Abstract:
A method and apparatus for calibrating rate sensor measurements to compensate for rate sensor scale factor non-linearities. An outer loop compensator compares current rate sensor scale factor estimates with the current scale factor non-linearity compensation, and deviations from the current non-linearity compensation are corrected in an updated compensation.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to the following co-pending and commonly assigned patent application(s), all of which applications are incorporated by reference herein: 
     application Ser. No. 09/212,454, entitled “AUTONOMOUS GYRO SCALE FACTOR AND MISALIGNMENT CALIBRATION,” filed on Dec. 16, 1998, by Rongsheng Li, Yeong-Wei Wu and Garry Didinsky, now U.S. Pat. No. 6,298,288. 
    
    
     STATEMENT OF RIGHTS OWNED 
     This invention was made with Government support. The Government has certain rights in this invention. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to systems and methods for spacecraft navigation, and in particular to a spacecraft attitude determination system for correcting gyro scale factor non-linearity. 
     2. Description of the Related Art 
     Satellite navigation systems typically include an attitude determination system. Attitude determination systems typically comprises one or more rate sensors (which provide measurements of the rotation rate of the spacecraft) and one or more attitude sensors (which measure the attitude of the spacecraft). Rate sensors may include mechanical gyros, ring laser gyros (RLGs), or similar devices. Attitude sensors include, for example, sun sensors, earth sensors, and/or star trackers. Typically, sun and earth sensors are used to provide a rough spacecraft attitude estimate (useful, for example in recovering from large spacecraft motions), while the star trackers provide a more accurate attitude estimates. 
     For agile spacecraft, gyro scale factor and misalignment errors contribute significantly to spacecraft attitude determination errors. To ameliorate this problem, a Kalman filter can be used to generate estimates of the spacecraft attitude, gyro scale factors and gyro misalignments. Using such estimates, substantial performance improvements can be obtained. However, the Kalman filters used in such designs typically assume that the gyro scale factors are constant across different measured angular rates. What is needed is an attitude control system that compensates for rate sensor scale factor errors, without rendering the Kalman filter algorithms unnecessarily complex. The present invention satisfies that need. 
     SUMMARY OF THE INVENTION 
     To address the requirements described above, the present invention discloses a method and apparatus for calibrating rate sensor measurements to compensate for rate sensor scale factor non-linearities. The method comprises the steps of generating a current rate sensor scale factor estimate; generating a deviation of the scale factor estimate from a current scale factor non-linearity correction mapping; generating an updated scale factor non-linearity correction mapping from the deviation of the scale factor estimate from the current scale factor non-linearity correction mapping; and mapping the rate sensor measurement according to the current scale factor non-linearity correction mapping. The apparatus comprises a plurality of modules that can be implemented in hardware or in software by one or more processors. The modules include a first module for estimating a gyro scale factor; a second module, communicatively coupled to the first module, for generating a deviation of the scale factor estimate from a current scale factor non-linearity correction mapping; a third module, communicatively coupled to the second module for generating an updated scale factor non-linearity correction mapping from the deviation of the scale factor estimate from the current scale factor non-linearity correction mapping; and a fourth module, communicatively coupled to the third module, for mapping the rate sensor measurement according to the current scale factor non-linearity correction mapping. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Referring now to the drawings in which like reference numbers represent corresponding parts throughout: 
     FIG. 1 illustrates a three-axis stabilized satellite or spacecraft; 
     FIG. 2 is a diagram depicting the functional architecture of a representative attitude control system; 
     FIG. 3 is a block diagram of an attitude determination system; 
     FIG. 4 is a graph illustrating typical gyro scale factor non-linearity errors; 
     FIG. 5 is a diagram illustrating an attitude determination system having an outer loop compensator for gyro scale factor non-linearity errors; 
     FIG. 6 is a diagram presenting a further illustration of how the gyro scale factor non-linearity correction can be generated; and 
     FIG. 7 is a flow chart presenting illustrative process steps that could be used to practice one embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     In the following description, reference is made to the accompanying drawings which form a part hereof, and which is shown, by way of illustration, several embodiments of the present invention. It is understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. 
     Attitude Control Systems 
     FIG. 1 illustrates a three-axis stabilized satellite or spacecraft  100 . The spacecraft  100  is preferably situated in a stationary orbit about the Earth. The satellite  100  has a main body  102 , a pair of solar panels  104 , a pair of high gain narrow beam antennas  106 , and a telemetry and command omni-directional antenna  108  which is aimed at a control ground station. The satellite  100  may also include one or more sensors  110  to measure the attitude of the satellite  100 . These sensors may include sun sensors, earth sensors, and star sensors. Since the solar panels are often referred to by the designations “North” and “South”, the solar panels in FIG. 1 are referred to by the numerals  104 N and  104 S for the “North” and “South” solar panels, respectively. 
     The three axes of the spacecraft  10  are shown in FIG.  1 . The pitch axis P lies along the plane of the solar panels  140 N and  140 S. The roll axis R and yaw axis Y are perpendicular to the pitch axis P and lie in the directions and planes shown. The antenna  108  points to the Earth along the yaw axis Y. 
     FIG. 2 is a diagram depicting the functional architecture of a representative attitude control system. Control of the spacecraft is provided by a computer or spacecraft control processor (SCP)  202 . The SCP performs a number of functions which may include post ejection sequencing, transfer orbit processing, acquisition control, stationkeeping control, normal mode control, mechanisms control, fault protection, and spacecraft systems support, among others. The post ejection sequencing could include initializing to assent mode and thruster active nutation control (TANC). The transfer orbit processing could include attitude data processing, thruster pulse firing, perigee assist maneuvers, and liquid apogee motor (LAM) thruster firing. The acquisition control could include idle mode sequencing, sun search/acquisition, and Earth search/acquisition. The stationkeeping control could include auto mode sequencing, gyro calibration, stationkeeping attitude control and transition to normal. The normal mode control could include attitude estimation, attitude and solar array steering, momentum bias control, magnetic torquing, and thruster momentum dumping (H-dumping). The mechanisms mode control could include solar panel control and reflector positioning control. The spacecraft control systems support could include tracking and command processing, battery charge management and pressure transducer processing. 
     Input to the spacecraft control processor  202  may come from a any combination of a number of spacecraft components and subsystems, such as a transfer orbit sun sensor  204 , an acquisition sun sensor  206 , an inertial reference unit  208 , a transfer orbit Earth sensor  210 , an operational orbit Earth sensor  212 , a normal mode wide angle sun sensor  214 , a magnetometer  216 , and one or more star sensors  218 . 
     The SCP  202  generates control signal commands  220  which are directed to a command decoder unit  222 . The command decoder unit operates the load shedding and battery charging systems  224 . The command decoder unit also sends signals to the magnetic torque control unit (MTCU)  226  and the torque coil  228 . 
     The SCP  202  also sends control commands  230  to the thruster valve driver unit  232  which in turn controls the liquid apogee motor (LAM) thrusters  234  and the attitude control thrusters  236 . 
     Wheel torque commands  262  are generated by the SCP  202  and are communicated to the wheel speed electronics  238  and  240 . These effect changes in the wheel speeds for wheels in momentum wheel assemblies  242  and  244 , respectively. The speed of the wheels is also measured and fed back to the SCP  202  by feedback control signal  264 . 
     The spacecraft control processor also sends jackscrew drive signals  266  to the momentum wheel assemblies  243  and  244 . These signals control the operation of the jackscrews individually and thus the amount of tilt of the momentum wheels. The position of the jackscrews is then fed back through command signal  268  to the spacecraft control processor. The signals  268  are also sent to the telemetry encoder unit  258  and in turn to the ground station  260 . 
     The spacecraft control processor also sends command signals  254  to the telemetry encoder unit  258  which in turn sends feedback signals  256  to the SCP  202 . This feedback loop, as with the other feedback loops to the SCP  202  described earlier, assist in the overall control of the spacecraft. The SCP  202  communicates with the telemetry encoder unit  258 , which receives the signals from various spacecraft components and subsystems indicating current operating conditions, and then relays them to the ground station  260 . 
     The wheel drive electronics  238 ,  240  receive signals from the SCP  202  and control the rotational speed of the momentum wheels. The jackscrew drive signals  266  adjust the orientation of the angular momentum vector of the momentum wheels. This accommodates varying degrees of attitude steering agility and accommodates movement of the spacecraft as required. 
     The use of reaction wheels or equivalent internal torquers to control a momentum bias stabilized spacecraft allows inversion about yaw of the attitude at will without change to the attitude control. In this sense, the canting of the momentum wheel is entirely equivalent to the use of reaction wheels. 
     Other spacecraft employing external torquers, chemical or electric thrusters, magnetic torquers, solar pressure, etc. cannot be inverted without changing the control or reversing the wheel spin direction. This includes momentum bias spacecraft that attempt to maintain the spacecraft body fixed and steer payload elements with payload gimbals. 
     The SCP  202  may include or have access to memory  270 , such as a random access memory (RAM). Generally, the SCP  202  operates under control of an operating system  272  stored in the memory  270 , and interfaces with the other system components to accept inputs and generate outputs, including commands. Applications running in the SCP  202  access and manipulate data stored in the memory  270 . The spacecraft  10  may also comprise an external communication device supporting a satellite command link for communicating with other computers at, for example, a ground station. If necessary, operation instructions for new applications can be uploaded from ground stations. 
     In one embodiment, instructions implementing the operating system  272 , application programs, and other modules are tangibly embodied in a computer-readable medium, e.g., data storage device, which could include a RAM, EEPROM, or other memory device. Further, the operating system  272  and the computer program are comprised of instructions which, when read and executed by the SCP  202 , causes the spacecraft processor  202  to perform the steps necessary to implement and/or use the present invention. Computer program and/or operating instructions may also be tangibly embodied in memory  270  and/or data communications devices (e.g. other devices in the spacecraft  10  or on the ground), thereby making a computer program product or article of manufacture according to the invention. As such, the terms “program storage device,” “article of manufacture” and “computer program product” as used herein are intended to encompass a computer program accessible from any computer readable device or media. 
     Attitude Determination System 
     FIG. 3 is a block diagram of an attitude determination system  300 . The attitude determination system  300  is communicatively coupled to the rate sensors (e.g. gyros)  320  and star trackers  218 . The gyros (which are typically part of the inertial reference unit  208 ) provide measurements of the rotation rate of the satellite,  100 . Typically, such measurements are taken in three separate orthogonal axes by three different instruments. Often, the gyros are integrated with accelerometers to comprise the inertial reference unit  208 . 
     The attitude determination system  300  includes a gyro data processor  302  communicatively coupled to the gyro(s)  320  to receive satellite rotation rate data. The gyro data processor processes the raw spacecraft rotation rate measurement data to provide processed rate data or changes in spacecraft attitude (delta angles). This data is provided to a gyro data correction module  304 . The gyro data correction module  304  further processes the spacecraft rotation rate data to account for gyro biases, gyro scale factors, and gyro misalignments. The estimates of the gyro biases, gyro scale factors, and gyro misalignments are provided by a Kalman filter  306 . 
     The attitude determination system  300  also includes an attitude propagation module  308  communicatively coupled to the gyro data correction module  304 . The attitude propagation module  308  accepts corrected gyro data (spacecraft  100  rotation rates or incremental angles) from the gyro data correction module  304  as well as estimated attitude corrections from the Kalman filter  306 , and generates an attitude estimate. 
     The Kalman filter generates the foregoing estimates from information provided by the attitude propagation module  308  (which provides data ultimately derived primarily from the gyro  320  data) and a star identification module  312  (which provides attitude data derived from the star trackers  218 ). The star identification module  312  provides the attitude information by comparing measured star positions from the star trackers  218  and star tracker data processor  310  with information in the star catalog  314 . 
     The foregoing elements create an inner loop  316  compensator which can provide reasonably good estimates of spacecraft  100  attitude, changes in scale factor linearity are not adequately accounted for in highly agile spacecraft applications. In some cases, the errors in spacecraft attitude determination induced by such errors exceed the minimum performance requirements. 
     FIG. 4 is a graph illustrating typical gyro scale factor non-linearity errors. The horizontal axis represents the rotation rate input into the gyro, and the vertical axis represents the scale factor error in parts per million (PPM). As shown in FIG. 4, gyro scale factor errors (in terms of parts per million) are largest for small angular rate inputs. FIG. 4 also shows that scale factor error is a function of the input rate. 
     FIG. 5 is a diagram illustrating an attitude determination system  500  having an outer loop  506  compensator for gyro scale factor non-linearity errors. In addition to the elements described in FIG. 3, the attitude determination system  500  includes a gyro scale factor non-linearity correction module  502  in communication with the gyro data processing module  302  and the gyro data correction module  304 . The gyro data correction module  502  accepts updated gyro non-linearity correction information and provides the current gyro non-linearity correction to a deviation module  504 . The deviation module  504  accepts the estimated gyro scale factor information from the Kalman filter  306  and the current gyro non-linearity correction, and computes an estimate of the deviation between the estimated gyro scale factor and the currently implemented correction. 
     An updated scale factor non-linearity correction is then created, as represented in block  506 , and provided to the gyro scale factor non-linearity correction module  502 . In one embodiment, the updated scale factor non-linearity correction is a lookup table relating the rate input measurement with the required correction (or compensated rate measurement), and an interpolator in block  502  generates the precise value for rate inputs between data points. In another embodiment, the correction is a curve fitted to the data points, and the value is determined by evaluating the fitted curve. 
     Preferably, the estimated gyro scale factor information is obtained at a plurality of different spacecraft  100  rotation rates using the inner loop  316 . The estimated scale factors are associated with the corresponding spacecraft  100  rates and collected. From time to time, the estimated scale factors and rotation rates can then be sorted and used to generate an updated scale factor that is a function of input rate. These operations can be performed periodically (e.g. weekly, monthly), or as the need arises. For example, temporal variations in the rate sensor scale factor estimates can be examined to determine if they are converging, and the updated scale factor and/or scale factor linearity mapping determined only if the estimates are sufficiently converged. Further, the foregoing operations can be performed in a processor on-board the satellite  100  or on the ground, or a combination of both. 
     FIG. 6 is a diagram presenting a further illustration of how the gyro scale factor non-linearity correction is generated. The Kalman filter  306  generates an estimate of the gyro scale factor, and that estimate is provided to the derivation module  504 . The gyro scale factor  600 A is indicated in FIG. 6 as a plot of a relationship between the measured angular rate ω meas  and the actual rate ω(since the Kalman filter does not provide an estimate of gyro scale factor non-linearity, the plot is a straight line, indicating that there is a linear relationship between the input rate ω and the measured angular rate ω meas ). The gyro scale factor non-linearity scale factor correction module  502  provides the current scale factor correction  600 B to the derivation module as well. The current scale factor correction is illustrated in FIG. 6 as a plot showing a relationship between the measured spacecraft angular rotation rates (perhaps after pre-processing) and the measured rate. This data is provided to differencer  602 . The difference between these two data sets represents the difference between the current scale factor non-linearity correction and the currently estimated scale factor, and is shown in plot  600 C. The sorter  604  sorts the data according to the input rate ω, resulting in the plot  600 D, and an updated non-linearity correction is formed in block  506 , resulting in plot  600 E. 
     FIG. 7 is a flow chart presenting illustrative process steps that could be used to practice one embodiment of the present invention. A rate sensor scale factor estimate is generated, as illustrated in block  702 . In one embodiment, this is accomplished by a Kalman filter  306 , however, other optimal estimation techniques can be used. A deviation of the scale factor estimate from a current scale factor non-linearity correction mapping is then determined, as shown in block  704 . In one embodiment this is accomplished by determining a difference between the scale factor estimate and a current scale factor non-linearity correction mapping and associating the difference with an estimated rate sensor measurement. 
     An updated scale factor non-linearity correction mapping is then generated from the deviation of the scale factor estimate from the current scale factor non-linearity correction mapping, as shown in block  706 . The mapping can take one or more of several forms, including a set of discrete data points relating the rate measurements and the non-linearity correction, or a continuous curve. In the case of the discrete mapping, corrections for data falling between representative values for rate measurements can be obtained by interpolation or extrapolation as required. In the case of curve fitting, a curve can be fit to the data points (e.g. exponential, power curve, or polynomial curve fitting routines using minimum mean squared error criteria). 
     Then, as depicted in block  708 , the rate sensor measurements are mapped according to the current scale factor non-linearity correction mapping. 
     In one embodiment, all of the foregoing operations are performed on a single spacecraft control processor  202  on the spacecraft  100  itself, however, this need not be the case. Any of the foregoing operations can be implemented in a special purpose processor with an associated memory (or shared memory with any of the other processors), or may be completely or partially implemented by a processor on the ground and by transmitting data between the satellite  100  and the ground station. 
     Conclusion 
     This concludes the description of the preferred embodiments of the present invention. The foregoing description of the preferred embodiment of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto. The above specification, examples and data provide a complete description of the manufacture and use of the composition of the invention. Since many embodiments of the invention can be made without departing from the spirit and scope of the invention, the invention resides in the claims hereinafter appended.