This is nfortunately limited to 2-dimensional state/measurements. In this case the covariance matrix is only 3 numbers, so the required linear algebra can be easily be done in a loop. The generic Kalman handles arbitrary dimensions, but requires general matrix multiplication and inversions, which are not easy to implement in Postgres.

Still, 2d is a useful special case, and if it addresses the problem at hand, there's no need to overbuild. (Even the 1d Kalman filter, which often boils down to exponential smoothing, is a useful special case.)