Defense Coordinate Systems

LASS TECH · SPACE TRAINING DIVISION

COORD SYS

Defense Coordinate Systems · Interactive Guide

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Absolute Coordinate Systems

ABSGeographic (Lat/Lon/Alt)

Position expressed in geodetic latitude φ, longitude λ, and height h above the WGS-84 ellipsoid. The global standard for all GPS-based warfare systems.

$$\varphi \in [-90°,\,+90°]\;(\text{N/S}),\quad \lambda \in [-180°,\,+180°]\;(\text{E/W})$$$$h \text{ — height above WGS-84 ellipsoid (metres)}$$

GEOGRAPHIC / WGS-84

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ABSECEF (Earth-Centred Earth-Fixed)

Cartesian X/Y/Z with origin at Earth's centre of mass. Z-axis through geographic North Pole. Used internally by GPS receivers and missile guidance systems.

$$X = (N+h)\cos\varphi\cos\lambda$$$$Y = (N+h)\cos\varphi\sin\lambda$$$$Z = \bigl(N(1-e^2)+h\bigr)\sin\varphi$$

ECEF FRAME

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ABSECI (Earth-Centred Inertial)

Inertial frame fixed to stars (vernal equinox). Does not rotate with Earth. Essential for ballistic missile and satellite trajectory computation.

ECI FRAME

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Relative / Local Frames

RELNED (North–East–Down)

Local tangent-plane frame centred on an observer. X→North, Y→East, Z→Down. Standard in INS, IMUs, radar trackers, and fire-control systems.

$$N = -\sin\varphi\cos\lambda\,\Delta X - \sin\varphi\sin\lambda\,\Delta Y + \cos\varphi\,\Delta Z$$$$E = -\sin\lambda\,\Delta X + \cos\lambda\,\Delta Y$$

NED LOCAL FRAME

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RELENU (East–North–Up)

Variant with Z pointing Up. Preferred in some western C2 systems and most mapping/GIS tools. Positive altitude is intuitive.

ENU LOCAL FRAME

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RELBody Frame

Fixed to a vehicle/weapon platform. x→nose, y→right-wing, z→down. Attitude (roll/pitch/yaw) describes rotation from NED to body. Critical for weapon aiming.

BODY FRAME

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RELSlant Range & AzEl

Polar representation from sensor to target. Azimuth θ measured clockwise from North. Elevation ε above local horizon. Used by radars, FLIR, and laser designators.

$$R = \sqrt{N^2+E^2+D^2}$$$$\text{Az} = \operatorname{atan2}(E,\,N)\;\in[0°,360°]$$$$\varepsilon = -\operatorname{atan2}\!\left(D,\,\sqrt{N^2+E^2}\right)$$

AZEL / SLANT RANGE

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Military Grid Systems

MILMGRS (Military Grid Reference System)

NATO standard for ground operations. Alphanumeric identifier: Grid Zone Designator (6° lon × 8° lat band) + 100 km square identifier + numerical easting/northing.

$$\underbrace{37\text{S}}_{\text{GZD}}\;\underbrace{\text{EB}}_{\text{100km sq}}\;\underbrace{12345\;67890}_{\text{Easting / Northing (10\,m precision)}}$$

MILUTM (Universal Transverse Mercator)

60 longitudinal zones, each 6° wide. Conformal projection preserving local shapes. Easting 0–1,000,000 m; Northing 0–10,000,000 m. Foundation of MGRS.

$$E = 500\,000 + k_0\,\nu\,(\lambda - \lambda_0)\cos\varphi$$$$N_S = 10^7\text{ m (southern hemisphere false northing)}$$

MILGEOREF (WGS-84 Reference)

Air-force targeting system. 15° quadrangles (letter+letter), subdivided to 1' intervals. Used in JDAM/cruise missile mission planning and strike packages.

Bearings & Directions

NAVTrue Bearing

Measured clockwise from True North (geographic North Pole). Required for all absolute navigation references. GPS outputs True bearing.

NAVMagnetic Bearing

Clockwise from Magnetic North. Requires declination correction. Varies by location and year. Used by aircraft and ship magnetic compasses.

$$\text{True} = \text{Magnetic} + \delta$$$$\delta > 0\;\text{(East)},\quad \delta < 0\;\text{(West)}$$

NAVGrid Bearing

Clockwise from Grid North (UTM zone central meridian). Differs from True by grid convergence angle γ. Used on all military map overlays.

$$\text{Grid} = \text{True} - \gamma$$$$\gamma \approx (\lambda - \lambda_0)\sin\varphi$$

NAVMils vs Degrees

Artillery and direct-fire weapons use angular mils (6400 mils = 360°). 1 mil subtends ~1 m at 1000 m — enabling rapid range/offset mental arithmetic.

$$1° = 17.778\;\text{mil}\quad(6400\;\text{mil} = 360°)$$$$\text{Mils} = \theta° \times \dfrac{6400}{360}$$

Observer Position

Lat φ 25.0°N

Lon λ 46.0°E

Target Position

Lat φ 31.0°N

Lon λ 52.0°E

Alt (km) 10 km

Bearing Reference

Declination +3.5°

Convergence +0.00°

Slant Range— km

True Bearing—°

Mag. Bearing—°

Grid Bearing—°

Elevation—°

NATO Mils (Az)—

NED N— km

NED E— km

NED D— km

UTM Zone—

UTM Easting—

UTM Northing—

MGRS—

Lat/Lon ↔ DMS ↔ DDM

Decimal°

DD—

DDM—

DMS—

Degrees ↔ NATO Mils

Degrees

Degrees—

NATO mils—

Radians—

True ↔ Magnetic ↔ Grid

True Brg

Decl

Convergence

True—

Magnetic—

Grid—

True mils—

Globe / LatLon

NED Frame

UTM / MGRS Grid

Bearings

Mode: GLOBE / LAT-LON

Obs: 25.0°N 46.0°E

Tgt: 31.0°N 52.0°E

Range: — km

Az True: —°

Keys: 1-4 modes · O orbit · D drift · T trail · L theme