Abstract:
An exemplary navigation system uses a master navigation component at a first location in a vehicle and a slave navigation component at a second location that is a variable displacement to the first location due to physical deformation of the vehicle. Static and dynamic location components provide static and dynamic information of the displacement between the first and second locations. An error estimator estimates errors in the navigational measurement data generated by the slave navigation component based on the navigational measurement data generated by the master navigation component and the displacement information provided by the static and dynamic location components. The master navigation component corrects the navigation measurement data of the slave navigation component based on the determined error and translates the corrected navigation measurement data of the slave navigation component into navigational measurement data in its coordinate system.

Description:
BACKGROUND  
       [0001]     Sensing systems on a vehicle require knowledge of navigation parameters, for example, velocity, position, and orientation, of the sensors to provide accurate measurements from the sensors while the vehicle is in motion. The vehicle comprises a high performance reference navigation system, for example, a master navigation system, to provide velocity, position, and orientation of the vehicle relative to a reference navigation coordinate system. The master navigation system is mounted in the vehicle but is usually physically separated from the sensing systems. As the vehicle is in motion, the vehicle bends. The bending of the vehicle causes instantaneous discrepancies between the position expressed by the master navigation system and the position experienced by the sensor. The difference between the position expressed by the master navigation system and the position experienced by the sensor is the “lever arm error.” The lever arms between the master navigation system and the sensing systems are nominally known. As one shortcoming, due to bending of the vehicle, errors are induced into the velocity, position, and orientation of the sensing system where outputs of the master navigation system are corrected based on the nominal lever arms.  
         [0002]     For example, in a synthetic aperture radar, an image is formed by combining signals from multiple sensors over a period of time while the radar is in motion. The lever arms between the master navigation system and the multiple sensors are nominally known. Where the vehicle bends, variations in the motion of the vehicle degrade the image. Data from the master navigation system is utilized to compensate the signals from the multiple sensors to form the image. The master navigation system employs the nominal lever arms to compensate the signals from the multiple sensors. While the vehicle is in motion, the position expressed by the master navigation system is different from the position experienced by the sensor as the master navigation system is separated from the sensing system. The difference is the lever arm error.  
         [0003]     One prior art solution to reduce the level arm error is to employ a high performance navigation system, for example, a slave navigation system, at a location of the sensing system to provide velocity, position, and orientation of the sensing system. As another shortcoming, it is costly to add additional high performance navigation systems into the vehicle. Another prior art solution to reduce the level arm error is to employ a smaller, lightweight, lower performance navigation system, for example, a slave navigation system, at a location of the sensing system. The slave navigation system at the location of the sensing system determines the velocity, position, and orientation of the sensing system relative to a coordinate system defined by the slave navigation system at the location of the sensing system. As yet another shortcoming, the coordinate system defined by the slave navigation system at the location of the sensing system differs from the reference coordinate system defined by the master navigation system of the vehicle. Where multiple sensing systems and multiple navigation systems are employed on the vehicle, the navigation systems employ multiple reference coordinate systems. It is desirable to obtain data from the sensing systems in the same coordinate system.  
         [0004]     Thus, a need exists for determining navigation parameters of a plurality of sensors on a vehicle relative to one coordinate system. 
     
    
     DESCRIPTION OF THE DRAWINGS  
       [0005]     Features of exemplary implementations of the invention will become apparent from the description, the claims, and the accompanying drawings in which:  
         [0006]      FIG. 1  is a representation of one implementation of an apparatus that comprises one or more vehicles, one or more master navigation components, one or more slave navigation components, one or more sensors, and one or more external positioning components.  
         [0007]      FIG. 2  is a representation of an exemplary process flow for providing corrected navigational parameters for the sensors from the master navigation component to the slave navigation components of the apparatus of  FIG. 1 .  
         [0008]      FIG. 3  is a representation of one implementation of one or more reference coordinate components and one or more rigid lever arm model components of the master navigation component, the slave navigation components, the sensors, the external positioning components, one or more incremental dynamic lever arm correction components, and one or more filters of the apparatus of  FIG. 1 .  
         [0009]      FIG. 4  is another representation of the apparatus of FIG. I comprising one or more navigation networks. 
     
    
     DETAILED DESCRIPTION  
       [0010]     Turning to  FIG. 1 , an apparatus  100  in one example comprises one or more vehicles  105 , one or more master navigation components  110 , one or more slave navigation components  115 ,  120 ,  125 , and  130 , one or more sensors  135 ,  140 ,  145 , and  150 , and one or more external positioning components  155  and  160 . The vehicle  105  in one example comprises a car, a tank, an airplane, an airship, or a space vehicle. The master navigation component  110  comprises a high performance navigation system to provide velocity, position, and attitude of the vehicle  105 . The master navigation component  110  employs accelerometers and gyroscopes to determine the velocity, position, and attitude of the vehicle  105 . For example, the master navigation component  110  comprises an Inertial Navigation System (“INS”).  
         [0011]     The slave navigation components  115 ,  120 ,  125 , and  130  in one example comprise one or more inertial sensors, for example, three linear accelerometers and three gyros, to determine position and attitude of the sensors  135 ,  140 ,  145  and  150 . For example, the slave navigation components  115 ,  120 ,  125 , and  130  comprise one or more Inertial Measurement Units (“IMUs”), as will be understood by those skilled in the art. The one or more sensors  135 ,  140 ,  145 , and  150  in one example comprise one or more synthetic aperture radars, one or more optical sensors, or one or more acoustic sensors. The external positioning components  155  and  160  comprise a Global Positioning System (“GPS”) receiver and a baro-altimeter. The master navigation component  110  and the slave navigation components  115 ,  120 ,  125 , and  130  comprise an instance of a recordable data storage medium  101 , as described herein.  
         [0012]     The master navigation component  110  employs one or more sensors to determine navigation measurement data for the vehicle  105 . The navigation measurement data for the vehicle  105  in one example comprises: inertial measurement data, positioning measurement data, air speed measurement data, and/or pressure altitude measurement data. In one example, the master navigation component  110  employs one or more inertial sensors to determine inertial measurement data for the vehicle  105 . In another example, the master navigation component  110  employs one or more pressure altitude sensors to determine pressure altitude measurement data for the vehicle  105 . In yet another example, the master navigation component  110  employs one or more GPS units to determine GPS measurements for the vehicle  105 . In yet another example, the master navigation component  110  employs one or more air speed sensors to determine air speed measurements for the vehicle  105 . The master navigation component  110  employs the navigation measurement data to determine a navigation and orientation solution for the vehicle  105  that describes the location/position of the vehicle  105  with respect to a reference coordinate system, for example, the Earth.  
         [0013]     The master navigation component  110  establishes a coordinate system, for example, a first coordinate system, with respect to the reference coordinate system based on the navigation measurement data for the vehicle  105 , as will be understood by those skilled in the art. In one example, the master navigation component  110  employs data from the external position component  155 , for example, GPS data, pressure altitude, or air data, to establish the coordinate system, as will be appreciated by those skilled in the art. In another example, the master navigation component  110  employs navigation measurement data from the slave navigation components  115 ,  120 ,  125 , and  130 , and positioning information from the external positioning components  155  and  160  to establish the coordinate system for the vehicle  105 . In yet another example, the master navigation component  110  employs the navigation measurement data from the slave navigation components  115 ,  120 ,  125 , and  130  to further refine the coordinate system established by the master navigation component  110  for the vehicle  105 . The master navigation component  110  employs the coordinate system and the navigation measurement data for the vehicle  105  to describe the orientation of the vehicle  105  as a function of time.  
         [0014]     The master navigation component  110  communicates with the slave navigation components  115 ,  120 ,  125 , and  130  to describe the position of the sensors  135 ,  140 ,  145 , and  150  relative to the coordinate system established by the master navigation component  110 , for example, the first coordinate system. The master navigation component  110  obtains navigation measurement data, for example, inertial measurement data, for the slave navigation components  115 ,  120 ,  125 , and  130  as a function of time. The master navigation component  110  comprises one or more error estimation components, for example, one or more Kalman filters, to estimate one or more errors in the navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130 . The master navigation component  110  corrects the navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130  based on the errors. The master navigation component  110  provides the corrected navigation measurement data to the slave navigation components  115 ,  120 ,  125 , and  130 , as illustrated by outputs  165 ,  170 ,  175 , and  180 . The slave navigation components  115 ,  120 ,  125 , and  130  employ the corrected navigation measurement data to improve estimations of navigation parameters (e.g., orientation, position, and velocity) of the sensors  135 ,  140 ,  145 , and  150 .  
         [0015]     The master navigation component  110  translates the navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130  from coordinate systems established by the slave navigation components  115 ,  120 ,  125 , and  130 , for example, one or more second coordinate systems, to the coordinate system established by the master navigation component  110 , for example, the first coordinate system, as will be appreciated by those skilled in the art. The master navigation component  110  provides as output  182 , navigation parameters for the master navigation component  110  in the coordinate system established by the master navigation component  110 , for example, the first coordinate system. The master navigation component  110  provides navigation parameters (e.g., orientations, velocities, and positions) of the sensors  135 ,  140 ,  145 , and  150  in the coordinate system established by the master navigation component  110 , as illustrated by the outputs  184 ,  186 ,  188 , and  190 . The master navigation component  110  provides the orientation of the coordinate reference system as output  192 .  
         [0016]     The master navigation component  110  estimates one or more lever arms (i.e. parameters used to model three dimensional distance vectors) between the master navigation component  110  and the slave navigation component  115 , the master navigation component  110  and the slave navigation component  120 , the master navigation component  110  and the slave navigation component  125 , and the master navigation component  110  and the slave navigation component  130 . The slave navigation components  115 ,  120 ,  125 , and  130  employ the estimation of the lever arms to determine dynamic motion of the sensors  135 ,  140 ,  145 , and  150  relative to the coordinate system established by the master navigation component  110 .  
         [0017]     The master navigation component  110  synchronizes the navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130  as a function of time provided by the slave navigation components  115 ,  120 ,  125 , and  130  with the navigation measurement data of the master navigation component  110 . In one example, the slave navigation component  115  provides a timestamp along with navigation measurement data for the slave navigation component  115 . The master navigation component  110  compares the navigation measurement data for the slave navigation component  115  with the navigation measurement data of the master navigation component  110  at a time described by the timestamp. In another example, the master navigation component  110  and the slave navigation components  115 ,  120 ,  125 , and  130  operate on a synchronized clock, for example, a clock  162 . In yet another example, the master navigation component  110  and the slave navigation components  115 ,  120 ,  125 , and  130  employ timing pulses to synchronize the navigation measurement data of the master navigation component  110  with the navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130 .  
         [0018]     The slave navigation components  115 ,  120 ,  125 , and  130  determine navigation parameters (e.g., orientation, position, and velocity) of the sensors  135 ,  140 ,  145 , and  150 . The slave navigation components  115 ,  120 ,  125 , and  130  compensate the output of the sensors  135 ,  140 ,  145 , and  150  based on the orientation, position, and/or velocity of the sensors  135 ,  140 ,  145 , and  150 . The slave navigation components  115 ,  120 ,  125 , and  130  communicate with the master navigation component  110  to provide the navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130  to the master navigation component  110 . The slave navigation components  115 ,  120 ,  125 , and  130  receive corrected navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130  from the master navigation component  110 . The slave navigation components  115 ,  120 ,  125 , and  130  employ the corrected navigation measurement data of the slave navigation components  115 ,  120 ,  125 , and  130  to describe the position of the sensors  135 ,  140 ,  145 , and  150  with respect to the coordinate system established by the master navigation component  110 . For example, the slave navigation component  115  employs the corrected navigation measurement data of the slave navigation component  115  to determine motion of the sensor  135  relative to the coordinate system established by the master navigation component  110 .  
         [0019]     An illustrative description of exemplary operation of the apparatus  100  is presented, for explanatory purposes.  
         [0020]     Turning to  FIG. 2 , in STEP  205 , the master navigation component  110  determines a navigation solution as a function of time for the vehicle  105 . In STEP  210 , the master navigation component  110  employs navigation measurement data and optional data from the external positioning component  155  to establish a coordinate system for the vehicle  105 , for example, a first coordinate system, in relation to the Earth. In STEP  215 , the master navigation component  110  receives navigation measurement data with respect to a coordinate system established by the slave navigation component  115 , for example, a second coordinate system, and time-tag from the slave navigation component  115  for the sensor  135 . The master navigation component  110  employs the time-tag to determine the navigation measurement data of the master navigation component  110  at a time described by the time-tag. In STEP  220 , the master navigation component  110  compares the navigation measurement data of the slave navigation component  115  at the time described by the time-tag to the navigation measurement data of the master navigation component  110  at the time described by the time-tag. The navigation measurement data of the master navigation component  110  at the time described by the time-tag in one example comprises navigation measurement data of the master navigation component  110  adjusted by one or more lever arms between the master navigation component  110  and the slave navigation components  115 ,  120 ,  125 , and  130 , as described herein.  
         [0021]     In STEP  225 , the master navigation component employs a Kalman filter to estimate errors in the navigation measurement data from the slave navigation component  115 . In STEP  230 , the master navigation component  110  corrects the errors in the navigation measurement data from the slave navigation component  115 . In STEP  235 , the master navigation component  110  translates the corrected navigation measurement data for the slave navigation component  115  from the coordinate system established by the slave navigation component  115 , (e.g., the second coordinate system) to the coordinate system established by the master navigation component  110  (e.g., the first coordinate system). In STEP  240 , the master navigation component  110  employs the corrected and translated navigation measurement data for the slave navigation component  115  in the first coordinate system to provide navigation parameters for the sensor  135 , for example, orientation, position, and velocity, in the coordinate system established by the master navigation component  110 .  
         [0022]     Turning to  FIG. 3 , the master navigation component  110  in one example comprises one or more reference coordinate components  305  and one or more rigid lever arm model components  310  and  340 . The reference coordinate component  305  establishes a coordinate system for the vehicle  105 . For example, the rigid lever arm model component  310  comprises a base-line static position for the slave navigation component  115 . The rigid lever arm model component  310  determines a base-line static lever arm for the slave navigation component  115  based on the base-line static position. The base-line static lever arm for the slave navigation component  115  comprises a three-dimensional position distance, or vector, between the master navigation component  110  and the slave navigation component  115 . The rigid lever arm model component  310  cooperates with the reference coordinate component  305  to project the base-line static lever arm for the slave navigation component  115  in the coordinate system established by the reference coordinate component  305  to determine a translated static lever arm for the slave navigation component  115 . The rigid lever arm model component  310  sends the translated static lever arm for the slave navigation component  115  as output  316  to a summing node  318 .  
         [0023]     The slave navigation component  115  determines navigation measurement data for the slave navigation component  115  in reference to a coordinate system established by the slave navigation component  115 . The slave navigation component  115  sends as output  320 , the navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the slave navigation component  115  to the summing node  318 . The summing node  318  combines the output  316  from the rigid lever arm model component  310  with the output  320  from the slave navigation component  115  to produce as output  322 , navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305 .  
         [0024]     The output  322  comprising the navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305  is enhanced through employment of an incremental dynamic lever arm correction component  324 . The incremental dynamic lever arm correction component  324  comprises a model describing reactions of the vehicle  105  during motion. The incremental dynamic lever arm correction component  324  employs the model to provide positions for the slave navigation components  115  and  120  in relation to the reactions of the vehicle  105  during motion. For example, while in motion, the vehicle  105  reacts by bending. The bending of the vehicle  105  alters a lever arm (i.e., the three-dimensional distance vector) between the master navigation component  110  and the slave navigation component  115 . As the vehicle  105  bends, the lever arm between the master navigation component  110  and the slave navigation component  115  changes.  
         [0025]     The incremental dynamic lever arm correction component  324  receives as input, an output  326  from the reference coordinate component  305 , and an output  327  from the slave navigation component  115 . The output  326  comprises the coordinate system established by the reference coordinate component  305 . The output  327  comprises the navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the slave navigation component  115 , similar to the output  320 . The incremental dynamic lever arm correction component  324  employs the outputs  326  and  327  to determine a dynamic lever arm for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305 . The incremental dynamic lever arm correction component  324  sends as output  328 , the dynamic lever arm for the slave navigation component  115  to the summing node  318 . The summing node  318  combines the outputs  316 ,  320 , and  328  to produce the output  322 . Thus, the summing node  318  generates the output  322  as comprising more accurate navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305  for the vehicle  105  in motion. The output  328  of the incremental dynamic lever arm correction component  324  obtains more accuracy through employment of a filter  330 , for example, a Kalman filter, as will be discussed herein.  
         [0026]     The filter  330  receives as input, the output  322  from the summing node  318 . The filter  330  compares the output  322  for a given timestamp (i.e., the navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305 ) with the navigation measurement data from the reference coordinate component  305  at the given timestamp. The filter  330  estimates errors in the output  322 . The filter  330  provides as output  332 , corrected navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305 . The slave navigation component  115  employs the output  332  to determine orientation, position, and velocity of the sensor  135  with respect to the coordinate system established by the reference coordinate component  305 . The slave navigation component  115  employs the output  332  to adjust the coordinate system established by the slave navigation component  115 . In addition, the filter  330  sends as output  334 , the corrected navigation measurement data for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305  to the incremental dynamic lever arm correction component  324 . The incremental dynamic lever arm correction component  324  employs the output  334  to correct the output  328 , the dynamic lever arm for the slave navigation component  115 . Thus, the incremental dynamic lever arm correction component  324 , the slave navigation component  115  and the filter  330  cooperate to iteratively align a coordinate system of the slave navigation component  115  with the coordinate system established by the reference coordinate component  305 .  
         [0027]     The slave navigation component  120 , the sensor  140 , the reference coordinate component  305 , rigid lever arm model component  340 , summing node  348 , incremental dynamic lever arm correction component  354 , and outputs  346 ,  350 ,  352 ,  358 ,  357 ,  362 , and  364  interact in a similar fashion to the slave navigation component  115 , the sensor  135 , the reference coordinate component  305 , the rigid lever arm model component  310 , the summing node  318 , the incremental dynamic lever arm correction component  324 , outputs  316 ,  320 ,  322 ,  326 ,  327 ,  328 ,  332  and  334 . The reference coordinate component  305 , the rigid lever arm model components  310  and  315 , incremental dynamic lever arm correction components  324  and  354 , and the filter  330 , comprise one or more instances of a recordable data storage medium  101 , as described herein.  
         [0028]     Referring still to  FIG. 3 , the slave navigation component  115  sends as output  366 , the navigation measurement data for the slave navigation component  115  to the incremental dynamic lever arm correction component  354 . The incremental dynamic lever arm correction component  354  employs the output  366  to provide increased accuracy of the dynamic lever arm for the slave navigation component  120  in reference to the coordinate system established by the reference coordinate component  305 . The slave navigation component  120  sends as output  368 , the navigation measurement data for the slave navigation component  120  to the incremental dynamic lever arm correction component  324 . The incremental dynamic lever arm correction component  324  employs the output  368  to provide increased accuracy of the dynamic lever arm for the slave navigation component  115  in reference to the coordinate system established by the reference coordinate component  305 .  
         [0029]     Referring again to  FIG. 3 , the filter  330  receives as input, navigation measurement data from the master navigation component  110 , and the slave navigation components  115  and  120 . The filter  330  receives as input, output  370  from the reference coordinate component  305 , the output  322  from the slave navigation component  115 , and the output  352  from the slave navigation component  120 . The filter  330  employs the outputs  322 ,  352 , and  370  to establish a coordinate system. For example, the filter  330  combines the outputs  322 ,  352 , and  370  to establish the coordinate system, as will be appreciated by those skilled in the art. The filter  330  estimates errors in navigation measurement data received from the reference coordinate component  305 , and the slave navigation components  115  and  120 , and corrects the errors.  
         [0030]     The filter  330  sends as output  372 , the corrected navigation measurement data with respect to the coordinate system established by the filter  330  to the reference coordinate component  305 . The reference coordinate component  305  employs the output  372  to adjust a coordinate system established by the reference coordinate component  305 . For example, the reference coordinate component  305  employs the output  372  to adjust a base-line coordinate system established by the reference coordinate component  305 . The filter  330  and the reference coordinate component  305  cooperate to align the coordinate system established by the reference coordinate component  305  and the coordinate system established by the filter  330 . The filter  330  sends the outputs  332 ,  334 ,  362 , and  364 , the corrected navigation measurement data with respect to the coordinate system established by the filter  330  to the slave navigation components  115  and  120 , and the incremental dynamic lever arm correction component  324  and  354 .  
         [0031]     Turning to  FIG. 4 , the vehicle  105  comprises a navigation network  402 . The navigation network  402  comprises a navigation network hub  410 , and one or more navigation components  415 ,  420 ,  425 , and  430 . The navigation components  415 ,  420 ,  425 , and  430  in one example comprise navigation components of varying degrees of accuracy. For example, the navigation components  415  and  420  comprise high performance navigation systems, similar to the master navigation component  110 , and the navigation components  425  and  430  comprise lower performance navigation systems, similar to the slave navigation components  115 ,  120 ,  125 , and/or  130 . The navigation components  415 ,  420 ,  425 , and  430  obtain navigation measurement data for the navigation components  415 ,  420 ,  425 , and  430  and determine navigation parameters (i.e., orientations, positions, and velocities) for the sensors  135 ,  140 ,  145 , and  150 .  
         [0032]     The navigation network hub  410  in one example receives the inertial measurement information from the navigation components  415 ,  420 ,  425 , and  430 . The navigation network hub  410  employs the navigation measurement data from the navigation components  415 ,  420 ,  425 , and  430  to establish a coordinate system for the vehicle  105 . The navigation network hub  410  determines one or more navigational parameters, for example, orientations, positions, and velocities, for the sensors  135 ,  140 ,  145 , and  150  with respect to the coordinate system established by the navigation network hub  410 . The navigation network hub  410  provides the navigation parameters (i.e. orientations, velocities, and positions) of the sensors  135 ,  140 ,  145 , and  150  in the coordinate system established by the navigation network hub  410 , as illustrated by outputs  482 ,  484 ,  486 , and  490 . The navigation network hub  410  provides the orientation of the coordinate reference system established by the navigation network hub  410  as output  492 . The navigation network hub  410 , and the navigation components  415 ,  420 ,  425 , and  430  in one example comprise one or more instances of a recordable data storage medium  101 , as described herein.  
         [0033]     The navigation network hub  410  and the navigation components  415 ,  420 ,  425 , and  430  communicate through employment of one or more instances of a network bus  495 . In one example, the network bus  495  comprises a high speed transmission bus. In another example, the network bus  495  comprises an Ethernet communication means. The navigation components  415 ,  420 ,  425 , and  430  in one example employ the network bus  495  to transmit navigation measurement data to the navigation network hub  410 . In one example, the navigation network hub  410  employs the network bus  495  to transmit corrected navigation measurement data  165 ,  170 ,  175 , and  180  to the navigation components  415 ,  420 ,  425 , and  430 . In another example, the navigation network hub  410  employs the network bus  495  to provide outputs  482 ,  484 ,  486 ,  488 ,  490 , and  492 . In yet another example, the navigation network hub  410  employs the network bus  495  to communicate with the external positioning components  155  and  160 . The navigation network hub  410  employs a standard protocol over the network bus  495  to provide a common interface to multiple external components, for example, the navigation components  415 ,  420 ,  425 , and  430 , the external positioning components  155  and  160 , and one or more vehicle computers (not shown).  
         [0034]     The apparatus  100  in one example comprises a plurality of components such as one or more of electronic components, hardware components, and computer software components. A number of such components can be combined or divided in the apparatus  100 . An exemplary component of the apparatus  100  employs and/or comprises a set and/or series of computer instructions written in or implemented with any of a number of programming languages, as will be appreciated by those skilled in the art.  
         [0035]     The apparatus  100  in one example employs one or more computer-readable signal-bearing media. The computer-readable signal-bearing media store software, firmware and/or assembly language for performing one or more portions of one or more embodiments of the invention. Examples of a computer-readable signal-bearing medium for the apparatus  100  comprise the recordable data storage medium  101  of the master navigation component  110 , the slave navigation components  115 ,  120 ,  125 , and  130 , the reference coordinate component  305 , the rigid lever arm model components  310  and  315 , incremental dynamic lever arm correction components  324  and  354 , the filter  330 , the navigation network hub  410 , and the navigation components  415 ,  420 ,  425 , and  430 . The computer-readable signal-bearing medium for the apparatus  100  in one example comprise one or more of a magnetic, electrical, optical, biological, and atomic data storage medium. For example, the computer-readable signal-bearing medium comprises floppy disks, magnetic tapes, CD-ROMs, DVD-ROMs, hard disk drives, and electronic memory. In another example, the computer-readable signal-bearing medium comprises a modulated carrier signal transmitted over a network comprising or coupled with the apparatus  100 , for instance, one or more of a telephone network, a local area network (“LAN”), a wide area network (“WAN”), the Internet, and a wireless network.  
         [0036]     The steps or operations described herein are just exemplary. There may be many variations to these steps or operations without departing from the spirit of the invention. For instance, the steps may be performed in a differing order, or steps may be added, deleted, or modified.  
         [0037]     Although exemplary implementations of the invention have been depicted and described in detail herein, it will be apparent to those skilled in the relevant art that various modifications, additions, substitutions, and the like can be made without departing from the spirit of the invention and these are therefore considered to be within the scope of the invention as defined in the following claims.