A novel linear whitening measurement device is presented in this paper that allows optimal echo path modelling using real time least mean square (LMS) system identification techniques. The device provides improved and accurate characterisation of the far-end echo path using only half-duplex speech during conversational calls. The in-service non-intrusive parallel digital adaptive filter measurement device (PDMD) is based on a class of in-service non-intrusive measurement devices (INMDs) for quality of service (QoS) assessment in public switched telephone networks (PSTNs). INMDs are usually based on LMS digital adaptive filters (DAFs). The modelling convergence rate is derived from the optimal Wiener weights, which defines the performance criterion. The novel PDMD utilises a parallel additional FIR-DAF set which is driven by the input speech and the stochastic behaviour of the LMS upon convergence is used to provide a linear whitening function on the input speech's power spectral density (PSD). Whitening the input speech improves the convergence rate. Software simulation is reported for conversational speech realisation and it is shown that the proposed device significantly improve the convergence rate by 23.8 dB after 1 second adaptation.