006 caused by the related mis-alignment components. Figures 12a,b show the north–south and east–west biases caused by roll and pitchmisalignments, respectively. The ordinate of Fig. 12shows the unit IR pixels and microradians. For IR chan-nels of the FY2 meteorological satellite, a one-pixelbias on the image is associated with a 140-�radian mis-alignment angle. In principle, misalignment parameters

FIG. 11. Trajectory of the FY2C spin axis on the J2000 O–X–Y plane in June 2006. Theordinate and abscissa show the projection of the unit spin vector of FY2C on the J2000 x andy axes, respectively. The date is labeled at the two terminals of the trajectory.

FIG. 10. The (a) X, (b) Y, and (c) Z components of the FY2C spin axis of J2000 in June 2006. The ordinate shows the projection ofthe unit spin vector of FY2C on the relative J2000 axes, while the abscissa is the date in June 2006.



should remain unchanged between the two maneuveroperations, as stated in section 3c. Actually, misalign-ment parameters absorb any deficiencies in the naviga-tion model and may change with time. Time series ofthe misalignment parameters and the associated earthdisk center position throughout the day appear in spe-cific patterns. Figure 9a shows the time series of theearth disk center column count on two successive days.The east–west shifts of the earth disk center columncount are mainly caused by inaccurate � angle predic-tion explained as pitch misalignment. Before real-timeimages are broadcasted, misalignments are compen-sated during image registration based on the historicalstatistics.

Figure 13 shows a histogram of the earth disk centerbias (deviation of forecasted values from the diagnosedvalues) in June 2006. Seven-hundred and ninety

samples were involved in this statistical analysis. Figure13a shows the bias in the north–south direction alone.The mean bias and standard deviation of the earth diskcenter line counts in June 2006 were 0.016 and 0.410,respectively. Figure 13b shows the east–west directionalone. The mean bias and standard deviation of theearth disk center column counts in June 2006 are 0.002and 0.201 pixels, respectively. These statistics show thatFY2C image navigation accuracy reaches 1 IR pixel (5km) at subsatellite point (SSP).

Histogram statistics in Fig. 13 show that image navi-gation quality is worse in the north–south directionthan in the east–west direction. This is mainly due tothe following:

1) The known quantities input into the image naviga-tion model are distributed over a 24-h period. Thus,

FIG. 13. Earth disk center forecast bias (actual minus forecast) in June 2006. (a) North–South directionalone. (b) East–West direction alone. The ordinate is the sample number per 0.02 pixel intervals, and theabscissa is the bias in pixels.

FIG. 12. Time series of the earth disk center bias of FY2C in June 2006 caused by the related misalignment components. (a)North–South bias caused by roll misalignment. (b) East–West bias caused by pitch misalignment. The ordinate is labeled with units ofIR pixels on the left side and microradians on the right side. The abscissa is the date in June 2006. A 1-pixel bias in the image isassociated with a 140-�rad misalignment angle.

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attitude and -misalignment parameters obtained bythe solution of the image navigation model are 24-hmean values. For the spin satellite, while there is aminor change in attitude over time, it is well main-tained over a time period of 1–2 days. As a result ofthe pressure of sunlight on the satellite, which isnot restricted to the center of mass of the satellite,the spin axis experiences precession and nutation(Sørensen 1997). Therefore, the instantaneous atti-tude deviates somewhat from the mean, which is themajor source of error.

2) As illustrated in section 5b, the earth disk center linecount is less accurate compared to the column.

3) Earth is surrounded by atmosphere. High-latitudeatmosphere is thinner in the winter hemisphere thanin the summer. Thus, the earth disk center obtainedby edge detections involves the effect of atmo-spheric thickness, and tends to deflect toward thesummer hemisphere side. During the spring or au-tumn, this deflection changes relatively faster withtime, requiring adjustments in the north–south di-rection.

Figure 14 shows observation images overlaid withlatitude–longitude grids, coastlines, and other geo-graphical symbols. The images in Fig. 14 are all visibleimages at 0456 UTC 8 June 2006 from FY2C. The reso-lution for the visible channel is 4 times better than theIR channel. Coastlines overlaid on the images are pre-dicted ones. Figure 14a is a full disk image, while theother images are local section images with raw visibleresolution. To show detail, the image pixel size in thelocal section images is zoomed to 10 times larger thanthe geographical symbol size. These images clearlyshow a good overlap between images and grids.

7. Summary discussion and algorithm features

This paper introduces the image navigation algo-rithm for FY2 meteorological satellites. The major fea-tures of the algorithm include the geometric formulasfor calculation of the � angle, the adoption of earthcenter line counts as one of the known quantities, theadoption of J2000 as the inertial coordinate system,compensations with historical error statistics, and thestable operation of the system.

For spin-stabilized satellites like FY2, the pointing ofthe satellite toward earth relies heavily on the � angle.During the observation process, the � angle is used notonly to make the radiometer open together with the sunpulse, but also to align the scan lines. Accurate � angleprediction helps not only in determining the earth diskcenter column counts in the east–west direction, but

also in reducing image deformation. FY2 accurately cal-culates and predicts the � angles with a geometric for-mulation, which is an important feature of the algorithm.

In the north–south direction, earth disk center linecounts are used as one of the known input qualities ofHP80’s formulation to measure the angles between thespin axis and observation vectors, and are sampled oncean hour. Considering the revolution of satellites aroundthe earth, the known quantities are homogenously dis-tributed in space. With a dynamic earth edge detectionprocedure, the earth disk center line counts can be ac-

FIG. 14. Full-resolution FY2C visible images with superimposedcoastal lines showing the FY2 image navigation results. (a) Fulldisk image of FY2C at 0456 UTC 8 Jun 2006. (b)–(e) Imagesections of FY2C at 0456 UTC 8 Jun 2006.



curately calculated. The good performance of the navi-gation model solution is also due to the input of knownqualities with homogenous distribution and high qual-ity. The adoption of the earth disk center line counts asone of the input quantities allows for this high level ofsuccess.

In the earth-fixed coordinate systems, attitude pa-rameters are not conserved over time. Therefore, imagenavigation equations must be solved in inertial coordi-nation systems. The adoption of J2000 as an inertialcoordinate system ensures the stable solution of thenavigation equations. All coordinate conversions arecarefully programmed to ensure their accuracy.

In this algorithm, the east–west biases of the earthdisk center column count are compensated for duringthe image registration stage based on historical statis-tics. This measure further improves image navigation inthe east–west direction.

Since observation parameters from the previous dayare used to derive parameters to control observationson the successive day, the stable operation of the entiresatellite system is essential for high-quality image navi-gation. Thus, every effort has been made to improveoperation stability, and as a result, FY2 has achieved a5-km-level image at SSP.

Acknowledgments. This research was supported byGrant 40275007 from the National Natural ScienceFoundation of China and Grant 863-2003AA133050from the Ministry of Science and Technology of China.

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Image Navigation for the FY2 Geosynchronous Meteorological