# Doppler effect to distance without using time-of-flight; can this be done?

• Ray_Xu
In summary: As the target moves away from the radar, the frequency difference will increase, until it reaches a certain limit (0Hz?) where the measuring distance would be a function of the frequency difference. Its not 100% clear to me, but that's the gist of it.If you want more information on the theory, I suggest you look into some books on RF theory or physics.In summary, Ray Xu thinks that if you have a way to sweep the output frequency, you may be able to determine the distance to a target based on the doppler shift and the speed your bike is moving at. Mike has no way to do this and suggests looking into books on RF theory or physics if you want to extend the theory

#### Ray_Xu

Hey all,

I'm a newbie here with a question regarding doppler shift. Before I ask, I only have a very basic understanding of the doppler effect.

So, my big question is: can a doppler shift measurement be converted to the distance between the source and target, without using the time of flight method?

What I'm trying to do here is using this product http://www.parallax.com/Store/Sensors/ObjectDetection/tabid/176/CategoryID/51/List/0/SortField/0/Level/a/ProductID/606/Default.aspx I want it to determine the distance to a target, based on the output of that radar module. Its intended to be used as a proximity sensor, but the datasheet says it can also be used to measure speed via the doppler effect. It may sound crazy, but I'm planning to mount this onto my bike for my own useful and safety purposes; as well as to gain more experience working with radars and doppler shift. Since this is going to be mounted onto my bike, I will know the speed I'm/the radar is traveling at. Not all targets in the radar's view will be stationary (ex: cars, pedestrians, etc); FYI.

But forget about my application here; I just want to know how to derive the distance based on doppler effect. I won't be able to modify any part of the radar as well. I also cannot use the time of flight method either.

So far, I *think* this can be done, however I'm not sure how to do it. My theory to this right now is assuming that my bike is moving and doppler shift is present, the frequency difference must cross 0Hz when I pass the target. There for, that means the distance must be a (slight?) function of the frequency di8fference; assuming I know the speed my bike is traveling at. Can anyone else help me extend on this?

Thanks,

Ray Xu

Hey Ray,

That's a pretty cool gadget. If you dig around in it, you may be able to find the output from the mixer. It will be the source of the fluctuations used to trip an alarm. If the unit has any range, you may be able to amplify it into a speaker or pair of headphones and listen to the cars go by.

As to Doppler radar, I think it's a matter of some expertise / investment to sort out the frequency shift while still acting as a range radar. But, if you have a way to sweep the output frequency, the return signal will differ from your current output frequency giving you a Doppler-like tone. This has often been used in altimeters.

What's cool about these projects is that you have an amazing signal processor just using your hearing.

Unfortunately, I cannot sweep the frequency. The unit only takes an "enable" signal and it continuously sends out "bursts" of RF energy at a fixed frequency and outputs a signal relative to the amount of doppler shift. I'm not so sure of using my hearing involved in this project; but it does sound interesting. I'm more inclined to mounting a LCD screen onto my handlebar so I can have a full 360 view on one screen. The LCD screen will plot the distance/speed of the target onto a polar coordinate plane; hence why I need the distance...

But anyways, sticking to the original topic, would my idea be plausible in determining the distance to the target based on the doppler shift and the speed my bike is moving at? Is there any way to extend my theory, if needed?

BTW, Mike, I'm just wondering; are you a member of DPRG? We both live in the same city...

I'm not familiar with DPRG, but I used to work with a very talented engineer named Ray Xu. I think he moved to Canada.

Anyway, I can't perceive a method to do ranging that doesn't involve time of flight, signal correlation, or frequency shift. Unless you can get deep in the heart of this little module, I don't think it will get you there.

Gunn diode based oscillators used to sweep a bit if you changed their supply voltage. I don't know if this one was based on that technology or not. The motion detectors for automatic doors used to be built this way.

Hey Mike,

Its cool that you worked with someone very talented in engineering before with my name!

Anyways, I think I'm not making myself clear in my theory... First, assume the relative speed between me and a target is fixed. When the target is moving towards my radar, the receiving frequency will be higher than the transmitting frequency; thus resulting in a frequency difference in the positive range. When the target is very close to the radar, the receiving frequency would be about the same as the transmitting frequency. When the target is moving away from the radar, the receiving frequency is lower than the transmitting frequency; thus resulting in a frequency difference in the negative range. If you plot the "general trend" of the "one-way distance from radar to target" vs "frequency difference relative to the transmitting frequency", you will see the line obviously doesn't all of a sudden swing from a positive frequency difference to the negative or vice versa. Instead, it should look like two connected logarithmic curves. So to find the distance, I can write up a mathematical function to determine the distance from the frequency difference.

But in the real world, the speed between me and a target will never be fixed. Because of that, I imagine that the relative speed between me and a target would affect the practical maximum/minimum Y-values of that function.

Am I correct on my theory? Is there any way to extend/make improvements? And since I haven't gone through Algebra 2 class in my high school yet; I may need some help on deriving the mathematical function...

Thanks,

Ray Xu

If you start out with a given distance between you and your target and that distance changes, you'll either gain phase rotations or loose them. This is a way to tell how much you've gained or lost towards target distance.

The trick is to tell whether your gaining or loosing. With a single mixer, all you see is the phase rotations going by. You cannot tell if the corresponding frequency is positive or negative.

The solution is to have a second mixer that's off by 90 degrees - either in the return signal, or in the local oscillator.

With this scheme, you'll have two "tones." One will lead, or lag, the other by 90 degrees depending on whether your moving towards the tartget or away from the target.

Then, you count up or down depending on the phase positions. Reference quadriture encoder for details.

Best Luck,

Mike

Hey Mike,

So the purpose of using two out-of-phased signals is to know the relative location of the target; either behind, near, in front, or etc relative to my position...correct? Will the amount of phase shift or any other aspect of the two signals give a clue about the distance from me to the target?

Like I said, I cannot risk to hack into that radar module; let alone that I don't have any experience working with very high frequency RF.

But, I'm still open to ideas and feedback...

Thanks,

Ray Xu

No, the two out of phase signals will let you know whether you're getting closer or further to the target. It hasn't a clue in which direction the target is.

In any case, you would need to get into the module and add a slightly delayed (90 deg) mixer.

Hey Mike,

Alright, thanks for the info. I'll think about it.

Ray Xu

## 1. What is the Doppler effect?

The Doppler effect is a phenomenon observed in waves, such as sound or light, where the frequency of the wave appears to change when the source and observer are in relative motion. This results in a shift in the perceived wavelength and can lead to changes in the perceived pitch or color of the wave.

## 2. How does the Doppler effect relate to distance?

The Doppler effect can be used to measure the distance between a source and an observer without using time-of-flight. This is because the amount of frequency shift is directly proportional to the distance between the source and observer. The greater the distance, the greater the observed shift in frequency.

## 3. Can the Doppler effect be used to measure distance without using time-of-flight?

Yes, the Doppler effect can be used to measure distance without using time-of-flight. This is commonly done in astronomy to measure the distance between stars and galaxies. However, it requires precise measurements and assumptions about the velocity of the source and observer.

## 4. What are the limitations of using the Doppler effect to measure distance?

The Doppler effect is most accurate when the source and observer are moving in a straight line. This means that any changes in the velocity or direction of either the source or observer can significantly affect the accuracy of the distance measurement. Additionally, the accuracy is also dependent on the precision of the instruments used to measure the frequency shift.

## 5. Are there other methods for measuring distance without using time-of-flight?

Yes, there are other methods for measuring distance without using time-of-flight. Some examples include using parallax measurements, which rely on the slight differences in the apparent position of an object when viewed from different locations, and using the luminosity of an object to estimate its distance based on its known brightness. Each method has its own limitations and is used in different contexts depending on the available data and resources.