Fig. 9-12. Observed Sun Sensor Data for GEOS-3 in Mission Mode, June 28, 1975

Fig. 9-12. Observed Sun Sensor Data for GEOS-3 in Mission Mode, June 28, 1975

GEOS-3 Sun sensors in mission mode. Correct angular measurements (NA and NB) were telemetered but the sensor head (ID) selected by onboard electronics was incorrect when the Sun was near the Earth horizon. (Similar problems were observed when the Sun traversed the field of view of two sensors.) Let SMi denote the measured Sun vector in body coordinates, assuming that the measurement corresponds to the ith sensor. Then the correct sensor selection minimizes the quantity

where XM and Xc are the measured and calculated values for any inertial reference vectors (e.g., nadir or magnetic field) and Sc is the calculated inertia! Sun vector. Note that this procedure can fail for certain geometries. For example, if the Sun sensor boresights are dispersed at a half cone angle 0 with respect to the spacecraft Z-axis, Eq. (9-34) is independent of / when \M is colinear with the Z-axis.

933 Central Body and Horizon/Terminator Identification

Data from horizon scanners, either those sensitive to the visible or the infrared portion of the electromagnetic spectrum, must be validated to reject spurious triggerings caused by the Sun, the Moon, or reflections from spacecraft hardware. For visible light sensors, a further test is required to distinguish between horizon and terminator crossings (Section 4.1).

Although most spurious triggerings are relatively simple to identify (Section 8.1), terminator crossings escape most preprocessing tests and normally are eliminated after the attitude computation by a data regeneration test [Joseph, 1972] or solution averaging (Section 11.2). However, a simple scalar test based on the arc length separation, a, between the Sun, S, and the triggering event, X, will suffice for both central body identification and terminator rejection for all cases for which the data regeneration test will succeed [Williams, 1972].

For any triggering, the angle a may be computed by applying the law of cosines to the spherical triangle shown in Fig. 9-13. Thus,

Figure 9-14 illustrates the terminator geometry for a central body, R, of angular radius p, less than half-lit {crescent). Alternatively, Fig. 9-14 illustrates the case for the central body more than half-lit {gibbous) if the Sun is at the opposite pole. Since the Sun is at a pole of the coordinate grid, the latitude lines are lines of rared sensors, the only restriction on a is that cos a = cos ß cos y + sin ß sin y cos$

The requirements for visible light data are more restrictive. First, consider the crescent geometry of Fig. 9-14. Note that the angles a, and ip on the figure are measured from the Sun. The small circle of constant a, is tangent to the terminator on the SR great circle and the small circle of constant a2 passes through the cusps or the points where the horizon and terminator intersect. Clearly, a triggering at latitudes Oq < a < a, can result only from the central body horizon. Triggerings at .latitudes a, <a < a2 can result from either the horizon or the terminator.* This is defined as the indeterminate case. Triggerings at latitudes a>a2 are necessarily spurious.

The angles a, and a2 may be calculated with the aid of the upper half of Fig. 9-15. The plane of the figure contains the vectors S and R with the spacecraft at the origin and the Sun along the + Y axis. By symmetry, this plane also contains X at the angle a = a,. Dc (89.15 deg) is the dark angle defined in Section 4.1.

Let Re be the vector from the center of the central body to the terminator crossing. Taking components of X and Re, perpendicular and parallel to the sunline, we obtain

with the result a, = arctan|^sinV'- "~jfsinDc)/{^osxp- ^-cosDc j j (9-39)

To compute a2, we note that when a = a2, X is located on both the horizon and the terminator. Points on the terminator are formed by rotating R© about the

'Data regeneration procedures will attribute this data unambiguously (and incorrectly) to a horizon crossing.

R COSOr a c

R COSOr a c

sunline. Clearly, all points on the terminator satisfy Eq. (9-38) for components parallel to the sunline,

Xcosa2 + R ®cos Dc= R cos The condition that X is on the horizon is simply

Therefore, we have the result

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