Patent Publication Number: US-7724188-B2

Title: Gimbal system angle compensation

Description:
FIELD 
   The present disclosure is generally related to gimbal system calibration and pointing angle compensation. 
   BACKGROUND 
   Where an antenna or a similar payload is installed on a gimbal system, such that the antenna is used to point at a selected target, overall pointing direction performance may be adversely affected by intrinsic errors that exist in various system locations, such as inboard, internal, and outboard locations of the gimbal system. Pointing performance after an antenna mapping calibration may still be sensitive to the gimbal angles of the gimbal system, especially in the case where the antenna needs to cover a large field of view. Many of the intrinsic errors are due to components of the gimbal system that are not readily measurable which can cause difficulty in calibration, control, and pointing accuracy. Pointing control and accuracy are particularly challenging for applications where the antenna is mounted on a moving platform (e.g., a satellite or a ship) and is pointing at a fixed or moving target. These errors may be even more difficult to correct where the gimbal system includes multiple gimbals (e.g., two or more two-axis gimbals). 
   SUMMARY 
   In a particular illustrative embodiment, a system includes a host vehicle interface adapted to be coupled to a host vehicle and to a gimbal system. The gimbal system includes a first gimbal coupled to the host vehicle interface, a platform coupled to the first gimbal, a second gimbal coupled to the platform, and a first directional payload interface coupled to the second gimbal. 
   In another particular illustrative embodiment, a method includes setting at least four nominal gimbal angles to point an antenna at a target based at least partially on location information associated with the target. The method also includes identifying a set of corrected gimbal angles based on the set of at least four nominal gimbal angles and based on a set of gimbal angle corrections. The method also includes pointing the antenna using the set of corrected gimbal angles. The set of gimbal angle corrections is determined based at least partially on one or more bore sight measurements of the antenna. 
   In another particular illustrative embodiment, a method includes pointing an antenna at a first target using an initial set of at least four gimbal angles and determining first bore sight pointing errors resulting from a pointing direction of the antenna relative to the first target. The method also includes estimating values of a plurality of independently observable error variables based on the first bore sight pointing errors. The method further includes determining a set of gimbal angle corrections based on the values of the plurality of independently observable error variables. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram of a first particular embodiment of a gimbal system; 
       FIG. 2  is a block diagram of a second particular embodiment of a gimbal system; 
       FIG. 3  is flow diagram of a particular embodiment of a method of performing gimbal calibration; 
       FIG. 4  is flow diagram of a particular embodiment of a method of using gimbal angle corrections to point a directional payload; 
       FIG. 5  is a flow diagram of a particular embodiment of a method of determining corrected gimbal angles; 
       FIG. 6  is a flow diagram of a particular embodiment of a method of adjusting gimbal angles; 
       FIG. 7  is a flow diagram of a second particular embodiment of a method of adjusting gimbal angles; 
       FIG. 8  is a flow diagram of a third particular embodiment of a method of adjusting gimbal angles; 
       FIG. 9  is a flow diagram of a particular embodiment of method of pointing an antenna; and 
       FIG. 10  is a general diagram that illustrates pointing error convergence associated with a method of applying adjusted gimbal angles based on estimated values of a plurality of independently observable error variables. 
   

   DETAILED DESCRIPTION 
   Referring to  FIG. 1 , a particular illustrative embodiment of a system  100  is illustrated. The system  100  includes a host vehicle interface  102 , a two-axis platform gimbal  104 , a platform  106 , and a two-axis antenna gimbal  110 . The platform  106  is supported by the platform gimbal  104 , and the platform  106  is coupled to a first antenna  108 . The antenna gimbal  110  is supported by the platform  106 , and the antenna gimbal  110  is coupled to a second antenna  112 . The first and second antennas  108 ,  112  may alternatively be substituted by other pointing devices, such as a laser or other directional payload. 
   The platform gimbal  104  includes a plate assembly  120 , a housing  122 , a shaft  124 , a second plate  126 , a second housing  128 , and a second shaft  130 . In a particular embodiment, the platform gimbal  104  has at least two axes, an azimuth axis and an elevation axis. In this embodiment, the first plate  120 , the housing  122  and the shaft  124  are related to an azimuth of the platform gimbal  104 , and the second plate  126 , the second housing  128 , and the second shaft  130  are related to an elevation of the platform gimbal  104 . Thus, both the azimuth and the elevation of the platform  106  relative to the host vehicle interface  102  can be adjusted using the platform gimbal  104 . 
   The antenna gimbal  110 , which is supported by the platform  106 , includes a first plate  140 , a first housing  142 , and a first shaft  144 . The antenna gimbal  110  also includes a second plate  146 , a second housing  148 , and a second shaft  150 . In a particular embodiment, the antenna gimbal  110  has at least two axes, an azimuth axis and an elevation axis. In this embodiment, the first plate  140 , the housing  142  and the shaft  144  are related to an azimuth of the antenna gimbal  110 , and the second plate  146 , the second housing  148 , and the second shaft  150  are related to an elevation of the antenna gimbal  110 . Thus, both the azimuth and the elevation of the second antenna  112  relative to the platform  106  can be adjusted using the antenna gimbal  110 . 
   The system  100  enables independent pointing of the first antenna  108  and the second antenna  112 , even while a host vehicle coupled to the host vehicle interface  102  is in motion. For example, the first antenna  108  can be pointed at a first target using the platform gimbal  104  and the second antenna  112  can be pointed at a second target using the antenna gimbal  110 . 
   Calibration of the system  100  by measuring errors related to each mechanical component may be difficult. However, in a particular embodiment, the system  100  can be calibrated based on bore sight measurements or other pointing error measurements taken with respect to the second antenna  112 . The pointing direction of the second antenna  112  is affected by 11 independently observable error variables, including: rotation of the host vehicle about x-, y-, and z-axes; non-orthogonality of the first shaft  124  and the second shaft  130  of the platform gimbal  104 ; rotation of the platform  106  about x-, y-, and z-axes; non-orthogonality of the first shaft  144  and the second shaft  150  of the antenna gimbal  110 ; and rotation of the second antenna  112  about x-, y- and z-axes. For some applications, rotation of the second antenna  112  about the z-axis is not applicable; thus, only 10 independently observable error variables may contribute to the pointing errors. In a particular embodiment, values of the independently observable variables can be estimated by measuring pointing error of the second antenna  112  related to various gimbal angles of the platform gimbal  104  and the antenna gimbal  110 . For example, pointing error measurements can be made by pointing the second antenna  112  at a target while the host vehicle is at different attitudes. In another example, pointing error measurements can be made by pointing the second antenna  112  at different targets. In still another example, pointing error measurements can be made by pointing the second antenna  112  at the same target using a different set of platform and antenna gimbal angles. The estimates of the independently observable variable values can be used to calibrate the system  100  by determining gimbal angle adjustments to be made during pointing of the first antenna  104 , the second antenna  112 , or both. 
   Referring to  FIG. 2 , a second particular illustrative embodiment of a system is illustrated. The system includes a host vehicle  202 , such as a satellite, a ship, an aerial vehicle or another movable vehicle. The host vehicle  202  is coupled by a host vehicle interface  206  to a first gimbal  210 . The first gimbal  210  supports a platform  220  via which equipment or tools can be coupled to the host vehicle  202 . For example, one or more platform interfaces, such as representative platform interface  222 , can be coupled to the platform  220 . The platform interface  222  supports a first directional payload  228 . In another example, one or more additional gimbals, such as a second gimbal  224 , a third gimbal  226 , or both, may be coupled to the platform  220 . The second gimbal  224  may be coupled to a second payload interface  230 , and the third gimbal, when present, may be coupled to a third payload interface  232 . The second payload interface  230  may support a second directional payload  234 , and the third payload interface  232  may support a third directional payload  236 . While three directional payloads are illustrated in  FIG. 2 , the system can include any number of directional payloads, including fewer than or more than three payloads. Likewise, while two additional gimbals are shown coupled to the platform, the platform can include any number of additional gimbals, including fewer than or more than two additional gimbals. In a particular embodiment, the system includes the first gimbal  210  and at least one additional gimbal, such as the second gimbal  224 . 
   The directional payloads  228 ,  234 ,  236  may include a tool or device adapted to be pointed toward a desired location. Illustrative, non-limiting examples of directional payloads  228 ,  234 ,  236  include antennas, lasers and optical devices (e.g., telescopes or cameras). The system may be used to control and direct one or more of the directional payloads  228 ,  234 ,  236  toward a beacon  260  or a target  270 . The beacon  260  may be used to provide alignment information with respect to one or more of the directional payloads  228 ,  234 ,  236  or the host vehicle  202  for navigation, direction, or calibration. In a particular embodiment, the beacon  260  provides a signal from a known location and the host vehicle  202  is a moving vehicle, such as a ship, an airplane, or a satellite. 
   In a particular embodiment, the first gimbal  210  has at least two axes of rotation and the second and third gimbals  224  and  226  each have at least two axes of rotation. Hence, the pointing direction (e.g., azimuth and elevation) of the first directional payload  228  relative to the host vehicle  202  may be adjusted by using the first gimbal  210  to change the orientation of the platform  220 . The pointing directions of the second directional payload  234  and the third directional payload  236  may be changed independently of each other and independently of the orientation of the platform  220  by adjusting the second gimbal  224  and the third gimbal  226 , respectively. For example, as the host vehicle  202  moves, the pointing direction of the first directional payload  228  may be maintained by adjusting gimbal angles of the first gimbal  210  to compensate for the movement of the host vehicle  202 . Additionally, the pointing direction of the second directional payload  234  may be maintained by adjusting the gimbal angles of the second gimbal  224  to compensate for the movement of the host vehicle and, if needed, the movement of the platform  220 . Similarly, the pointing direction of the third directional payload  236  may be maintained by adjusting the gimbal angles of the third gimbal  226  to compensate for the movement of the host vehicle  202  and, if needed, the movement of the platform  220 . 
   The system also includes a control interface that includes or communicates with a controller  204 . The controller  204  may be located onboard the host vehicle  202  or remote from the host vehicle  202 . For example, where the host vehicle  202  is a satellite, all of or a portion of the controller  204  may be located at a ground station (not shown), all of or a portion of the controller  204  may be onboard the satellite, or any combination thereof. The controller  204  includes gimbal compensation logic  250 , a beacon tracking module  252 , an antenna mapping module  254 , and a host vehicle attitude module  256 . In a particular embodiment, the controller  204  includes one or more processors and memory. The one or more processors may execute computer instructions stored in the memory to implement and execute the various functions of the controller, such as the functions exemplified by the modules  252 ,  254 ,  256  and the logic  250  illustrated in  FIG. 2 . 
   In a particular embodiment, the multiple gimbal arrangement illustrated in  FIG. 2 , enables independent pointing of the directional payloads  228 ,  234 ,  236  at separate targets as the host vehicle  202  moves. However, each gimbal may introduce error in the pointing of the directional payloads  228 ,  234 ,  236 . For example, pointing errors due to non-orthogonality of the azimuth and elevation axis of each gimbal may be present. Additionally, other pointing errors may be related to the gimbal angles of each gimbal  210 ,  224 ,  226 , the control system, attitude information related to the host vehicle  202  or platform  220 , and so forth. In an illustrative embodiment, a pointing direction of each directional payload is controlled by adjusting gimbal angles of the gimbals  210 ,  224 ,  226  to account for a set of independently observable values. 
   In an exemplary embodiment, the independently observable error variables include at least one error variable related to one or more of an attitude of the host vehicle  202 , an attitude of the platform, an attitude of the antenna or other type of pointing device, orthogonality of axes of the antenna gimbal, or orthogonality of axes of the platform gimbal. For example, the pointing direction of the second directional payload  234  may be determined based on error values related to host vehicle rotation about x-, y-, and z-axes; an error value related to non-orthogonality of axes of the first gimbal  210 ; error values related to platform rotation about x-, y-, and z-axes; an error value related to non-orthogonality of axes of the second gimbal  224 ; error values related to the second directional payload&#39;s rotation about x-, and y-axes. The second directional payload&#39;s rotation about a z-axis may also be considered in some embodiments. As used herein, the term exemplary indicates an example and not necessarily an ideal. 
   The independently observable error variables may be estimated based on bore sight measurements related to the respective directional payload. For example, estimates of the independently observable error variable values for the second gimbal  224  and the first gimbal  210  may be determined based on bore sight measurements related to the second directional payload  234 . The independently observable error variable values may be used to determine corrected gimbal angles to point the directional payloads  228 ,  234 ,  236  at specified targets. 
   During operation, the controller  204  receives sensory information and provides control information and direction, in order to control and adjust the directional payloads  228 ,  234 ,  236 . In a particular embodiment, the beacon tracking module  252  receives sensory information detected from one or more of the directional payloads  228 ,  234 ,  236  and communicates the received sensory information to the controller  204  via the controller interface  240 . The beacon tracking module  252  processes the received sensor data and based on the received sensor data, the beacon tracking module  252  can provide updated target location and the difference between the commanded pointing direction and the tracked pointing direction. Alternatively, the antenna mapping module  254 , based on the knowledge of target location, can command an antenna scanning motion with which, together with receiving antenna on the ground, the true antenna boresight where the maximum antenna signal power occurs relative the commanded antenna boresight can be determined. In both cases, the boresight difference data is provided to the gimbal compensation logic  250  as calibration measurement data. The gimbal compensation logic  250  estimates values of the independently observable error variables to calibrate the system so that corrected gimbal angles can be determined for other pointing directions, other host vehicle orientations, other platform orientations, or any combination thereof, and the directional payloads  228 ,  234 ,  236  can be pointed in a desired direction, such as at the target  270 . In a particular embodiment, the values of the independently observable error variables are determined based on an estimation algorithm that estimates the values based on bore sight measurements from antenna mapping, beacon tracking or another measurement related to the pointing direction of one of the directional payloads  228 ,  234 ,  236 . 
   The host vehicle attitude module  256  receives and processes attitude information related to the host vehicle  202 . The host vehicle attitude information can be provided to the gimbal compensation logic  250  to adjust the gimbal angles of one or more of the gimbals  210 ,  224 ,  226 . For example, the host vehicle attitude information can be used to maintain the pointing direction of the first directional payload  228  by adjusting the gimbal angles of the first gimbal  210 . Additionally, the host vehicle attitude information, information about adjustments made to the first gimbal angles, or both, may be provided to the gimbal compensation logic  250  to determine adjusted gimbal angles for the second gimbal  224 , the third gimbal  226 , or both to maintain a pointing direction of the respective directional payloads  234 ,  236  when the orientation of the platform  220  is changed. 
   The antenna mapping module  254  provides antenna scanning motion profiles and processes the corresponding received power profile at a target to produce boresight error data that may be used to calibrate the gimbals, and to direct and control an antenna, such as an antenna at one or more of the directional payloads  228 ,  234 , or  236 . In a particular embodiment, the antenna mapping module  254  includes logic or instructions to determine gimbal angle error values, either directly obtained or derived from bore sight pointing errors. For example, the antenna mapping module  254  may determine the strength of a signal transmitted to a target, such as the target  270 . The antenna mapping module  254  may compare the determined signal strength to a maximum or peak signal strength that may be measured or predetermined. 
   The gimbal angle error values may be used by the gimbal compensation logic  250  to determine gimbal angle corrections, which may be used to adjust the pointing direction of an antenna. In a particular embodiment, the antenna mapping module  254  determines the gimbal angle values based on multiple positions of the gimbals. For example, the gimbal angle error values of the first gimbal  210  and the second gimbal  224  may be determined based on pointing the second directional payload  234  at two or more beacons at different locations, such that the gimbal angles of the first and second gimbals  210 ,  224  are different for pointing at each beacon. In another example, the gimbal angle error values of the first gimbal  210  and the second gimbal  224  are determined based on different orientations of the host vehicle  202  while pointing the second directional payload  234  at one or more beacons, such that the gimbal angles of the first and second gimbals  210 ,  224  are different for pointing at each host vehicle orientation to gain linearly independent measurement data. 
   In a particular embodiment, the gimbal compensation logic  250  determines one or more gimbal angle correction values based on the error values of the gimbals  210 ,  224 ,  226  and gimbal angles when the error measurements are taken. For example, the gimbal compensation logic  250  may determine gimbal angle correction values for the first gimbal  210  based on a bore sight measurement of the first directional payload  228 . In another example, the gimbal compensation logic  250  determines gimbal angle correction values for the first gimbal  210 , the second gimbal  224 , or both, based on a bore sight measurement of the second directional payload  234 . In yet another example, the gimbal compensation logic  250  determines gimbal angle correction values for the first gimbal  210 , the third gimbal  226 , or both, based on a bore sight measurement of the third directional payload  236 . The gimbal angle error correction values may be used by the gimbal compensation logic  250  to adjust gimbal angles of the gimbals  210 ,  224 ,  226  to control pointing of the directional payloads  228 ,  234 ,  236 . 
   In a particular embodiment, the gimbal angle compensation logic  250  is adapted to receive host vehicle attitude data from the host vehicle attitude module  256  to adjust the attitude of one or more of the directional payloads, such as the first directional payload  228 , to maintain a first specified pointing direction and to adjust the attitude of another directional payload, such as the second directional payload  234 , to maintain a second specified pointing direction. As shown, the gimbal compensation logic  250  may control one, two, or all of the directional payloads  228 ,  234 ,  236 . The gimbal compensation logic  250  may also maintain a specified pointing direction for each of the directional payloads  228 ,  234 , and  236  independently of the pointing direction of the other directional payloads and independently of the orientation of the host vehicle  202 . Further, the gimbal compensation logic  250  can calibrate the gimbal system, including the first gimbal  210 , the second gimbal  224 , the third gimbal  226 , or any combination thereof, based on beacon tracking measurements or bore sight measurements of one or more of the directional payloads  228 ,  234 ,  236 . For example, the gimbal compensation logic  250  may determine gimbal angle correction values to adjust various gimbal angles of the gimbals  210 ,  224 ,  226  to compensate for pointing errors in the system. 
   Referring to  FIG. 3 , a particular embodiment of a method of performing gimbal calibration is illustrated. The method relates to calibrating a gimbal system including at least two gimbals, where each gimbal has at least two axes. The method includes, at  304 , performing an initial analysis of a gimbal system as part of a manufacturing process  302 . Based on the manufacturing process  302  and the initial analysis  304 , an initial estimate of values of gimbal variables  306  are determined. The initial estimate of values of gimbal variables  306  may include estimates of independently observable error values related to each gimbal of the gimbal system. Based on the initial estimate of the values of various variables  306 , an estimate of gimbal angle corrections  310  is determined, at  308 . 
   At  314 , a calibration process begins. The calibration process  314  includes providing a calibration input  316 . For example, the calibration input can include information to a specific pointing direction of a directional payload coupled to the gimbal system. To illustrate, the calibration input may include host vehicle location data, host vehicle attitude data, and data specifying a calibration target. The calibration input  316  and the gimbal angle corrections  310  may be used, at  312 , to determine pointing angles  320  for each gimbal of the gimbal system. For example, the gimbal pointing angles  320  can include platform gimbal angles  350  and antenna gimbal angles  352 . 
   At  322 , the directional payload (e.g., an antenna, laser, or other directional device) is pointed by setting the gimbal angles of the gimbal system to the pointing angles  320 . The method further includes, at  324 , measuring a pointing error of the directional payload. For example, the pointing error can be measured by performing antenna mapping, beacon tracking or other pointing device detection and error correction calculations. The pointing error measurements are collected, at  326 , and used, at  328 , to generate an estimate of adjusted gimbal angle corrections  330 . Additionally, the pointing error measurements are used to determine, at  340 , whether the pointing accuracy is acceptable. If the pointing accuracy is acceptable, the calibration process ends, at  342 . If the pointing accuracy is not acceptable, at  340 , then the calibration process is repeated in an iterative fashion, at  344 . 
   Additionally, the settings for subsequent calibrations may be adjusted, at  346 . The calibration settings may use the same or a different calibration input. For example, the host vehicle location, the host vehicle attitude, or the calibration target location may be changed for subsequent calibrations. The calibration settings may also use adjusted gimbal angle corrections  330  rather than the estimated gimbal angle corrections  308  to determine the pointing angles  320 , at  312 . Additionally, other factors such as diurnal effects (e.g., effects of heating and cooling each day) may be accounted for by performing subsequent calibrations at various times during the day. Thus, the next calibrations may be delayed until a time when the diurnal effects can be accounted for. For example, the pointing error measurements  324  may be determined at a plurality of different times during the calibration phase. In a particular illustrative embodiment, the time period between determining two or more pointing error measurements is selected to reduce influences of cyclic errors on gimbal angle corrections and adjustments. In another particular illustrative embodiment, for each pointing error measurement, multiple consecutive data points can be taken to reduce the influence of measurement noise. 
   Referring to  FIG. 4 , a particular embodiment of a method of using gimbal angles corrections to point a directional payload is illustrated. The method includes identifying a mission target  402  and providing a target input  404  specifying the mission target  402 . The target input  404  may include host vehicle location data  406 , host vehicle attitude data  408 , target location data  410 , other data to specify the mission target  402 , or any combination thereof. The target input  404  and gimbal angle corrections  412  are used, at  411 , to determine pointing angles  416 . The pointing angles  416  may include pointing angles related to more than one gimbal of a gimbal system. In a particular illustrative embodiment, the gimbal system includes at least two gimbals, a platform gimbal and an antenna gimbal. Additionally, each gimbal includes at least two axes, an azimuth axis and a elevation axis. Thus, the pointing angles  416  may include platform gimbal angles  418  specifying an azimuth angle and an elevation angle, and antenna gimbal angles  420  specifying an azimuth angle and an elevation angle. 
   In a particular embodiment, the gimbal angle corrections  412  are determined by an iterative calibration process, such as the calibration method illustrated in  FIG. 3 . For example, the gimbal angle corrections  412  can be based on a set of independently observable error values that are estimated based on measurements of pointing error related to the directional payload. 
   The method also includes pointing the antenna or other directional payload using the pointing angles, at  422 . For example, the platform gimbal angles  418  can be used to adjust the orientation of a platform gimbal and the antenna gimbal angles can be used to adjust the orientation of an antenna gimbal. 
   After the pointing direction of the antenna or other pointing device has been set based on pointing angles  416 , the method determines the accuracy of the pointing. For example, an error in the pointing direction may be determined based on bore sight measurements. If the accuracy is acceptable, at  424 , then successful pointing for the mission has been accomplished and the method ends, at  426 . If the accuracy is not acceptable, at  424 , then the method proceeds to perform a calibration of the gimbal system, at  428 . A particular illustrative method of performing gimbal calibration is shown with respect to  FIG. 3 . 
   Referring to  FIG. 5 , a method of determining corrected gimbal angles is shown. The method includes initializing a set of gimbal angles, at  502 . The gimbal angles may be initialized based on estimates of gimbal angle error and the relative position and attitude of a target and a system associated with a pointing device (such as a host vehicle and a gimbal system that includes at least two, two-axis gimbals). The method also includes, at  504 , measuring a pointing error of the pointing device, such as an antenna, a laser, an optical device, or another pointing device. At  508 , the measured pointing error is compared to a threshold  506 . If the pointing error is less than the threshold  506 , then the method is completed at  510 . 
   If the measured pointing error is not less than the threshold  506 , then the method proceeds to  512  where a set of independently observable error variable values are determined. The independently observable error variable values may be determined based on measurements of the pointing error. For example, the pointing error measurement may include a bore sight measurement to determine an actual pointing direction of the pointing device. The actual pointing direction and the expected pointing direction based on the gimbal angles may be used to estimate error values related to independently observable error variables. For example, where the system associated with the pointing device includes a host vehicle, a first gimbal coupled to the host vehicle and supporting a platform, and a second gimbal coupled to the platform supporting the pointing device, the independently observable error variables may include rotation of the host vehicle about an x-, y- or z-axis; non-orthogonality of the first gimbal; rotation of the platform about an x-, y-, or z-axis; non-orthogonality of the second gimbal; rotation of the pointing device about an x-, y-, or z-axis; or any combination thereof. 
   The method further includes, at  514 , determining corrected gimbal angles. The corrected gimbal angles may be determined based on the independently observable error variable values. For example, the corrected gimbal angles may be gimbal angles that minimize or reduce pointing error based on the independently observable error variable values. The method also includes, at  516 , applying the corrected gimbal angles to point the pointing device. The method may repeat iteratively, by returning to  504  to again measure the pointing error, until the pointing error is less than the threshold accuracy  506 . 
   Referring to  FIG. 6 , a method of adjusting gimbal angles is shown. In a particular embodiment, the method is used with respect to a gimbal system that includes at least two, two-axis gimbals moveably coupling a pointing device (e.g., an antenna, a laser, or an optical device) to a host vehicle (e.g., a satellite, aircraft, or ship), such as the systems illustrated in  FIGS. 1 and 2 . The method includes, at  608 , determining an initial set of gimbal angles  610  based on an estimate of independently observable error variable values  602 , target coordinates  604  for a pointing device, and host vehicle attitude data  606 . The independently observable error values may be estimated based on analysis of the gimbal system after manufacturing, based on previous measurements related to the error values, or any combination thereof. The initial set of gimbal angles  610  can be determined by calculating an azimuth and an elevation angle for each gimbal based on the target coordinates  604  and the host vehicle attitude data  606  and accounting for the estimates of the independently observable error variables  602 . In an illustrative embodiment, the independently observable error variable values  602  include error values related to rotation of host vehicle about an x-, y- or z-axis; an error value related to non-orthogonality of the first gimbal; error values related to rotation of the platform about an x-, y-, or z-axis; an error value related to non-orthogonality of the second gimbal; error values related to rotation of the pointing device about an x-, y-, or z-axis; or any combination thereof. 
   The method also includes, at  612 , pointing the pointing device, which may be an antenna, at a target based on a set of gimbal angles. During a first pass through the method, the set of gimbal angles may be the initial set of gimbal angles  610 . In a particular embodiment, pointing the pointing device at the target includes, at  614 , adjusting the gimbal angles of a platform gimbal and of an antenna gimbal. 
   The method may also include, at  618 , determining bore sight pointing errors  620  resulting from a pointing direction of the antenna relative to the target. The bore sight pointing errors may be detected by performing an adjustment of the pointing device with respect to a bore sight maximum signal sensing measurement and by determining differences in direction between the bore sight maximum point and the prior target point to determine the bore sight pointing errors  620 . The bore sight pointing measurement may be observed and used to identify gimbal angles needing adjustment. In a particular embodiment, a mapping matrix  616  is used in connection with performing the bore sight measurement to provide mapped pointing errors with respect to each of the gimbal angles. 
   At  624 , the bore sight pointing error data  620  is compared to a pointing error threshold  622 . If the pointing error  620  is less than the threshold  622 , then the method terminates at  626 . If the pointing error  620  is not less than the threshold  622 , then the method continues to  630 . At  630 , the method estimates a plurality of independently observable error values  634  based on the bore sight pointing errors  620 . In a particular embodiment, values of the independently observable error variables may be estimated, at  632 , based on the bore sight pointing errors using a mapping matrix  628 . 
   The method may also include, at  636 , determining a set of gimbal angle corrections  638  based on the independently observable error variable values  634 . The gimbal angle corrections  638  may be used, at  640 , to determine an adjusted set of gimbal angles  650  for pointing the antenna to compensate for the measured bore sight pointing errors. The adjusted set of gimbal angles  650  may be used to adjust the pointing of the antenna to point at the target (or at a new target) based on the adjusted set of gimbal angles  650 . The method may iterate until the observed bore sight pointing errors  620  are less than the threshold  622 . After the threshold accuracy  622  is achieved, new gimbal angle corrections  638  may be calculated based on the estimated independently observable error variable values  634  to point the pointing device based on other target coordinates or other host vehicle attitude data  606 . 
   Referring to  FIG. 7  a method of adjusting gimbal angles is shown. In a particular embodiment, the method may be used with respect to a gimbal system including two or more gimbals, each having two or more axes, such as the gimbal systems illustrated in  FIGS. 1 and 2 . The method of  FIG. 7  illustrates calibrating the gimbal system based on multiple attitudes of a host vehicle coupled to the gimbal system. To maintain a pointing direction using the gimbal system as the host vehicle attitude changes, gimbal angles of the gimbal system are adjusted to maintain the pointing direction. 
   The method includes, at  704 , pointing an antenna at a target based on the initial set of gimbal angles  702 . For example, the initial set of gimbal angles  702  may specify an azimuth angle and an elevation angle for each of the two or more gimbals of the gimbal system. The method further includes, at  706 , determining bore sight pointing errors  708  resulting from a pointing direction of the antenna relative to the target. The method also includes, at  710 , estimating values of a plurality of independently observable error variables based on the bore sight pointing errors  708  to produce the independently observable error variable values  712 . In a particular illustrative embodiment, the independently observable error variables include variables related to error that can be observed based on bore sight measurements with respect to the antenna (or other pointing device). For example, where the gimbal system includes a host vehicle interface, a platform gimbal coupled to the host vehicle interface and supporting a platform, and an antenna gimbal coupled to the platform supporting the antenna, the independently observable error variables may include rotation of the host vehicle about an x-, y- or z-axis; non-orthogonality of the first gimbal; rotation of the platform about an x-, y-, or z-axis; non-orthogonality of the second gimbal; rotation of the pointing device about an x-, y-, or z-axis; or any combination thereof. 
   The method also includes, at  714 , determining a set of gimbal angle corrections  716  for pointing the antenna. The gimbal angle corrections  716  adjust the initial gimbal angles  702  to account for the independently observable error variable values  712 . 
   The method also includes, at  720 , pointing the antenna at the target based on a subsequent set of gimbal angles  718 . The subsequent set of gimbal angles  718  may include gimbal angles to point at the target from a different location or based on a different host vehicle attitude than the initial set of gimbal angles  702 . 
   In a particular embodiment, the method further includes, at  722 , determining bore sight pointing errors  724  resulting from a pointing direction of the antenna relative to the target using the subsequent set of gimbal angles  718 . The method may also include, at  726 , estimating the values of the plurality of independently observable error variables based on the bore sight pointing errors  724  to produce a second set of independently observable error variable values  728 . 
   The second set of independently observable error variable values  728  may be used, at  730 , to determine a second set of gimbal angle corrections  732  for pointing the antenna. The method may also include, at  734 , determining an adjusted set of gimbal angles  736  based on the second set of gimbal angle corrections  732 . 
   In a particular embodiment, a next set of gimbal angles is provided to point the antenna, at  750 . The next set of gimbal angles may point at the same target from a different location of the antenna (or host vehicle) or from a different orientation of the host vehicle. Alternately, the next set of gimbal angles may point to a different target. 
   In a particular embodiment, the adjusted set of gimbal angles  736 , the first set of gimbal angle corrections  716 , the second set of gimbal angle corrections, other gimbal angle corrections or adjusted gimbal angles, or any combination thereof, may be used, at  738 , to determine representative gimbal angle corrections  740 . The representative gimbal angle corrections  740  are used to control the gimbal system with respect to pointing of an antenna or other pointing device. 
   Referring to  FIG. 8 , another illustrative embodiment of a method of adjusting gimbal angles is shown. In a particular embodiment, the method may be used with respect to a gimbal system that includes at least two, two-axis gimbals moveably coupling a pointing device (e.g., an antenna, a laser, or an optical device) to a host vehicle (e.g., a satellite, aircraft, or ship), such as the systems illustrated in  FIGS. 1 and 2 . The method illustrated in  FIG. 8  relates to calibrating the gimbal system using two or more sets of target coordinates. 
   The method includes, at  804 , determining an initial set of gimbal angles  806  based on target coordinates  802  of a first target. The method also includes, at  808 , pointing an antenna at the first target based on the initial set of gimbal angles  806 . The method further includes, at  810 , determining bore sight pointing errors  812  resulting from a pointing direction of the antenna relative to the target. For example, the bore sight pointing errors  812  may indicate that a peak signal strength of the antenna is not aligned with the first target. 
   Based on the bore sight pointing errors  812 , values of independently observable error variables  816  may be estimated, at  814 . In an illustrative embodiment, the independently observable error variable values  816  include error values related to rotation of the host vehicle about an x-, y- or z-axis; an error value related to non-orthogonality of the first gimbal; error values related to rotation of the platform about an x-, y-, or z-axis; an error value related to non-orthogonality of the second gimbal; error values related to rotation of the pointing device about an x-, y-, or z-axis; or any combination thereof. The values of the independently observable variables  816  may be estimated based on a set of boresight pointing errors  812  obtained from measuring the location of the peak signal strength of the antenna relative to the target direction as determined by the current values of the independently observable variables  816  and other associated knowledge. The method also includes, at  818 , determining a set of gimbal angle corrections  820  for pointing the antenna based on the independently observable error variables  816 . 
   The method may also include, at  824 , determining a second set of gimbal angles  826  to point at a second or subsequent target  803 . The second set of gimbal angles  826  may be determined taking into consideration the previously determined gimbal angle corrections  820 , or without considering the previously determined gimbal angle corrections  820 . 
   The method also includes, at  828 , pointing an antenna at the second target based on the second set of gimbal angles  826 , and, at  830 , determining bore sight pointing errors  832  resulting from a pointing direction of the antenna relative to the second target. Based on the bore sight pointing errors  832 , values of the independently observable error variables  836  may be estimated, at  834 . The independently observable error variables  836  may be the same as the previous independently observable variables  816 , or may include different variables. For example, the first bore sight pointing errors  812  may be used to determine values of a first subset for the independently observable variables, and the second bore sight pointing errors  832  may be used to determine values of a second subset of the independently observable variables. 
   The method also includes, at  838 , determining a second set of gimbal angle corrections  840  for pointing the antenna based on the independently observable error variables  836 . The method may iteratively determine additional gimbal angle corrections based on different target coordinates by providing coordinates of a next target  844 . Additionally, a representative set of gimbal angle corrections  850  may be determined, at  842 , based on the first gimbal angle corrections  820 , the second gimbal angle corrections  840 , subsequent gimbal angle corrections based on iterations of the method, or any combination thereof. The representative gimbal angle corrections  850  may be used to point the antenna during operation. 
   Referring to  FIG. 9 , a method of pointing an antenna is shown. The method includes, at  902 , determining a set of at least four nominal gimbal angles to point an antenna at a target based at least partially on location information associated with the target. In a particular embodiment, the set of at least four nominal gimbal angles is used to position a first gimbal coupled to a host vehicle and a second gimbal coupled to the first gimbal. In addition, the set of at least four nominal gimbal angles may be determined based at least partially on attitude information related to the host vehicle and the coordinates of a first target. The set of at least four nominal gimbal angles may include an azimuth and an elevation angle for a first gimbal, and an azimuth and an elevation angle for a second gimbal. In an illustrative embodiment, the set of at least four nominal gimbal angles is determined by, at  904 , determining values of a plurality of independently observable error variables based on one or more bore sight measurements, and, at  906 , determining gimbal angle corrections by applying the values of the independently observable error variables to a mapping matrix. 
   The method also includes, at  908 , identifying a set of adjusted or corrected gimbal angles based on the set of at least four nominal gimbal angles and based on a set of gimbal angle corrections. The gimbal angle corrections may be determined based at least partially on one or more bore sight measurements of the antenna. 
   In a particular embodiment, the method further includes, at  910 , pointing the antenna using a gimbal system that receives the set of corrected gimbal angles. Thus, the method conveniently uses readily available bore sight measurements of a pointing device, such as an antenna, to determine independently observable error variable values to adjust the gimbal angles to compensate for errors in pointing of the pointing device. 
     FIG. 10  depicts a graph that illustrates representative pointing error data expected based on simulation of the calibration methods and systems previously discussed. The graph shows convergence of calibration data related to calibrating pointing of an antenna mounted on two gimbals with each of them having two axes. Simulated pointing error convergence data  1002  illustrates that North-South error decreases as the number of calibrations increases. Similarly, the simulated error convergence data  1104  illustrates that East-West error decreases as the number of calibrations increases. The calibration simulation is based on using bore sight observations to determine values of a set of independently observable error variables. Specifically, the independently observable error variables simulated include: rotation of a host vehicle about an x-, y- or z-axis; non-orthogonality of a first gimbal mounted to the host vehicle; rotation of a platform mounted to the first gimbal about an x-, y-, or z-axis; non-orthogonality of a second gimbal mounted to the platform; and rotation of the antenna mounted to the second gimbal about an x- or y-axis. 
   The disclosed double gimbal system calibration approach is useful for applications with moving host vehicles, such as satellite applications where multiple mission functionality is desired. For example, a first 2-axis platform gimbal can compensate for motion of the satellite based on real-time commands while a secondary 2-axis antenna gimbal can be used for target tracking based on the relatively stable platform afforded by the platform gimbal system. The teachings of this disclosure can be expanded for use with more than two 2-axis gimbal components, such as for a gimbal system including three or more gimbals. The calibration approach disclosed beneficially provides operational flexibility to support a robust calibration technique without requiring a user to provide multiple geometrically diverse calibration targets. Thus, calibration target selection is simplified.