Material for : A Neural Implementation of the Kalman Filter

This approach is equivalent to asking the question, what position, z(t), would the maximum likelihood decoder choose given the noisy bump of activity I(t)? This idea is illustrated in figure 1. Here the red line corresponds to bump at the location of the actual stimulus, U(x(t)). This is then corrupted by noise to give the noisy input profile shown in grey (note that this example uses a high noise setting for illustrative purposes). Finally, the black line denotes U(z(t)), the maximum likelihood location of the bump given the noisy input activity. Thus, the addition of noise has lead to a shift in the position of the input bump.