Homework: working through details of a sensor network application.

Due: 2/14.
What to turn in: a paper.

Consider a set of 3 microphones.  The microphones' positions are:
s1 in (0,0); s2 in (4, 3); s3 in (6, -4). Remember, the attenuation of sound in air is, roughly, proportional to the inverse of the square of the distance traveled by the sound wave.

1. At one point, the microphones sense the following acoustic powers: z1=0.1; z2=0.0588; z3=0.0556. Assuming the acoustic power of the source object is 1, where is the source object in a 2-dimentional plane? Show your reasoning and assumptions.

2. Write a function x = locate(z1, z2, z3) that, given a set of 3 microphone measurements, returns the location [x,y] of the source object. Suggestion: do it as an actual program, so that you can test it. Comment on the effect of measurement errors and rounding errors in your approach.

3. Now consider a much larger network of microphones, consisting of hundreds of nodes. When a sound happens, a number of microphones, possibly much larger than 3, detect that sound. You, as this network's designer, face the decision about what to do with all those measurements. Should they all be forwarded to the central server? Should there be some kind of self-filtering? How? Explain and comment on tradeoffs.

4. Take the initial 3 microphones again and your locate function as the core of a smart spotlight that always points in the direction of a moving human speaker inside a room. What else would it take to develop this smart spotlight? Show your design through one or more diagrams.