Observation (encoding) model

The observation model is the half of a state-space decoder that links the hidden state to the neural measurement — the encoding model turned around for inference. In a Gaussian Kalman decoder it is the matrix C plus noise covariance Q that maps kinematics to expected firing rates; in a spiking decoder it is a conditional-intensity or Poisson model. Its quality sets a ceiling on decoding: no filter can recover information that the observation model fails to represent, and a mis-specified C injects systematic bias that the dynamics prior then smooths but cannot remove.

Two design choices dominate practice. First, the direction of the relationship: motor decoders usually write firing rate as a function of kinematics (an 'inverse' encoding model) because that keeps the filter linear-Gaussian and the parameters interpretable as tuning. Second, stationarity: real tuning drifts across hours and days as electrodes move and neurons appear and disappear, so a fixed observation model degrades and must be recalibrated or adapted — one of the central engineering problems of chronic BCI.