LC-8000 Series

The LC-8310 high-sensitivity GPS speedometer calculates speed from the Doppler effect of the carrier wave output from GPS satellites.
The Doppler effect is a phenomenon where the frequency of waves, such as radio waves, light, and sound waves, is observed to differ when there is a velocity difference between the source of the waves and the observer. When the source and observer are moving closer together, the frequency is observed to be higher, and when they are moving apart, it is observed to be lower. The Doppler effect for radio waves and light is expressed by the following formula.

The carrier frequency of GPS satellites (L1 band fs=1.5754 GHz) is managed with very high precision, so by measuring this frequency and applying it to the aforementioned formula, the speed V can be determined.
However, GPS satellites are moving at high speeds. Additionally, due to the influence of the Earth's rotation, it is not possible to determine the ground speed using only the carrier frequency of a single GPS satellite.
Therefore, as shown in the following diagram, by measuring the carrier frequencies from multiple (four or more) GPS satellites and applying positioning calculations similar to those for location, the speed of the moving object can be determined with high accuracy.

Because this method is largely unaffected by the ionosphere, it is possible to calculate the velocity of a moving object with extremely high accuracy compared to methods that calculate velocity from changes in position.
The accuracy of the horizontal component is 0.03 m/s at 2σ and 0.08 m/s at 3σ.
However, the accuracy of the vertical component is not limited to this; because satellites are unidirectional in principle, the accuracy is approximately three times worse compared to the horizontal component. From the image above, it can be seen that the moving object is receiving radio waves at different Doppler shift frequencies from multiple satellites.

When these relationships are formalized,
Δ fd1 = 1/ λ(V0 - V1)・u1
Δ fd2 = 1/ λ(V0 - V2)・u2
Δ fd3 = 1/ λ (V0 - V3)・u3
Δ fd4 = 1/ λ (V0 - V4)・u4
Δ fd5 = 1/ λ (V0 - V5)・u5
This is the result.
Here, λ is the wavelength of the carrier wave emitted from the satellite, approximately 0.19 m, fb is the receiver's clock error (Hz), and un(n = 1..5) is the unit vector in the line of sight between the satellite and receiver positions, calculated using the following formula.
un = ρ n/| ρ n| (n = 1..5)
ρ n = [(Npn - Np0), ( Epn - Ep0), ( Dpn - Dp0)] ^T (n = 1..5)

By solving for Vo in these equations, we can obtain the velocity of the moving object.

In urban areas with obstacles such as trees and buildings, similar to public roads, the influence of multipath causes significant noise in the Doppler speed output, as shown in the figure. Additionally, when passing through areas where satellites cannot be observed, such as under elevated bridges, it becomes impossible to measure speed using GPS alone.
By fusing speed information from GPS with speed calculated from the IMU's 3-axis accelerometer/3-axis gyro at an appropriate ratio, we achieve very smooth and high-precision speed output even in multipath environments, as compared to using GPS alone, as shown in the figure below.
Furthermore, even in locations where speed cannot be measured using GPS alone, such as when passing under elevated bridges, we can output continuous speed and high-precision speed during short-term GPS satellite loss by performing speed interpolation processing using the IMU.

LC-8000 Series

High-precision data measurement - The principle of speed measurement using GPS.

Stabilized Measurement - Correction Processing by IMU