This paper deals with optimal (minimal variance) filtering in an errors-in-variables framework. Differently from many other contexts, errors-in-variables models treat all variables in a symmetric way (no partition of the variables into inputs and outputs is required) and assume additive noise on all the variables. The filtering technique described in this paper can be easily implemented in a recursive way and does not require the use of a Riccati equation at every update. The results of Monte Carlo simulations have shown the effectiveness and consistency of the approach.