There are two types of GNSS:
- Traditional single-point GPS: 10m accuracy, usually found in phones
- RTK (Real-Time-Kinematics) GPS. centimeter accuracy. It talks to a base station. Each module gives its
(x, y).
GPS
A GPS needs to talk to at least 4 satellites to run a trillateration process to determine its current pose. Process: TODO
A GPS module’s performance is affected by:
- Atmospheric delay: signals can be delayed as they pass through the ionosphere and troposphere.
- Multipath errors: signals can bounce off surfaces like buildings or mountains
- Satellite geometry: misalignment of satellite can reduce accuracy
A consumer grade GPS is 10m accuracy 95% of the time
RTK GPS
RTK (Realtime-Kinematics) GPS needs an extra ground station that sends correction data to itself. The general workflow is:
- A GPS Ground stateion is a known location. Its location is determined during a survey-in
- The GPS ground station gets its GPS reading from the 4 satelelltes through trillateration.
- Using its known location, the GPS ground station calculates the impacting factors such as the Atmospheric Delay, etc.
- An RTK-GPS module is a.k.a a rover. It connects to a nearby GPS ground station. The baseline distance is typically 10-20km.
- The GPS ground station start to send correction data that contains the impacting factors to the RTK-GPS data real time.
Another crucial technique RTK GPS uses is Carrier Phase Ambiguity resolution. The carrier wave is a high frequency sinusoidal wave. In the illustration below, we can determine the distance between a satellite and a rover using the number of phases. Here, the total number of wavelength is $\phi = \alpha + \beta + N$. We aim to solve for N:
N: an integer that represents a fixed number of wavelengths. This number is unknown at the moment- The L1 carrier wave is transmitted at 1575.42 MHz, its wavelength is 19cm.
- $\alpha$ is the fractional number of wavelengths. E.g., if the total distance is in total 10.5 wavelengths. $\alpha = 0.5$
- $\beta$ is the “accumulated number of observed wavelengths during the measurement period.” As the receiver moves and the satellite orbits the earth, $\beta$ shrinks when the two gets closer, and expands when the two gets farther apart.
Longitude - Latitude System
Longitude and latitude is a very well-known concept. Some drawbacks are:
- Requires many significant digits to represent a location precisely
- Not directly in meters
- The polar areas have a singularity, because longitude
0 - 180 degconverges there. So any longitude value could be assigned to the north pole, but in the meantime, large changes in the longitude would happen, too.
UTM Coordinates
The Universal Transverse Mercator (UTM) coordinate system can better handle the significant digits issue better. Singularity issue? Its workflow is:
- Projects the globe onto a map
- Segment the map into 60 parts (longitude) and 20 parts (latitude).
- So each zone is 6 deg longitudinally, 8 deg latitudinally.
- The 20 latitudes are represented by a letter in
C to X, exludingIandO- Zone
33Trepresents zone33in the T latitudinal region
- Zone
- Each zone has a coordinate frame
x = left = east, y=up=norh - The center line is x = 500km
- UTM has opposite north directions in the southern hemisphere
Advantages:
- Directly in meters!
- Fewer sigificant digits are required
500kmis a common scale requires 6 significant digits. So to represent centimeters, one needs 8 significant digits (FP64)
Drawbacks include:
- Region number are required in representation
- So cross-zone operations should be handled separately. But some RTK systems help us handle this.
- Distortions are large in the polar zones
RTK GPS in Autonomous Vehicles
In an autonomous vehicle, we use two RTK GPS modules (蘑菇头) so we know the mid point (x, y, z), and its heading $\theta$. This set up is also known as DUAL GNSS Compassing. Usually, GPS signals come in at 1hz.
There are three ways to mount the RTK. The angle between the line and the heading of the car is an “extrinsic rotation”:
