This paper deals with oesophageal speech enhancement using Kalman Filtering. Such an exceptionally special type of voice is due to the laryngectomy undergone by those persons with larynx cancer. Kalman filtering is known as an effective speech enhancement technique. In this context, several approaches have been developed in the past. One of the most important steps in the speech enhancement using Kalman filtering is the estimation of parameters of the signal parameters and noise. Coloured noise is considered in this kind of voice. Two approaches have been carried out in this paper in order to estimate the noise parameters: firstly, the measurement noise is estimated using AR model of oesophageal voice during the period of silence and the model noise process is not considered. Secondly, the model and measurement noise process is estimated theoretically in recursive procedure.