Abstract:
A vehicular position and attitude can be accurately determined from GPS signals by positioning a master and two slave orthogonally disposed receiver antennas rigidly mounted together enabling the rotation of the slave receiver antennas about the master antenna. The slave antennas are rotated and then dither back and forth so that differential phase measurements between the slave antennas and the master antenna is nulled in carrier phase alignment of the GPS signals for determining azimuth angles and elevation angles to the GPS satellites for determining the position and attitude of the vehicle.

Description:
FIELD OF THE INVENTION 
     The invention relates to the field of attitude reference determination of moving vehicles. More particularly, the present invention relates to attitude reference determination of spacecraft providing carrier integer cycle ambiguity resolution. 
     BACKGROUND OF THE INVENTION 
     Aircraft and spacecraft vehicles require methods and apparatus for accurately determining respective positions during flight missions. Position determination has been improved using the Global Position System (GPS) that includes a constellation of orbiting GPS satellites broadcasting ephemeral signals to receivers. The receivers may be fixed at a ground base or carried onboard a moving ground, airborne or space vehicle. Position determinations resulting in determined points in space as well as an attitude reference using GPS is well known in the art. During GPS position determination applications, a range distance between a receiver and a GPS satellite is determined by measuring the time it takes for the pseudo random signal to travel the distance from the GPS satellite to the receiver. Knowing four range measurements from four respective different GPS satellites to the receiver, the receiver position can be uniquely determined by well known spatial reference frame computational processes. The receiver position is the location of the receiver in three dimensional X, Y, Z space. The attitude of a vehicle is an angular orientation that requires the position of at least three receiver antennas to achieve centimeter level accuracy. However, the accuracy of these range measurements is of the order of several meters and therefore the range measurements are not precise enough for determining the attitude of the vehicle as an angular orientation reference. Another measurable quantity of the GPS signal is the carrier phase that is a fractional part of a carrier cycle. The carrier phase needs to be precisely determined for improved accuracy of the position determination. Before the fractional carrier phase measurements at the antennas can be converted into receiver to satellite ranges, knowledge of the integer cycles spanning these ranges is required. The integer cycles can be ambiguously determined due to a lack of precise range determinations. A number of approaches currently exist to resolve this integer cycle ambiguity. However, the current methods suffer various computational problems limiting the ability to effectively determine the carrier cycles. Earlier software based approaches utilize an integer search method attempting to minimize a cost function. The software based approaches check different sets of integer values that can number in millions for antennas separated by just a few meters. The problems that arise with this software based approach include the existence of nonunique solutions that create the possibility of converging to a wrong set of integers. Also, due to existence of a very large set of integer combinations, processing takes large amount of time to check all of the integer possibilities. This limits the reaction time of an agile vehicle. Further, most search algorithms may not always converge to a solution. Another current approach utilizes integer resolution algorithms that use additional information due to motion of the vehicle to determine the integer cycle of the carrier. These integer resolution algorithms possess the same inherent computational problems that are not significantly reduced. These and other disadvantages are solved or reduced using the invention. 
     SUMMARY OF THE INVENTION 
     An object of the invention is to provide a method for attitude reference determination. 
     Another object of the invention is to provide a method for determining elevation angles and azimuth angles to pseudo stars. Another object of the invention is to provide a method for determining elevation angles and azimuth angles to pseudo stars for attitude reference determination. 
     Yet another object of the invention is to provide a method for determining elevation and azimuth angles to GPS satellites by rotating receiver antennas about a reference axis and dithering the antennas along an orthogonal axes for carrier phase alignment of the received GPS signals. 
     Still another object of the invention is to provide a method for positioning receiver antennas in carrier phase alignment of GPS signals by rotation about a reference axis and dithering the receiver antennas along orthogonal axes for determining a position and attitude in inertial space. 
     A further object of the invention is to provide a method for positioning receiver antennas by rotation about an attitude axis and dithering along orthogonal axes for receiving GPS signals in carrier phase alignment when the antennas are orthogonally positioned for determining the attitude axis. 
     The invention is a method directed to positioning receiver antennas in carrier phase alignment of GPS signals for determining coelevation and azimuth angles to GPS satellites. The coelevation and azimuth angles can be used for determining the attitude of the vehicle in an inertial reference frame from known GPS satellite lines of sight. The method can be preferably used for determining the attitude of a airborne or spaceborne craft receiving GPS signals from GPS satellites functioning as pseudo star references. The method is practiced using a GPS receiver system and signal processing algorithms that determine the attitude of an arbitrary ground receiver, aircraft or spacecraft. In the preferred form,,the system uses a master antenna and two dependent slave antennas, each of which having a respective receiver for receiving the GPS signals. The antennas are orthogonally aligned respecting each other and are controlled to undergo prescribed motions relative to each other. A fractional phase of the GPS carrier signal received at each of two dependent slave antennas is measured relative to the master antenna. Processing of the measured carrier signal is used to eliminate the integer cycle ambiguity for determining the attitude reference by computing two noncolinear lines of sight vectors. The method comprises of means to determine more than one noncolinear unit vector along the lines of sight from the master antenna to GPS satellites functioning as pseudo stars. 
     The method includes signal processing steps to compute the unit vectors in two coordinate systems. The two coordinate systems are an earth centered inertial coordinate system and a local coordinate frame system attached to the craft. The signal processing steps are provided to compute the attitude from the direction cosine matrix between the local coordinate system and the earth centered inertial coordinate system. The system preferably includes the set of three antennas mounted on a rigid frame forming essentially two orthogonal directions. A first orthogonal direction extends from the first master antenna to the second x axis slave antenna along an x axis. A second orthogonal direction extends from the master antenna to a third y axis antenna along a y axis. The system provides motors for rotating the rigid frame about a vertical z axis extending through the master antenna. Each of the second and third slave antennas are controlled to undergo back-and-forth dither motion along respective orthogonal lines respectively extending from the master antenna to the second and third antennas. A controller rotates the frame about the z axis for positioning the rigid frame while controlling the two slave antennas to respectively undergo the dither motion along the x axis and y axis. A system includes a microprocessor that continuously measures the differential carrier phase between the master antenna and the x axis antenna and between the master antenna and y axis antenna. Signal processing steps of the differential phase data enables determination of the unit vectors along the line of sights from the master antenna and various GPS satellites. The lines of sight data is used for accurately determining the attitude reference of the vehicle. The position and attitude can be determined without resolving carrier phase ambiguity. These and other advantages will become more apparent from the following detailed description of the preferred embodiment. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 depicts a satellite coordinate system. 
     FIG. 2 depicts equiphase geometry of receiver antenna locations. 
     FIG. 3 depicts generic hardware for the preferred embodiment. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     An embodiment of the invention is described with reference to the figures using reference designations as shown in the figures. Referring to FIG. 1, three GPS receiver antennas R 1 , RA, and R 3  are mounted on the vehicle, not shown, having a position and attitude in inertial space. The receiver antenna R 1  is a first master antenna on a vehicle that has a relative attitude and a position in inertial space. The R 2  receiver antenna is a second slave antenna. The receiver antenna R 3  is a third slave antenna. The attitude of the vehicle is defined with respect to a local orthogonal coordinate frame with the origin point at R 1 . A line extending between receivers R 1  and R 2  defines a local x axis. A line extending between receivers R 1  and R 3  defines a local y axis. A z axis extends through the master receiver R 1  and is defined by the right-hand rule of the cross-product between the x axis and y axis. The x axis, y axis and z axis form a reference frame for attitude determination. A curved arrow around the z axis indicates that the antennas can be rotated about the z axis through the full 360 degrees providing a capability to position R 2  and R 3  slave antennas at any desired angular position in the local x-y plane. An R 1  line of sight is the vector from master antenna R 1  to a GPS satellite S. 
     The angle θ is an azimuth angle and the angle φ is a coelevation angle of the line of sight to the GPS satellite S functioning as a pseudo star. The azimuth angle and coelevation angle define the R 1  line of sight relative to the x, y and z local axes which are relative to a vehicle, not shown, having a position and attitude in inertial space. The positions R 2 ′ and R 3 ′ show the new locations of antennas R 2  and R 3  after being rotated through the azimuth angle θ. The double-headed arrows through R 2 ′ and R 3 ′ indicate that the R 2  and R 3  antennas can be controlled to undergo linear dither motion relative to the master antenna R 1  at the origin point. 
     Referring to FIGS. 1 and 2, the equiphase geometry of the antennas R 1  and R 3  is obtained after the antennas have been rotated through an angle θ about the z axis. In this configuration, the antenna R 2  occupies the new location R 2 ′ and the antenna R 3  occupies the new location R 3 ′. Before undergoing the rotation θ, the path length between R 1  and the satellite S can be represented in terms of an integer number of cycles n 1  plus a fractional phase φ 1 , that is, as (n 1 +φ 1 )λ, where λ is the wavelength of a GPS carrier signal. Similarly, before the rotation through the angle θ, the path length R 3  and the satellite S is (n 3 +φ 3 )λ. After rotation through the angle θ, the antennas R 2  and R 3  are positioned at the new R 2 ′ and R 3 ′ positions, respectively. At the R 3 ′ location, path lengths R 1  to S and R 3 ′ to S are exactly the same, that is, n 1 =n 3  and φ 1 =φ 3  at which location, there is a 90° degree angle between a baseline L B  and both the path lengths R 1  to S and R 3 ′ to S. This property of equal path lengths is utilized to determine the azimuth angle θ, by forcing the measurement of the fractional phase difference (φ 1 −φ 3 ) at R 1  and R 3  to go to zero in carrier phase alignment. The receiver antenna R 2  is dithered linearly as the fractional phase φ 2  is measured continuously. The coelevation angle φ is determined from changes in the fractional phase φ 2  as the receiver antenna R 2  travels from a point nearest to the receiver antenna R 1  to a point farthest from R 1 . 
     Referring to all of the Figures, and particularly to FIG. 3, receiver antennas R 2  and R 3  are disposed on the R 2  boom and the R 3  boom, respectively, forming an orthogonal structure that is mounted to a vehicle having an attitude of a spacecraft that is to be determined. The R 1  motor is secured to the vehicle and an angular position sensor can sense the relative angle of the R 2  and R 3  booms relative to the attitude of the vehicle. An R 1  rotational drive motor is used to rotate the booms so as to rotate the slave receiver antennas R 2  and R 3  about master receiver antenna R 1 . A microprocessor can provide for controlling a rotational motion controller that controls the R 1  rotational motor. The microprocessor can be further programmed to execute code correlation, range measurements, carrier phase measurements and attitude determinations. The R 1  rotation motor is connected to the R 1  boom and the R 2  boom using a shaft assembly providing a full 360 degrees of rotational freedom about the local z axis. The R 1  receiver has an antenna mounted at the junction of R 2  boom and the R 3  boom, forming the origin of the local x axis, y axis and z axis local coordinate system. The R 2  and R 3  receiver antennas are respectively mounted on R 2  and R 3  booms and at a nominal distance of L B  from the R 1  receiver antenna. The R 2  receiver antenna is connected to an R 2  linear dither motor that provides the capability of linearly moving the R 2  receiver along the R 2  boom relative to the R 1  receiver. Similarly, the R 3  receiver antenna is mounted on the R 3  boom and is connected to an R 3  linear dither motor also providing linear motion relative to the R 1  receiver antenna. The R 1  rotational drive motor and the R 2  and R 3  linear dither motors have angular position sensors that feed into the microprocessor. The microprocessor controls the position of the booms through the rotational motion controller. The microprocessor processes signals to perform GPS code correlation, range measurements, carrier phase measurements and attitude determination. 
     The microprocessor is used for determining the attitude of a vehicle, including roll, pitch and yaw angles with respect to a inertial frame of reference. The attitude of a vehicle can be determined when at least two noncolinear vectors, from the vehicle to known points in space, are available. For example, a unit vector, which lies along the R 1 -S line of sight (LOS) between antenna R 1  and the satellite S, can be defined by its components [l 1 l 2 l 3 ] in an inertial coordinate system X I , Y I , Z I . The same unit vector, along the R 1 -S line of sight, can also be represented by [sin φ cos θ, sin φ sin θ, cos φ] in the local X, Y, Z coordinate system. By definition, a vector in the local x, y, z coordinate system can be transformed to the inertial x I , y I , z I  coordinate system using a direction cosine matrix denoted by C B   I .          [           sin                 φ                 cos                 θ               sin                 φ                 cos                 θ               cos                 φ           ]     =       [     C   B   I     ]                [           l   1               l   2               l   3           ]                            
     When angles θ and φ are known for two independent noncolinear lines of sight vectors from antenna R 1  to GPS satellites, then the attitude matrix C B   I  can be determined. The system provides the means to compute azimuth angle θ and the coelevation angle φ from the fractional phase measurements made at the multiple antennas without the need to know integer number of cycles. When a receiver R 1  is located at the origin and R 2 , R 3  at a known distance L B  from R 1  along the local x, y axes, ranges R 1 -S and R 3 -S can be represented as R 1 -S=(n 1 +φ 1 )λ, where n 1  equals the integer cycles of the carrier signal and φ 1  equals the fractional phase that is measured. Similarly R 3 -S=(n 3 +φ 3 )λ. The desired azimuth angle θ can be expressed by an azimuth angle equation.          sin                 θ     =         [       (       n   3     -     n   1       )     +     (       ϕ   3     -     ϕ   1       )       ]                   λ       L   B                              
     In the azimuth angle equation, integer cycles are not observable from the fractional phase measurements and constitute a fundamental limitation in fully utilizing the high-resolution phase data for attitude determination. To illustrate this point, phase of a periodic signal can readily be determined with one percent accuracy. Therefore, measuring the L 1  phase of a GPS L 1  carrier signal at 1575.42 MHz can provide a spatial resolution of roughly 0.19 cm, which for a baseline of 1 meter translates into an attitude resolution of 0.10 degrees. However, this level of accuracy is possible only if integer cycles n 1  and n 3  in the azimuth angle equation are known. Hence, the integer number of cycles are eliminated and thereby provide a means to determine attitude with fractional phase measurements. 
     The set of three GPS receivers R 1 , R 2 , R 3  are mounted in a plane defined by the R 1 -R 2  line and the R 1 -R 3  line, respectively, for forming the x and y axes of the local coordinate system. The z axis is through the origin defined by the right-hand rule of x into y. The line-of-sight from the R 1  origin to a GPS satellite S is defined by spherical coordinates φ and θ. Means are provided to be able to rotate the antenna assembly about the z axis. It is seen that after a positive rotation of θ about the z axis, the difference in path lengths R 1 -S and R 2 -S would be a maximum and at the same time, receiver antennas R 1  and R 3  would be equidistant from the satellite, with a path length difference equal to zero. However, when a mechanized control system simultaneously nulls the phase difference between one of the pairs and maximizes on the other, the angle θ would still not be determined uniquely due to integer cycle ambiguity. The fractional phase difference between a pair of receiver antennas would be zero as long as the path length difference is an integer multiple of a wavelength. This means that, depending upon the length of the baseline L B  between the receivers, and the coelevation φ, there could be multiple values of θ in the 0° to 360° range for which the phase difference would be zero. To solve this problem, the relative linear dither motion between the pairs R 1 -R 2  and R 1 -R 3  is used. When the null phase difference is maintained between a pair of receiver antennas while the receivers are in relative linear motion along a line joining them, then both the receiver antennas must be equidistant from the satellite, and the angle θ is determined uniquely from a z axis angular position sensor reading for an angle relative to the vehicle. The coelevation angle φ can be solved by computation based on relative phase measurements. The rotational capability about the z axis is provided. After angle θ has been determined, the fractional phase φ 2  at antenna R 2  undergoing relative linear motion is measured. The coelevation angle φ can then be computed using the coelevation equation.          cos                 φ     =           [       (       n   2     +     ϕ     2      i         )     -     (       n   2     +   k   +     ϕ     2      f         )       ]                   λ       L   dither       =         [       ϕ     2      i       -     (     k   +     ϕ     2      f         )       ]                   λ       L   dither                                
     In the coelevation equation, k is the number of integer cycles elapsed as the antenna R 2  travels between the two extremes of the dither cycle that is continuously tracked between the measurements. And φ 2i  and φ 2f  are the fractional phases measured at the two extremes of the dither motion, and dither is the dither amplitude. This process of determining azimuth angle θ and coelevation angle φ is repeated with a second satellite to obtain the two noncolinear line of sight vectors. Further processing of this data provides the attitude of the vehicle. 
     The system could also include linear dither position sensors for measuring the dither length of the R 2  and R 3  receiver antennas. In the alternative method, the antenna structure could be attached to a vehicle through a gimbal system that provides the antenna structure with a three axis rotational freedom relative to the vehicle. After angle θ has been determined, antenna structure is rotated about the R 1 -R 3 ′ axis until null phase difference is obtained between R 1 -R 2 ′. The elevation angle φ is read directly from the angular position sensor along R 1 -R 3 ′ axis. Also, a pseudo star can be any transmitter having a predetermined inertial position transmitting a signal modulating a carrier. Those skilled in the art can make enhancements, improvements, and modifications to the invention, and these enhancements, improvements, and modifications may nonetheless fall within the spirit and scope of the following claims.