6.2 Baselines
Baselines
We’ve discussed baselines previously – they are essentially a vector that represents the difference in position of two points.
Imagine you have two GNSS receivers that are capable of reading the phase observable, one is on mark 1 and one is one mark 2. You could get an autonomous position on them using code pseudo ranging or DGPS, but we know these are subject to significant errors. Getting a more accurate position means we need to use the phase observable to create a baseline between the two marks. But for now, let’s assume that we have collected the positions of the two marks.
The two receivers are shown in Figure 6.2(a), in a Cartesian coordinate system, and they each have a known position. To calculate the baseline, it’s a simple case of calculating the hypotenuse of two right angled triangles.
The first hypotenuse (or distance) we need to calculate is the horizontal distance between marks 1 and 2, which is simple given we can quickly determine our and values by subtracting the position of mark 1 from the position of mark 2. We can then use Pythagoras’ Theorem to solve for the hypotenuse:
c2 = a2 + b2
Where c = Hypotenuse
a =
b =
Substituting into Pythagoras’ Theorem this gives:
We can now project or push this hypotenuse up to the level of mark 1, and by using the value – the difference between the heights of the marks in this case, we can make another right angle triangle. This time we have:
Thus, our baseline between mark 1 and mark 2 can be described by the equation:
But because we are attempting to measure the positions of the marks more accurately than the code observable can provide, we need another way to determine the baseline without starting positions of the marks.
Imagine if we knew a way to determine the distance between two objects using the actual GNSS signals? Oh wait….
The phase observable
Note: If you need a refresher on signals, head back to Chapter 3 as we won’t be discussing all the basics again here.
The phase observable section of GNSS signals is the carrier wave – the blank wave that is modulated with the binary code to become the modulated carrier wave. The code is unique to each satellite in most systems (remember that GLONASS is the exception).
The carrier wave is a 3D wave, and is a right hand polarised wave. This means if we were able to look down the centre of the wave in the direction it was travelling, it would appear to rotate in a clockwise direction, as shown in Figure 6.2(b).
When the carrier wave gets to the GNSS receiver, the first measurement that it observes is a partial wave, which is also referred to as a partial phase, and is represented by or by upper case Greek letter delta (used to indicate change or difference) and lower case Greek letter Lambda (wavelength) .
The GNSS receiver is in theory able to measure this partial phase quite accurately – to around of the wavelength. This equates to around 2mm for GPS L1 or L2 signals.
The remainder of the signal is a number of full wa