## 1 Introduction  
The measurement of the depth-averaged velocity in sediment-laden flow is a prerequisite for many research works on river engineering, such as river-bank erosion and sediment transportation. Two-dimensional quantitative information of the depth-averaged velocity field helps investigate dynamic flow structures in complicated turbulent phenomena. The information enables us to compute vorticity, deformation, and other quantities, which are directly related to the dynamics of coherent flow structures [1]. However, traditional measuring instruments, such as hot-wires and laser-Doppler anemometers, are of one-point measurements, not capable of illustrating an instantaneous spatial flow structure. The conventional Doppler algorithm has a problem on the angular error, which confines the measurement only to the velocity component along ultrasonic beams. Parallel alignment of the ultrasonic beam to the flow direction is required, which is not always feasible in many applications. It is challenging research to scientists and hydraulic engineers for a long time [2]. Optical PIV is now widely adopted as a reliable method that can obtain quantitative information on a spatial flow structure [3]. However, light cannot penetrate through turbid water because it rapidly attenuates when travelling in turbid flow, which affects its application in sediment-laden flow. To overcome those disadvantages and meet the requirements of high-precision measurements, ultrasonic imaging techniques have been introduced into the field of PIV for their distinct advantages in terms of cost and non-transparent fluid penetration. For example, the ultrasonic PIV (UIV) technique has been used to measure the time-average velocity field in silt carrying flow under moderately concentrated flow conditions [4]. In addition, UIV can measure the instantaneous flow velocity field of single-phase turbulent pipe flow [5]. In this paper, an implementation based on ultrasound imaging is developed. A UIV system is built by integrating a medical ultrasound instrument and a measurement algorithm of particle velocimetry with ultrasound images. The combination of ultrasound imaging technique and a digital PIV method can generate a new measurement technique of two-dimensional, two-component, depth-averaged velocity field appropriate for sediment-laden flow conditions [6]. Compared with Doppler-based techniques, an advantage of the UIV is its ability to measure the flow velocity components in both parallel and perpendicular directions to the ultrasonic beam. In general, it has excellent performance on simplicity, accuracy, and accessibility, while it does not have the limitations of the Doppler-based algorithm [7]. Even with ultrasonic particle image velocimetry, flow velocity measurement algorithms still face a major challenge. When the concentration of sandy water is high enough, algorithms based on the PTV method of tracking individual particles can no longer meet the measurement requirements, because there is not only In-Plane Motion but also Out-of-Plane Motion in the acoustic plane of ultrasound images, which brings instability to the calculation, as shown in Figure 1. On the other hand, there are a large number of particles in turbid water. Their motion trajectories cross each other, which causes uncertainty in the analysis of particle motion and greatly reduces the tracking robustness. PIV matching algorithms based on cross-correlation method are widely used for simplicity. For improving the accuracy and efficiency of the flow field measurement, the multigrid deformation algorithm is used to calculate the flow velocity with ultrasonic particle images of sandy water streams with volume sediment concentration less than 5% [4]. Cross-correlation is also applied in photoacoustic flowmetry for deep tissue measurement of blood flow velocity at physiological speeds ranging from 3 to 25 mm/s [8].