Parameter estimation of an integrate-and-fire model based on symbolic analysis

Based on symbolic analysis, a new parameter estimation method of an Integrate-and-Fire model (IFM) is proposed. With varying threshold modulations, the IFM can output many kinds of spike-trains. And their dynamics can be described using circle map. We present a new method to get the symbols of the IFM, instead of currently practiced method of directly measuring the phase. Using the formalism of Markov chain, a cost function has been given in this paper to find the optimal parameters of the model. The minimum of this function yields a good estimate for the model parameters. The computer simulations prove that the method is effective even when the symbol sequence is short and corrupted by a significant amount of noise.