## 1 Introduction  
In recent years, home weight training exercises have received a lot of attention. Wearable products have also become an important tool to help people improve the quality of exercise. In terms of exercise data quantification, with the rapid development of Wearable Fitness Trackers (WFTs) and Smartphone Pedometer Apps (SPAs), people are keeping an eye on their health through heart rate, fitness, and sleep tracking [1]. In 2004, [PERSON] [2] developed an inertial navigation system algorithm based on a low-cost inertial measurement unit to implement a nonlinear data fusion algorithm using a Distribution Approximation Filter (DAF). Gyroscopes are often used for system positioning in many applications, but gyroscopes generate error drift, a low-frequency drift phenomenon over time [3], which accumulates very large orientation errors over time, so that an attitude positioning system cannot use only one gyroscope to achieve accurate orientation. The causes of integration drift can be divided into two categories: one is the linear increase of drift due to the integration of the original offset in the signal, and the other is the integration of noise in the signal [4]. In the long term, both accelerometer and magnetometer have no drift. Inputting the accelerometer and magnetometer data into Kalman Filter (KF) can compensate the drift of gyroscope, so it can be used to determine the orientation, but both of them have more obvious short-term noise [5]. Many studies have used data from inertial measurement units (IIMUs) for human posture recognition using machine learning models. [PERSON] [6] used a one-dimensional Hadamard wavelet transformation and a feature extraction method based on one-dimensional LBP (Local binary patterns) to compute valuable eigenvalues in acceleration and angular velocity signals, and used a sequential minimization algorithm and a stochastic forest method to classify activities in the USC-HAD (USC human activity dataset) and IMSB (IM-Sporting Behaviors) datasets. No IMU-based device was presented in this work. [PERSON] [7] trained and tested different supervised machine learning models based on 14 participants, including k-NN (k-nearest neighbors) algorithm and SVM (Support Vector Machine), using accelerations and angular velocities of one sensor with an highest accuracy of 96.4% and of two sensors with 97.6% accuracy to classify four fitness sports. No exercise prescription variables, such as exercise sets, training capacity, workout capacity, training period, explosive power, etc. were considered. Many research papers have combined data from cell phones and wearable sensors to automatically capture features using deep learning algorithms, effectively saving manual feature processing [8]. [PERSON] [9] mentioned that many papers use IMU data into a CNN (Convolutional Neural Network) to achieve posture recognition, and he proposed another CNN algorithm to calculate the pace trajectory. In his work, the developed IMU device was worn on a shoe for foot motion tracking. The literature [10] proposes a real-time segmentation and classification algorithm that can identify physical exercise and works well in both indoor and outdoor environments. This proposed algorithm achieved a 95% classification accuracy for five indoor and outdoor exercises. No exercise prescription variables were considered in [10]. [PERSON] and [PERSON] [11] trained a machine learning model with accelerometer data to classify 36 types of fitness exercises. The data were collected using a GeneActiv 3D accelerometer, which can be used as a wrist-worn or be attached with straps to other body locations. In many cases, IMUs have been used to develop multimodal algorithms, and [PERSON] et al. [12] designed a smart fitness device that uses acceleration and angular velocity signals read by IMUs to perform automatic motion tracking and analyze weight training exercises. Their device was mounted on the dumb bell. The repetitions of dumb bell exercise were detected by a peak/valley detector.