A frequency modulation continuous wave (FMCW)-based system includes an emitter to transmit at least one linearly modulated wave of radiation to a scene and a receiver to receive a reflection of the transmitted wave from one or multiple objects located at different locations in the scene. The system interferes a copy of the wave outputted by the emitter with the reflection of the transmitted wave received by the receiver to produce a beat signal with spectrum peaks corresponding to reflections from the different locations at the scene. The beat signal is distorted due to the non-linearity of the modulation. The system includes a processor to detect a number of spectrum peaks in the distorted beat signal and, only in response to detecting multiple spectrum peaks, jointly determine coefficients of a basis function approximating the non-linearity of the modulation and distances to the different locations at the scene having the objects causing the reflection resulting in the spectrum peaks in the distorted beat signal.