Inertial Navigation Technology Explained: Positioning Principles from 1D to 3D

Introduction to Inertial Technology

(2) Principle of Inertial Navigation

Inertial navigation is a fundamental navigation and positioning technology based on Newton’s laws of classical mechanics. It determines the position, velocity, and attitude of a moving object by measuring its acceleration and angular velocity without relying on any external reference signals.

The basic relationships are expressed as:

Where:

• a = acceleration vector

• v = velocity vector

• r = position vector

• t = time

Through continuous integration of acceleration and angular rate data, an Inertial Navigation System (INS) can calculate real-time motion information such as displacement, velocity, and orientation.

1D (One-Dimensional) Navigation

In a simplified one-dimensional navigation scenario, only one accelerometer is required.
It measures linear acceleration along a single axis (e.g., the direction of motion of a train).

Key principle:
By integrating acceleration once, you obtain velocity; by integrating velocity again, you obtain position.

2D (Two-Dimensional) Planar Navigation

For planar motion such as that of a train or vehicle:

• Two accelerometers are used to measure lateral and longitudinal accelerations.

• A gyroscope is added to measure the real-time heading angle (orientation).

• The acceleration data are projected onto the X and Y axes and integrated to calculate velocity and position in 2D space.

Applications:
Ground vehicles, railway systems, robotics, marine vessels, and other navigation systems that require position tracking in a flat plane.

3D (Three-Dimensional) Navigation

For full three-dimensional navigation:

• Three accelerometers measure acceleration along the X (lateral), Y (longitudinal), and Z (vertical) axes.

• Three gyroscopes measure angular motion around each of these axes.

Combining these six sensors allows the system to calculate complete 3D motion and attitude information, including roll, pitch, and yaw angles.

Core Components:

• Accelerometer (measures linear acceleration)

• Gyroscope (measures angular velocity)

• Mounting frame with roll, pitch, and azimuth motors

This configuration forms the basis of modern Inertial Measurement Units (IMUs) and Inertial Navigation Systems (INS) used in:

• Aerospace and aviation

• Autonomous vehicles

• Ships and underwater navigation

• Drones (UAVs)

• Defense and missile guidance

• Industrial robotics and mapping systems

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