Doppler Velocity Estimation of Overlapping Linear-Period-Modulated Ultrasonic Waves Based on an Expectation-Maximization Algorithm

The occurrence of an overlapping signal is a significant problem in performing multiple objects localization. Doppler velocity is sensitive to the echo shape and is also able to be connected to the physical properties of moving objects, especially for a pulse compression ultrasonic signal. The expectation-maximization (EM) algorithm has the ability to achieve signal separation. Thus, applying the EM algorithm to the overlapping pulse compression signals is of interest. This paper describes a proposed method, based on the EM algorithm, of Doppler velocity estimation for overlapping linear-period-modulated (LPM) ultrasonic signals. Simulations are used to validate the proposed method. 1. Introduction Recently, acoustic systems have been used in many industrial and educational applications because such systems have the advantages of a variety of acoustic transducers, low cost, small size, and simple hardware. For example, ultrasonic distance measurement is a modern and relatively flexible approach for environment recognition. The ultrasonic distance measurement determination uses the time-of-flight (TOF) approach, which is the time for sound waves to travel between the sound source and the objects. In general, TOF can simply be computed by performing a cross-correlation between the transmitted and received signals [1]. As a result, TOF can be measured by the maximum peak during a storage time. A linear-frequency-modulated (LFM) signal, which has a linear variation in an instantaneous frequency with time, is an example of a pulse compression signal used for ultrasonic distance measurement [1]. However, for the case of the distance measurement of the moving object, the LFM signal is unsuitable because of the shifted frequency of the Doppler effect. The problem is that the cross-correlation cannot completely be achieved between the transmitted and received signals. Therefore, a linear-period-modulated (LPM) signal, the period of which is linearly swept with time, has been demonstrated to solve the Doppler-shift problem of the LFM signal [2, 3]. A LPM signal can be used in the cross-correlation by providing the TOF with the Doppler-shift compensation via Doppler velocity estimation [4]. However, the Doppler-shift problem is more challenging for the multiple-echoes case. The overlapping signals due to many objects will exhibit many Doppler velocities. If each Doppler velocity can be completely separated, then the Doppler velocity can be estimated for each individual echo. In the case of a pulse compression signal, the LFM echoes can be discriminated by the use