Does the Kalman filter incorporate a Heisenberg-like uncertainty principle?

In the case of mechanical systems, applying the Kalman filter involves combining model based prediction (using an apriori known dynamical model) with real-world noisy observations of the positions and velocities of the system. The algorithm weights the apriori prediction and current observation in proportion to the uncertainty (covariance) of the model and observation. Indeed, the aposteriori uncertainty (covariance) decreases to an equilibrium value on applying the algorithm iteratively as the number of observations of the positions and velocities of the systems grows. This indicates a bound on the available resolution of the filter even as we accrue an arbitrarily large number of observations.

Is there a direct correspondence between the filtering algorithm and the Heisenberg uncertainty principle in quantum mechanics? A similar classical-quantum correspondence indeed exists in the case of purely predictive models of the Langevin systems or potential flows with additive Brownian noise, but I’m not aware of any work in the case of observations of noisy dynamics.