## 1 Introduction
Depth cameras are able to measure the depth information (RGB-D) of each pixel and use depth information to generate 3D scene models compared with conventional 2D cameras. This makes depth cameras more precise in distance measurement and spatial analysis; therefore, it is more suitable for fields such as human activity recognition and movement quality assessment. In addition, depth cameras are also affordable and have the advantages of being non-invasive, portable, and low cost [12]. In recent years, with the continuing progress and development of artificial intelligence, some automated FMS measurement methods have emerged. [PERSON] et al. proposed a CNN-LSTM model to achieve the classification of functional movements [13]. [PERSON] et al. used a CNN model to classify the electromyographic (EMG) signals of functional movements, in which the classification accuracies of squat, stride, and straight lunge squat were 91%, 89%, and 90%, respectively, [14]. Deep learning algorithms can automatically extract a set of movement features, which can improve the accuracy of activity recognition. However, they require large amounts of training data, which is time-consuming, and the network structures of deep learning models are more complex and less interpretable. Meanwhile, better results have been achieved in the field of movement quality assessment by training multiple weak classifiers to form a strong classifier in machine learning methods. An automated FMS assessment method based on the AdaBoost.M1 classifier was proposed by [PERSON] et al. [15]. FMS assessment can be achieved by training weak classifiers and combining them into a strong classifier. [PERSON] et al. used a random forest model to assess the arm movements of stroke patients by randomly selecting samples to form multiple classifiers [16]. The classification labels were then predicted by a voting method using a minority-majority approach. This method requires a smaller amount of data and is based on the interpretability of a machine learning method with manually extracted features. In summary, we propose an automated FMS assessment method based on an improved Gaussian mixture model in this study. First, we perform feature extraction on the FMS dataset collected with two Azure Kinect depth sensors; then, the features with different scores (1 point, 2 points, or 3 points) are trained separately in a Gaussian mixture model. Finally, FMS assessment can be achieved by performing maximum likelihood estimation. The results show that the improved Gaussian mixture model has better performance compared to the traditional Gaussian mixture model. It provides fast and objective evaluation with real-time feedback. In addition, we further explore the application of datasets acquired using depth cameras in the field of FMS and validate the feasibility of FMS assessment based on depth cameras. This research makes a significant contribution to the field by introducing an automated FMS assessment method and exploring the potential of depth cameras in enhancing the evaluation process. These advancements overcome the limitations of traditional methods by providing an objective and efficient FMS assessment method. The implications of our findings extend to various domains, including sports medicine, rehabilitation therapy, and performance optimization.