# Parameter Testing and System of Skiing Aerial Skills under the Background of Artificial Intelligence

Authors: Dan Wang
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Skiing aerial skills are a perfect combination of gymnastics tossing technology and skiing technology. It pursues technology and aesthetics in the process of completing the action, and is a sporting event with strong skills and high viewing. However, the training of ski aerial skills is more difficult, and there is no qualified training mode, which may be detrimental to the long-term development of the overall strength of ski aerial skills. Therefore, based on the shortcomings of the current stage, this paper proposed a ski aerial skill movement detection system. The system mainly assists the MTi sensor to obtain the sports shape parameters of the skier’s sports information and then analyzes the obtained data to find out the approximate data of each parameter when the skiing succeeds and fails, as well as the relationship between acceleration and speed. The experimental results showed that the maximum resultant acceleration and resultant velocity are obtained at the lowest point of the landslide. At a certain stage of the air, the resultant acceleration is always around 10 m/s2 due to gravity. The shoulder joint angle of the skier at the moment of introduction is about 163.2° for success and about 167.6° for failure. The inclination of the trunk is about 30.4° when the action is successful at the moment of landing, while the inclination of the trunk is about 38.4° when the action fails, and the angle of the hip joint in the successful and failed actions is about 138.5° and 153.8°, respectively.


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## Body

## 1. Introduction

With the rapid development of competitive sports, many modern sciences and technologies are combined with sports for sports scientific research and training and play an increasingly important role in improving the performance of athletes. At present, the main method of scientific training at home and abroad is to use modern information acquisition technology to obtain human body motion information parameters, which are used to guide training after comprehensive analysis. Due to the complexity of human motion and the necessity of training real-time diagnosis, it is required that the device for acquiring human motion information has high accuracy and real-time performance. Skiing aerial skills are a high-skill, high-difficulty, and high-risk sport. Any technical flaws may lead to the failure of sports movements or even injuries to athletes. The signal extraction and data processing research of the ski aerial skill test system is very important to the digital research of the standard movements of the athletes in each technical link.In order to better study the parametric test and analysis system for ski aerial skills, some researchers have studied from a single aspect, among which Kim has studied the aerodynamic and kinematic aspects related to ski jumping, by using various measurement sensors to obtain and analyze the information of the entire platform [1]. Sands studied the possible hazards of trampoline by analyzing various parameters of trampoline’s aerial action and then applied it to skiing [2]. Dhruv studied mathematical optimization methods to find optimal interactions between articulating body parts [3]. Jaam identified appropriate aerial motor skills by studying normative values of motor skills tests for children aged 4–12 [4]. But, none of them found a suitable algorithm to validate their research.Based on the development of artificial intelligence, scholars have developed some artificial intelligence algorithms in order to find the optimal algorithm to test the parameters of skiing aerial skills. Among them, Youssef has studied artificial intelligence algorithms in the modeling, selection and model, control, fault diagnosis, and output estimation. The important role of artificial intelligence algorithms in photovoltaic systems was proved by a comprehensive comparison with traditional methods [5]. Wang proposed a region growing image processing method to study the seeds of region growing [6]. Ekici proposed a multizone optimization method to support decision-making across tall buildings. Proposed approaches include parametric modeling and simulation of tall buildings and machine learning and optimization as an artificial intelligence approach [7]. Hassabis examined the role of artificial intelligence in neuroscience [8]. Makridakis examined the impact of the AI revolution on companies and employment [9]. But, they did not apply the algorithm to skiing.Based on the existing technology, this paper developed a system for detecting the action parameters of ski aerial skills and proposed a contact detection method to obtain the kinematic information of the athlete’s entire action process, so as to realize the real-time analysis of the athlete’s action. The innovation of this paper is that this paper used the MTi sensor to detect the movement parameters of five skiers in real time and used multiple drones to shoot at the same time. By comparing and analyzing the sports data and states of athletes at various time nodes, the standardization of skiing actions can be further analyzed.


## 2. Ski Aerial Skills under the Background of Artificial Intelligence

### 2.1. Artificial Intelligence

Artificial intelligence (AI) can be explained in two ways. On the one hand, AI originates from the continuous progress and development of human beings. On the other hand, it is a computer imitating certain human behaviors [10]. Artificial intelligence is the study of how to use computers to simulate certain human thought processes and intelligent behaviors. There are many application fields of artificial intelligence, mainly in agriculture, communication, medical care, social security, transportation, service industry, financial industry, big data processing, and so on, as shown in Figure 1.Figure 1
Artificial intelligence application areas.


### 2.2. Ski Aerial Skills Motion Detection System

The skiing aerial skill movement consists of four parts: assisting, taking off, flipping in the air, and landing. It requires “stable, difficult, accurate, and beautiful” in the completion of the action. The so-called “stability” refers to the stability when landing, which is one of the keys to winning the athlete; the so-called “difficult” means that the movements are technically complex and highly skilled; the so-called “beauty” means that it does not only look at the result but not the process in some projects, but also depend on both the result and the whole process, and it pays attention to the beauty and artistry of the athletes’ movements. For those who watch the game, ski aerial skills sports have a great viewing experience. However, for athletes, it is necessary to have good coordination, balance, sense of direction, good air feel, and strong explosive qualities. In the process of exercising, athletes have to not only overcome and adapt to the difficulties brought by the climate, wind direction, snow quality, and other natural conditions in the snow field, but also overcome the inconvenience caused by the weight of clothing and snow gear [5]. At the same time, the project is a sport with a high error rate, and athletes have a high possibility of sports injuries. Moreover, the motion morphological parameters of human motion information are mainly composed of dynamics, kinematics, and EMG information, as shown in Figure 2.Figure 2
Composition diagram of human motion information.Aiming at the characteristics of skiing aerial skills, combined with the knowledge of sports biomechanics, advanced sensing technology, information acquisition, and ergonomics, a contact method for acquiring key parameters such as acceleration, velocity, angular velocity, and angle was proposed and a prototype test system for skiing aerial skills was constructed. The system displays all the data in the form of two-dimensional curves while acquiring the kinematic parameters of the skiers in real time. A large number of experiments have proved that not only can the system obtain real-time and accurate data information of athletes, but also this data information can reflect some key posture features in the movement process, thus verifying the reliability and practicability of the system [11, 12].Aiming at the technical characteristics of ski aerial skills and the shortcomings of the current motion video analysis system, this paper designed a test system based on attitude sensors. The system consists of four modules, and the four modules communicate through wireless signals. The kinematic parameters such as acceleration and angular velocity of athletes during exercise can be obtained in real time, and data information such as speed, angle, and angular acceleration of athletes can be obtained through certain algorithms. These four modules are shown in Figure3.Figure 3
Ski aerial skills test system.The signal acquisition module in Figure3 is worn on the waist of the athlete during the test, which can collect and store the data information of human body movement in real time and transmit the data information to the PC receiving module through wireless signals. The remote control module controls the signal acquisition module through wireless signals, so as to minimize the inconvenience caused by the athlete’s operation of the signal acquisition module. When receiving the synchronization signal sent by the receiving module of the PC, the camera will record the time point, so as to realize the synchronization of collecting data and shooting video. The PC receiver module is connected with the host computer, and this module communicates the PC with the other three modules through wireless signals [13]. When the host computer sends and receives the command, the PC receiver module starts to receive data.The signal acquisition module is the core part, which can collect and store data information. The structure of this module is shown in Figure4. The MTi sensor and wireless module are connected to the microprocessor through serial port 1 and serial port 2, respectively. The memory transmits data with the microprocessor through the SPI interface. Since the microprocessor integrates the AD converter, the power detection module can directly input the analog signal into the microprocessor [14].Figure 4
Block diagram of the signal acquisition module.The data information measured by the placement position of the module should best reflect the movement posture of the athlete, and the waist should be the center of mass and the center of the human body. Obviously, the motion information here can best reflect the motion posture of the human body. To accurately obtain the posture information of the movement, it must be ensured that the selected position is more conducive to the fixation of the module and will not fall off the athlete. Throughout the whole process of freestyle skiing, the waist of the athlete should be the part with the smallest range of motion of the human body. Moreover, the module is designed in the form of a belt, which is tied to the waist of the athlete during exercise and is very convenient to wear, and the belt part is made of elastic material, which can be properly scaled [15].Since the module is to be worn on the body, the interference of the instrument to the athlete’s movements should be minimized, and the athlete should not be injured. Therefore, the module is designed to be small in size and light in weight. At the same time, the shell of the module is made of plastic with not too much hardness, which not only reduces the weight and ensures the safety of athletes, but also takes into account the aesthetics of the module.The block diagram of the synchronization signal acquisition module and the PC receiver module is shown in Figure5.Figure 5
Structure block diagram of synchronization signal acquisition module and PC receiver module.
(a)(b)It can be seen from Figure5 that, in the synchronization signal acquisition module, when the synchronization signal sent by the PC receiving module is received, the signal indicator light will flash, and the camera will record this time point. Thereby, the synchronization of the collected data and the captured video is realized. The camera is an auxiliary analysis tool, which can assist the coaches to analyze the data information, so as to guide the athletes in a targeted manner. The PC receiver module mainly realizes the following functions: data stored in the signal acquisition module is received; synchronization signals to the synchronization signal module are sent; the signal acquisition module is debugged; data through the host computer software is processed and visualized [16, 17].The remote control module can realize the control of the signal acquisition module. At the same time, the stop of the signal acquisition is completed by the timing of the internal microprocessor of the module, thereby minimizing the inconvenience caused by the athlete’s operation of the signal acquisition module. The structural block diagram of the remote control module is shown in Figure6.Figure 6
Block diagram of remote control module structure.


### 2.3. MTi Sensor

The sensor in this system adopts MTi sensor. It is a gyroscope-enhanced heading and attitude measurement system that is a miniature, integrated MEMS inertial measurement sensor. MTi sensors have the advantages of small size, light weight, high precision, convenient operation, and easy development, so they are widely used in robotics, aerospace, automotive, marine industries, and other fields [18,19].The physical properties and positioning performance parameters of the MTi sensor are shown in Table1, and the main performance parameters are shown in Table 2.Table 1
MTi sensor physical properties and positioning performance parameters.
WeightVolumeOperating voltagePower consumptionOperating temperature50 g58∗58∗23 mm5 V350 mW-15∼50 °CDynamic rangeAngular velocity resolutionStatic accuracy (roll)Static accuracy (heading)Dynamic accuracy3D all angles0.05 deg<0.4 deg<0.8 deg2 degRNSTable 2
MTi sensor performance parameters.
projectAngular velocityAccelerationGeomagnetic fieldDimensionThree-dimensionalThree-dimensionalThree-dimensionalFull range±1250 deg/s±20 g/s±800 mGaussLinearity0.1% of FS0.1% of FS0.2% of FSZero point stability5 deg/s0.02 m/s20.5 m GaussNoise density0.1 deg/s√Hz0.1 m/s√Hz0.5 m GaussAxis calibration error0.1 deg0.1 deg0.1 degWidth40 Hz30 Hz10 HzThe coordinate system that defines the sensor itself is the S (Sensor) coordinate system, also known as the carrier coordinate system, and its coordinate system is aligned with the housing of the MTi sensor. The reference coordinate system based on geomagnetism is theG (geomagnetism) coordinate system, also known as the inertial reference coordinate system. The G coordinate system is a right-handed Cartesian coordinate system, which is defined as follows. The positive direction of the X-axis points to the geomagnetic north pole; the Y-axis is determined according to the definition of the right-handed coordinate system; the positive direction of the Z-axis points vertically upward. Since the data (acceleration and angular velocity) measured by the MTi sensor are all defined in the S coordinate system, in order to analyze the movement of skiing aerial skills, some data need to be transformed into the G coordinate system.The direction cosine matrix output mode is adopted in this system. The direction cosine matrix is also called the transformation matrix method. It consists of nine parameters in total, which is a method of representing the attitude rotation matrix by the direction cosine of the vector. The direction cosine matrix represents the relationship between two coordinate systems rotating around a fixed point, and its variation law can be described by the differential formula of the direction cosine matrix. The transformation matrix is shown in formula (1), which represents the transformation matrix from the sensor coordinate system to the inertial reference frame coordinate system.(1)RGS=abcdefghi=R11R12R13R14R15R16R17R18R19=RSGT.In order to facilitate the description and analysis of the athlete’s movements, it is necessary to transform the acceleration into theG coordinate system. The transformation method is shown in formula (2). Among them, AS is the three-dimensional acceleration or angular velocity vector in the S coordinate system, and AG is the corresponding three-dimensional acceleration vector in the G coordinate system. For the angular velocity, there is no need for coordinate transformation.(2)AG=RSGTAS.Since the acceleration signal output by the MTi sensor contains a certain trend term, and the acceleration output by the sensor contains a gravitational acceleration g, these are uniformly defined as the DC component of the signal. The DC component needs to be removed when calculating the speed by integration. A common practice is to approximate the mathematical expectation of the signal in place of the DC component.(3)x¯=1N∑i=1Nxi.In the formula,xii=1,…,N is the acceleration signal collected by the sensor. Therefore, the signal formula after removing the DC component is(4)xi′=xi−x¯.However, the method cannot completely remove the DC component in most cases.at is the acceleration signal with the DC component removed in the time domain, and Aω is obtained by Fourier transform. According to the properties of Fourier transform, if at⟶Aωq, as shown in formula (5), the left end is the acceleration integral formula and ω is the frequency.(5)∫−∞atdt↔1iωAω.By integrating the accelerations in the three directions by the method, the corresponding speedvxi,vyi,vzi can be obtained. Among them, i is the label of the signal sequence, and the combined speed is as follows:(6)vi=vxi2+vyi2+vzi2.Although the angular velocity output by the MTi sensor is in the S coordinate system, it is not necessary to perform coordinate transformation on the angular velocity. Therefore, the angular acceleration can be obtained by directly differentiating the angular velocity. Then, trapezoidal integration is used to find the angle with the following formula:(7)θi=θi−1+12×Fs×yi−1+yi,(8)ai=Fs∗yi−yi−1,where yi is the angular velocity and i=1,2,...,N and N are the signal sequence lengths. Fs is the sampling frequency. The angles and angular accelerations in other directions can be obtained by formulas (7) and (8).The Kalman filter mainly includes the process of prediction and update. Kalman filter is an algorithm that utilizes the linear system state formula to optimally estimate the state of the system by inputting and outputting observation data of the system. According to the model of Kalman filter, assuming that the current state of the system isa,(9)xa|a−1=Axa−1|a−1+Bua.Among them,xa|a−1 refers to the result of predicting the current state through the previous state; xa−1|a−1 refers to the optimal result of the previous state; ua is the current control amount. If P represents covariance, the covariance formula is as follows:(10)Pa|a−1=APa−1|a−1AT+Q.Among them,Pa|a−1 corresponds to the covariance of xa|a−1, Pa−1|a−1 corresponds to the covariance of xa−1|a−1, and Q refers to the covariance matrix.According to the predicted valuexa|a−1 and the current measured value Z(a), the optimal estimated value xa|a of the current state can be obtained. Among them, KGa is the Kalman gain in the a state:(11)KGa=Pa|a−1HTHPa|a−1HT+R,xa|a=xa|a−1+KGaZa−Hxa|a−1.After obtaining the optimal estimated value in the current state, the covariance transformation matrixPa|a of the current state xa|a is updated.(12)Pa|a=1−KGaHPa|a−1.When dealing with nonlinear relationships, an extended Kalman filter is required. The basic idea is to linearize the nonlinear system and then perform Kalman filtering. Assuming the state vectorx∈Rn of the process, its state formula is expressed as follows:(13)xa=fxa−1,ua−1,ωa−1.Then the observed variablez∈Rm is expressed as(14)za=hxa,va.Among them,ωa,va represents the process excitation noise and observation noise, respectively, and f and h are nonlinear functions. In practical applications, ωa,va at different times has its own value, which can be assumed to be 0 when used, and then formulas (13) and (14) can be expressed as follows:(15)x˜a=fx˜a−1,ua−1,0,z˜a=hx˜a,0.Among them,x˜a refers to the posterior estimate in a stochastic process. The basic operation process of the extended Kalman filter is basically the same as that of the discrete Kalman filter.However, the obtained motion signals always contain some noise signals. In order to reduce the interference of the noise signals and better analyze the movements of the athletes, it is necessary to remove the noise in the signals, so as to restore the real movement information of the athletes. According to the characteristics of these signals, wavelet decomposition and reconstruction denoising method are used in this paper to denoise all motion signals of athletes. The signal contaminated by noise is(16)xk=sk+nk.In the formula, x(k) is the signal with noise, s(k) is the real signal, n(k) is the noise, andk is the number of sampling points. Then the decomposition formula is(17)ckj=∑nhn−2kcnj−1,dkj=∑ngn−2kcnj−1.In the formula,k=1,2,...,N and N are discrete sampling points; ckj is the scale coefficient; dkj is the detail coefficient. The purpose of denoising can be achieved by decomposing the signal containing noise into different frequency bands at a certain scale, retaining the frequency band where the useful signal is located, and performing wavelet reconstruction. Inverse wavelet transform is performed to obtain the estimate of the original signal, and the reconstruction formula is(18)ckj−1=∑nhn−2kcnj+∑ngn−2kdnj.


## 2.1. Artificial Intelligence

Artificial intelligence (AI) can be explained in two ways. On the one hand, AI originates from the continuous progress and development of human beings. On the other hand, it is a computer imitating certain human behaviors [10]. Artificial intelligence is the study of how to use computers to simulate certain human thought processes and intelligent behaviors. There are many application fields of artificial intelligence, mainly in agriculture, communication, medical care, social security, transportation, service industry, financial industry, big data processing, and so on, as shown in Figure 1.Figure 1
Artificial intelligence application areas.


## 2.2. Ski Aerial Skills Motion Detection System

The skiing aerial skill movement consists of four parts: assisting, taking off, flipping in the air, and landing. It requires “stable, difficult, accurate, and beautiful” in the completion of the action. The so-called “stability” refers to the stability when landing, which is one of the keys to winning the athlete; the so-called “difficult” means that the movements are technically complex and highly skilled; the so-called “beauty” means that it does not only look at the result but not the process in some projects, but also depend on both the result and the whole process, and it pays attention to the beauty and artistry of the athletes’ movements. For those who watch the game, ski aerial skills sports have a great viewing experience. However, for athletes, it is necessary to have good coordination, balance, sense of direction, good air feel, and strong explosive qualities. In the process of exercising, athletes have to not only overcome and adapt to the difficulties brought by the climate, wind direction, snow quality, and other natural conditions in the snow field, but also overcome the inconvenience caused by the weight of clothing and snow gear [5]. At the same time, the project is a sport with a high error rate, and athletes have a high possibility of sports injuries. Moreover, the motion morphological parameters of human motion information are mainly composed of dynamics, kinematics, and EMG information, as shown in Figure 2.Figure 2
Composition diagram of human motion information.Aiming at the characteristics of skiing aerial skills, combined with the knowledge of sports biomechanics, advanced sensing technology, information acquisition, and ergonomics, a contact method for acquiring key parameters such as acceleration, velocity, angular velocity, and angle was proposed and a prototype test system for skiing aerial skills was constructed. The system displays all the data in the form of two-dimensional curves while acquiring the kinematic parameters of the skiers in real time. A large number of experiments have proved that not only can the system obtain real-time and accurate data information of athletes, but also this data information can reflect some key posture features in the movement process, thus verifying the reliability and practicability of the system [11, 12].Aiming at the technical characteristics of ski aerial skills and the shortcomings of the current motion video analysis system, this paper designed a test system based on attitude sensors. The system consists of four modules, and the four modules communicate through wireless signals. The kinematic parameters such as acceleration and angular velocity of athletes during exercise can be obtained in real time, and data information such as speed, angle, and angular acceleration of athletes can be obtained through certain algorithms. These four modules are shown in Figure3.Figure 3
Ski aerial skills test system.The signal acquisition module in Figure3 is worn on the waist of the athlete during the test, which can collect and store the data information of human body movement in real time and transmit the data information to the PC receiving module through wireless signals. The remote control module controls the signal acquisition module through wireless signals, so as to minimize the inconvenience caused by the athlete’s operation of the signal acquisition module. When receiving the synchronization signal sent by the receiving module of the PC, the camera will record the time point, so as to realize the synchronization of collecting data and shooting video. The PC receiver module is connected with the host computer, and this module communicates the PC with the other three modules through wireless signals [13]. When the host computer sends and receives the command, the PC receiver module starts to receive data.The signal acquisition module is the core part, which can collect and store data information. The structure of this module is shown in Figure4. The MTi sensor and wireless module are connected to the microprocessor through serial port 1 and serial port 2, respectively. The memory transmits data with the microprocessor through the SPI interface. Since the microprocessor integrates the AD converter, the power detection module can directly input the analog signal into the microprocessor [14].Figure 4
Block diagram of the signal acquisition module.The data information measured by the placement position of the module should best reflect the movement posture of the athlete, and the waist should be the center of mass and the center of the human body. Obviously, the motion information here can best reflect the motion posture of the human body. To accurately obtain the posture information of the movement, it must be ensured that the selected position is more conducive to the fixation of the module and will not fall off the athlete. Throughout the whole process of freestyle skiing, the waist of the athlete should be the part with the smallest range of motion of the human body. Moreover, the module is designed in the form of a belt, which is tied to the waist of the athlete during exercise and is very convenient to wear, and the belt part is made of elastic material, which can be properly scaled [15].Since the module is to be worn on the body, the interference of the instrument to the athlete’s movements should be minimized, and the athlete should not be injured. Therefore, the module is designed to be small in size and light in weight. At the same time, the shell of the module is made of plastic with not too much hardness, which not only reduces the weight and ensures the safety of athletes, but also takes into account the aesthetics of the module.The block diagram of the synchronization signal acquisition module and the PC receiver module is shown in Figure5.Figure 5
Structure block diagram of synchronization signal acquisition module and PC receiver module.
(a)(b)It can be seen from Figure5 that, in the synchronization signal acquisition module, when the synchronization signal sent by the PC receiving module is received, the signal indicator light will flash, and the camera will record this time point. Thereby, the synchronization of the collected data and the captured video is realized. The camera is an auxiliary analysis tool, which can assist the coaches to analyze the data information, so as to guide the athletes in a targeted manner. The PC receiver module mainly realizes the following functions: data stored in the signal acquisition module is received; synchronization signals to the synchronization signal module are sent; the signal acquisition module is debugged; data through the host computer software is processed and visualized [16, 17].The remote control module can realize the control of the signal acquisition module. At the same time, the stop of the signal acquisition is completed by the timing of the internal microprocessor of the module, thereby minimizing the inconvenience caused by the athlete’s operation of the signal acquisition module. The structural block diagram of the remote control module is shown in Figure6.Figure 6
Block diagram of remote control module structure.


## 2.3. MTi Sensor

The sensor in this system adopts MTi sensor. It is a gyroscope-enhanced heading and attitude measurement system that is a miniature, integrated MEMS inertial measurement sensor. MTi sensors have the advantages of small size, light weight, high precision, convenient operation, and easy development, so they are widely used in robotics, aerospace, automotive, marine industries, and other fields [18,19].The physical properties and positioning performance parameters of the MTi sensor are shown in Table1, and the main performance parameters are shown in Table 2.Table 1
MTi sensor physical properties and positioning performance parameters.
WeightVolumeOperating voltagePower consumptionOperating temperature50 g58∗58∗23 mm5 V350 mW-15∼50 °CDynamic rangeAngular velocity resolutionStatic accuracy (roll)Static accuracy (heading)Dynamic accuracy3D all angles0.05 deg<0.4 deg<0.8 deg2 degRNSTable 2
MTi sensor performance parameters.
projectAngular velocityAccelerationGeomagnetic fieldDimensionThree-dimensionalThree-dimensionalThree-dimensionalFull range±1250 deg/s±20 g/s±800 mGaussLinearity0.1% of FS0.1% of FS0.2% of FSZero point stability5 deg/s0.02 m/s20.5 m GaussNoise density0.1 deg/s√Hz0.1 m/s√Hz0.5 m GaussAxis calibration error0.1 deg0.1 deg0.1 degWidth40 Hz30 Hz10 HzThe coordinate system that defines the sensor itself is the S (Sensor) coordinate system, also known as the carrier coordinate system, and its coordinate system is aligned with the housing of the MTi sensor. The reference coordinate system based on geomagnetism is theG (geomagnetism) coordinate system, also known as the inertial reference coordinate system. The G coordinate system is a right-handed Cartesian coordinate system, which is defined as follows. The positive direction of the X-axis points to the geomagnetic north pole; the Y-axis is determined according to the definition of the right-handed coordinate system; the positive direction of the Z-axis points vertically upward. Since the data (acceleration and angular velocity) measured by the MTi sensor are all defined in the S coordinate system, in order to analyze the movement of skiing aerial skills, some data need to be transformed into the G coordinate system.The direction cosine matrix output mode is adopted in this system. The direction cosine matrix is also called the transformation matrix method. It consists of nine parameters in total, which is a method of representing the attitude rotation matrix by the direction cosine of the vector. The direction cosine matrix represents the relationship between two coordinate systems rotating around a fixed point, and its variation law can be described by the differential formula of the direction cosine matrix. The transformation matrix is shown in formula (1), which represents the transformation matrix from the sensor coordinate system to the inertial reference frame coordinate system.(1)RGS=abcdefghi=R11R12R13R14R15R16R17R18R19=RSGT.In order to facilitate the description and analysis of the athlete’s movements, it is necessary to transform the acceleration into theG coordinate system. The transformation method is shown in formula (2). Among them, AS is the three-dimensional acceleration or angular velocity vector in the S coordinate system, and AG is the corresponding three-dimensional acceleration vector in the G coordinate system. For the angular velocity, there is no need for coordinate transformation.(2)AG=RSGTAS.Since the acceleration signal output by the MTi sensor contains a certain trend term, and the acceleration output by the sensor contains a gravitational acceleration g, these are uniformly defined as the DC component of the signal. The DC component needs to be removed when calculating the speed by integration. A common practice is to approximate the mathematical expectation of the signal in place of the DC component.(3)x¯=1N∑i=1Nxi.In the formula,xii=1,…,N is the acceleration signal collected by the sensor. Therefore, the signal formula after removing the DC component is(4)xi′=xi−x¯.However, the method cannot completely remove the DC component in most cases.at is the acceleration signal with the DC component removed in the time domain, and Aω is obtained by Fourier transform. According to the properties of Fourier transform, if at⟶Aωq, as shown in formula (5), the left end is the acceleration integral formula and ω is the frequency.(5)∫−∞atdt↔1iωAω.By integrating the accelerations in the three directions by the method, the corresponding speedvxi,vyi,vzi can be obtained. Among them, i is the label of the signal sequence, and the combined speed is as follows:(6)vi=vxi2+vyi2+vzi2.Although the angular velocity output by the MTi sensor is in the S coordinate system, it is not necessary to perform coordinate transformation on the angular velocity. Therefore, the angular acceleration can be obtained by directly differentiating the angular velocity. Then, trapezoidal integration is used to find the angle with the following formula:(7)θi=θi−1+12×Fs×yi−1+yi,(8)ai=Fs∗yi−yi−1,where yi is the angular velocity and i=1,2,...,N and N are the signal sequence lengths. Fs is the sampling frequency. The angles and angular accelerations in other directions can be obtained by formulas (7) and (8).The Kalman filter mainly includes the process of prediction and update. Kalman filter is an algorithm that utilizes the linear system state formula to optimally estimate the state of the system by inputting and outputting observation data of the system. According to the model of Kalman filter, assuming that the current state of the system isa,(9)xa|a−1=Axa−1|a−1+Bua.Among them,xa|a−1 refers to the result of predicting the current state through the previous state; xa−1|a−1 refers to the optimal result of the previous state; ua is the current control amount. If P represents covariance, the covariance formula is as follows:(10)Pa|a−1=APa−1|a−1AT+Q.Among them,Pa|a−1 corresponds to the covariance of xa|a−1, Pa−1|a−1 corresponds to the covariance of xa−1|a−1, and Q refers to the covariance matrix.According to the predicted valuexa|a−1 and the current measured value Z(a), the optimal estimated value xa|a of the current state can be obtained. Among them, KGa is the Kalman gain in the a state:(11)KGa=Pa|a−1HTHPa|a−1HT+R,xa|a=xa|a−1+KGaZa−Hxa|a−1.After obtaining the optimal estimated value in the current state, the covariance transformation matrixPa|a of the current state xa|a is updated.(12)Pa|a=1−KGaHPa|a−1.When dealing with nonlinear relationships, an extended Kalman filter is required. The basic idea is to linearize the nonlinear system and then perform Kalman filtering. Assuming the state vectorx∈Rn of the process, its state formula is expressed as follows:(13)xa=fxa−1,ua−1,ωa−1.Then the observed variablez∈Rm is expressed as(14)za=hxa,va.Among them,ωa,va represents the process excitation noise and observation noise, respectively, and f and h are nonlinear functions. In practical applications, ωa,va at different times has its own value, which can be assumed to be 0 when used, and then formulas (13) and (14) can be expressed as follows:(15)x˜a=fx˜a−1,ua−1,0,z˜a=hx˜a,0.Among them,x˜a refers to the posterior estimate in a stochastic process. The basic operation process of the extended Kalman filter is basically the same as that of the discrete Kalman filter.However, the obtained motion signals always contain some noise signals. In order to reduce the interference of the noise signals and better analyze the movements of the athletes, it is necessary to remove the noise in the signals, so as to restore the real movement information of the athletes. According to the characteristics of these signals, wavelet decomposition and reconstruction denoising method are used in this paper to denoise all motion signals of athletes. The signal contaminated by noise is(16)xk=sk+nk.In the formula, x(k) is the signal with noise, s(k) is the real signal, n(k) is the noise, andk is the number of sampling points. Then the decomposition formula is(17)ckj=∑nhn−2kcnj−1,dkj=∑ngn−2kcnj−1.In the formula,k=1,2,...,N and N are discrete sampling points; ckj is the scale coefficient; dkj is the detail coefficient. The purpose of denoising can be achieved by decomposing the signal containing noise into different frequency bands at a certain scale, retaining the frequency band where the useful signal is located, and performing wavelet reconstruction. Inverse wavelet transform is performed to obtain the estimate of the original signal, and the reconstruction formula is(18)ckj−1=∑nhn−2kcnj+∑ngn−2kdnj.


## 3. Experiment of Parameter Testing and System for Ski Aerial Skills

### 3.1. Ski Aerial Skills Track Model

Through on-the-spot inspection, the field situation of ski aerial skills is shown in Figure7. The freestyle skiing aerial skill field includes the following five areas: the gliding area, the level area, the uphill area, the air area, and the landing area. The downhill area is the starting point of the athlete’s competition, and the slope is between 25° and 27°; the slope of the uphill area is between 65° and 70°; the slope of the landing area is between 35° and 38°, and the athlete will land on the landing area after completing the aerial movements.Figure 7
Ski aerial skills field model.The movement of ski aerial skills consists of four stages: assist, take-off, flying, and landing. The take-off stage refers to the moment when the athlete starts to prepare for the jump, after entering the upper wave area until the moment before the tail of the double board completely leaves the platform. The aerial stage refers to the moment when the athlete’s double tails completely leave the platform to the moment before the snowboard hits the ground. A total of 5 skiers were invited this time, and their basic information is shown in Table3.Table 3
Basic information for skiers.
AthleteHeight (cm)Weight (kg)Age1172752621757327317168264178702851746925


### 3.2. Field Experiment and Data

In order to better illustrate the accuracy and practicability of the system, 5 skiers were accompanied to the experimental ski resort for field experiments. Data collection was carried out on these 5 ski aerials. At the same time, the cameras in the system were shot synchronously for auxiliary analysis. Aerial skills are scored based on the athlete’s movement in the air and landing smoothness. It is known from the principles of human kinematics that the completion of the flipping action in the air is related to the speed of the flight, and the stability of the landing is closely related to the attitude when landing. The parameter testing and analysis system for skiing aerial skills can obtain the acceleration and angular velocity information of the whole movement process and obtain the relevant parameter information such as velocity and angle through the numerical integration and differential operation of the acceleration and angular velocity signals.Figure8 shows the three-dimensional acceleration parameters in the G coordinate system during the process from the starting point to the landing point. The picture distinguishes three curves and compares the trend of acceleration in three directions.Figure 8
Acceleration of ski movements. (a) X-axis acceleration. (b) Y-axis acceleration. (c) Z-axis acceleration. (d) Resultant acceleration.
(a)(b)(c)(d)Through analysis, it is known that the combined acceleration obtained by the athlete at the lowest point of the landslide reaches the maximum value, as shown at pointa in Figure 8(d). At the same time, after the athlete is in the air, the athlete is only affected by one gravitational acceleration. Therefore, the resultant velocity in the figure is about 10 m/s2, which is consistent with the athlete receiving only a vertical downward gravitational acceleration. Since the athlete is subjected to a very large force at the moment of landing, the acceleration of the athlete will have a sudden change at this time. Point b is the landing point of the athlete. Between 6 s and 7 s, the combined acceleration of the athlete is always around 10 m/s2, so the interval is the athlete’s vacating stage, which is consistent with the time of the video shot. However, (a), (b), and (c) in Figure 8 are the three-dimensional accelerations in the G coordinate system, respectively.Figure9 shows the velocities in the X, Y, and Z-axis directions of the athlete’s G coordinate system, which are obtained from the accelerations in Figure 8, respectively. It can be seen from Figure 9 that, before the introduction, the speed trend in the X and Y directions is increasing. In this stage, the Z-axis speed reaches point a; that is, when the athlete reaches the lowest point of the landslide, only the Z-axis direction is affected by gravity when in the air. Therefore, the speed of X and Y axes remains basically unchanged, while the speed of Z-axis decreases at a constant speed. There is a sudden change in the Z-axis acceleration when landing; that is, point b is the landing point.Figure 9
Speed of skiing action.
(a)(b)(c)In addition, this experiment also analyzed multiple data parameters of the skier’s movements, mainly the introduction of the skier and the standard degree of landing movements. The experimental data are shown in Figure10.Figure 10
Various movements of the skier’s introduction and landing. (a) Parameters at launch. (b) Parameters at landing.
(a)(b)From Figure10(a), it can be seen that, in the absence of external interference, all the sports indicators of the five skiers have significant differences in the results at the moment of introduction. At the moment of introduction, the shoulder joint angle succeeded at about 163.2° and failed at about 167.6°. For the influence factors of the instant index of the skier on the action result, it can be analyzed that the vertical speed of the center of gravity and the slow assist speed are the key factors that cause the failure of the action. Because the length of the assist distance is proportional to the assist speed, the speed of the assist speed affects the speed of the athlete’s center of gravity, and the speed of the center of gravity is affected by the horizontal speed of the center of gravity and the vertical speed of the center of gravity.From Figure10(b), it can be seen that the trunk inclination angle of the skier was about 30.4° when the landing action was successful, and the trunk inclination angle was about 38.4° when the action failed. One of the reasons for the failure of the movement is that the athlete’s torso inclination is too large when the athlete lands, and the upper body leans back. The hip angles were around 138.5° and 153.8° in the successful and failed movements, respectively.


### 3.3. Recommendations

According to the kinematic characteristics of the landing stage, training methods are found to improve sports performance, the landing posture from take-off, flying, and aerial movements are adjusted, the speed of the center of gravity in the three-dimensional direction is maintained, the changing angle of each joint is adjusted, and landing stability is improved. The young athletes of skiing aerial skills strengthen the targeted training of the hip and knee joints, improve the joint angle control, and help improve the landing stability during the landing stage. In the training of skiers, unstable landing caused by excessive lateral drift is avoided.


## 3.1. Ski Aerial Skills Track Model

Through on-the-spot inspection, the field situation of ski aerial skills is shown in Figure7. The freestyle skiing aerial skill field includes the following five areas: the gliding area, the level area, the uphill area, the air area, and the landing area. The downhill area is the starting point of the athlete’s competition, and the slope is between 25° and 27°; the slope of the uphill area is between 65° and 70°; the slope of the landing area is between 35° and 38°, and the athlete will land on the landing area after completing the aerial movements.Figure 7
Ski aerial skills field model.The movement of ski aerial skills consists of four stages: assist, take-off, flying, and landing. The take-off stage refers to the moment when the athlete starts to prepare for the jump, after entering the upper wave area until the moment before the tail of the double board completely leaves the platform. The aerial stage refers to the moment when the athlete’s double tails completely leave the platform to the moment before the snowboard hits the ground. A total of 5 skiers were invited this time, and their basic information is shown in Table3.Table 3
Basic information for skiers.
AthleteHeight (cm)Weight (kg)Age1172752621757327317168264178702851746925


## 3.2. Field Experiment and Data

In order to better illustrate the accuracy and practicability of the system, 5 skiers were accompanied to the experimental ski resort for field experiments. Data collection was carried out on these 5 ski aerials. At the same time, the cameras in the system were shot synchronously for auxiliary analysis. Aerial skills are scored based on the athlete’s movement in the air and landing smoothness. It is known from the principles of human kinematics that the completion of the flipping action in the air is related to the speed of the flight, and the stability of the landing is closely related to the attitude when landing. The parameter testing and analysis system for skiing aerial skills can obtain the acceleration and angular velocity information of the whole movement process and obtain the relevant parameter information such as velocity and angle through the numerical integration and differential operation of the acceleration and angular velocity signals.Figure8 shows the three-dimensional acceleration parameters in the G coordinate system during the process from the starting point to the landing point. The picture distinguishes three curves and compares the trend of acceleration in three directions.Figure 8
Acceleration of ski movements. (a) X-axis acceleration. (b) Y-axis acceleration. (c) Z-axis acceleration. (d) Resultant acceleration.
(a)(b)(c)(d)Through analysis, it is known that the combined acceleration obtained by the athlete at the lowest point of the landslide reaches the maximum value, as shown at pointa in Figure 8(d). At the same time, after the athlete is in the air, the athlete is only affected by one gravitational acceleration. Therefore, the resultant velocity in the figure is about 10 m/s2, which is consistent with the athlete receiving only a vertical downward gravitational acceleration. Since the athlete is subjected to a very large force at the moment of landing, the acceleration of the athlete will have a sudden change at this time. Point b is the landing point of the athlete. Between 6 s and 7 s, the combined acceleration of the athlete is always around 10 m/s2, so the interval is the athlete’s vacating stage, which is consistent with the time of the video shot. However, (a), (b), and (c) in Figure 8 are the three-dimensional accelerations in the G coordinate system, respectively.Figure9 shows the velocities in the X, Y, and Z-axis directions of the athlete’s G coordinate system, which are obtained from the accelerations in Figure 8, respectively. It can be seen from Figure 9 that, before the introduction, the speed trend in the X and Y directions is increasing. In this stage, the Z-axis speed reaches point a; that is, when the athlete reaches the lowest point of the landslide, only the Z-axis direction is affected by gravity when in the air. Therefore, the speed of X and Y axes remains basically unchanged, while the speed of Z-axis decreases at a constant speed. There is a sudden change in the Z-axis acceleration when landing; that is, point b is the landing point.Figure 9
Speed of skiing action.
(a)(b)(c)In addition, this experiment also analyzed multiple data parameters of the skier’s movements, mainly the introduction of the skier and the standard degree of landing movements. The experimental data are shown in Figure10.Figure 10
Various movements of the skier’s introduction and landing. (a) Parameters at launch. (b) Parameters at landing.
(a)(b)From Figure10(a), it can be seen that, in the absence of external interference, all the sports indicators of the five skiers have significant differences in the results at the moment of introduction. At the moment of introduction, the shoulder joint angle succeeded at about 163.2° and failed at about 167.6°. For the influence factors of the instant index of the skier on the action result, it can be analyzed that the vertical speed of the center of gravity and the slow assist speed are the key factors that cause the failure of the action. Because the length of the assist distance is proportional to the assist speed, the speed of the assist speed affects the speed of the athlete’s center of gravity, and the speed of the center of gravity is affected by the horizontal speed of the center of gravity and the vertical speed of the center of gravity.From Figure10(b), it can be seen that the trunk inclination angle of the skier was about 30.4° when the landing action was successful, and the trunk inclination angle was about 38.4° when the action failed. One of the reasons for the failure of the movement is that the athlete’s torso inclination is too large when the athlete lands, and the upper body leans back. The hip angles were around 138.5° and 153.8° in the successful and failed movements, respectively.


## 3.3. Recommendations

According to the kinematic characteristics of the landing stage, training methods are found to improve sports performance, the landing posture from take-off, flying, and aerial movements are adjusted, the speed of the center of gravity in the three-dimensional direction is maintained, the changing angle of each joint is adjusted, and landing stability is improved. The young athletes of skiing aerial skills strengthen the targeted training of the hip and knee joints, improve the joint angle control, and help improve the landing stability during the landing stage. In the training of skiers, unstable landing caused by excessive lateral drift is avoided.


## 4. Conclusion

Aiming at the characteristics of ski aerial skills, this paper developed a set of snow aerial skills detection system that can obtain the movement parameters of skiers during the movement process. This paper divided the movement stages according to the characteristics of the freestyle skiing aerial skills movement process, and verified the reliability and practicability of the detection system through field experiments. However, there are still some problems in the information acquisition system used in this paper to detect motion parameters, and the types of sensors in the system should be optimized. For example, in the motion with high speed parameter requirements, it is necessary to select a speed sensor that directly measures the speed to avoid the error in the process of calculating the speed by the acceleration integral. The number of sensors was increased, the sensors in multiple positions on the athlete’s body were configured, and multipoint motion parameters were obtained. Moreover, the system will provide a data basis for coaches to guide athletes in training. With the development, a complete database of elite athletes may be established in the future to provide the necessary data basis for the comparative analysis of athletes’ training.



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*Source: 8190398-2022-09-15.xml*