Automotive Radar Relative Velocity Calculator & Formula

This online Automotive Radar Relative Velocity Calculator allows you to compute the relative velocity of targets detected by automotive radar systems, which are widely used in Advanced Driver Assistance Systems (ADAS) applications such as Adaptive Cruise Control (ACC). By inputting parameters like transmitted frequency, received frequency, and speed of the vehicle, the calculator will provide you with the relative velocity of the target.

Automotive Radar Relative Velocity Calculator

Example Calculation:

Scenario : An Adaptive Cruise Control (ACC) system is tracking a car ahead. The radar operates at 77 GHz (standard Long Range Radar band). The signal processing unit detects a Doppler frequency shift of 10.26 kHz. We need to calculate how fast we are closing in on the car ahead.

INPUTS:

• Transmitted Frequency (fc) = 77 GHz
• Doppler Frequency Shift (fd) = 10.26 kHz

Constant:

• Speed of Light (c) = 3 x 10^8 meters/second

OUTPUT:

• Wavelength (λ) = 0.00389 meters
• Vrel = 19.987 meters/second
• Vrel = 71.95 kilometers/hour

Automotive Radar Relative Velocity Formula

Following formula can be used to calculate the relative velocity in automotive radar systems:

Where:

• vr = Relative Velocity (meters/second)
• c = Speed of light (approximately 3 x 10^8 meters/second)
• fd = Doppler Frequency Shift (Hertz)
• fc = Carrier Frequency (Hertz)

References

1. Handbook of Driver Assistance Systems. Springer, 2016. Winner, Hermann, et al.
2. ETSI (European Telecommunications Standards Institute) Standard EN 301 091.
3. Introduction to mmWave Sensing: FMCW Radars. Whitepaper from Texas Instruments.