Goals:

• Construct some movement kernels for estimation of spatial priors
• Incorporate a dynamic spatial prior in your decoder

In the previous module, we applied the decoder to each time bin independently, using a flat spatial prior. In effect, this assumes that the place representation can move around arbitrarily from one time step to the next. Clearly, however, a rat cannot move around arbitrarily but instead moves subject to smoothness and continuity constraints! We can use this domain knowledge to improve the performance of our decoder.

Our approach will be similar to Kalman filtering, in that we can construct a model of the rat's movement. We can then use this model to generate a prediction of the rat's position $P(\hat{x}_t)|P(\hat{x}_{t-1})$. The hat is meant to indicate that these are all estimates since the decoder does not have access to the rat's true position $x$.