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LORD 6253-4220, User Manual

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LORD 6253-4220 User Manual Download Page 75

3DM

®

-GX5-25

User Manual

UTC (Coordinated Universal Time)
The primary time standard for world clocks and time. It is similar to Greenwich Mean Time (GMT).

V

Vector
a measurement with direction and magnitude with refernce from one point in space to another

Velocity
The rate of change of position with respect to time. Also called speed.

W

WAAS (Wide Area Augmentation System)
An air navigation aid developed to allow aircraft to rely on GPS for all phases of flight, including pre-
cision approaches to any airport.

WGS (World Geodetic System)
a protocol for geo-referencing such as WGS-84

Y

Yaw
In navigation yaw is what occurs when rotational force is applied at a distance forward or aft from the
center of gravity of the platform, causing it to move around the center axis of a sensor or platform frame
origin.

75

Summary of Contents for 6253-4220

Page 1: ...LORD User Manual 3DM GX5 25 Attitude and Heading Reference System AHRS ...

Page 2: ... 2017 LORD Corporation 3DM 3DM DH 3DM DH3 3DM GX2 Ask Us How DEMOD DC DVRT EmbedSense FAS A G Link Little Sensors Big Ideas LORD Microstrain Live Connect LXRS MathEngine MicroStrain MXRS Node Commander SensorCloud SG Link Strain Wizard TC Link V Link Wireless Simplicity Hardwired Reliability and WSDA are trademarks of LORD Corporation Document 8500 0012 Revision C Subject to change without notice ...

Page 3: ...ve Help Menu 13 3 4 Sensor Communication 14 3 5 Satellite Link 15 3 6 Sensor Settings 15 3 6 1 Saving Configurations 16 3 7 Data Monitoring and Recording 17 3 8 View Recorded Data 18 4 Sensor Measurements 21 4 1 Direct Sensor Measurements IMU Outputs 22 4 2 Computed Outputs 24 4 3 Sensor Reference Frames 26 4 3 1 Geodetic Frame 26 4 3 2 North East Down NED Frame 27 4 3 3 Sensor Frame 28 4 3 4 Plat...

Page 4: ...7 2 Mag Adaptive 41 5 8 Communications Bandwidth 42 5 9 Platform Frame Transformation 42 5 10 Estimation Filter Operation 42 5 11 Estimation Filter Convergence 43 5 11 1 Initial Convergence 43 5 11 2 Output Uncertainty 43 5 12 Vibration Isolation 44 5 13 IMU Sensor Calibration 44 5 14 Temperature Compensation 44 5 15 Import and Export Settings 44 6 Sensor Installation 46 6 1 Sensor Mounting 46 7 O...

Page 5: ...uide 53 8 2 Repair and Calibration 57 8 3 Maintenance 57 8 4 Technical Support 58 9 Parts and Configurations 59 9 1 Standard Configurations 59 9 2 Accessories 61 9 3 Sales Support 61 10 Specifications 62 11 Reference Diagrams 64 11 1 Sensor Dimensions and Origin 64 11 2 Power Supply Specifications 65 11 3 Communication and Power Cables 66 12 Reference Documents 68 13 Glossary 69 ...

Page 6: ... bias tracking auto zero update options ZUPT and user adjustable sensor noise factors All sensors are fully temperature compensated and calibrated over the full operating temperature range The use of Micro Electro Mechanical System MEMS technology allows for small lightweight devices Sensors are integrated into customer systems using serial communication protocols such as RS422 RS232 and USB The L...

Page 7: ...ed and are mathematically aligned to an orthogonal coordinate system The combination of sensors environmental compensation and dual on board processing with an Auto Adaptive Extended Kalman Filter EKF allows the 3DM GX5 25 to perform well in a wide variety of applications that require low noise drift gain and offset errors The 3DM GX5 25 communicates through a serial connection and is monitored by...

Page 8: ...ts and ordering information see Parts and Configurations on page 59 Item Description Model LORD Sensing Part Number Included with Sensor Purchase A 3DM GX5 25 InertialSensor AHRS 8G 300 DPS 6253 4220 MIP Monitor Software Suite http www microstrain com software For additionaloptions available see Specifications on page 62 USB Connectivity Kit B USB Communication Cable 6212 3004 RS232 Connectivity K...

Page 9: ...25 include a device status indicator and the device information label The table below describes the basic status indicator behavior The device information label includes the sensor frame diagram axis orientation which will be critical during device installation see Sensor Frame on page 28 Indicator Behavior Device Status device status indicator OFF no power applied rapid flash streaming data slow ...

Page 10: ...ystem and includes all functions needed for sensor configuration and data acquisition Users may also utilize the LORD Sensing MIP Data Communications Protocol DCP to write custom software applications with expanded or specific feature sets needed for the application MIP Monitor includes a message building tool that can be used to streamline this process For more information see OEM System Integrat...

Page 11: ...strain com software 2 Download and open the MIP Monitor zip file 3 Run the setup exe file and follow the on screen prompts to completion 4 Download and open the Inertial Drivers zip folder to install the hardware drivers required for operating the sensor 5 Run the msi file and follow the on screen prompts to completion 6 Download and open the Iron Calibration zip file to facilitate magnetometer fi...

Page 12: ...wer supplies within the operating range of the sensor or damage or injury could result Once power is applied the sensor is on and active see Specifications on page 62 To acquire sensor data the following components are needed 3DM GX5 25 sensor communication cable power cable as applicable for RS232 communications and a host computer with LORD Sensing MIP Monitor installed Figure 5 System Connectio...

Page 13: ...ncludes selections for data sampling recording device settings opening windows selecting which open window to view and advanced features such as selecting the communications mode The icon toolbar includes buttons for Help Menu access where all related documentation is available in Web Resources device refresh and data sampling and recording Figure 6 Main Window Display 3 3 1 Interactive Help Menu ...

Page 14: ... Open the MIP Monitor software 3 The sensor should appear in the device list automatically when the software is running The list includes the device information and communication port assignment If the sensor is not automatically discovered use the refresh button Figure 8 Sensor Communication NOTE If data is not actively being exchanged between the sensor and host computer the status message may d...

Page 15: ...these include calculated measurements Estimation Fil ter and direct inertial sensor measurements IMU AHRS b Message Format first sub menu tab Under each main menu tab there are additional sub menu tabs including the Message Format tab which allows the user to select the meas urement type to be displayed and recorded b1 and the data rate in samples second b2 c Measurement parameters Available sub m...

Page 16: ... device is powered on select Settings Save Current Settings First adjust the sensor settings to the desired values Next select Settings Save Current Settings from the main window Figure 10 Save Sensor Settings The settings will now remain intact when the sensor is powered off and then on again To recall the last saved settings select Settings Load Startup Settings To revert the settings back to th...

Page 17: ... for monitoring and recording Each view corresponds to one of the main categories in the Device Settings window For example the 3DM GX5 25 includes Sensor Data Monitoring for the IMU AHRS measurements and EF Monitoring for the Estimation Filter outputs During viewing and recording only the outputs that are selected in the Message Format tab of the Device Settings menu are displayed and recorded se...

Page 18: ...the example below the y axis of the graph indicates data points the x axis is the measurement units and there is a tab for each measurement 1 Right click on the device in the MIP Monitor software main window and select Sensor Data Monitor 2 Click the blue Start Streaming icon to start sampling Figure 12 Data Streaming 3 8 View Recorded Data Recorded data is stored in either Binary bin or Comma Sep...

Page 19: ...ecord data select the Arm Recording icon at any time 2 Select the type of data file to generate Binary or CSV The CSV file is the most common and can be viewed and processed by data editors such as Microsoft Excel 3 To save a settings file when creating a data file check the box next to this option This settings file is the same as selecting Export Settings from the Settings menu NOTE If the data ...

Page 20: ...cording press the Arm Recording button again and select OK in the confirmation prompt window 5 Select the Stop Streaming icon to end sampling 6 Use the red X in the upper right of the sensor monitoring window to exit monitoring mode 20 ...

Page 21: ... Delta theta change in angular rate and Delta velocity change in velocity Temperature and pressure sensors provide environmental information for measurement compensation and altitude estimations information can be read directly but is not used internally for attitude or navigation estimations on the 3DM GX5 25 Computed estimations for attitude and heading reference systems AHRS are available outpu...

Page 22: ...s All measurements are temperature compensated and are mathematically aligned to an orthogonal coordinate system The IMU sensors can be read directly to report stand alone inertial measurements or computed measurements Because the sensor system is digital the analog voltage readings from the sensors are converted into a digital equivalent value based on the volt to bit scale of the internal analog...

Page 23: ...ree axis acceleration readings in engineering units Magnetic Field Gauss G three axis magnetic field readings in engineering units Angular Rate radian second three axis rotational velocity reading from gyro scope in engineering units Delta Angle Theta radians time integral of angular rate with configurable time period Delta Velocity g seconds time integral of acceleration with configurable time pe...

Page 24: ...s for how the estimations are made These settings are available at Settings Device EF With the Help window open accessed with the Help button mousing over context sensitive settings provides a detailed explanation of the setting Figure 16 Estimation Filter Settings Figure 16 Estimation Filter Settings All of the estimation filter outputs are available to record and most but not all are available t...

Page 25: ...d scale read ings and one sigma uncertainty estimations also available Compensated Angular Rate radians second measured angular rate corrected using the estimated gyroscope scale factor and bias with reference to either the sensor or vehicle frame depending on settings Gravity Vector meter second2 estimated WGS84 gravity vector with reference to either the sensor or vehicle frame depending on sett...

Page 26: ... reference ellipsoid Latitude ranges from 90 degrees at the South Pole to 90 degrees at the North Pole Longitude ranges from 180 to 180 degrees with 0 degrees being the prime meridian The 180 180 degree switchover occurs in the middle of the Pacific Ocean and includes a section of the International Date Line The model takes into account the oblateness of the Earth s surface A point P on or above t...

Page 27: ...he East vector along the line of latitude and the Down vector normal to and towards the tangent plane Figure 18 North East Down Frame The assumption when using the NED frame is that the local surface can be reasonably approximated by a flat plane For most applications this assumption is valid and provides a more intuitive reference frame for expressing attitude information than a global frame The ...

Page 28: ...sor biases and corrections in this frame When no sensor to platform frame transformation has been provided see Platform Frame on page 29 The orientation of the sensor frame with respect to the local NED frame can be viewed in the MIP Monitor software at View 3D Attitude menu This window displays the orientation of the sensor in relationship to north and shows measurement origination for accelerati...

Page 29: ...tform frame In the following example the user has defined the desired reference point on the platform frame to be located at the front bumper of the vehicle In accordance with aircraft co ordinate systems the platform frame is oriented with the x axis pointed in the forward direction of travel the z axis pointed down and the y axis pointed towards the passenger side The sensor has been mounted fac...

Page 30: ...eleration compensated angular rate and gravity vector It also affects the following IMU outputs acceleration angular rate magnetic field vector delta Theta and delta velocity see Computed Outputs on page 24 Transformed acceleration is expressed at the location of the sensor but within the platform frame For example if the sensor is offset from the center of gravity CG and the platform is undergoin...

Page 31: ...et the gyroscope baseline place the sensor or sensor platform in the desired home position Allow 2 3 minutes for the sensor to warm up and for the temperature to stabilize for the best bias capture Select Settings Capture Gyro Bias Figure 22 Gyro Bias Capture The sensor must remain stationary for about twenty seconds while the outputs are being measured A status message will appear when the captur...

Page 32: ...onding LORD Sensing MIP Data Communications Protocol DCP command see the DCP Manual NOTE The filter must be initialized and have a valid attitude output If the attitude is not valid an error will be returned The Tare Mounting Pitch Roll assumes that the X axis is co aligned with the X axis of the vehicle To tare the pitch roll select the sensor name in the MIP Monitor software main window then sel...

Page 33: ... the magnetometer scale factor scale factor tracking for purposes of auto calibration To enable select the sensor name in the MIP Monitor software main window then select Settings Device Estimation Filter EF Tracking and check the white box to the left of Enable EF Mag Hard Iron Auto Calibration and Enable EF Mag Soft Iron Auto Calibration Auto Calibration only takes place if the magnetometer is u...

Page 34: ...on software which is included in the MIP Monitor software suite see Software Installation on page 11 This command also resets the auto calibration coefficients The Capture command should only be executed after the vehicle has undergone a series of maneuvers typical of actual operating conditions These maneuvers are necessary to establish the magnetometer offset and scale factors For more informati...

Page 35: ...To mitigate this effect when using the 3DM GX5 25 magnetometer to aid in heading estimations a field calibration of the magnetometer after final installation is highly recommended This can be accomplished using LORD Sensing MIP Hard and Soft Iron Calibration software The following are instructions for field calibrating the magnetometers 1 Connect and power on the sensor as normal and open the MIP ...

Page 36: ...rm as much as possible to simulate actual use without exposing it to excessive magnetic sources such as driving over railroad tracks or near steel pilings The intention is to get a baseline of the platform in a neutral environment that still accounts for the platform itself in all orientations For stationary platforms the baseline may include significant magnetic influences that will be present du...

Page 37: ... write the values to the sensor memory 8 Cycle power to the sensor if prompted and then use the Refresh button if needed to re establish communication with the sensor 9 Start a calibration verification by clicking the Start Streaming Data button next to Verify Calibration Figure 28 Verify Calibration Rotate the device in all orientations in the same way as during calibration When completed click t...

Page 38: ... Filter Aiding menu select the sensor name in the MIP Monitor software main window then select Settings Device Estimation Filter EF Aiding 1 Heading Aiding has three options including None Magnetometer and External Heading Mes sage 2 Pitch Roll Aiding has two options including None and Gravity Vector Figure 29 EF Aiding Options Menu 38 ...

Page 39: ...d e g when stationary or traveling in the same direction at a constant velocity If the setting is the magnetometer there will be no drift but the accuracy will only be as good as the magnetometer measurement The external heading message setting means the heading is derived from one of two possible external messages provided by the user 1 0x0D 0x17 or 2 0x0D 0x1F in the LORD Sensing MIP Data Commun...

Page 40: ...n run 5 7 Adaptive Anomaly Rejection 5 7 1 Gravity Adaptive Enabling this feature allows the filter to stabilize attitude readings when undergoing linear accelerations The bandwidth setting determines the cutoff frequency of the filter applied to linear acceleration changes see Communications Bandwidth on page 42 The high and low limits determine the trigger points at which the stabilization is ap...

Page 41: ...d this setting select the sensor name and then Settings Device Estimation Filter Mag Adaptive Manual Adaptive default setting Enter user set fixed values Auto Adaptive Automatically estimates the values internally It is important to have accurate location information lat long in order to have an accurate value for the local magnetic field magnitude NOTE For best results perform a hard and soft iro...

Page 42: ...ference System AHRS solution that incorporates the strengths of the individual sensors while minimizing their weaknesses In a conventional system Attitude and Heading Reference System AHRS several sources of error exist when making attitude estimates First the algorithm assumes the acceleration vector is dominated by Earth s gravity with only transient linear accelerations When long duration linea...

Page 43: ...ividual states given what it knows about the statistical properties of the noise sources of the various sensors and also provide feedback to the user as uncertainty values 5 11 Estimation Filter Convergence 5 11 1 Initial Convergence After a successful initialization a period of convergence for the Kalman filter states occurs Roll and pitch angles typically converge very quickly Heading accelerome...

Page 44: ...tions of internal sensor damage may be seen as excessive measurement offsets or drift when the sensor is in a neutral motionless position 5 14 Temperature Compensation All sensor conversion and calibration formulas include temperature compensation All computed outputs and IMU sensor outputs are automatically adjusted for local temperature 5 15 Import and Export Settings The import and export setti...

Page 45: ...3DM GX5 25 User Manual Figure 33 Import Export Settings Menu 45 ...

Page 46: ...read lock are recommended There are two additional holes used for precise alignment with 2mm dowel pins One of the holes is slotted to allow for relaxed pin positioning accuracy The sensor can be mounted in any orientation as required for the application see Sensor Reference Frames on page 26 The axes are labeled on the face of the sensor for reference and the sensor measurement origin is shown in...

Page 47: ...t format The commands and data are divided into four command sets and three data sets corresponding to the internal architecture of the device The protocol is packet based All commands replies and data are sent and received as fields in a message packet The packets have a descriptor type field based on their contents so it is easy to identify if a packet contains commands replies or data To view o...

Page 48: ...MIP Monitor main window 7 1 1 Packet Builder The sensor must be in the Standard communications mode to use this feature Figure 35 Packet Builder 7 1 2 Sensor Direct Mode The MIP Monitor software can be used to put the sensor in a mode that allows direct programmatic access to the internal Inertial Measurement Unit IMU The IMU has its own processor and protocol commands and native data outputs from...

Page 49: ...de select Advanced Communications Sensor Direct from the MIP Monitor main window Once in this mode the device status message will indicate Sensor Direct Mode Figure 36 Sensor Direct Mode To exit Sensor Direct Mode select the Refresh button in the MIP Monitor at any time or use Advanced Communication menu to select the Standard operating mode Figure 36 Sensor Direct Mode 49 ...

Page 50: ...2 communication or a USB connector for USB communications Alternately the micro DB9 can be purchased from LORD Sensing with flying leads or the connector by itself can be purchased from the manufacturer Ulti Mate Connector Inc See Parts and Configurations on page 59 for a list of available options For the cable diagram see Sensor Dimensions and Origin on page 64 The connector interface includes co...

Page 51: ...ect 3DM GX5 25 and then select document from the list NOTE When setting the sensor to begin sampling on start up verify that the sensor is sampling by reading the status indicator on the device see Interface and Indicators on page 9 or by viewing the serial data stream from the host computer If communication with MIP Monitor is established the sampling will stop to facilitate device configuration ...

Page 52: ...t on page 58 7 5 Using Wireless Adapters In some applications it can be very useful to set up wireless communications between the sensor to the host computer One way this can be accomplished is by connecting the serial output of the sensor to a serial to wireless converter and then connecting the wireless receiver to the host computer For more information and an example refer to the Using RS232 Bl...

Page 53: ...3DM GX5 25 User Manual 8 Troubleshooting 8 1 Troubleshooting Guide 53 ...

Page 54: ...hnical Support on page 58 2 COMMUNICATION no communication to sensor 2 1 sensor not found in MIP Monitor In MIP Monitor use the Refresh button to look for the sensor again If the sensor is still not found try cycling power to the sensor and refreshing 2 2 communication cable not connected or miswired Check remove and reconnect communications and power cables as applicable Replace or rewire as need...

Page 55: ...ing data could result 3 4 sensor data not recorded Verify data recording has been activated In MIP Monitor the device status information field will indicate Recording Data If the sensor isn t recording activate in the software Verify specific measurements have been enabled for sampling and recording NOTE Data is recorded in time sequence If measurements are set to different sample rates not all ti...

Page 56: ...3DM GX5 25 User Manual Problem Possible cause and recommended solution conditions outside of its operating specifications 56 ...

Page 57: ...from defective material and workmanship for a period of one 1 year from the original date of purchase LORD Sensing will repair or replace at its discretion a defective product if returned to LORD Sensing within the warranty period This warranty does not extend to any LORD Sensing products that have been subject to misuse alteration neglect accident incorrect wiring mis programming or use in violat...

Page 58: ...s http www microstrain com support_overview aspx For further assistance our technical support engineers are available to help with technical and applications questions Technical Support sensing_support LORD com Phone 802 862 6629 SKYPE microstrain orientation support Live Chat is available from the website during business hours 9 00 AM to 5 00 PM Eastern Time US Canada 58 ...

Page 59: ...RD Sensing Sales Department Table 4 Model Numbers describes the standard models available at the time this manual was published Once a model is selected the part number is further defined by desired configuration and interface options The model determines the first four digits of the product part number the options are indicated in the last four digits Figure 39 Standard Part Numbers Table 4 Model...

Page 60: ...anual The same options are available in each model and are indicated in the last four digits of the product part number For a list of the starter kit contents see Components on page 1 Figure 39 Standard Part Numbers 60 ...

Page 61: ...5 Sensor Accessories Description Manufacturer part number A Series or P Series 9 pin male Micro D connector Ulti Mate PR09N05 Table 6 Sensor Mating Connector 9 3 Sales Support Products can be ordered directly from the LORD Sensing website by navigating to the product page and using the Buy feature http www microstrain com inertial For further assistance our sales team is available to help with pro...

Page 62: ...ard 2 g 4 g 20 g 40 g optional 300 sec standard 75 150 900 optional 2 5 Gauss Non linearity 0 02 fs 0 02 fs 0 3 fs Resolution 0 1 mg 0 003 sec Bias instability 0 04 mg 8 hr Initial bias error 0 002 g 0 04 sec 0 003 Gauss Scale factor stability 0 03 0 05 0 1 Noise density 25 µg Hz 2 g 0 005 sec Hz 300 sec 100 µGauss Hz Alignment error 0 05 0 05 0 05 Adjustable bandwidth 225 Hz max 250 Hz max Offset...

Page 63: ...source 4 to 36 V dc V dc Power consumption 500 mW typ Operating temperature 40 C to 85 C Mechanical shock limit 500 g calibration unaffected 1000 g bias may change 5000 g survivability MTBF TBD Physical Specifications Dimensions 36 0 mm x 36 6 mm x 11 1 mm Weight 16 5 grams Enclosure material Aluminum Regulatory compliance ROHS CE Integration Connectors Data power output micro DB9 Software MIP Mon...

Page 64: ...roduct installation and troubleshooting For more information contact LORD Sensing Technical Support see Technical Support on page 58 11 1 Sensor Dimensions and Origin This diagram describes the sensor physical specification including the measurement point of origin Figure 40 3DM GX5 25 Sensor Origin 64 ...

Page 65: ...aximum load V ac maximum load Input power saving at no load 0 3 W maximum DC voltage rating DC load capacity maximum Ripple peak to peak maximum Regulation 5 line and load Efficiency average Circuit protection auto restart Safety approvals cUL UL SAA CE C Tick Environmental Parameters Operating temperature 0 C to 40 C Storage temperature 25 C to Humidity to 90 Emissions FCC Class B EN55022 Class B...

Page 66: ...Power Cables These diagrams describe the cables included in the 3DM GX5 25 connectivity kits Only one is included in each kit depending on the type of kit ordered Figure 41 RS232 Communications and power cable Figure 42 USB Communications cable 66 ...

Page 67: ...3DM GX5 25 User Manual Figure 43 Connecter interface cable sold separately PN 6224 0100 67 ...

Page 68: ... documents are continuously updated and may provide more accurate information than printed or file copies Document Where to find it 3DM GX5 25 support documentation http www microstrain com documents inertial NIST Calibration Procedures http www nist gov calibrations ASTM Testing Procedures http www astm org Standard standards and publications html Table 7 Document Resources 68 ...

Page 69: ...ve technology refers to the ability of a filter to selectively trust a given measurement more or less based on a trust threshold when com pared to another measurement that is used as a reference Sensors that have estimation filters that rely on adaptive control elements to improve their estimations are refered to as an AKF AHRS Attitude and Heading Reference System A navigation device consisting o...

Page 70: ... Complementary Filter CF A term commonly used for an algorithm that combines the readings from multiple sensors to produce a solution These filters typically contain simple filtering elements to smooth out the effects of sensor over ranging or anomalies in the magnetic field Configuration A general term applied to the sensor indicating how it is set up for data acquisition It includes settings suc...

Page 71: ... describe the orientation of an object in space such as the x y and z or pitch roll and yaw Euler angles can also represent a sequence of three elemental rotations around the axes of a coordinate system Extended Kalman Filter EKF Used generically to describe any estimation filter based on the Kalman Filter model that can handle non linear elements Almost all inertial estimation filters are fundame...

Page 72: ...the current mean and covariance to produces an estimate of a system s current state that is statistically more precise than what a single measurement could pro duce L LOS Line of Sight Describes the ideal condition between transmitting and receiving devices in a wireless network As stated it means they are in view of each other with no obstructions M Magnetometer A type of sensor that measures the...

Page 73: ... up or down with respect to the sensor or platform frame origin Position The spatial location of an object PVA acronym for Position Velocity Attitude Q Quaternion Mathematical notation for representing orientation and rotation of objects in three dimensions with respect to the fixed earth coordinate quaternion Quaternions convert the axis angle representation of the object into four numbers and to...

Page 74: ...rocess of taking measurements from a sensor or device Sampling rate rate at which the sensors are sampled Sampling Rate the frequency of sampling Sensor a device that physically or chemically reacts to environmental forces and conditions and produces a pre dictable electrical signal as a result Sigma In statistics sigma is the standard deviation from the mean of a data set Space Vehicle Informatio...

Page 75: ...ct to time Also called speed W WAAS Wide Area Augmentation System An air navigation aid developed to allow aircraft to rely on GPS for all phases of flight including pre cision approaches to any airport WGS World Geodetic System a protocol for geo referencing such as WGS 84 Y Yaw In navigation yaw is what occurs when rotational force is applied at a distance forward or aft from the center of gravi...

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