Math! Solving problems, making friends…

A few months ago there was an interesting article about AlphaGo and deep learning.  What made the solution interesting is that AlphaGo determined a new strategy for playing Go, e.g. it wasn’t just replicating the best of current players, it was creating something new.

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So this got me thinking about sensor placement. Let’s say you are building an autonomous vehicle; you give it radar, LIDAR, cameras, heck even and a person walking 5 feet in front of the car with a red flag. But how do you know what the best configuration of those sensor is? This is where math and deep learning can come to the rescue.

It’s research, dam the budget!

With research vehicles it is common to go high end with the sensors and processors. Often the number of sensors are far in excess of what the final vehicle will have; the question then becomes “If you train your controller using 10 sensor and the final vehicle will only have 3 do you have to retrain?”

So here is the insight, in regression there is the concept of a synthetic variable. E.g. you can take the raw data X and put X^2 into the equation. What if, for sensor data, you optimize for sensor position?

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Trig and Geometry!

Step 1: Train your model using the full set of sensors. Train it until you reach the highest confidence level you can.

Step 2: Define the set of equations that will take your original sensor data and use them to create “artificial” sensor at arbitrary locations. E.g. if you have 10 LIDAR sensors, then it could be that
AS_1 = func(X1,Y1,Z1) = func(L1,L2,L4,L6)
AS_2 = func(X2,Y2,Z2) = func(L3,L4,L7)
AS_3 = func(X3,Y3,Z3) = func(L2,L6,L9,L10)

Step 3: Using the already trained data train the new sensor array

Step 4: Optimize the models as a function of the sensor placement and number of sensors

Sensor fusion before the sensors…

I think of this approach as “sensor fusion before the sensors”. What is interesting about this approach is that it is possible that we could discover a combination of sensors (and yes this should be done with multiple sensors) that has a higher accuracy and lower costs than we expect.

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