Mixed signal neuromorphic circuits represent a promising technology for implementing compact and ultra-low power prosthetic devices that can be directly interfaced to living tissue. However, to accurately emulate the dynamical behavior of the biological tissue, it is necessary to determine the optimal set of specifications and bias parameters for these circuits. In this paper we show how this can be done for a silicon neuron design, by applying a statistical Data Assimilation method (DA). We present a conductance-based silicon neuron based on the Mahowald-Douglas (MD) design and use the DA method to estimate its state variables and the ion channels parameters, so that it can accurately emulate the properties of biological neurons involved in the Central Pattern Generators (CPGs) responsible for producing the respiratory and heart-rate rhythms. While previous work has shown how DA well-estimates and predicts parameters from membrane voltage measurements using a semi-empirical Hodgkin-Huxley neural model, here we show how the same method is suitable for simplified Very Large Scale Integration (VLSI) circuit designs and demonstrate how it allows us to reliably predict the response of the MD neuron to different input current profiles.