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Measure relative velocity between two objects with 50-150 meter distance

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I am looking to find an approach to measure the relative velocity between two objects in real-time. There is no contact between the objects. The relative velocity will act as input to a control system that will try actively to keep this distance constant.

One object is allowed to carry instruments, but the other object can not be instrumented. The distance between the two objects will normally vary between 50 and 150 meters (or a bit less). The object to measure is made of metal, but I need a "spot" measurement, meaning that I need to be able to "point" at a specific coordinate of the object and get the relative velocity from that exact coordinate.

The accuracy requirements are not defined fully yet, but it should probably be down to a few centimeters per second (preferably millimeters).

(I assume this sounds like an adaptive cruise control system as used in cars, which it is not, but perhaps similar problem)

Can anybody point me in the right direction? Is some sort of laser measurement possible?

Be gentle, I'm a software guy and a newbie to hardware/electronics :)

I would suggest re-wording your question and tell us exactly what you are doing. Don't generalize on it, as this leaves open to many general questions. Plus, people can leverage their experiences better if they have the real world task in mind, not just a generic problem to be solved.
That sounds really tough. Radar can work to the max distance and beyond, with the accuracy you need, but can't be focused to a point measurement. IMO, a laser system is the only practical method- Google "laser rangefinder". I don't know how good the resolution will be for any affordable system. Is there a budget?
Does the problem situation allow the measurement of the angle between the two objects?
... Say from a third, static position, where you can observe the two moving objects.
Do you require that one of the measuring positions is to be located on one or the other of the moving objects?
Thanks for your input!

smanches: yes, you are right, it does make it hard to provide answers, but I am not allowed to reveal the exact usage...

Conrad: thanks for the tip, I did already look for laser rangefinder. Any in particular you can recommend? The budget is not defined yet, but the requirements and performance is more important than the price (to some level).

user_88: Well, yes, the measurement could be done from an angle between the two objects, and no, I don't require that one of the measuring positions is located on one of the objects. Does this help you in suggesting some other solution than laser rangefinder?
... Say you had a spotting scope, and could devise a method to aim the scope at one of your objects, and then you were able to activate a servo-mechanism that would keep the scope trained on the object as it moved along at an unknown velocity.
The angular motion of the spotting scope as it rotated and followed the target object would be directly related to the velocity of the object.:
This is possible due to the following:
where S= the length of the arc that the target travels .... which is approximately a straight line path ... at any reasonable radius.
R= the radius length from the observing scope to the target
Θ= the angle, from a reference, of the target
The time derivative of the previous equation yields:
where V= the tangential velocity .... what you require
R is constant, same as above
ω= the rotational, angular velocity with respect to the observing point

The only possible objection to this concept is that the object will be traveling in a straight line, rather than following the arc of a circle.
However, as the radius of the distance from the observation point to the target increases to a large enough value, the arc of the circle will approximate a straight line, for all practical purposes.

Consequently, the problem at hand is to find some method to track the angular position of the moving object, and convert it to a form that is useful for your purposes. Relative velocity is just the difference between the velocities of the two objects.

One possible line of thought to achieve the new objective might be to get a CCD and attach it to the focal point of the spotting scope. Software manipulation of the target image within the scope would have to be converted into a signal that rotated the scope as the target moved along.
Thanks user_88,

That is a very interesting idea! As you mention, to make this work I would need to find a way to track the object. With CCD you mean a camera, right? And use this to implement some image analysis method to track the object?

Thanks a lot for your efforts and opinion!
As far as I see you want to design something like a moving target intercept point device.

If speed and true direction are known you just have to calculate for the correct angle of intercept which can be solved by simple triangulation.

Normally speed won't vary much with air targets, but direction (and height) might vary a great deal.

A target tracking radar (for semiactive homing) therefor supplies target speed and relative angle for the missile tracking radar to intercept the target in a "dog tail curve".

Boncuk, thanks for your inputs!

FYI, the problem is not for air targets/missiles, it is for an industrial automation task (sorry I cannot be more informative, I am not allowed to provide details on the actual application).
CCD .... charge coupled device ... It was originally developed for telescopes and astronomical viewing. Currently used in retail camera manufacturing, with some degree of success.

... There is admittedly a missing link, as related to your objective. The fundamental problem is that the target image must be constrained to stay centered on the the CCD screen. This 'centering action' must be accomplished by driving a servomotor as it rotates the scope assembly about an axis.

The practicality of constructing a tracking mechanism may determine the outcome of the project.
Thanks user_88,

I agree. The tracking is probably the risky part that will make this feasible or not. I do have some experience in computer vision, so I guess my next step should be to make investigations on the feasability of making a robust tracking system.
Just an idea, but it might trigger some gizmoes.

How about using something similar to a stereographic optical system to foucus on the "target" for a matching image?

Both sensors must be turned individually and have a decent distance between them for calculations.

Thanks Boncuk,

Yes, I have been thinking about that myself, but since the distance between the two objects is typically between 50 and 150 meters, I am not confident whether the accuracy of a stereo optical system will be within requirements? As you say I would need a "decent" distance between the sensors/cameras, and I do have some limitations there. Theoretically I belive the distance would need to be as much as 10 meters, and that is a bit too much.

It might be possible though...
I don't think the distance between the optical sensors has to be as much as 10m. Just look at autofocussing cameras.

They focus 100% with the optics a few centimeters apart. :)

1 to m should suffice. It's the calculations which have to be superaccurate.

If you can describe the problem closer without sacrificing the secret about it we'll probably get to a workable solution quicker.

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Allright, I might be missing something here.

Are you suggesting to use 2x visible cameras for stereo calculations? And you would put them ~1 meter apart in a fixed stereo rig?

Would you locate the stereo rig on one of the objects, or watching the two objects from a distance/an angle?

I'm not exactly sure how to describe the problem without revealing too there anything in particular that is unclear?
Hi torbjoen,

I really don't have a clue what exactly you want to know.

Here's a sketch using optical sensors for two objects moving on the same plane.

Example: Object A moves at a speed of 3m/sec, object B moves at 3.5m/sec. So the relative speed of object B is 0.5m/sec higher than that of object A.

By the angular difference of one sensor pair the distance between sensors and object can be calculated.

The speed can be measured by the known distance to the object course and the angular change of the tracking device over time.

Using the relative speed of the "overtaking" object the collision point can be exactly predicted (provided the speed remains constant). Otherwise calculations have to be updated in short invervals.

May be that helps defining your problem clearer.



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Thanks Boncuk,

I see your point now. Sounds like a good suggestion. The tracking-part seems to still be the challenge, and I assume that should be some sort of vision based algorithm.
Thanks Boncuk,

I see your point now. Sounds like a good suggestion. The tracking-part seems to still be the challenge, and I assume that should be some sort of vision based algorithm.

No, it's just spheric arithmetics. :)

The rest has been done already by optical tracking systems being used for terrain observation and surveillance.

I forgot the name of the company. It is located in Austria and offers a burglar tracking solution. The target is being tracked by several optical systems (depending on terrain and building layout) overlapping in radius and never looses contact with it.

Their slogan: "If the burglar doesn't know where he is the system can tell him."

May be I'll find the company's name after opening some drawers in my brains.


Oh really? I am very interested in locating that company to check out their solution.

If you remember their name, please let me know :)
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