In this work we introduce the Mean Field Games (MFG) as a framework to develop a nonlinear estimator. This can be viewed as an extension of particle filtering, where now each particle acts as a rational player. To this effect, all the players are associated with a cost function and its minimizer is the estimate. The main results presented in the papers are twofold: the introduction of MFG in estimation theory and the derivation of explicit Kalman-like formulas. Computer simulations are performed to illustrate the method. In particular we provide an example where our estimator converges whereas both the extended Kalman filter and the particle filter diverge.