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In this paper, we investigate the problem of modeling time-series as a process generated through (i) switching between several independent sub-models; (ii) where each sub-model has heteroskedastic noise, and (iii) a polynomial bias, describing nonlinear dependency on system input. First, we propose a generic nonlinear and heteroskedastic statistical model for the process. Then, we design Maximum Likelihood (ML) parameters estimation method capable of handling heteroscedasticity and exploiting constraints on model structure. We investigate solving the intractable ML optimization using population-based stochastic numerical methods. We then find possible model change-points that maximize the likelihood without over-fitting measurement noise. Finally, we verify the usefulness of the proposed technique in a practically relevant case study, the execution-time of odometry estimation for a robot operating radar sensor, and evaluate the different proposed procedures using both simulations and field data.