Orthogonal Projection vs PCI
I have completed simulators which emulate the performance of a centralized localization scheme (where all microphone clusters communicate with a single computer) and that of a distributive localization scheme (where microphones collaborate).
I also created a statistics test bench which shows the performance of the algorithm.
The red line shows the centralized scheme of localization, and the blue one shows the distributive scheme of localization. Bias is the distance between the source location and the scheme’s estimate. Because my distributive scheme is iterative, I also kept track of the number of estimates it took for the method to converge. Each point of data on this graph is the average of 100 trials.
The x-axis gives the maximum error in the time-delay measurement.
The graphs tell us 3 things. First, we know the limit of the noise that either system can manage with. Both systems fall apart at around the same level of noise. Second, since the curves are for the most part on top of each other, the two methods are comparable (very good news). Third, it will take anywhere between 18-20 estimates to ascertain a solution. This means, for a 4-sensor network, each sensor makes 4 or 5 calculations–making this method very fast. There is also no need to fiddle with a random variable, unlike with the centralized method.
Here’s where things get interesting. My question now is this: What happens when we try a new microphone geometry? We’ve been working so far with this:
What happens when we try something like this?
With 8 microphones in a cluster, we can no longer use the notion of cones to come up with the intersection. Now we have at least 4 cones to contend with. With noise, we’d need an estimator just to get the vector.
But what if we can find another way to do it? Thinking back on what the time delay lets us do:
We have an arc of all possible directions, which ranges from 0 to 180 degrees. The black vector is the vector given from the time delay. The green and orange vectors compose the black vector. If we can come up with a scheme that properly translates these vectors, we’ll have no need for a cone.
And so begins the next task.
Orthogonal Projection – Resolved
I’ve come up with a resolution to the ring convergence problem. Will post the formula later.
MATLAB report:
| 13-Jul-2008 17:17:33 ——————— Source Location [0.059564,1.0961,8.1876] Ring convergence found Applying relaxation term. Estimate=[0.055027,1.113,8.1881] Statistics: Injected Gaussian Noise with mean=0 and variance=0.001 Estimates Needed=45 Bias=0.00030764 |
