# Coordinate Transformation. Magellan ZXW Eurocard, ZXW Sensor

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The ZXW Sensor and ZXW Eurocard are high-precision GPS receivers designed for demanding surveying and mapping applications. These receivers offer advanced features such as real-time kinematic (RTK) positioning, differential correction, and data logging. They are ideal for a wide range of applications, including construction, surveying, mapping, and geospatial data collection.

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7

**Coordinate Transformation**

This chapter discusses the coordinate transformation features of your receiver.

## Background

GPS determines the three-dimensional positions of surveyed points based on the

WGS84 datum. These coordinates are either presented as geocentric Cartesian coordinates (X,Y,Z) values or geodetic coordinates (latitude, longitude, ellipsoidal height).

There are circumstances where it would be desirable to have positions represented in a different reference frame or format, i.e. based on a different datum or projected onto a plane (grid coordinates).

The ZXW-Receivers provide the following on-board tools to transform WGS84 coordinates into various formats and reference frames:

**1.**

**Datum-to-Datum Transformation**

Using this feature, WGS84 coordinates can be transformed into coordinates based on another datum.

**2.**

**Datum-to-Grid Conversion**

With this tool, a grid system can be defined to convert geodetic coordinates into grid coordinates.

**3.**

**Elevation Modeling**

Using an on-board geoid model, ellipsoidal heights can be transformed into orthometric heights using this capability.

**Coordinate Transformation 93**

Table 7.1 provides an overview of user coordinate transformation functions for your

receiver.

** Table 7.1. **User Coordinate Transformation Functionalities

**Transformation**

Datum to Datum

Datum to Grid

Elevation Modeling

**Description**

3D (7-parameter) datum transformation between two Cartesian XYZ systems associated with the WGS84 datum and local datum defined by the user.

Data projected from a geodetic system, associated with WGS-84 or a user-defined datum and a specified grid system.

Map Projections Supported

• Mercator (EMER)

• Transverse Mercator (TM83)

• Oblique Mercator (OM83)

• Sterographic (Polar and Oblique) (STER)

• Lambert Conformal Conic (2 standard parallels) (LC83)

Special Map Projections Specific to NAD27

• Transverse Mercator 27 (TM27 and TMA7)

• Oblique Mercator 27 (OM83)

• Lambert Conformal Conic 27 (LC27)

Interpolation of geoidal undulations

The remainder of this chapter describes in more detail the coordinate transformation features of your receiver.

## Datum to Datum

The receiver normally computes and outputs positions in the WGS-84 coordinate reference frame. However, it is possible to output positions in NMEA messages in a number of different pre-defined datums, as well as in a user defined datum.

To set the receiver to output positions in a different datum, use the $PASHS,DTM command. Once set to a different datum, then all position outputs in NMEA messages such as GGA and GLL and the position displayed on the LED screen are referenced

to the chosen datum. For a list of Datums, refer to Appendix A, **Reference Datums & **

If the list of datums does not include a datum of interest to you, you can define a datum and load it on the receiver, using the $PASHS,UDD command along with the

$PASHS,DTM command. Prior to using these commands, define the required parameters including the length of the semi-major axis and amount of flattening in the reference ellipsoid and the translation, rotation, and scale between the user defined system and WGS-84.

**94 ZXW- Receivers Operation and Reference Manual**

**The rotation and scale parameters are only available in version ZC00 or later.**

The generic formula used to translate and rotate from coordinate system 1 to coordinate system 2 is as follows: x y z

2

=

∆x

∆y

∆z

+

(

1 + m

×10

– 6

)

–

1

ε rz

ε rz

–

ε ry

1

ε rx

ε ry

–

ε rx

1 x y z

1 where e rx

= e x expressed in radians, similarly for e ry

and e rz

.

Example: Define local datum as the WGS-72 datum

Send the following commands to the receiver:

**$PASHS,UDD, 0,6378135.0, 298.26,0,0,4.5,0,0,-0.554,0.23**

**$PASHS,DTM,UDD**

This implements the transformations listed in Table 7.2 and below.

** Table 7.2. **Ellipsoid Parameters for WGS-72 and WGS-84

**Datum**

WGS-72

WGS-84

**Reference **

**Ellipsoid**

WGS-72

WGS-84

**a[m] 1/f**

6378135.0

6378137.0

298.26

298.257223563

x y z

WGS84

∆x=∆y=0

ε x

=

ε y

=0

∆z= 4.5 meters m= 0.23 x 10

**-**6

ε z

= –2.686

x 10

**-**6 radians = –0.”554 in the following equation:

=

0

0

4,5

+

(

1 + 0,23

×10

– 6

)

1

2,686

×10

– 6

0

– 2,686

×10 0

1

0

0

1 x y z

1WGS72

After issuing the $PASHS,DTM,UDD command, the receiver internally transforms positions * from* the reference datum (WGS-84)

*the user-defined datum. In standard text books, however, the datum transformations are given*

**to***local datums*

**from***WGS-*

**to**84. To simplify entering the transformation parameters, the translation, rotation, and scale parameters are defined * from* the local datum

*WGS-84.*

**to****Coordinate Transformation 95**

Figure 7.1 illustrates the change in the coordinate systems.

** Figure 7.1. **Rotation and Translation Between Coordinate Systems

After transforming the datum, the receiver computes geodetic coordinates in the defined system. All coordinates output by the receiver are in this new system.

**Do not forget to issue the $PASHS,DTM,UDD command after defining the transformation parameters with the $PASHS,UDD command. Otherwise, the newly entered parameters are not used.**

## Datum to Grid

Use this transformation to generate coordinates in an <x,y> rectangular system, based on the user’s location and mapping requirements or local standard. You can select any projection along with any base datum for output.

Convert geodetic coordinates into grid coordinates by defining a grid system utilizing one of the supported projection types (Figures 7.2 - 7.6).

CAUTION

**Although almost any projection or combination of datums and projections is mathematically possible, some are inappropriate with respect to the project scope or geographic area.**

**96 ZXW- Receivers Operation and Reference Manual**

To set the receiver to supply grid coordinates:

1.

Select the projection type that best fits your needs.

2.

Define the grid system, using this projection type, with the $PASHS,UDG command. This command defines the grid system to be used.

3.

Enable the grid system with the $PASHS,GRD,UDG command. The receiver computes grid coordinates in the system defined.

4.

To access the grid coordinates, use either the $PASHQ,GDC command to query for one output of the current coordinates, or use the

$PASHS,NME,GDC command to set the receiver to continuously output the current coordinates.

There is one exception when configuring the receiver to compute and output grid coordinates. If you are interested in computing and outputting WGS-84 based UTM coordinates, there is no need to define the grid system in the receiver. The parameters for WGS84 UTM are pre-set in the receiver. To use them, set the receiver to output grid coordinates using either the $PASHQ,UTM command to query for one output of the current coordinates, or the $PASHS,NME,UTM command to set the receiver to continuously output the current coordinates.

**Check the GDC message for the currently assigned datum.**

**Coordinate Transformation 97**

**Projection Types**

The following graphics represent the different types of projections available for the receiver.

** Figure 7.2. **Mercator

**98 ZXW- Receivers Operation and Reference Manual**

** Figure 7.3. **Transverse Mercator

**Coordinate Transformation**

** Figure 7.4. **Oblique Mercator

**99**

** Figure 7.5. **Stereographic

** Figure 7.6. **Lambert Conformal Conic

**Elevation Modeling**

In addition to computing and outputting geodetic and cartesian coordinates in different systems, the receiver can compute and output elevations in different systems.

By default, the receiver computes and outputs ellipsoidal heights. In some messages, the geoid separation is included, computed from the internal global model, relative to

WGS-84.

**100 ZXW- Receivers Operation and Reference Manual**

To set the receiver to compute and output orthometric heights, use the

$PASHS,HGT,GEO command. After setting this command, the receiver outputs orthometric heights using the internal global geoid model. Be aware that the internal geoid model used in this calculation is very coarse. Orthometric heights derived from this model could be in error by a meter or more.

**If separation is included in the message, it is calculated by adding the difference between WGS-84 and a user- or pre-defined datum to the WGS-84-based geoid separation. An exception to this is the **

**GGA message which ONLY outputs WGS-84 based geoid heights and separation, as per NMEA specifications.**

**Coordinate Transformation 101**

**102 ZXW- Receivers Operation and Reference Manual**

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### Key Features

- Real-time Kinematic (RTK) Positioning
- Differential Correction
- Data Logging
- High-Precision Positioning
- Advanced Signal Processing
- Multiple Data Output Options
- User-Friendly Interface
- Flexible Configuration Options

### Related manuals

### Frequently Answers and Questions

###### What are the power requirements for the ZXW Sensor?

###### What is the accuracy of the RTK solution?

###### How do I set up a differential base station?

###### What is the difference between RTK and Fast RTK?

###### How do I download data from the receiver?

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#### Table of contents

- 23 Introduction
- 23 Overview
- 24 Functional Description
- 25 Technical Specifications
- 26 Performance Specifications
- 26 Receiver Options
- 28 Option [B] RTCM Base
- 28 Option [U] RTCM Remote
- 28 Option [E] Event Marker
- 28 Option [M] Remote Monitoring
- 28 Option [F] Fast Data Output
- 28 Option [T] Point Positioning
- 29 Option [3] Observables-1, 2, 3
- 29 Option [J] RTK Rover
- 29 Option [K] RTK Base
- 29 [I] Instant RTK
- 29 [G] Reserved for Future Options
- 30 [H] 5 Hz Synchronized RTK
- 30 [N] Reserved for Future Options
- 30 Option [Y] SBAS
- 31 Equipment
- 31 Hardware Description
- 31 ZXW-Eurocard
- 34 RF Connector
- 34 Antenna
- 34 Power Requirements
- 34 Environmental Specifications
- 34 Mounting Requirements
- 35 Heat Sink Requirements
- 36 Modem Support
- 36 ZXW-Sensor
- 38 Mounting Dimensions
- 39 Power/Input/Output Connector
- 40 Power Requirements
- 40 Environmental Specifications
- 40 RF Connector
- 41 Serial/Power Cable
- 41 Antenna
- 41 On-Board Battery
- 41 Radio Interference
- 42 Development Kits
- 47 Getting Started
- 47 Hardware Setup
- 47 Applying Power
- 47 Receiver Initialization
- 47 Receiver Communication
- 48 Monitoring
- 48 Satellite Tracking
- 49 Position
- 49 Setting Receiver Parameters
- 49 Saving Parameter Settings
- 49 Data Recording
- 50 Default Parameters
- 55 Operation
- 55 Receiver Initialization
- 55 Setting Receiver Parameters
- 56 Saving Parameter Settings
- 56 Data Modes
- 57 Downloading the Data
- 57 Data Logging through Serial Port
- 58 Elevation Masks
- 58 Secondary Elevation Mask
- 59 Zenith Elevation Mask
- 60 Session Programming
- 61 Position Mode
- 61 ALT Fix Mode
- 62 Daisy Chain Mode
- 62 Point Positioning
- 62 Remote Monitoring
- 63 Event Marker
- 64 Time Tagging the Shutter Signal
- 64 Closed-Loop Technique (Advanced Trigger)
- 65 1PPS Out
- 65 Data Output
- 66 Transferring Data Files
- 67 Synchronization to GPS Time
- 67 Default Parameters
- 71 Multipath Mitigation
- 72 Evaluating Correlator Performance
- 74 Signal-to-Noise Ratio
- 75 Antenna Reduction
- 77 Differential and RTK Operations
- 78 Base Stations
- 78 Setting Up a Differential Base Station
- 79 Setting Up an RTK Base Station
- 79 RTCM 18 & 19
- 80 RTCM 20 & 21
- 81 Magellan DBEN Format
- 82 CMR or CMR Plus Format
- 83 Setting Up a Combined Differential & RTK Base Station
- 84 Advanced Base Station Operation
- 84 Recommended Advanced Parameter Settings for Base Stations
- 84 Antenna
- 84 Message Rate
- 85 Required Differential Update Rates
- 88 Mask Angle
- 88 Base Station Position
- 89 Base Station Antenna Offset
- 89 Using Reference Station ID
- 89 Reference Station Health
- 89 Other RTCM Messages
- 90 Using a PC Interface
- 90 Using a Handheld Interface
- 91 Remote Stations
- 91 Setting Up a Differential Remote Station
- 91 Setting Up an RTK Remote Station
- 91 Using RTCM Messages
- 92 Using Magellan DBN or CMR Messages
- 93 Advanced Remote Station Operation
- 93 Base Station Data
- 94 Base Data Latency
- 95 Differential Accuracy vs. Base Data Latency
- 95 Chosing Between Fast RTK and Synchronized RTK
- 97 Float and Fixed Solutions
- 98 Carrier Phase Initialization
- 99 Mask Angles
- 99 Auto Differential Mode
- 100 RTCM Messages
- 103 Understanding RTK/CPD
- 103 Monitoring the CPD Rover Solution
- 104 How to Tell If the Integer Ambiguities are Fixed
- 104 Data Link Monitor
- 104 CPD Solution Output and Storage
- 105 Real-time Solution Output
- 105 Vector Solution Output
- 106 Solution Storage
- 107 Troubleshooting
- 108 System Performance Optimization
- 109 Ambiguity Fix: $PASHS,CPD,AFP
- 110 Dynamics: $PASHS,CPD,DYN
- 111 Fast CPD: $PASHS,CPD,FST
- 111 Multipath: $PASHS,CPD,MTP
- 111 DBN Message Interval: $PASHS,CPD,PED and CPD Update Rate: $PASHS,CPD,PER
- 112 Initialization: $PASHS,CPD,RST
- 112 Base Position Coordinates Selection: $PASHS,CPD,UBS
- 112 Base Station Elevation Mask: $PASHS,ELM
- 113 Universal RTCM Base Station
- 113 Instant-RTK
- 114 CMR Format
- 114 Setting Up Your Receivers to Use CMR Format
- 115 Coordinate Transformation
- 115 Background
- 116 Datum to Datum
- 118 Datum to Grid
- 120 Projection Types
- 122 Elevation Modeling
- 125 Command/Response Formats
- 127 Receiver Commands
- 127 Set Commands
- 127 Query Commands
- 132 ALH: Almanac Messages Received
- 133 ALT: Set Ellipsoid Height
- 133 ANA: Post-Survey Antenna Height
- 133 ANH: Set Antenna Height
- 134 ANR: Set Antenna Reduction Mode
- 135 ANT: Set Antenna Offsets
- 136 BEEP: Beeper Set-up
- 137 CLM: Clear/Reformat PCMCIA Card
- 138 CSN: Satellite Signal-to-Noise Ratio
- 139 CTS: Port Protocol Setting
- 139 DOI: Data Output Interval
- 140 DRI: Data Recording Interval
- 140 DSC: Store Event String
- 140 DSY: Daisy Chain
- 141 ELM: Recording Elevation Mask
- 142 EPG: Epoch Counter
- 142 FIL,C: Close a File
- 142 FIL,D: Delete a File
- 143 FIX: Altitude Fix Mode
- 143 FLS: Receiver File Information
- 145 FSS: File System Status
- 146 HDP: HDOP Mask
- 147 INF: Set Session Information
- 149 INI: Receiver Initialization
- 150 ION: Set Ionospheric Model
- 150 ION: Query Ionospheric Parameters
- 152 LPS: Loop Tracking
- 153 LTZ: Set Local Time Zone
- 153 MDM: Set Modem Parameters
- 155 MDM,INI: Initialize Modem Communication
- 156 MET: Meteorological Meters Setup
- 156 MET,CMD: Meteorological Meters Trigger String
- 157 MET,INIT: Meteorological Meters Initialization
- 157 MET,INTVL : Meteorological Meters Interval
- 158 MST: Minimum SVs for Kinematic Survey
- 158 MSV: Minimum SVs for Data Recording
- 158 OUT,MET: Start Meteorological Meters Process
- 159 OUT, TLT: Start Tiltmeter Process
- 159 PAR: Query Receiver Parameters
- 162 PDP: PDOP Mask
- 162 PEM: Position Elevation Mask
- 163 PHE: Photogrammetry Edge (Event Marker Edge)
- 164 PJT: Log Project Data
- 164 PMD: Position Mode
- 165 POS: Set Antenna Position
- 166 POW: Battery Parameters
- 167 PPO: Point Positioning
- 167 PPS: Pulse Per Second
- 168 PRT: Port Setting
- 169 PWR: Sleep Mode
- 170 RCI: Recording Interval
- 170 REC: Data Recording
- 171 RID: Receiver ID
- 172 RNG: Data Type
- 172 RST: Reset Receiver to default
- 173 RTR: Real-Time Error
- 173 SAV: Save User Parameters
- 174 SEM: Secondary Elevation Mask
- 174 SES: Session Programming
- 178 SID: Serial Number
- 178 SIT: Set Site Name
- 178 SPD: Serial Port Baud Rate
- 179 STA: Satellite Status
- 180 SVS: Satellite Selection
- 181 TLT : Tiltmeter Set-up
- 181 TLT,CMD: Tiltmeter Trigger String
- 182 TLT,INIT : Tiltmeter Initialization
- 182 TLT,INTVL: Tiltmeter Interval
- 183 TMP: Receiver Internal Temperature
- 183 TST:Output RTK Latency
- 184 UNH: Unhealthy Satellites
- 184 USE: Use Satellites
- 184 VDP: VDOP Mask
- 184 WAK: Warning Acknowledgment
- 185 WARN: Warning Messages
- 189 WKN: GPS Week Number
- 190 Raw Data Commands
- 190 Set Commands
- 191 Query Commands
- 194 CBN: CBEN Message
- 199 CMR: CMR Message
- 201 Compact Measurement Record Packet
- 201 Observables (Message Type 0)
- 203 L2 Data
- 204 DBN: DBEN Message
- 208 EPB: Raw Ephemeris
- 210 MBN: MBN Message
- 214 OUT: Enable/Disable Raw Data Output
- 215 PBN: Position Data
- 217 RAW: Query Raw Data Parameter
- 219 RWO: Raw Data Output Settings
- 220 SAL: Almanac Data
- 221 SNV: Ephemeris Data
- 224 NMEA Message Commands
- 224 Set Commands
- 225 Query Commands
- 228 ALL: Disable All NMEA Messages
- 228 ALM: Almanac Message
- 231 CRT: Cartesian Coordinates Message
- 233 DAL: DAL Format Almanac Message
- 235 DCR: Delta Cartesian Message
- 237 DPO: Delta Position Message
- 239 GDC: User Grid Coordinate
- 242 GGA: GPS Position Message
- 245 GLL: Latitude/Longitude Message
- 246 GRS: Satellite Range Residuals
- 248 GSA: DOP and Active Satellite Messages
- 251 GSN: Signal Strength/Satellite Number
- 252 GST: Pseudo-range Error Statistic Message
- 253 GSV: Satellites in View Message
- 256 GXP: Horizontal Position Message
- 257 MSG: Base Station Message
- 263 NMO: NMEA Message Output Settings
- 264 PER: Set NMEA Send Interval
- 265 POS: Position Message
- 268 PTT: Pulse Time Tag Message
- 269 RMC: Recommended Minimum GPS/Transit
- 271 RRE: Residual Error
- 273 SAT: Satellite Status
- 276 TAG: Set NMEA Version
- 276 TTT: Event Marker
- 277 UTM: UTM Coordinates
- 280 VTG: Velocity/Course
- 282 XDR: Transducer Measurements
- 284 ZDA: Time and Date
- 286 RTCM Response Message Commands
- 286 Set Commands
- 286 Query Commands
- 288 Query: RTCM Status
- 291 AUT: Auto Differential
- 291 BAS: Enable Base Station
- 291 EOT: End of Transmission
- 292 INI: Initialize RTCM
- 292 IOD: Ephemeris Data Update Rate
- 292 MAX: Max Age
- 293 MSG: Define Message
- 293 MSI: Query RTCM Message Status
- 294 OFF: Disable RTCM
- 294 QAF: Quality Factor
- 294 REM: Enable Remote RTCM
- 295 SEQ: Check Sequence Number
- 295 SPD: Base Bit Rate
- 296 STH: Station Health
- 296 STI: Station ID
- 297 TYP: Message Type
- 298 CPD Commands
- 298 Set Commands
- 298 Query Commands
- 301 CPD: RTK Status
- 304 AFP: Ambiguity Fixing
- 305 ANT: Antenna Parameters
- 306 CMR: CMR Received Mode
- 306 DLK: Data Link Status
- 309 DYN: Rover Dynamics
- 310 ENT: Use Current Position
- 310 EOT: End of Transmission
- 311 FST: Fast CPD Mode
- 311 INF: CPD Information
- 313 MAX: Max Age for CPD Correction
- 313 MOD: CPD Mode
- 314 MTP: Multipath
- 315 OBN: Vector Solution Information
- 318 OUT: Solution Output
- 319 PEB: Base Broadcast Interval
- 319 PED: DBEN/CMR Transmission Period
- 320 PER: CPD Update Interval
- 320 POS: Set Base Position
- 321 PRO: Select RTK Format
- 322 PRT: Port Output Setting
- 322 RST: Reset CPD
- 322 STS: CPD Solution Status
- 323 UBP: Use Base Position
- 324 UCT Commands
- 325 DTM: Datum Selection
- 326 FUM: Fix UTM Zone
- 327 FZN: Set UTM Zone to Fix
- 327 GRD: Datum-to-Grid Transformation Selection (Map Projection)
- 328 HGT: Height Model Selection
- 329 UDD: User-Defined Datum
- 330 UDG: User-Defined Datum-to-Grid Transformation
- 335 SBAS Commands
- 336 SBA: SBAS Raw Data
- 337 OUT: WAAS Almanac Data
- 338 SBA: Tracking Mode
- 338 Automatic Mode
- 340 SSO: Set SBAS Satellite Search Order
- 341 Reference Datums & Ellipsoids