Hello,
I was curious to learn more about the relationship between resolution and accuracy and how the chirp parameters can influence accuracy. I'll split this up in three parts: range, velocity, and azimuth/elevation. I realize this is long, but I think there is some fundamental understanding here which I feel is not clear regarding the different between resolution and accuracy and how this is effected in particular configurations.
I would both be interested in explanations as well as pointers to relevant literature. If the description is not clear please say so.
Range
- Range resolution is given by c / B, so this is directly influence by the chirp design
- speed of light / bandwidth
- How does chirp design then play into the accuracy? Hypothetically if we have two objects near one another, if they can't be resolved then one would think the detection would be somewhere in the middle of their actual ranges. If this is the case this causes some discrepancy between the "measured range" and the "actual range".
- E.g. two objects at 1.1 and 1.2 meters range, if we suppose the range resolution is 0.2m, then what is measured for these two objects, 1.15m?
- This site has some comments on how range accuracy can be written as a function of the resolution
- range accuracy = range resolution / sqrt(2 * SNR)
Velocity
- Velocity resolution is given by lambda / 2T_F
- wavelength / 2 times frame time
- where frame time is chirp duration * num chirps
- Question very similar to range. How is velocity accuracy influenced by resolution/chirp parameters that influence resolution?
- As an example, take the following image from TI's "The fundamentals of millimeter wave radar sensors"
- Suppose the radar is moving left and obj1 and obj2 are stationary. The relative velocity of obj1 and obj2 are both due to the radar moving left. If both objects have the same angle to the radar, their doppler should also be the same. These two object should be distinguishable by angle of arrival, but their range and doppler will be the same, how will this be handled?
- Suppose the radar is moving left and obj1 and obj2 are stationary. Suppose now they have slightly different angles to the radar, such that their dopplers are different. Let's consider this in 2D, if one is at +30 deg and the other at -45deg and the radar moves along 0 deg at 1m/s, their radial speeds will be ~0.86 and ~0.71. How will this be measured? They're at the same distance so range isn't different, and it is definitely possible that velocity resolution is >0.15m/s, but they are 75deg different. Will this result in 2 reflection with range/velocity accuracy to FFT bin width, or will they somehow be merged since velocity, while different, is not actually resolvable?
- Since all radial speed here is a result of our own motion, there is a ground truth value for any points direction, can we say anything about the accuracy in a case like this?
- As an example, take the following image from TI's "The fundamentals of millimeter wave radar sensors"
Azimuth/Elevation
I figure this is one of the simplest of the bunch, given that (as far as I know) neither resolution nor accuracy are affected by chirp.
- Resolution, according to the a TI intro to mmwave radar videos, is limited by the antenna configuration
- Accuracy should be, in part, limited by the number of FFT bins (64). E.g. 120 deg FOV / 64 bins results in FFT bin width of 1.875 degrees
