This paper presents a formant tracking linear prediction (LP) model for speech processing in noise. The main focus of this work is on the utilization of the correlation of the energy contours of speech, along the formant tracks, for improved formant and LP model estimation in noise. The approach proposed in this paper provides a systematic framework for modelling and utilization of the inter-frame correlation of speech parameters across successive speech frames; the within frame correlations are modelled by the LP parameters. The formant tracking LP model estimation is composed of three stages: (1) a pre-cleaning spectral amplitude estimation stage where an initial estimate of the LP model of speech for each frame is obtained, (2) a formant classification and estimation stage using probability models of formants and Viterbi-decoders and (3) an inter-frame formant de-noising and smoothing stage where Kalman filters are used to model the formant trajectories and reduce the effect of residue noise on formants. The adverse effects of car and train noise on estimates of formant tracks and LP models are investigated. The evaluation results for the estimation of the formant tracking LP model demonstrate that the proposed combination of the initial noise reduction stage with formant tracking and Kalman smoothing stages, results in a significant reduction in errors and distortions.