# Local positioning system

Let me start by stating that I am a student with very little experience so I am starting at square one, so please bear with me.

Requirements

I am looking to create a local positioning system between 1 transmitters and N receivers (3-6 most likely). This is in a outdoor space about 10m x 10m and I only care about 2D location. I would like accuracy to be within 0.2m or so. The area will be very flat and open and the only disturbance will be the sound of a small engine. The transmitter will be moving with the receivers remaining stationary (that's how I imagine it anyways). The inherent design of the systems requires the transmitter to be moving very slowly, roughly walking speed or slower.

Current Idea

Given my accuracy limitations GPS is out of the question, and given the idea of a moving transmitter I decided an IR sensor would not give me the multiple directions for multiple receivers I require. After all this I decided an ultrasonic sensor would most likely give me the result I require. As you can probably tell I'm still stuck in the design phase and want to solidify an idea that would give me closet to the desired results.

Question

Am I correct in thinking that I can use a combination of ultrasonic transmitters/receivers to triangulate the location of the moving transmitter? Is there possibly a better system for what I'm trying to do?

I wish I could bring more technical questions to the table, but the more technical information I look up the more I realize I need to understand the fundamentals of what I am trying to accomplish first. I have very little practical information, so even links to readings or videos would be greatly appreciated.

Differential GPS may be able to get you good enough accuracy.

• Especially if the problem is objects positions relative to each other rather than absolute position on the entire planet, as multiple identical GPS's would hopefully be subject to very similar local errors. Sep 25 '14 at 12:43

As a "Robotics" engineer myself, I can tell you right now that it is not a trivial problem. Your system of transmitters and receivers will work with at minimum 1 transmitter and 2 receivers, any more will just help with the redundancy and fusion of measurements to reduce error (get a more accurate position estimate and with lower uncertainty).

There are formula (essentially it is just trigonometry) but first you must get the time stamp (synchronized as close as possible, to get the best accuracy) from each of the receiver units, which gives you a "radius" for each receiver. These radii will overlap, and there will be a weird gap in between them all. This is basically where your transmitter is/was at the time of the signal.

The time taken for the ultrasonic ping to reach each receiver gives you the distance, because the time taken multiplied by the speed of sound in ambient air at whatever temperature you estimate, gives you an approximate distance traveled.

That works if you have synchronisation of clocks, without that you can do a difference between each receiver and their known locations to work out the same thing as before, using similar information.

You may be able to find examples/formula/concepts for this in robotics textbooks which cover topics on "Localisation". My professor (Prof. Peter Corke) has a nice textbook called Robotic Vision and Control which you may enjoy.

Personally I'd stick a high-def camera up a pole and use OpenCV, then just tell each subject where it is via a simple radio link.

Depending on your budget and how much time you can invest in this aspect of your project, the mentioned answers (computer vision, differential carrier-phase GPS, ultrasound) are all potentially viable.