Mobile Robot, Sound Localization, and Neural Network

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tians

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Currently I am working on my final project. My final project title is “Design and Implementation of Mobile Robot Sound Tracker Based on Artificial Neural Network”.

I want to make it embedded with battery as the supply.

Any idea where should I learn first? Where should I start first?
Should I use Microcontroller Atmel AVR or Microchip PIC?
What Neural Network type I work to?
 
The Hider Robot in the above link "looks" complex but is really a simple state machine. Just because a microchip looks simple on the outside it's far more complex than any MSI, LSI IC design.
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It looks impressive and it is, but practical not really. A teeny tiny PIC10F222 can outperform it.
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Microcontroller’s RAM is limited and I need a lot RAM for float type data.
I use float type data to store Neural Network Weights.

How to store float type data to External RAM?
 
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