ARTICLE IN PRESS Flow Measurement and Instrumentation ( ) – Flow Measurement and Instrumentation www.elsevier.com/locate/flowmeasinst A new velocity estimation method using spectral identification of noise St´ ephane Fischer a,∗ , Philippe Schmitt b , Denis Ensminger b , Far` es Abda b , Anne Pallares b a Ultraflux R&D, 17, rue Ch. Jeanneret, 78306 Poissy Cedex, France b Institut de M´ ecanique des Fluides et des Solides (IMFS) UMR 7507, 2 rue Boussinguault, 67000 Strasbourg, France Received 31 October 2006; received in revised form 10 February 2007; accepted 21 June 2007 Abstract In all measurement techniques one seeks accuracy and precision. In ultrasonic Doppler velocimetry, those qualities strongly depend on signal to noise ratio of the Doppler signal and on the performance of the velocity estimator. The most widely used estimation method in ultrasonic coherent Doppler velocimetry is the pulse pair method. Its success is due to the computation efficiency of the algorithm combined to an unbiased estimator. Unfortunately, for a wide range of experimental fluid flows, the pulse pair estimation is less efficient, especially for clear water or concentrated mud where the signal to noise ratio can be very low, or for highly turbulent flows where the Doppler signal has a broad spectrum. Our approach is based on the treatment of the Doppler spectral information. It uses a simple parametric identification inspired by theoretical models and experimental observations. It acts through noise subtraction and subsequent cutting. Thus, we have developed a fast velocity estimation algorithm superior to the pulse pair one in terms of accuracy. The robustness of the method was evaluated by adding different levels of white Gaussian noise to an experimental Doppler signal. The results demonstrate an increase of noise immunity up to one decade compared to the pulse pair method. c  2007 Elsevier Ltd. All rights reserved. Keywords: Frequency estimation; Doppler signal; Spectral analysis; Standard deviation 1. Introduction There are several methods for flow velocity profile evaluation. One of the most commonly used is the pulsed ultrasound technique: the estimation of the flow velocity at different depths along a profile can be obtained by Doppler evaluation from the backscattered acoustic signals. Hence, every sample volume is defined by the ultrasonic beam geometry and by the range gated backscattered echo [1]. The measured ultrasonic signal is the result of reflection on moving scatterers in the insonified volume. Several techniques can be used to extract Doppler information from the volumes [2]. They are classified in two main categories, the narrowband and the broadband Doppler. The broadband method is based on evaluation of the time lag between the reflected acoustic signals from two successive pings. Narrowband methods include coherent and incoherent Doppler. The latter method consists in estimating the Doppler shift from echoes of the single-pulse ping. Every ping generates ∗ Corresponding author. Tel.: +33 01 39 79 26 40. E-mail address: stephane.fischer@gmail.com (S. Fischer). one estimation of the velocity profile. This method is robust and allows long measurement ranges, but the velocity resolution error requires long averaging times. Our newly developed method is based on coherent Doppler. For this technique, phase changes from successive pings are observed for each insonified volume [3]. It guarantees good spatial resolution and low variance, but has a main drawback consisting in the well-known “range–velocity” limit. Using this method, the Doppler signal is obtained from the quadrature demodulated signal by collecting a vector of samples where each sample is taken within a Pulse Repetition Frequency (PRF) period. Different vectors associated with the adjacent volumes within the measured profile are obtained by considering the corresponding roundtrip travel times. The measured signal can be modelled as a complex zero-mean Gaussian process with additive complex white Gaussian noise in a first approximation. For each volume, velocity is proportional to the Doppler signal first spectral moment. The major difficulty is due to the random phase of each backscattered echo inducing a random spectral density [4], even if there is no noise. The most used technique for estimation of the first spectral moment is the 0955-5986/$ - see front matter c  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2007.06.008 Please cite this article in press as: Fischer S, et al. A new velocity estimation method using spectral identification of noise. Flow Measurement and Instrumentation (2007), doi:10.1016/j.flowmeasinst.2007.06.008