Optimisation of the Nelder-Mead Simplex Method for Its Implementation in A Self-Mixing Laser Displacement Sensor

A laser diode self-mixing sensor enabling us to perform displacement measurements under moderate feedback has been designed with a resolution up to 32 nm. In this paper, we focus on the signal processing required to reach such a resolution and notably on the Nelder-Mead simplex method we used for the joint estimation of parameters like the linewidth enhancement factor and feedback level described by the coupling factor. Further more, influence of initial step size λ of Nelder Mead method on the reduction in the convergence time as well as on the possibilities of introducing parallelism in the algorithm have been studied for implementation in a future integrated sensor. This analysis leads to optimize the number of optical power samples necessary for joint estimation, the adaptations of Nelder-Mead method and its parameter λ on our application, all of which result in the consequent reduction in computing time necessary for convergence to the optimum values.