For a battery driven terminal, the power amplifier (PA) efficiency must be optimized. Consequently, non-linearities may appear at the PA output in the transmission chain. To compensate these distortions, one solution consists of using a digital detector based on a Volterra model of both the PA and the channel and a Kalman filter (KF) based algorithm to jointly estimate the Volterra kernels and the transmitted symbols. Here, we suggest addressing this issue when dealing with cognitive radio (CR). In this case, additional constraints must be taken into account. Since the CR terminal may switch from one sub-band to another, the PA non-linearities may vary over time. Therefore, we propose to design a digital detector based on an interacting multiple model combining various KF based estimators using different model parameter dynamics. This makes it possible to track the time variations of the Volterra kernels while keeping accurate estimates when those parameters are static. Furthermore, the single and multicarrier cases are addressed and validated by simulation results. Our solution corresponds to a compromise between computational cost and bit-error-rate performance.