Continuous-time errors-in-variables filtering

We consider estimation problems for a continuous-time linear system with a state disturbance and additive errors on the input and the output. The problem formulation and the estimation principle are deterministic. The derived filter is identical to the stochastic Kalman filter. The problem formulation with additive error on both the input and the output, however, is more symmetric then the classical Kalman filter one and allows interpretation in terms of misfit and latent variables.