Tracking high-inclination satellites with noise-affected signals

Abstract

In the satellite tracking system and method, a three-point peaking technique is used to determine the direction of a satellite 50, including the signal source. A Kalman filter is used to minimize the effects of noise in the received signal during the three-point peaking operation. This determination may be made on an ongoing basis. Once the position of a satellite 50 has been determined twice over a time interval, its future position may be estimated using the Kalman filter by an adaptive continuous step tracking technique. The adaptive continuous step tracking technique assumes that the satellite moves evenly over time as seen by the antenna.

Description

[Technical field]

[0001] The field of the invention relates to satellites, and more particularly to tracking satellites in a nominally geostationary orbit around the Earth. This application is related to U.S. Patent No. 6,657,588, filed March 12, 2002, and incorporated herein by reference in its entirety. [Background technology]

[0002] The use of satellites for communication is well known. In principle, a satellite may be placed in a circular orbit in the equatorial plane, at a distance from the center of the Earth such that the orbital period is equal to the Earth's rotation period. If the direction of revolution around the Earth is the same as the direction of the Earth's rotation, the satellite will appear to remain stationary to an observer on Earth.

[0003] In general, even if it were possible to initially place a satellite into such a perfect orbit, the orbit cannot be strictly circular and in the equatorial plane; external forces such as the gravity of the moon and sun, asymmetries in the Earth's gravitational field, and radiation pressure on the satellite's large solar panel array all act to gradually change the orbital elements over time. Station-keeping maneuvers may be employed to maintain the apparent position of the satellite within defined limits.

[0004] Satellites move according to Kepler's laws, so that any given ellipticity of the orbit will cause the satellite to move fastest at perigee and slowest at apogee. In general, a satellite's orbital plane may be inclined with respect to the equatorial plane, so that even if the satellite is in a strictly circular orbit, it will appear to move primarily in a north-south direction, with a small east-west component, as viewed from the center of the Earth.

[0005] The beamwidth of the ground station antenna may be wide enough that the signal strength remains constant enough that the ground station antenna can remain fixed, even with the inevitable apparent motion of the satellite.

[0006] Some applications may require a ground station antenna with higher gain. This reduces the antenna beam width and, as a result, may require the ground station antenna to track the apparent motion of the satellite to avoid large fluctuations in received signal strength. Secondly, it may become uneconomical or impossible to keep the satellite in geostationary orbit by station keeping operations even when the satellite is otherwise operating. In this case, the satellite service life may be increased by including the ability to track the apparent motion of the satellite by the ground station antenna.

[0007] For nominally geostationary satellites, the apparent motion of the satellite is relatively slow, with a periodicity of approximately one sidereal day. In general, received signal strength can be maximized from time to time by performing a series of steps in azimuth and elevation to "climb" to a position of maximum received signal strength. These step tracking techniques require many back and forth movements of the antenna in both azimuth and elevation, which can cause excessive wear on the drive system. Because the results of each measurement are generally compared only to the immediately preceding measurement, the technique is not always reliable and can fail completely in the presence of severe atmospheric scintillation or precipitation attenuation. Recovery from these conditions generally requires human intervention.

[0008] It is desirable to reduce the number of movement requests required to peak the antenna in order to increase drive system reliability and reduce routine maintenance. It is also desirable to determine satellite orientation with greater accuracy and reduce the sensitivity of the antenna peaking process to scintillation and other variations in received signal level.

[0009] For higher frequencies and many locations, the antennas cannot peak on the satellites during periods of significant rain attenuation. Antenna positioning systems require techniques to maintain antenna-to-satellite alignment when normal antenna peaking is not possible due to rain attenuation. Summary of the Invention

[0010] The present disclosure provides an improved antenna positioning method and system. The following summary is not intended to define every aspect of the present disclosure, and other features and advantages of the present disclosure will become apparent from the following detailed description, including the drawings. It is understood that the present disclosure is intended to relate as an integrated document, and that all combinations of features described herein are contemplated, even if the combinations of features are not found together in the same sentence, paragraph, or section of the present disclosure. In addition, the present disclosure includes, as an additional aspect, all embodiments of the present invention narrower in scope than the variations specifically mentioned herein in any way.

[0011] As disclosed herein, a method for tracking a satellite signal source using an antenna includes determining an orientation of the antenna to receive a maximum signal level from a satellite during a collection phase, by rotating an RF axis of the antenna in a single plane through three or more predetermined measurement angles, measuring the signal level at each angle, retaining the three measured signal levels and corresponding angular positions of the predetermined measurement angles such that the measured signal level at the second angular position exceeds the measured signal level at both the first angular position and the third angular position, determining a set of coefficients of a quadratic function relating the measured signals to angular positions, using the coefficients of the quadratic function to determine a first angular position that maximizes the signal level from the signal source, storing the determined angular position, and repeating the preceding steps in an orthogonal plane to provide a second angular position; periodically performing the determining an orientation of the antenna to receive a maximum signal level process to obtain a set of first determined angular positions and a set of second determined angular positions; submitting the set of angular positions to a Kalman filter to generate a filtered output; and estimating a position of the satellite using the filtered output.

[0012] The method may further include submitting the periodically determined angular positions that are above a predetermined noise threshold to a Kalman filter, and further submitting the estimates of the satellite's position to the Kalman filter to generate predicted azimuth and elevation angles for the antenna.

[0013] In the method, the first angular position is an elevation angle and the second determined angular position is an azimuth angle. Additionally, the method may include rotating an RF axis of the antenna in a single direction from a first predetermined measurement angle of the three or more predetermined measurement angles through a set of remaining signal measurement angles of the three or more measurement angles.

[0014] Additionally, the method may include determining a first source position at time t0, a second source position at time t1, and estimating a third source position at a subsequent time t2 by linear extrapolation. Further, the method may include periodically estimating further source positions based on the previously estimated source positions and submitting the estimates to a Kalman filter. Further, the method may include calculating subsequent source positions using a set of equations expressing source positions in geocentric spherical coordinates as a function of time.

[0015] As disclosed herein, an apparatus for tracking a satellite signal source using an antenna having a predetermined beamwidth includes an antenna driver adapted to rotate an RF axis of the antenna in a single plane through three or more predetermined measurement angles, a receiver that measures a signal level at each angle, and a controller configured to: retain the three measured signal levels of the predetermined measurement angles and corresponding angular positions such that the measured signal level at the second angular position exceeds the measured signal level at both the first angular position and the third angular position; determine a set of coefficients of a quadratic function relating the measured signals to the angular positions; determine an angular position that maximizes the signal level from the signal source using the coefficients of the quadratic function; repeat the preceding steps in an orthogonal plane to provide a signal source position; periodically perform the determining of the orientation of the antenna to receive the maximum signal level process to obtain a set of first determined angular positions and a set of second determined angular positions; submit the set of angular positions to a Kalman filter to generate a filtered output; and estimate a position of the satellite using the filtered output.

[0016] The controller may be further configured to periodically submit the determined angular positions above a predetermined noise threshold to the Kalman filter. Additionally, the controller may be further configured to submit an estimate of the satellite's position to the Kalman filter to generate a predicted azimuth and elevation angle for the antenna. Additionally, the first angular position is an elevation angle and the second determined angular position is an azimuth angle. Additionally, the controller may be further configured to point the antenna to rotate the RF axis in a single direction from a first predetermined measurement angle of the three or more predetermined measurement angles through a set of remaining signal measurement angles of the three or more measurement angles. Additionally, the controller may be further configured to determine a first signal source position at time t0, a second signal source position at time t1, and estimate a third signal source position at a subsequent time t2 by linear extrapolation. Additionally, the controller may be further configured to periodically estimate further signal source positions based on the previously estimated signal source positions and submit the estimates to the Kalman filter. [Brief description of the drawings]

[0017] [Figure 1] 1 shows a system for controlling the position of a ground station antenna to track a nominally geostationary satellite, according to an illustrative embodiment of the present invention. [Diagram 2] 2 illustrates typical movement in azimuth of a ground station antenna resulting from a three-point peaking algorithm operating within the system of FIG. 1 under a particular embodiment. [Diagram 3] 2. The results of a quadratic function fit using the quadratic equation whose coefficients are provided by the system of FIG. 1 under the particular embodiment of FIG. 2 and the peak azimuth angle provided by these coefficients are shown. [Figure 4] 3 shows a typical movement in elevation angle of a ground station antenna resulting from a three-point peaking algorithm operating in the system of FIG. 1 under the same specific embodiment as FIG. 2. [Diagram 5]4 shows the results of a quadratic function fit using the quadratic equation whose coefficients are provided by the system of FIG. 1 under the particular embodiment of FIG. 4 and the peak elevation angle provided by these coefficients. [Figure 6] 2 illustrates a typical movement in azimuth of a ground station antenna using an adaptive continuous step tracking technique in the system of FIG. 1 under another specific embodiment. [Figure 7] FIG. 7 illustrates a typical movement in elevation angle of a ground station antenna using an adaptive continuous step tracking technique in the system of FIG. 1 under the same specific embodiment as FIG. 6. [Figure 8] 8 shows the linearly extrapolated movement in azimuth and elevation of the ground station antenna using an adaptive continuous step tracking technique in the system of FIG. 1 under the same specific embodiment as FIGS. 6 and 7. [Figure 9] 10 illustrates a tracking movement in azimuth using the tracking technique in the system of FIG. 1 under another specific embodiment. [Figure 10] 10 shows a tracking motion in elevation using the tracking technique in the system of FIG. 1 under the same specific embodiment as FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] This application is related to US Pat. No. 6,657,588, filed Mar. 12, 2002, which is incorporated herein by reference in its entirety.

[0019] A satellite tracking system 10 generally shown in accordance with an illustrated embodiment of the present invention may include an antenna 40, a drive controller module 35, a signal processing module (device) 30, and a controller module 20 (FIG. 1). Each of the drive controller 35, the signal processing device 30, and the controller 20 may be implemented with one or more processors having associated computer-readable data storage media. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, such as, for example, a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. Thus, the term "processor" as used herein may refer to any of the foregoing structures, any combination of the foregoing structures, or any other structure or apparatus suitable for implementing the techniques described herein.

[0020] The antenna 40 may have an RF axis 42. If a satellite includes the signal source, the antenna may be aligned such that an outward extension of the RF axis 42 passing through the satellite 50 results in maximum received signal strength at the antenna output. Energy received by the antenna for a suitable length of time may be measured by a suitable receiver 31.

[0021] If the satellite contains the receiver and a ground antenna transmits towards the satellite, maximum received signal strength will be obtained at the satellite by aligning the antenna so that the outward extension of RF axis 42 passes through the satellite 50. The energy received at the satellite over an appropriate length of time can be measured by a suitable receiver contained within the satellite.

[0022] At an angular position θ, the reduction in antenna gain can be given by the following equation: G(θ)=12(|θ-θ0|) 2 (1)

[0023] Here, θ is the direction of the RF axis 42, and θ BW is the angle encompassing the angular region 44 within which the gain is reduced by no more than 3 dB from the gain along the RF axis.

[0024] Generally, antenna peaking refers to pointing an antenna so that its RF axis is aligned with the path from the antenna to the satellite. The three-point peaking technique described below provides a unique method for aligning the RF axis of the antenna 40 with the satellite 50.

[0025] In the illustrated embodiment, a three-point peaking technique may be used to determine the direction of the satellite 50 that contains the signal source. This determination may be made at any time.

[0026] Once the position of satellite 50 has been determined twice over a time interval, its future position may be estimated by an adaptive continuous step tracking technique, which assumes that the satellites move evenly over time as seen by antenna 40.

[0027] The three-point peaking technique may be used from time to time to improve the alignment of the RF axis 42 of the antenna 40 with the satellite 50. Successive determinations of the position of the RF axis 42 of the antenna 40 may be tabulated as a function of time.

[0028] Because the apparent motion of satellites 50 is periodic over time, that motion can be predicted by orbit tracking techniques that use the tabulated positions of antenna 40 to determine the coefficients of equations that describe the orbital motion of satellites 50. The accuracy is sufficient that additional determinations of satellite positions, such as may be obtained by a three-point peaking technique, are only required to improve the accuracy of the predictive equations in the orbit tracking techniques.

[0029] First, the three-point peaking technique is described and contrasted with the conventional step tracking technique.

[0030] In the conventional "hill-climbing" step tracking technique, the antenna is moved in small steps in both directions along two orthogonal axes. For convenience and simplicity, the movements are typically in azimuth and elevation. At each position, the received signal level is averaged over a suitable length of time to obtain an average level, which is compared with the average level at the previous position. If the level drops, the antenna is moved two increments in the opposite direction and the measurement is repeated. If the level rises, the antenna is moved one increment in the same direction. This process is repeated until the average level rises and then the antenna is moved in the same direction, causing the average level to fall. The optimal position along this axis is assumed to be the position that provided the maximum average level. The entire procedure is repeated along the orthogonal axis.

[0031] In any antenna positioning system, the accuracy with which the antenna's RF axis can be aligned with the path between the antenna and the satellite is limited in each of the orthogonal axes by the greater of the respective resolver resolution and the minimum increment of antenna movement achievable by the antenna drive system. Thus, conventional "hill climbing" step tracking cannot determine the position of the RF axis with a precision better than this limit.

[0032] The three-point peaking technique moves the antenna in each of two orthogonal axes, typically azimuth and elevation, by fixed increments that can be expressed as integer multiples of the resolver resolution. The fixed increments must equal or exceed the smallest increment of antenna movement achievable by the antenna drive system in each axis.

[0033] Under the illustrated embodiment of the invention, the three-point peaking technique first measures the average level received by the antenna at its current location by integrating the received signal for a period of typically 10 seconds.

[0034] The controller 20 calculates an azimuth step size 25, which is typically 15% of the 3 dB full beamwidth. When the antenna RF axis is initially aligned with the satellite, an offset of this magnitude reduces the received signal strength by a measurable amount (0.27 dB).

[0035] The antenna 40 is commanded to move in azimuth by a step size of 25 in the direction determined by the direction index 26. The average level received by the antenna at the actual azimuth angle attained by the antenna is measured by integrating the received signal for typically 10 seconds. The actual azimuth angle of the antenna is indicated. If the average level drops, the direction index 26 is complemented (i.e., inverted) and the antenna is commanded to move twice the step size of 25 in the opposite direction. If the average level rises, the antenna is commanded to move by a step size of 25 in the same direction. The process is repeated until the average level rises and then falls. The last three actual azimuth positions bracket the antenna azimuth angle that maximizes the received signal strength. In effect, the movement (i.e., rotation) of the antenna 40 caused the satellite 50 to describe an arc across the RF axis 42 of the antenna 40. Only these three actual antenna positions and their corresponding levels are retained.

[0036] According to equation (1), the received signal level can be expressed as the quadratic equation L(α)=c0+c1*α+c2*α 2 where L(α) is the received signal strength and α is the azimuth or elevation angle of the antenna. By differentiating and setting dL(α) / dα=0, the equation α pk =-c1 / (2*c2), the antenna direction of the peak signal reading is defined according to

[0037] The actual azimuth angles that determine the quadratic equation (1) are separated by approximately the step size of 25 degrees, but the peak azimuth angle α pk is determined with a precision greater than the resolver resolution.

[0038] The antenna 40 then rotates in azimuth at a calculated peak azimuth angle α pk The resulting actual antenna azimuth angle is limited by the greater of the azimuth resolver resolution and the minimum increment of antenna movement achievable in azimuth by the antenna drive system.

[0039] The peaking process described for the azimuth movement is then repeated in elevation. As stated above, according to equation (1), the received signal level is given by the quadratic equation L(ε)=c0+c1*ε+c2*ε 2 where L(ε) is the received signal level, ε is the actual antenna elevation angle, and the coefficients c0, c1, and c2 define a quadratic equation in the elevation angle. The antenna elevation angle ε corresponding to the maximum signal strength pk At ε, the slope dL(ε) / dε is zero. Therefore, the elevation angle that provides the maximum received signal level is ε pk =-c1 / (2·c2).

[0040] The antenna is then tilted at a calculated peak elevation angle ε pk The resulting actual antenna elevation angle is limited by the greater of the elevation resolver resolution and the minimum increment of antenna movement achievable in elevation by the antenna drive system.

[0041] α pk and ε pk It is emphasized that provides an estimate of the direction from the antenna 40 to the actual satellite position 50 with an accuracy that exceeds that achievable by the antenna due to the inherent limitations of the drive system.

[0042] The three-point peaking algorithm determines the direction α0, ε0 from the antenna to the actual position of the satellite at a single time t0. Generally, subsequent satellite motion may cause the angle between the antenna's RF axis and the path between the antenna and the satellite to increase.

[0043] In the illustrated embodiment, the motion of the satellite reduces the antenna gain by an amount G(θ) given by equation (1). It may be desirable to use a three-point peaking technique to realign the RF axis of the antenna with the path between the antenna and the satellite. This may result in a second direction α1, ε1 from the antenna to the actual position of the satellite at a single time t1.

[0044] For complete generality, subsequent satellite motion may be small enough that the reduction in antenna gain G(θ) remains within tolerance. After a suitable time has elapsed, it may be desirable to use a three-point peaking technique to realign the RF axis of the antenna with the path between the antenna and the satellite. This procedure may yield a second direction (α1, ε1) from the antenna to the actual position of the satellite at a single time t1.

[0045] In the illustrated embodiment, the RF axis 42 of the antenna 40 may be realigned with the path between the antenna 40 and a satellite 50 using a three-point peaking technique whenever the average received signal level integrated over one minute drops by an established threshold, such as 0.3 dB, as a result of satellite motion, or whenever more than an established interval, such as three hours, has elapsed since the previous alignment. Each alignment procedure involves detecting a corresponding time t i Direction α to the actual position of the satellite at t , ε i provides for an independent decision-making process.

[0046] It will be apparent to one skilled in the art that since the motion of the satellite as observed from the antenna has a period of one sidereal day, knowledge of the antenna positions α0, ε0 at time t0 and the antenna positions α1, ε1 at a subsequent time t1 allows for the estimation of the antenna positions α, ε at a time t following time t1.

[0047] The advantages of this adaptive continuous step tracking technique are explained with reference to an illustrated embodiment.

[0048] The rate of change of azimuth angle dα / dt and elevation angle dε / dt are calculated from the two previous antenna positions α0, ε0 and α1, ε1 and their corresponding times t0 and t1. The antenna positions α, ε are calculated for times t following t1 using the calculated rates of change of azimuth and elevation angles.

[0049] In the illustrated embodiment, the antenna is commanded to move to a calculated position α, ε whenever the calculated position differs from the actual antenna position by an amount determined by the greater of the respective resolver resolution or the minimum increment of antenna movement achievable by the antenna drive system.

[0050] Because the apparent motion of a satellite is not linear in azimuth and elevation, and may not be uniform in these coordinates over time, the angle between the antenna's RF axis and the path between the antenna and the satellite calculated by linear extrapolation as described above will ultimately increase.

[0051] In the illustrated embodiment, the satellite motion reduces the received signal level by an amount G(θ) given by equation (1). By time t2, this reduction may be greater than an established threshold, such as 0.3 dB, and the angular separation between the antenna's RF axis and the path between the antenna and the satellite may be reduced by a three-point peaking technique. The new antenna position is α2, ε2 at time t2.

[0052] Throughout the interval from t1 to t2, the antenna is required to move in azimuth and elevation only according to the linearly extrapolated position calculated by the adaptive continuous step tracking technique. At no time throughout this interval does the received signal level drop by more than the established threshold.

[0053] The antenna position at any time t following t2 can be calculated as a linear extrapolation of the antenna positions at times t1 and t2. Knowledge of the antenna positions α0, ε0 at time t0 is not necessary and may be discarded.

[0054] In the illustrated embodiment, after time t2, the antenna positions α1, ε1 at time t1 are denoted as antenna positions α0, ε0 at time t0. Similarly, the antenna positions α2, ε2 at time t2 are denoted as antenna positions α1, ε1 at time t1.

[0055] From this description, it can be said that the adaptive continuous step tracking technique approximates the actual apparent motion of the satellite 50 as seen by the antenna 40 by a series of linear extrapolations. Each linear extrapolation is calculated from two previous determinations of the antenna positions α, ε, as may be obtained by the three-point peaking technique. Each linear extrapolation is an approximation of the actual apparent satellite path that is good enough that misalignment of the antenna RF axis with the antenna-to-satellite path does not cause the receive level to drop by more than a threshold drop.

[0056] Orbital tracking techniques calculate the antenna positions α, ε by using simple equations that express the satellite position in geocentric spherical coordinates as a function of time.

[0057] The three-point peaking technique uses the corresponding time t i The antenna position α i , ε i The number of entries in the table may be significantly reduced by an adaptive successive step tracking technique.

[0058] The antenna position, which may be expressed in Earth coordinates such as latitude and longitude, is assumed to be known to a reasonable accuracy.

[0059] Assuming that the satellites are in nearly geostationary orbits, the distances of the satellites from the center of the Earth are known with reasonable accuracy. i , ε i is transformed into the geocentric spherical coordinate system by the coordinate transformation 23, and the corresponding time t i θ in i , φ i A table 27 of the above can be obtained.

[0060] It can be shown that for a real satellite in a nearly geostationary orbit, the satellite position can be described in geocentric spherical coordinates (ρ, θ, φ) with reasonable accuracy by the following three equations: ρ=a*(1-ecc*cos(κ*t-ω)) (2) θ=2*ecc*sin(κ*t-ω)-0.25*inc 2 *sin(2*κ*t)+θ0(3) φ=inc*sin(κ*t)+φ0(4)

[0061] Here, ecc is the eccentricity, inc is the inclination (radians), a is the semimajor axis of the satellite orbit (6.61006 Earth radians), ω is the argument of perigee (radians), κ is (2*π) / 86164.09, t is the time from the ascending node, θ0 is the offset of θ, and φ0 is the offset of φ. Since the origin of time is unknown, time t is expressed as t=t c -t0, where t c is the clock time and t0 is the epoch that has to be determined.

[0062] The trajectory tracking technique is a least squares method that calculates the time t i θ in i and φ i Determine the coefficients in equations (2)-(4) that best represent the tabulated values ​​of θ. Because the periodicity of equations (2)-(4) is one sidereal day (86164.09 seconds), the coefficients cannot be determined until the tables span a sufficient fraction of a sidereal day. Without loss of generality, the illustrated embodiment uses θ i and φ i It is assumed that the tabulated values ​​are obtained over a period not shorter than six hours.

[0063] The first coefficient processing application 21 may be obtained using a least squares technique, by application of a three-point peaking technique at any time, or as directed by an adaptive continuous step tracking technique, both as described above. i and t iBy applying equation (4) to the tabulated values ​​of θ, the satellite inclination angle inc, epoch t0, and offset φ0 can be determined.

[0064] After determining the satellite inclination angle inc, epoch t0, and offset φ0, the second term of equation (3) is i The second coefficient processing application 22 may then be obtained using a least squares technique, by application of a three-point peaking technique at any time, or as directed by an adaptive continuous step tracking technique, both as described above. i and t i By applying the tabulated values ​​of Eq. (3) as modified above, the satellite eccentricity ecc, argument of perigee ω, and offset θo may be determined.

[0065] After determining the four orbital parameters (inc, ecc, ω, and t0) and offsets (θ0, φ0), the geocentric coordinates of the satellite are calculated for any clock time t c These coordinates can then be transformed by an inverse coordinate transformation 24 into the satellite's ground coordinates α, ε as seen from any ground location.

[0066] In particular, this transformation from geocentric coordinates to the position of antenna 40 provides a means for RF axis 42 of antenna 40 to remain aligned with the path from antenna 40 to satellite 50 as the direction to the satellite changes over time.

[0067] In general, the geocentric coordinates may be transformed to obtain earth surface coordinates α, ε for any other terrestrial location, thereby providing a means by which the RF axis of the antenna at this second location may remain aligned with the path from this second location to the satellite as the satellite appears to move over time.

[0068] Every few hours, or in any other desired manner, the alignment of the RF axis 42 of the antenna 40 with the path from the antenna to the satellite 50 may be tested and possibly improved by invoking a three-point peaking technique. As mentioned above, the antenna position (at this time t n In n , ε n is the geocentric spherical coordinate θ n and φ n and added to the table 27 of θ, φ, and t. The table size is n This may be constrained by discarding table elements that were retrieved earlier than some selected interval. The period of time for elements to be retained in table 27 may suitably be chosen to be a few days.

[0069] The orbital elements of a satellite change gradually over time due to the gravitational effects of the Sun and Moon, the effects of radiation pressure on the satellite's solar panels, and momentum changes imposed during station-keeping maneuvers. The orbital elements, as may be determined by application of orbit tracking and three-point peaking techniques, are gradually and automatically corrected to accommodate these effects.

[0070] If the antenna position is known and the shaft angle resolvers are correctly initialized, the offset φ0 should be zero. This arises from the observation that the satellite's orbital plane must contain the center of the Earth. Although orbit tracking techniques can tolerate substantial initialization errors in the shaft angle resolvers, a non-zero offset φ0 gives a useful indication that the initialization of one or both shaft angle resolvers should be corrected. By definition, the offset θ0 is the satellite longitude.

[0071] Illustrated Example of Three-Point Peaking Technique The three-point peaking technique may be illustrated by assuming a satellite 50 located at 80.90° West longitude with an inclination angle of 2.8° and a moderate eccentricity of 0.00034. The antenna has a 3 dB beamwidth of 0.22° and is located at 33° North and 96.6° West. The antenna 40 may be moved in both azimuth and elevation with an accuracy of 0.01°. This technique may be implemented, for example, by the controller 20.

[0072] Data can be provided for the illustrated embodiment by a simulation program that includes an accurate representation of the main lobe 44 of the antenna 40. The received signal contains additive white Gaussian noise (AWGN). The received C / N ratio of the simulation is lower than would normally be expected for a typical satellite beacon 50 and antenna 40.

[0073] The received signal strength is plotted as the upper trace (Figures 2 and 4). The three-point peaking algorithm begins at 981 minutes 50 seconds (first black diamond, Figure 2). The received signal level is measured for the next 10 seconds. The average received signal level for the current azimuth angle of 152.92° is available at 982 minutes 00 seconds. As required by the three-point peaking technique, the azimuth angle is reduced by the azimuth angle step size to 151.89°. The received signal level is measured for another 10 seconds. The average received signal level for the new azimuth angle is available at 982 minutes 10 seconds. Since the second average signal level is lower than the first, the antenna azimuth angle is increased by twice the azimuth angle step size to 151.95°. The average received signal level for this azimuth angle is available at 982 minutes 20 seconds. Because the average level has increased, the azimuth angle is again increased by the azimuth angle step size to 151.98°. The average received signal level for this azimuth angle is available at 982 minutes 30 seconds. After the average level has decreased, there are two 10 second averages, the first and fourth, which bracket the third average. The second 10 second average and its corresponding azimuth angle are ignored.

[0074] The coefficient of a quadratic equation in azimuth angle is calculated that includes all three retained averages. The locus of points defined by this quadratic equation can be plotted by a solid curve (FIG. 3). All four 10 second averages are plotted as black diamonds. From the quadratic equation, the peak azimuth angle α pk calculates to 151.949°.

[0075] The antenna 40 is then moved to an azimuth angle of 151.95°, so that the antenna reaches a calculated peak azimuth angle α pk The peaking process is repeated in elevation (Figure 4). Only three 10 second averages are needed to bracket the peak elevation. The coefficients of a quadratic equation in elevation that includes all three averages are calculated. The locus of points defined by this quadratic equation can be plotted by a solid curve (Figure 5). From the equation for the quadratic curve, the peak elevation angle ε pk is calculated to be 48.914°. The antenna 40 is then moved to an elevation angle of 48.91°, which causes the antenna to reach the calculated peak elevation angle ε pk The entire peaking process took 70 seconds.

[0076] In this particular embodiment, the three-point peaking algorithm determines the azimuth and elevation angles of the RF axis 42 to be 151.949° and 48.914°, respectively. The antenna 40 is then moved to the maximum possible accuracy to azimuth and elevation angles of 151.95° and 48.91°, respectively. Illustrated Implementation of the Adaptive Continuous Step Tracking Technique

[0077] The adaptive continuous step tracking technique can be illustrated by assuming a satellite 50 located at 80.9° West with an inclination angle of 2.8° and a moderate eccentricity of 0.00034. The antenna has a 3 dB beamwidth of 0.22° and is located at 33° North and 96.6° West. The antenna 40 can be moved in both azimuth and elevation with an accuracy of 0.01°.

[0078] Data can be provided for the illustrated embodiment by a simulation program that includes an accurate representation of the main lobe 44 of the antenna 40. The received signal contains additive white Gaussian noise (AWGN). The received C / N ratio of the simulation is lower than would normally be expected for a typical satellite beacon 50 and antenna 40.

[0079] The adaptive continuous step tracking technique is illustrated by plotting the received signal strength (light grey line), the one minute average received signal strength (thick line), the satellite azimuth and elevation angles (continuous thin lines), and the antenna azimuth and elevation angles (stepped lines) over time (Figures 6 and 7). The antenna peaks in azimuth and elevation as indicated by the black diamonds. The antenna motion extrapolated according to the adaptive continuous step tracking technique is shown as a series of linear movements (Figure 8). The antenna position immediately after each three-point peak is indicated by the black diamonds.

[0080] In the illustrative embodiment, the antenna RF axis is initially aligned with the path from the antenna 40 to the satellite 50, with an accuracy limited by the resolution of the controller (0.01°). For illustrative purposes only, initialization is performed at an arbitrary time of 300 minutes.

[0081] Any subsequent movement of the satellite that may occur is unknown since only one direction determination to the satellite 50 has been made, and therefore the antenna 40 remains stationary in azimuth and elevation.

[0082] In this exemplary embodiment, satellite 50 is moving fast enough that the one minute average received signal level drops by 0.6 dB within a few minutes. Application of the three-point peaking technique aligns RF axis 42 of antenna 40 with satellite 50 to within the accuracy possible with controller 35. Receive level and antenna position are not indicated during application of the three-point peaking technique.

[0083] Once the second peaking is complete, the antenna position is known at two times, approximately six minutes apart in this exemplary embodiment. The gradients dα / dt and dε / dt are calculated. Every minute thereafter, the extrapolated azimuth and elevation angles are calculated and the antenna 40 is moved to this position within the accuracy possible in the controller 35 (stepped lines, Figures 6 and 7).

[0084] Because the apparent motion of satellite 50 is not linear in azimuth and elevation, nor uniform in these coordinates over time, the angular separation between RF axis 42 and the path from antenna 40 to satellite 50 will increase. In this exemplary embodiment, the one minute average receive level drops 0.6 dB at the time shown at about 318 minutes, approximately 13 minutes after the previous peaking. The three-point peaking technique is applied to realign RF axis 42 to the path between antenna 40 and satellite 50 within the accuracy possible with controller 35.

[0085] As before, the gradients dα / dt and dε / dt are calculated from the antenna peaking which occurred at approximately 305 minutes and 318 minutes. The previous values ​​of the peak azimuth and elevation angles are discarded. Every minute thereafter, the extrapolated azimuth and elevation angles are calculated and the antenna 40 is moved to this position within the accuracy possible in the controller 35 (stepped lines, Figures 6 and 7).

[0086] Because the time increment is larger (13 minutes), it is expected that the gradients dα / dt and dε / dt are known with greater accuracy. As a result, the calculated antenna position can remain properly aligned with the satellite for a longer period of time. In this exemplary embodiment, the antenna does not require peaking again until more than two hours have passed.

[0087] The period between successive peaking of the antenna in azimuth and elevation decreases as the rate of change of the apparent satellite azimuth and elevation angles slows and reverses sign. Simulations show that the adaptive continuous step tracking technique continues to approximate the satellite motion by a series of linear extrapolations.

[0088] If the signal is affected to a greater extent by noise, mainly short-term and long-term atmospheric path loss variations (and the azimuth and elevation angles are smaller), this noise can significantly degrade the quality of the estimated orbit and require many more samples to try to stay within an acceptable error range. Improvements can be obtained by submitting the sequence of estimated peaks (set of determined angular positions) from the three-point peaking technique to a Kalman filter (e.g. of Benedict-Bordner type) for each axis (azimuth, elevation) to produce a better estimate of the true position of the satellite in the presence of noise. During the acquisition phase, the resulting (set of) estimated peaks is fed to the filter. The output of the filter is used instead of a linear extrapolation to project the movement in time, giving a more faithful pointing angle during the acquisition phase. The output of the filter(s) is also fed to the orbit estimation algorithm, giving a better input set and a more accurate ephemeris output. When the system transitions to predictive mode, the output azimuth and elevation angles from the propagated predictions are submitted to a Kalman filter to keep them synchronized to the target's current trajectory.

[0089] In addition, because heavy rainfall and other anomalies can impede the quality of the results, only estimated peaks in the actual measured signal that are above a certain noise threshold (e.g., within 2 dB of clear sky level) are submitted to the Kalman filter. This prevents noise caused by atmospheric losses from corrupting the input data. The output of the filter is used in place of the measured peaks to attempt to track the satellites more closely.

[0090] This results in a more accurate tracking approach with more robust rejection of rain fade noise, which is important for geostationary satellites with sufficient inclination angles to move away from the current line of sight in time for rain or other atmospheric events.

[0091] Illustrated embodiment of the trajectory tracking technique The orbital tracking technique can be illustrated by assuming a satellite 50 with an inclination angle of 3.0° and a moderate eccentricity of 0.00040. The antenna has a 3 dB beamwidth of 0.22° and is located at 33° North and 96.6° West. The antenna 40 can be moved in both azimuth and elevation with an accuracy of 0.01°.

[0092] Data can be provided for the illustrated embodiment by a simulation program that includes an accurate representation of the main lobe 44 of the antenna 40. The received signal includes additive white Gaussian noise (AWGN).

[0093] The orbit tracking technique can be illustrated by plotting the received signal strength (FIGS. 9 and 10) along with the antenna azimuth angle as a function of time (FIG. 9) and the antenna elevation angle as a function of time (FIG. 10).

[0094] In this illustrative embodiment, RF axis 42 is first aligned with the path from antenna 40 to satellite 50 using a three-point peaking technique. For purposes of illustration only, initialization occurs at an arbitrary time on the 345.0th day.

[0095] After a few minutes, the one-minute average receive level has dropped enough that the antenna's RF axis must be realigned on the path to the satellite. Upon completion of this second peaking, the antenna position is known at two times, and the azimuth gradient dα / dt and elevation gradient dε / dt are calculated according to an adaptive continuous step tracking technique. Every minute, the extrapolated azimuth and elevation angles are calculated and the antenna is moved to this position as determined by the accuracy of the drive control system 35.

[0096] At times, the average receive level may drop enough that the adaptive continuous step tracking technique requires the RF axis of the antenna to be realigned with the path to the satellite by a three-point peaking technique.

[0097] Since both the antenna position and antenna orientation in the Earth coordinate system are known, each pair of antenna azimuth and elevation values ​​obtained from each three-point peaking is converted to θ and φ in the geocentric spherical coordinate system as required by orbit tracking techniques, and a table is formed by storing the values ​​of θ, φ, and time.

[0098] The antenna position is determined by an adaptive successive step tracking technique until at least six θ and φ pairs spanning at least six hours (0.15 days) have been entered into the table.

[0099] In this exemplary embodiment, the satellite's apparent motion and antenna beamwidth are such that six or more pairs of θ and φ are obtained within the first six hours (0.15 days). All subsequent antenna positions are determined by orbital tracking techniques.

[0100] In this exemplary embodiment, the orbital tracking technique aligns the antenna RF axis 42 to the antenna-to-satellite path every 3 hours (0.125 days). The calculated values ​​of θ and φ are added to a table and used to refine the estimated orbital parameters. The time of each antenna peaking and the resulting peak azimuth and elevation angles are shown as open diamonds (FIGS. 9 and 10).

[0101] In this illustrative example, the orbital elements determined over the first 12 hours (0.5 days) reveal a gradual increase in misalignment of the RF axis with the antenna-to-satellite path. Three-point peaking at approximately 16 hours (345.65 days) into the simulation refines the orbital elements, which results in the RF axis being well aligned with the antenna-to-satellite path for the remainder of the two-day simulation.

[0102] Advantages over conventional technologies The above-described system 10 offers many advantages over the prior art. Fewer antenna movement commands are required to peak the antenna 40 using the three-point peaking technique than using conventional step tracking. The technique is inherently robust in the presence of signal variations due to atmospheric scintillation and precipitation because it does not rely on tiny differences in received signal strength resulting from small movements near the peak of the antenna pattern.

[0103] The antenna 40 steps from one side of the peak down to the other, so that in most cases the drive system 35 moves in only one direction to take all measurements. The load on the drive system 35 is typically in the same direction while taking all data points, so backlash is removed during the three-point peaking process. Similarly, errors in the shaft angle resolver output resulting from twisting of the coupling to the resolver and loads from the shaft angle resolver bearings are always included in the calculated peak position with the same sign.

[0104] Furthermore, the three-point peaking technique determines the orientation of the RF axis 42 with greater accuracy than is achievable from either the resolution of the shaft angle resolver or the smallest increment of antenna movement possible with the antenna drive system 35.

[0105] Generally, the antenna will peak regardless of antenna position, any errors including large errors in the initialization of the shaft angle resolver, and any nonlinearities in the shaft angle resolver output, as long as the output is a single-valued function of position relative to the relevant portion of the antenna with a 3 dB beamwidth.

[0106] The adaptive continuous step tracking technique has several advantages over conventional methods: It significantly reduces the number of alignments between the RF axis 42 and the path between the antenna 40 and the satellite 50 required to maintain adequate received signal levels, which is particularly effective for large antennas tracking satellites with significant tilt or eccentricity.

[0107] A satellite's motion in azimuth and elevation is most linear over time when the satellite appears to move fastest. With prior art methods, the antenna must be frequently re-peaked during these periods. The adaptive continuous step tracking technique eliminates much of this peaking activity, and the antenna moves in azimuth and elevation with the precision of the antenna drive system 35.

[0108] Since the direction of azimuth and elevation motion each reverses only twice a day, it follows that most antenna motion requests are in the same direction as the previous request, except for antenna peaking. This greatly reduces stress and wear on the antenna drive system and positioning system. In general, the adaptive continuous step tracking technique is effective despite antenna position, any errors, including large errors in shaft angle resolver initialization, and any nonlinearity in the shaft angle resolver output, as long as the output is a single-valued function of position for the range of azimuth and elevation satellite motions.

[0109] In addition to the benefits provided by the three-point peaking and adaptive continuous step tracking techniques, the orbital tracking technique further improves tracking accuracy and reduces the number of RF axis and satellite path alignments required to maintain adequate received signal levels. If necessary, antenna re-peaking can be discontinued during periods of precipitation attenuation or excessive atmospheric scintillation activity.

[0110] The orbital tracking technique calculates the relevant orbital elements of the satellite and moves the antenna according to Kepler's laws. The orbital tracking technique automatically corrects the satellite's orbital elements to include the effects of orbital changes resulting from various forces, such as the gravity of the sun and moon, and station keeping activities.

[0111] Additionally, the offset term φhd0 provided by the orbit tracking technique indicates the accuracy with which the shaft angle resolver was initialized. The offset term θ0 provided by the orbit tracking technique corresponds to the satellite longitude.

[0112] Using orbital tracking techniques, the antenna moves to remain aligned with the satellite for days without re-peaking the antenna. Orbital tracking techniques also provide the ability to transfer tracking data from the antenna location to any other location on Earth. Orbital tracking techniques, whose output is a single-valued function of position over the range of satellite motion in azimuth and elevation, are effective despite moderate errors in shaft angle resolver initialization and non-linearities in shaft angle resolver resolution, as long as the errors do not excessively distort the satellite path as seen by the antenna.

[0113] The steps of the various exemplary processes, methods, modules, and algorithms described in connection with the embodiments disclosed herein may be implemented as a combination of electronic hardware, computer software, or both. Any features and functions described as modules or components may be implemented together in an integrated logic device or separately as separate but interoperable logic devices (e.g., processors). To clearly illustrate this interchangeability of hardware and software, the steps of the various exemplary processes, methods, and algorithms have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the particular application and design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in various ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the invention.

[0114] When implemented in software, the techniques may be realized at least in part by a computer-readable data storage medium including program code, the program code including instructions that, when executed, perform one or more of the methods described above. The computer-readable data storage medium may be non-transitory and may form part of a computer program product, the part of which may include packaging materials. The computer-readable medium may include memory or data storage media, such as random access memory (RAM), such as synchronous dynamic random access memory (SDRAM), read-only memory (ROM), non-volatile random access memory (NVRAM), electrically erasable programmable read-only memory (EEPROM), flash memory, magnetic or optical data storage media, etc. The techniques may additionally or alternatively be realized at least in part by a computer-readable communication medium, which carries or communicates program code in the form of instructions or data structures, such as propagated signals or waves, and which may be accessed, read, and / or executed by a computer.

[0115] Particular embodiments of a method and apparatus for tracking satellites have been described for the purpose of illustrating how the invention may be made and used. It is to be understood that other variations and modifications of the invention and its various aspects of implementation will be apparent to those skilled in the art, and that the invention is not limited by the particular embodiments described. It is therefore intended to cover the invention and any and all modifications, variations, or equivalents that fall within the true spirit and scope of the basic underlying principles disclosed and claimed herein.

Claims

1. 1. A method for tracking a satellite signal source using an antenna, comprising: determining an orientation of the antenna to receive a maximum signal level from the satellite during a collection phase; rotating an RF axis of said antenna in a single plane through three or more predetermined measurement angles; measuring the signal level at each angle; retaining three measured signal levels and corresponding angular positions of the predetermined measurement angle such that the measured signal level at a second angular position exceeds the measured signal level at both the first angular position and a third angular position; determining a set of coefficients of a quadratic function relating the measured signal to the angular position; using the coefficients of the quadratic function to determine a first angular position that maximizes a signal level from the signal source; storing said determined angular position; And repeating the preceding steps in an orthogonal plane to provide a second angular position; said determining by periodically performing the determining of the orientation of the antenna to receive a maximum signal level process to obtain a set of first determined angular positions and a second determined angular positions; submitting the set of angular positions to a Kalman filter to generate a filtered output; using the filtered output to estimate a position of the satellite; and The method comprising:

2. The method of claim 1 , further comprising submitting periodically determined angular positions that are above a predetermined noise threshold to the Kalman filter.

3. The method of claim 2 , further comprising submitting the estimates of the positions of the satellites to a Kalman filter to generate predicted azimuth and elevation angles for the antenna.

4. The method of claim 1 , wherein the first angular position is an elevation angle and the second determined angular position is an azimuth angle.

5. 2. The method of claim 1, further comprising rotating the RF axis of the antenna in a single direction from a first predetermined measurement angle of the three or more predetermined measurement angles through a set of remaining signal measurement angles of the three or more measurement angles.

6. Time t ０ First signal source position at time t １ and determining the position of the second signal source at a subsequent time t by linear extrapolation. ２ and estimating a third signal source position in the signal source region.

7. The method of claim 6 , further comprising: periodically estimating further signal source positions based on previously estimated signal source positions; and submitting the estimates to a Kalman filter.

8. The method of claim 1 , further comprising: calculating a subsequent signal source position using a set of equations expressing the signal source position in geocentric spherical coordinates as a function of time.

9. 1. An apparatus for tracking a satellite signal source using an antenna having a predetermined beamwidth, comprising: an antenna driver adapted to rotate an RF axis of the antenna in a single plane through three or more predetermined measurement angles; a receiver for measuring the signal level at each angle; A controller, retaining three measured signal levels and corresponding angular positions of the given measurement angle such that the measured signal level at a second angular position exceeds the measured signal level at both the first angular position and a third angular position; determining a set of coefficients of a quadratic function relating the measured signal to the angular position; using the coefficients of the quadratic function to determine an angular position that maximizes a signal level from the signal source; repeating the preceding steps in an orthogonal plane to provide a signal source location; periodically performing the determining of the orientation of the antenna to receive a maximum signal level process to obtain a set of first determined angular positions and a second determined angular positions; submitting the set of angular positions to a Kalman filter to generate a filtered output; using the filtered output to estimate the position of the satellite; The controller configured to: The apparatus comprising:

10. The apparatus of claim 9 , wherein the controller is further configured to periodically submit the determined angular positions that are above a predetermined noise threshold to the Kalman filter.

11. 10. The apparatus of claim 9, wherein the controller is further configured to submit the estimates of the positions of the satellites to a Kalman filter to generate predicted azimuth and elevation angles for the antenna.

12. 10. The apparatus of claim 9, wherein the first angular position is an elevation angle and the second determined angular position is an azimuth angle.

13. 10. The apparatus of claim 9, wherein the controller is further configured to orient the antenna to rotate the RF axis in a single direction from a first predetermined measurement angle of the three or more predetermined measurement angles through a set of remaining signal measurement angles of the three or more predetermined measurement angles.

14. The controller determines whether a time t ０ First signal source position at time t １ and linearly extrapolating to a subsequent time t ２ The apparatus of claim 13 , further configured to estimate a third signal source position in

15. The apparatus of claim 14 , wherein the controller is further configured to periodically estimate further source positions based on previously estimated source positions and submit the estimates to a Kalman filter.

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