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Monitoring the performance is a crucial task for elite sports during both training and competition. Velocity is the key parameter of performance in swimming, but swimming performance evaluation remains immature due to the complexities of measurements in water. The purpose of this study is to use a single inertial measurement unit (IMU) to estimate front crawl velocity. Thirty swimmers, equipped with an IMU on the sacrum, each performed four different velocity trials of 25 m in ascending order. A tethered speedometer was used as the velocity measurement reference. Deployment of biomechanical constraints of front crawl locomotion and change detection framework on acceleration signal paved the way for a driftfree integration of forward acceleration using IMU to estimate the swimmers velocity. A difference of 0.6 ± 5.4 cm·s^{−1} on mean cycle velocity and an RMS difference of 11.3 cm·s^{−1} in instantaneous velocity estimation were observed between IMU and the reference. The most important contribution of the study is a new practical tool for objective evaluation of swimming performance. A single bodyworn IMU provides timely feedback for coaches and sport scientists without any complicated setup or restraining the swimmer's natural technique.
The advent of new technologies has changed the perception of athletic achievement. In swimming, the narrow gap between record holders, points to the growing importance of devising new tools to assess selfimprovement and optimize the training process. However, the biomechanical analysis of swimming remains inadequately explored due to complications of kinematics measurements in water.
To date, the most common practice for performance monitoring in swimming is using videobased systems. A video sequence is captured and postprocessed through digitization [
The second category of techniques uses tethered monitoring. An early version of such a system was developed by Craig
During the past two decades inertial measurement units (IMUs) have been proven to be powerful tools in human movement analysis [
Considering the velocity as the most intuitive metric of swimmers' performance, this study aimed to propose a new method to measure swimming velocity in front crawl, using a single bodyworn inertial sensor. We hypothesize that the swimmer's instantaneous velocity can be estimated accurately from IMU measurements when the average velocity of the swimmer over the trial is known. Driftfree integration of acceleration was certified in this study by assuming some simple locomotion constraints of the front crawl. Experimental protocols and statistical tools are introduced to assess the validity of the cycle and instantaneous velocity estimation method.
Eleven elite and nineteen recreational swimmers took part in this study. Their attributes are shown in
Each swimmer performed consecutive 25 m frontcrawl trials in four different increasing velocity trials from 70% to 100% of their best personal 100 m timing recorded one month before the measurement. In case the performance time was different more than ±5% from the targeted time, the swimmer repeated the trial. They were asked to position in the water at the edge of the pool for starts.
The swimmers were equipped with one waterproofed inertial sensor (Physilog^{®}, BioAGM, La TourdePeilz, Switzerland) including a 3D accelerometer (±11 g) and a 3D gyroscope (±900 °/s) and embedded data logger recording at 500 Hz. The sensor was worn on the sacrum inside the pocket of a custom designed swimming suit with a Velcro closing as shown in
As reference system, a tethered apparatus (SpeedRT^{®}, ApLab, Rome, Italy) [
Instantaneous velocity is estimated by integrating the forward acceleration signal in the global frame (
By starting the trials from a relatively motionless posture in water, the initial sacrum acceleration
At each time step
The time integration in
Any deviation from the conditions of
Accordingly the rotation axis is presented as in
So if we suppose that the drift is linearly increased through one cycle with
Therefore, the corrected orientation of
The instantaneous forward acceleration in global frame can be calculated according to
The instantaneous velocity
We used the geometric moving average (GMA) change detection algorithm [
For velocity drift removal, we assumed the average trend of
Detrending was done by subtracting the average of upper and lower trend curves from the original velocity curve.
A twofold validation of the proposed velocity estimation method is presented in this section. In the first step, we provided the statistics to assess the cycle mean velocity estimated using our system
In the second step we investigated the efficiency of our method in measuring the instantaneous velocity. The root mean squared (RMS), maximum and corresponding relative error of instantaneous velocity was calculated. As these calculations require similar time sampling of proposed and reference systems, the instantaneous velocity curve calculated by our method was downsampled to 100 Hz prior to error calculations. Besides, an indirect measure of accuracy of our system in instantaneous velocity measurement was provided by assessment of intracyclic velocity variation (IVV). In fact, the concurrent validity of our method was assessed by investigating IVV of the two groups of swimmers (Elite and Recreational), estimated by the two systems. IVV is computed as in
We have proposed a new wearable system and dedicated algorithms to measure front crawl velocity and described its validation procedure against a reference tethered device.
A significant correlation was observed between the two systems (Spearman's
The two systems differed by 3.5% in assessment of
The Bland–Altman plot showed the 95% limits of agreement lower than 10.8 cm·s^{−1} between the two systems in
As regards validation of instantaneous velocity, an RMS difference of 11.3 cm·s^{−1} was observed that is comparable to the precision of the reference system. The maximum instantaneous error was 18.2 cm·s^{−1} that corresponds to a relative error of 9.7%. One source of the difference between the velocity estimated by our method and the velocity measured by the reference is a small artifact due to the nonrigidness of the swimming suit. Nevertheless, the custom designed swimming suit used to fix the sensor did not allow the sensor to move drastically and kept the artifact within a tolerable range. Moreover, during high accelerations when the artifact is more pronounced, the random bias of accelerometer is less significant (higher signal to noise ratio) which leads to acceptable results [
Indirect validation of instantaneous velocity by IVV in
Another observation from
The ability of the inertial sensor to distinguish the variability of the movement of the subjects with different performance levels propounds the application of the inertial system in the study of swimming velocity. The capacity of our system to detect IVV changes also provides important evidence that our velocity drift removal method does not cancel out the velocity variations. Indeed, different swimming trial regimes were recognized based on changes of acceleration magnitude. These regimes are treated separately to mitigate the effect of the velocity drift and thereof variation of velocity signal was well maintained.
Signal segmentation using GMA is the core of drift removal in our method. Therefore, investigating the effect of changing the segmentation threshold in GMA can be illustrative of the method's robustness. To this end, the threshold in the GMA algorithm was shifted 5%. The effect of this change on the estimation is shown in
Our dataset includes only one type of initial condition (swimming starts from a relatively motionless posture in water followed by a wall push) that is a subset of possible initial conditions in swimming. However, the study of other initial condition was not feasible within the scope of our experiment for practical reasons. Since the tethered reference only measures the velocity in forward direction of swimming, comparison of the multi lap data with turns between the IMU and the tethered device was not realizable. Although diving from the start block was a possibility, we avoided it for two practical considerations. Firstly, during the diving period calculation of the parallax effect on the velocity measured by the tethered reference is not possible. Secondly, avoiding the dives we could collect more stroke cycles which augments the statistical power of our study.
The algorithm we proposed in this paper, despite providing timely results, should not be misinterpreted as being real time. The data stream of one complete lap serves as the input of our algorithm since the correction is performed per lap. For a near realtime implementation of our method a crucial step is to determine the cycle mean velocity without using prior information about pool length.
The proposed method presents a reliable IMUbased system that can be practically used to measure the swimming velocity as the most intuitive metric of the athlete's performance. The system is usercentric meaning that several athletes can wear their own sensor at a time without interfering with the other athletes' measurements. Development of such a tool can help coaches pinpoint the strengths and weaknesses of the athletes during workout sessions and design an optimal personal training plan for athletes to improve their performance.
Accurate measurement of swimming velocity allowed the assessment of intracycle variability, an important determinant of swimming efficiency. Analysis of swimming velocity along with other parameters such as coordination [
The authors wish to thank Arash Salarian for his technical advice. The work was supported by Swiss National Science Foundation (SNSF), grant No. 320030127554.
The inertial sensor with water proofing box and its placement. The global frame
Angular velocity in
Intermediate steps of velocity profile calculation (
A typical result of velocity calculation using IMU (Solid line) compared to the reference tethered apparatus (dotted line).
BlandAltman plot, representing mean (xaxis) and difference (yaxis) between the
Statistics of the measurement population. All variables are presented as mean ± standard deviation. V_{100} shows the average of best personal 100 m timing.
Elite  6  5  20.3 ± 3.3  177.8 ± 9.6  69.2 ± 10.5  1.68 ± 0.17 
Recreational  12  7  15.5 ± 2.8  171.3 ± 11.5  60.2 ± 12.2  1.34 ± 0.27 
Average velocity of the trials as measured by the two systems are shown under Measured Mean Velocity column. Cycle mean velocity (

 

Reference (m·s^{−1})  IMU (m·s^{−1})  Error (cm·s^{−1})  nPVI (%)  
Trial1  333  1.1 ± 0.1  1.1 ± 0.1  0.8 ± 5.2  3.9 
Trial2  347  1.2 ± 0.1  1.2 ± 0.1  1.1 ± 5.4  3.6 
Trial3  370  1.4 ± 0.2  1.4 ± 0.2  0.7 ± 4.9  3.1 
Trial4  398  1.6 ± 0.2  1.6 ± 0.2  −0.1 ± 5.8  3.4 
Total  1448  1.4 ± 0.2  1.4 ± 0.2  0.6 ± 5.4  3.5 
Comparison of intracyclic velocity variation (IVV) between the two systems for elite and recreational groups in different trials. ^{a}


 

Mean  Std  Mean  Std  Accuracy  Precision  
Trial1  Elite  109  14.4 ^{a}  3.9  11.8 ^{a}  3.7  2.6 *  1.7 
Recreational  224  19.7 ^{a}  6.2  17.8 ^{a}  7.1  1.8  4.5  
Trial2  Elite  111  17.5 ^{b}  2.7  12.3 ^{b}  4.2  5.1 *  2.3 
Recreational  236  23.3 ^{b}  4.6  20.6 ^{b}  4.9  2.7 *  3.5  
Trial3  Elite  117  17.2  3.7  12.7  4.6  4.6 *  3.1 
Recreational  253  20.6  3.6  18.5  5.1  2.0  3.8  
Trial4  Elite  120  13.7 ^{b}  5.6  9.7 ^{b}  6.6  4.1 *  2.1 
Recreational  278  19.6 ^{b}  3.4  15.4 ^{b}  6.2  4.2 *  4.0 
The effect of changing the segmentation threshold of geometric moving average (GMA) by a factor of 5% on velocity estimation. Estimation error in the cycle mean velocity (MEAN ± SD) and instantaneous velocity (RMS) are presented.
 

Cycle Mean ( 
Instantaneous  



0.15

0.3 ± 8.2  16.8 
0.25

0.5 ± 6.8  12.9 
Correction; To make the paper easier to read, Equation (10) on page 12392 is listed again in the below. (PDF, 18 KB)