LC-8000 series

The LC-8310 high-sensitivity GPS speedometer determines speed from the Doppler effect of the carrier wave output from GPS satellites.
The Doppler effect is a phenomenon in which the frequency of a wave (such as radio waves, light, or sound waves) is observed to differ when there is a speed difference between the source and the observer. The frequency is observed to be higher when the source and observer are close together, and lower when they are far apart. The Doppler effect of radio waves and light is expressed by the following equation:

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

Because this method is largely unaffected by the ionosphere, it can 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 operate in only one direction, 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, like public roads, multipath interference causes significant noise in the Doppler-based velocity output, as shown in the diagram. Furthermore, when passing through areas where satellites cannot be observed, such as elevated bridges, it becomes impossible to measure velocity using GPS alone.
By combining speed information from GPS with speed data obtained from the IMU's 3-axis accelerometer/3-axis gyroscope in an appropriate ratio, we achieve extremely smooth and highly accurate speed output, even in multipath environments, compared to using GPS alone, as shown in the figure below.
Furthermore, even in locations where GPS alone cannot measure speed, such as when passing over an elevated bridge, the use of an IMU enables speed interpolation processing, ensuring continuity of speed output and providing highly accurate speed output even in the event of short-term loss of GPS satellites.

最終更新日:2023/04/04