2 Point Direction and Distance Measurement

So, I am looking to start a robotics project, but I was looking for advice for one key part. I'd like to build a robot that can follow you as you walk around. So the basic idea of the project is to have some form of beacon, carried or placed by the user, and the robot will direct itself towards the beacon and move towards it. Now the constraints that make it more complicated are that 1) I'd like it to work "anywhere" (We'll assume 2 dimensions for now), so the only two points allowed are the Robot and the beacon. I'd like it to not require additional set-up. 2) I'd like it to not require direct line of sight. I'm assuming a max range, even if it isn't even a very long max range (I'd be happy with a just a few meters), but I'd like it to not automatically fail if something is between the beacon and the robot. 3) The beacon should be relatively low power. I'd like it to be something that a person could carry on their person without difficultly. 4) I'd like it to not cost a fortune.

What are the methods to determine relative direction and distance with only 2 points? I'm not even sure what to call this, so any information would help. I have no clue what type of signal to use for the beacon, or where to even start looking, but I imagine that there is at least some form of established technology for this?

Given 2 points you can determine the direction of the beacon, but as you have no other reference it tells you nothing more.

If you use an internal compass (I2C or so) you also have a north direction, whihc can be combined with the direction of the beacon, which will give you a line of points the robot can be on.

To determine the distance you need to have a way to tell the relative signal strength, OR measure the distance by measuring the time it takes a pulse to go back and forth.

Think of how ships knew their location (or not) when they saw only one light house in the dark...

robtillaart: Given 2 points you can determine the direction of the beacon, but as you have no other reference it tells you nothing more.

If you use an internal compass (I2C or so) you also have a north direction, whihc can be combined with the direction of the beacon, which will give you a line of points the robot can be on.

To determine the distance you need to have a way to tell the relative signal strength, OR measure the distance by measuring the time it takes a pulse to go back and forth.

Think of how ships knew their location (or not) when they saw only one light house in the dark...

I was thinking of the relative signal strength for the distance. How exactly would you determine the beacon direction?

If all you're going to do is move towards it, you don't need much of a distance measurement. Only when you get too close.

There's a way to use a sonic or ultrasonic pulse beacon with two receivers to determine approximate direction. Similar to binaural direction detection. They say a person with normal hearing can determine the direction of a sound within 3 degrees. And that's with ears what, 8 inches apart? Look at this youtube video for an example.

Certainly a light of any kind, infrared-ultraviolet, and a phototransistor or photodiode could work. There are several ways to determine direction. Solar tracking algorithms should work for this. Except line of sight would be necessary. You might be able to work around that with an algorithm. If you lose the beacon, continue in the same direction for a while or something.