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Inertial Sense Navigation Glossary

This glossary defines terminology used in inertial navigation, GNSS positioning, and Inertial Sense navigation systems.

Navigation Systems

IMU (Inertial Measurement Unit)

A sensor device containing:

  • gyroscopes
  • accelerometers

It measures angular velocity and linear acceleration, which are used to estimate motion and orientation.

AHRS (Attitude and Heading Reference System)

A system that estimates orientation using IMU and magnetometer data.

Outputs typically include:

  • roll
  • pitch
  • heading

INS (Inertial Navigation System)

A navigation system that computes:

  • position
  • velocity
  • orientation

by integrating IMU measurements over time.

Strapdown INS

A modern INS architecture where the IMU is rigidly attached to the vehicle and navigation equations are solved in software.

This contrasts with older gimbaled INS systems.

GNSS (Global Navigation Satellite System)

Satellite navigation systems providing global positioning and timing.

Examples include:

  • GPS
  • GLONASS
  • Galileo
  • BeiDou

GNSS-INS Integration

Combining GNSS and inertial measurements to provide:

  • robust positioning
  • high-rate navigation
  • improved reliability

Dead Reckoning

Position estimation obtained by integrating velocity and heading over time without external measurements.

Sensor Fusion

The process of combining measurements from multiple sensors to estimate system state more accurately.

Navigation State Variables

Position

Vehicle location expressed as:

  • Latitude
  • Longitude
  • Altitude

This geodetic representation is often called LLA.

Position can also be expressed in Earth-fixed Cartesian (ECEF) coordinates:

p_ecef = [X, Y, Z]

or in local coordinates:

p = [North, East, Down]

Velocity

Rate of change of position.

In the navigation frame:

v = [v_N, v_E, v_D]

Velocity can also be expressed in Earth-fixed Cartesian (ECEF) coordinates:

v_ecef = [v_X, v_Y, v_Z]

Attitude

The orientation of a vehicle relative to a reference frame.

Representations include:

  • Euler angles
  • quaternions
  • direction cosine matrices

Coordinate Frames

Body Frame

Coordinate frame fixed to the IMU.

Typical convention:

X → Forward
Y → Right
Z → Down

A local Earth-referenced coordinate frame used for navigation.

Common choice:

NED (North-East-Down)

NED Frame

Local tangent plane coordinate system:

X → North
Y → East
Z → Down

ECEF Frame

Earth-Centered Earth-Fixed coordinate system.

Origin:

Earth's center of mass.

Coordinates are represented as:

[X, Y, Z]

in meters, fixed to Earth.

LLA (Latitude, Longitude, Altitude)

Geodetic position representation on the Earth reference ellipsoid.

Common units:

  • latitude/longitude in degrees
  • altitude in meters

LLA is often used as an alternative to ECEF coordinates depending on the application.

ECI Frame

Earth-Centered Inertial coordinate frame that does not rotate with Earth.

Used primarily in orbital mechanics.

Sensor Frame

Coordinate frame defined by the axes of the IMU sensors.

Vehicle Frame

Coordinate frame aligned with the vehicle body.

Attitude Representations

Euler Angles

Orientation defined by three sequential rotations:

Roll  (φ)
Pitch (θ)
Yaw   (ψ)

Limitations:

  • gimbal lock near ±90° pitch

Quaternion

A four-element representation of orientation:

q = [q_w, q_x, q_y, q_z]

Advantages:

  • no singularities
  • efficient for filtering

Direction Cosine Matrix (DCM)

3×3 rotation matrix that converts vectors between coordinate frames.

Example:

C_bn

Transforms body frame vectors into navigation frame.

Strapdown Navigation Equations

Attitude Propagation

Orientation updated using gyro measurements:

q̇ = ½ Ω(ω) q

where

ω = angular rate vector
Ω = quaternion rate matrix

Velocity Equation

Velocity evolves as:

v̇ = C_bn f_b + g_n - (2Ω_ie + Ω_en)v

where:

  • f_b = specific force
  • g_n = gravity vector
  • Ω_ie = Earth rotation rate
  • Ω_en = transport rate

Position Equation

Position updated by integrating velocity:

ṗ = v

IMU Measurement Terms

Angular Rate

Rotation rate measured by gyroscopes.

Units:

deg/s
rad/s

Specific Force

Acceleration measured by accelerometers excluding gravity.

Linear Acceleration

True acceleration of the body.

Magnetic Field

Earth magnetic field measured by magnetometers for heading estimation.

Barometric Pressure

Atmospheric pressure measurement used for altitude estimation.

Sensor Error Models

Bias

Constant offset in sensor output.

measurement = truth + bias

Bias Instability

Slow variation of sensor bias over time.

Often characterized using Allan variance.

Angular Random Walk (ARW)

Gyroscope white noise causing attitude error growth.

Units:

° / √hr

Error growth:

σ_angle = ARW √t

Velocity Random Walk (VRW)

Accelerometer white noise causing velocity error growth.

Units:

m/s / √hr

Scale Factor Error

Error in sensor gain.

measurement = (1 + scale_factor_error) * truth

Misalignment Error

Small angular errors between sensor axes and the reference coordinate frame.

Cross-Axis Sensitivity

Sensor response to motion on another axis.

Allan Variance Terms

Allan Variance

A time-domain method used to analyze sensor noise processes.

Allan Deviation

Square root of Allan variance.

Used to identify noise characteristics.

Bias Instability (Allan)

Estimated from the minimum of the Allan deviation curve.

Conversion:

bias_instability = Allan_min / 0.664

Rate Random Walk

Low-frequency gyro noise process.

Quantization Noise

Noise introduced by digital resolution limits.

GNSS Terminology

Pseudorange

Measured distance between receiver and satellite based on signal travel time.

Carrier Phase

High precision measurement of GNSS signal phase.

Used for centimeter-level positioning.

RTK (Real-Time Kinematic)

Carrier-phase GNSS positioning using base station corrections.

Accuracy:

1–2 cm

Base Station

Stationary GNSS receiver that provides correction data.

Rover

GNSS receiver whose position is being estimated.

Differential GNSS (DGNSS)

Positioning method using corrections from a reference station.

Satellite Ephemeris

Precise orbital data describing satellite position.

Dilution of Precision (DOP)

Measure of satellite geometry quality.

Types include:

  • GDOP
  • PDOP
  • HDOP
  • VDOP

GNSS Measurement Models

Pseudorange Equation

ρ = r + c(dt - dT) + I + T + ε

where:

  • r = geometric range
  • dt = receiver clock bias
  • dT = satellite clock bias
  • I = ionospheric delay
  • T = tropospheric delay
  • ε = measurement noise

Carrier Phase Measurement

Φ = r + c(dt - dT) + λN + ε

where:

  • λ = carrier wavelength
  • N = integer ambiguity

Kalman Filtering

Kalman Filter

An optimal recursive estimator used to estimate system state.

Extended Kalman Filter (EKF)

A nonlinear version of the Kalman filter commonly used in navigation.

State Vector

Vector of estimated system variables.

Example INS state:

x = [position, velocity, attitude, biases]

Process Model

Mathematical model predicting how system state evolves.

Measurement Model

Relates sensor measurements to system state.

Covariance Matrix

Represents uncertainty in the state estimate.

Innovation

Difference between predicted and measured observation.

innovation = measurement − prediction

Observability

Ability to estimate a state variable from available measurements.

INS/GNSS Integration

Loosely Coupled Integration

INS and GNSS are integrated at the position/velocity level.

Tightly Coupled Integration

GNSS measurements integrated at the pseudorange level.

Allows operation with fewer satellites.

Deep Coupling

GNSS tracking loops assisted directly by INS measurements.

Lever Arm

Offset between IMU and GNSS antenna.

r_lever = position_GNSS − position_IMU

Time Synchronization

Alignment of timestamps between sensors.

Navigation Performance Metrics

CEP (Circular Error Probable)

Radius containing 50% of position errors.

RMS Error

Root-mean-square error of measurements.

Drift Rate

Rate at which inertial navigation error grows without external aiding.

Inertial Sense Protocol

DID (Data Identifier)

Numeric identifier defining a data structure in the Inertial Sense binary protocol.

Examples include:

DID_INS_1
DID_IMU
DID_GPS

Data Set

Binary structure containing navigation or configuration data.

ISB (Inertial Sense Binary)

Binary communication protocol used by Inertial Sense devices.

NMEA

ASCII protocol used for GNSS data output.

Example:

$GPGGA

Software Tools

SDK

Software development kit used to integrate Inertial Sense devices.

EvalTool

Graphical interface used to visualize and configure devices.

CLTool

Command-line tool used to communicate with devices.

Hardware Products

IMX

Inertial Sense navigation module containing:

  • IMU
  • magnetometer
  • barometer
  • navigation processor

GPX

Multi-band GNSS receiver used with IMX modules.

Rugged Systems

Industrialized versions of Inertial Sense modules.

Common Abbreviations

Acronym Meaning
IMU Inertial Measurement Unit
INS Inertial Navigation System
GNSS Global Navigation Satellite System
AHRS Attitude and Heading Reference System
ARW Angular Random Walk
VRW Velocity Random Walk
RTK Real-Time Kinematic
EKF Extended Kalman Filter
NED North-East-Down
ECEF Earth-Centered Earth-Fixed
LLA Latitude, Longitude, Altitude