Application of Wheel Speed Sensors in Inertial Navigation Systems | Enhancing INS Accuracy with Odometer Data

Wheel speed sensors (wheel speed sensors) are often used as auxiliary sensors in inertial navigation systems (INS) to improve navigation accuracy and suppress accumulated errors of inertial sensors. The wheel speed gauge calculates the longitudinal speed of the vehicle by measuring the wheel speed (combined with tire radius and slip ratio correction), providing independent speed information. When GPS signals are lost (such as in tunnels or underground garages), INS can continuously estimate the vehicle's position through dead reckoning by combining the speed data of the wheel speed meter, and compare it with the accelerometer integration results of INS to correct the speed error. In heading calculation, the wheel speed gauge can indirectly calculate the rate of change of heading angle by measuring the speed difference between the left and right wheels (wheel speed difference), providing compensation for the calibration of inertial navigation heading angle.

Taking the change of heading angle as an example, this article briefly introduces how to indirectly calculate the rate of change of heading angle through the data obtained from the wheel speed meter.

1.       Basic principles

Assuming that the vehicle has a rigid body and only moves in a horizontal plane (ignoring pitch and roll), there is no lateral slip at the contact point between the tires and the ground (only considering longitudinal rolling), and the left and right wheelbase (wheel spacing) is a fixed value. The relationship between wheel speed and linear speed is shown in the following equation:

When the vehicle turns, the left and right wheels move around the same instantaneous center of rotation (ICR), The vehicle angular velocity   is the rate of change in heading angle.

The difference in linear velocity between the left and right wheels is generated by the rotation of the vehicle around the ICR, satisfying the following relationship:

where：  : the wheel spacing ，  : the turning radius

Therefore, there is a difference in linear velocity between the left and right wheels：   

The rate of change in heading angle (angular velocity) is:       

2.       Factors affecting the measurement accuracy of wheel speed gauge and algorithm correction

In practical applications, the following issues may lead to inaccurate measurement data of the wheel speed gauge, affecting the error compensation of the azimuth angle in INS.

a)       Track B

The actual wheelbase may vary due to load or suspension deformation and requires regular calibration. The above formula assumes that the left and right wheels are symmetrical, so the model needs to be adjusted for asymmetric vehicles.

b)      Slip and error compensation

In wet and slippery road surfaces or off-road environments, or when the vehicle accelerates or brakes rapidly, it may cause tire slippage, resulting in a wheel speed difference that does not match the true angular velocity. Therefore, it is necessary to combine the acceleration and angular velocity data of IMU (Inertial Measurement Unit) to detect the slip state; Dynamically adjust the weight of the wheel speed gauge through multi-sensor fusion algorithm (Kalman filter algorithm) to reduce the impact of slip-on navigation.

3.       Actual use cases

I3500 is an integrated navigation system (GNSS/INS) produced by Micro-Magic Inc, consisting of high-performance MEMS sensors, high-precision GNSS systems, and high-performance microprocessors. Can be connected to an external odometer, DVL and other auxiliary navigation information, with built-in high reliability integrated navigation algorithms, can output real-time information such as speed, position, and attitude of the carrier.

Data input/output

Integrated navigation accuracy index

Conclusion

The wheel speed gauge complements the inertial navigation system by providing independent speed information, significantly improving the navigation reliability of vehicles in complex environments. Its core values are reflected in:

Ø  Short term accuracy: high-frequency speed data suppresses INS error accumulation.

Ø  Redundant design: Maintain basic navigation capability in the event of GPS failure.

Ø  Cost effectiveness: Significant improvement in navigation performance achieved at a lower cost.

In the future, with the advancement of multi-sensor fusion algorithms such as deep learning assisted filtering, The application of wheel speed sensors in autonomous driving and unmanned systems will be further deepened.

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