# Nomenclature¶

These are the most common definitions in AHRS:

**Altitude** is the distance along the ellipsoidal normal between the surface
of the ellipsoid and a
point of interest above it.

**Attitude** is the orientation of a vehicle or other object relative to a
known reference, which could be a frame, the horizon, a direction of motion, or
even another object. The heading of the object cn be omitted in the definition
of its attitude.

**Body Frame** matches the frame of the platform the sensors are mounted on.
The origin coincides with the center of gravity of the platform. The Y-axis
points forward of the moving platform, while the Z-axis points upwards. The
X-axis completes the right-hand system pointing in traverse direction. Some
literature names it **b-frame**.

**Earth-Centered Earth-Fixed Frame** (ECEF) has its origin and z-axis aligned
to the ECI frame, but rotates along with the Earth. Therefore is Earth-Fixed.
Some literature names it **e-frame**.

**Earth-Centered Inertial Frame** (ECI) has the origin at the center of mass of
the Earth. The X-axis points towards the vernal equinox
in the equatorial plane. The Z-axis is along the rotation axis of the Earth.
The y-axis completes with a right-hand system. Some literature names it **i-frame**.

**East-North-Up Frame** (ENU) is an LLF with the X-axis pointing East, Y-axis
pointing to the true North, and the Z-axis completes a right-hand system
pointing up (away from Earth.)

**Elevation** is the height above or below a fixed reference point. In
Geography, it is most commonly the height of a terrain above (or below) the sea
level.

**Geodetic** (also ellipsoidal or curvilinear) **coordinates** in the ECEF are
defined for positioning elements on or near the Earth.

**Inertial Measurement Unit** is a device fitted with inertial sensors
(accelerometers and gyroscopes) measuring a body’s specific force
and angular rate.

**Inertial Navigation System** is a navigation architecture consisting of an
IMU, and a computer to continuously estimate a device’s positoin and orientation using dead reckoning.

**Latitude** is the angle in the meridian plane from the equatorial plane to
the ellipsoidal normal at he point of interest.

**Local-Level Frame** (LLF) is the local navigation frame, whose origin
coincides with the sensor frame. Some literature names it **l-frame**.

**Longitude** is the angle in the equatorial plane from the prime meridian to
the projection of the point of interest onto the equatorial plane.

**Meridian** is the half of a creat circle on Earth’s surface terminated by the
poles.

**North-East-Down Frame** (NED) is an LLF with the X-axis pointing to the true
North, Y-axis pointing East, and the Z-axis completing the right-hand system
pointing Down.

**Orientation** is the rotation needed to place an object from a reference
placement to its current placement, neglecting its position or location in
space.

**Rectangular coordinates** in the ECEF represent position of a point with its
x, y, and z vector components aligned parallel to the corresponding e-frame
axes.

**Strapdown** INS has accelerometers rigidly mounted parallel to the body axes
of the vehicle. In this application the gyroscopes do not provide a stable
platform; they are instead used to sense the turning rates of the craft.

## Abbreviations¶

AACGM | Altitude-Adjusted Corrected Geomagnetic Coordinates |

ADC | Analog-to-Digital Converter |

ADEV | Allan deviation |

AHRS | Attitude and Heading Reference System |

AoA | Angle of Arrival |

AoD | Angle of Departure |

AR | Angular Rate |

atan | Arctangent |

atan2 | Arctangent (four quadrants) |

AUV | Autonomous Underwater Vehicle |

AVAR | Allan variance |

BIH | Bureau International de l’Heure |

BPF | Band-Pass Filter |

CD | Centered Dipole |

CGM | Corrected Geomagnetic Coordinates |

CIRS | Conventional Inertial Reference System |

CRS | Conventional Celestial Reference System |

CTP | Conventional Terrestrial Pole |

CTRS | Conventional Terrestrial Reference System |

DCM | Direction Cosine Matrix |

DoD | Department of Defense |

DoF | Degrees of Freedom |

DR | Dead Reckoning |

ECEF | Earth-Centered Earth-Fixed |

ECIF | Earth-Centered Inertial Frame |

EGM | Earth Gravitational Model |

EGNSS | Enhanced GNSS |

EKF | Extended Kalman Filter |

ENU | East-North-Up |

ESA | European Space Agency |

EU | European Union |

GNSS | Global Navigation Satellite System |

GPS | Global Positioning System |

GTRF | Galileo Terrestrial Reference Frame |

gyro | Gyroscope |

HP | High Performance |

HPF | High-Pass Filter |

IAU | International Astronomical Union |

IC | Integrated Circuit |

IERS | International Earth Rotation and Reference Systems Service |

IGRF | International Geomagnetic Reference Field |

IMU | Inertial Measurement Unit |

INS | Inertial Navigation System |

INU | Inertial Navigation Unit |

CIRAS | Coriolis Inertial Rate and Acceleration Sensor |

ITRF | International Terrestrial Reference Frame |

KF | Kalman Filter |

lat | Latitude |

LLF | Local-level Frame |

lon | Longitude |

LPF | Low-Pass Filter |

MagCal | Magnetic Calibration |

MARG | Magnetism, Angular Rate, and Gravity |

MCU | Micro-Controller Unit |

MEMS | Micro-electromechanical Systems |

MLT | Magnetic Local Time |

MOEMS | Micro-opto electromechanical Systems |

MST | Microsystem Technology |

μC | Microcontroller |

NED | North-East-Down |

PF | Particle Filtering |

PIGA | Pendulous Integrating Gyroscopic Accelerometer |

QD | Quasi-Dipole |

QUEST | Quaternion Estimator |

RHR | Right-Hand Rule |

SCI | Serial Communications Interface |

SI | Système International d’unités |

SLERP | Spherical Linear Interpolation |

SOA | Silicon Oscillating Accelerometer |

SVD | Singular Value Decomposition |

TFG | Turning Fork Gyroscope |

UART | Universal Asynchronous Receiver / Transmitter |

UAV | Unmanned Aerial Vehicle |

UKF | Unscented Kalman Filter |

UT | Universal Time |

WGS | World Geodetic System |

WMM | World Magnetic Model |

ZUPT | Zero Velocity Update |