Data processing: vehicles – navigation – and relative location – Navigation – Employing position determining equipment
Reexamination Certificate
1998-07-29
2001-03-27
Louis-Jacques, Jacques H. (Department: 3614)
Data processing: vehicles, navigation, and relative location
Navigation
Employing position determining equipment
C701S213000, C701S216000, C701S220000, C701S200000, C342S063000, C342S064000, C342S357490
Reexamination Certificate
active
06208937
ABSTRACT:
CROSS-REFERENCE TO RELATED APPLICATIONS
(Not applicable)
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT
(Not applicable)
BACKGROUND OF THE INVENTION
This invention relates generally to integrated GPS-inertial navigation systems and more specifically to GPS-inertial navigation systems augmented with direction-finding apparatus.
The velocity {right arrow over (&ngr;)} of interest in navigating a vehicle relative to the earth using an inertial navigation system is defined by the equation:
({right arrow over (d&ngr;)}/dt)
N
={right arrow over (a)}
sf
+{right arrow over (g)}−{right arrow over (W)}×({right arrow over (W)}×{right arrow over (R)})−({right arrow over (W)}+{right arrow over (w)})×{right arrow over (&ngr;)} (1)
The vector ({right arrow over (d&ngr;)}/dt)
N
is the rate of change of the vehicle's velocity relative to the earth expressed in an inertial navigation system frame of reference. An example of a model-based inertial navigation system frame of reference is a local-level system with origin fixed at the point of tangency to the ellipsoidal model of the earth's gravity potential surface at the present position of the vehicle. The ellipsoidal model of the earth's gravity potential surface is called the normal gravity potential (See Heiskenan & Moritz, “Physical Geodesy”, Page 67, W. H. Freeman & Co., 1967). The vector {right arrow over (a)}
sf
is the specific-force acceleration experienced by the inertial navigation system (INS) on board the vehicle. The vector {right arrow over (g)} is the gravity vector. The vector {right arrow over (W)} is the rotation rate of an earth-fixed frame of reference relative to an inertial frame (i.e. earth's rotation rate vector). The vector {right arrow over (R)} is the position vector of the vehicle from the center of the earth. The vector {right arrow over (w)} is the rotation rate of the inertial navigation system frame relative to the inertial frame.
If the vehicle is stationary with respect to the earth, the equation above becomes:
{right arrow over (a)}
sfg
+{right arrow over (g)}−{right arrow over (W)}×({right arrow over (W)}×{right arrow over (R)})=0 (2)
Here {right arrow over (a)}
sfg
is the specific-force acceleration that balances gravity and the acceleration resulting from the earth's rotation and causes the vehicle to be stationary with respect to the earth. The specific-force acceleration—{right arrow over (a)}
sfg
in the stationary case is sometimes referred to as the plumb bob gravity since its direction coincides with that of a plumb bob suspended at the vehicle's present position:
{right arrow over (a)}
sfg
=−{right arrow over (g)}+{right arrow over (W)}×({right arrow over (W)}×{right arrow over (R)}) (3)
The vector {right arrow over (a)}
sfg
is only approximately aligned with the local geodetic vertical {right arrow over (U)} which is orthogonal to the normal gravity potential surface of the earth (i.e. the ellipsoidal surface model). The vector {right arrow over (a)}
sfg
deviates from the vector {right arrow over (U)} by what is called the deflection of the gravity vertical. The vector {right arrow over (U)} is the vertical axis of what is called the local geodetic frame that is comprised of the orthogonal east, north and vertical axes. The deflection of the vertical is the difference in the slope of the ellipsoidal model of the earth's gravity potential surface with respect to the slope of the actual gravity potential surface, which is called the geoid. The plumb bob gravity is orthogonal to the surface of the geoid.
The vector {right arrow over (a)}
sfg
is used to establish the orientation of the level axes of a gravity-based inertial navigation system frame relative to the inertial instrument reference axes during initial alignment of the inertial system. The three orthogonal axes of the inertial system instrument frame usually correspond to the sensing axes of the accelerometers and gyros of the inertial system. The local north component of the earth rate vector {right arrow over (W)} is used to determine the orientation of the inertial navigation frame with respect to the instrument frame in the local level plane relative to the local north axis (i.e. the azimuth orientation). This is achieved by observing the direction of the earth's rotation rate vector about the local north axis during the gyrocompassing phase of initial alignment of the inertial system using a combination of gyro and accelerometer measurements. After initial alignment the orientation of the gravity-based inertial navigation frame relative to the model-based frame differs by small amount due to various sources of error.
After initial alignment, when an inertial navigation system is integrated with a GPS navigation system, the differences in the measurements of position and velocity between the INS and the GPS system can be used to periodically correct the “drift” errors in the inertial system computed position, velocity and orientation with respect to the earth. In addition various causes of such errors, such as due to inertial instrument errors in can also be corrected. In such a situation, a GPS-INS navigation system has been demonstrated to have extremely small errors in position and velocity in actual flight tests. In addition, the error in knowledge of the orientation of the inertial instrument frame, and consequently the gravity-based inertial navigation frame, with respect to the earth is quite small. However, an error does exist in the orientation of the gravity-based inertial system navigation frame about the local north and east geodetic axes. This error which is called the tilt, is caused primarily by the deflection of the gravity vertical. If the highest accuracy navigation performance for a GPS-INS or INS-only (free-inertial) system is to be realized, some means must be developed for conveniently and effectively determining the deflection of the vertical throughout any region of interest. Such data can then be employed for constructing a deflection of the vertical database that can be used to compensate the inertial navigation system accelerometer measurements of force such that the deflection of the vertical has a much reduced effect on the accuracy of the navigation solution.
BRIEF SUMMARY OF THE INVENTION
The invention is a method and apparatus for generating navigation data. The method comprises the steps of (a) determining the position vector for one or more observation points in an earth-fixed reference frame and (b) determining either (1) the position vector for a target point in the earth-fixed reference frame from directions in either a model-based or a gravity-based reference frame from the one or more observation points to the target point or (2) the directions in either a model-based or a gravity-based reference frame from the one or more observation points to the target point from the position vector for the target point in the earth-fixed reference frame.
The model-based reference frame has a vertical axis with a specified orientation with respect to a normal to an ellipsoidal model of the earth and horizontal axes with specified orientations with respect to the earth-fixed reference frame. The gravity-based reference frame has a vertical axis with a specified orientation with respect to the gravity vector and horizontal axes with specified orientations with respect to the earth-fixed reference frame.
The apparatus for practicing the method for generating navigation data comprises an inertial navigation system, a GPS antenna and receiver, and direction-finding apparatus. The axes of maximum sensitivity for the accelerometers and gyros of the inertial navigation system define an instrument reference frame which is referenced to the gravity-based reference frame. The GPS antenna is fixed in the body reference frame, and the direction-finding apparatus is fixed in a direction-finder reference frame. There is at least
Litton Systems Inc.
Louis-Jacques Jacques H.
Malm Robert E.
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