Accurate state estimates are important for the success of model predictive control (MPC). State estimates are obtained using a model, but, in real plants, there will always be model plant mismatch (MPM), which affects these estimates. In this work, we present a multiple-model (MM)-based approach to obtain unbiased state estimates in the presence of MPM. Necessary assumptions on the source of mismatch and models used are presented. It is shown that unbiased output estimates do not guarantee unbiased state estimates. Our approach is shown to provide unbiased state estimates when all the assumptions are met using a froth flotation system. A model identification -based control approach using our multiple model estimation approach with a conventional MPC was tested on the froth flotation system and was found to successfully provide offset-free reference tracking when all the necessary assumptions for unbiased state estimation were met. A nonlinear offset-free MPC was also tested on the froth flotation system but was not able to provide offset-free reference tracking, because some necessary conditions were not met.