The proposed system consists of 2 parts: a resistive pressure-sensitive mat constructed with an FSR sensor array and the electronic system. The mat is composed of 3 layers. One layer contains thin and flat copper wires distributed in a column arrangement along a flexible 3D printed grid; another layer is composed of the same copper wires but distributed in a row arrangement on another flexible 3D printed grid. A third layer is placed between the layers consisting of Velostat material, a pressure-sensitive material that behaves as a resistor whose value drops whenever pressure is exerted upon it. In this way, variations on the resistance values on every intersection of rows and columns when pressure is exerted over the mat can be measured. Some typical characteristic problems with Velostat material are repeatability, nonlinearity, and hysteresis [23,24]. For this application, however, these features are not relevant because high precision is not needed; the mat only needs to be able to detect a heavy body placed on it (average human body weight). More information about the development of this mat is documented on the work of Medrano et al [25].

Figure 1 shows the different layers of an FSR matrix with smaller dimensions (4 rows and 4 columns). Figure 2 shows an example of the placement of the overlapped layers. The total sensing area of the mat used for this study is 30×30 cm, with 16 rows and 16 columns, 1 cm width each. This way, the area of each of the individual FSR sensors is equal to 1 cm². In Figure 3, a developed mat is shown.

Due to the number of operations needed for a full scan of the mat, a high frequency microprocessor must be used for data processing, as the time complexity of these operations grows in exponential order. The STM32F103C8T6 microprocessor (STMicroelectronics) was selected due to its 72 MHz CPU frequency, with which a sampling frequency of 200 Hz is achieved. Other microprocessors with lower CPU frequencies (like the ATmega328P, Microchip Technology Inc) would not achieve the desired sampling frequency. Also two 16-1 multiplexers 74HC4067 are needed for an efficient scan process of the whole mat. For data transmission, a Bluetooth HC-05 module is used. Bluetooth technology was selected due to its ease of connection with different devices, especially with smartphones and tablets, which offers health care professionals the choice of an easy-to-transport monitoring device. Other electronic elements included in the system are a TP4056 battery-charging module and a Lipo battery of 3.7 V and 150 mAh capacity, allowing continuous functioning of the system for up to 2 hrs. A block diagram of the proposed system is shown in Figure 4.

The algorithm used for this system consists of calculating the summation of every FSR sensor of the mat. For each FSR sensor, the voltage value obtained by the analog-to-digital converter of the microcontroller is given in bits (from 0 to 4095), and this resulting value is used for the calculations. A threshold is used for the system to decide whether a person is standing on the mat or not. To calculate an appropriate value for this threshold, data were collected from 16 volunteers (5 female and 11 male), with an average weight of 74.81 (SD 15.25) kg and foot size of 26.93 (SD 1.94) cm. The volunteers were asked to stand on the mat barefoot in 4 different positions: with both feet standing still and on their forefoot and with one foot standing still and on their forefoot. Maximum values of pressure exerted on FSR sensors were used as reference for normalization, and the minimum value for activation of FSR sensors was considered as no volunteer standing on the mat.

Using such criteria, on average when standing still over the mat with both feet subjects activated 71.66% of the FSR sensors, and when standing on their forefoot with both feet, 28.9% of the FSR sensors were activated. When standing still and on their forefoot with only one foot an activation of 40.37% and 18.40% of the FSR sensors was registered, respectively. The minimum value of FSR sensors activation is registered when standing on one foot on their forefoot, with a value of 12.09%. All results are summarized in Table 1. By taking these results into account, and if it is assumed that volunteers may land first with one foot on their forefoot after a jump, a proper threshold should be proposed below the minimum value of FSR sensors activation. For this study, a threshold of 9% of FSR sensors activation is used. This threshold was chosen to be at three-quarters between the zero FSR sensor activation and the minimum FSR sensor activation recorded, to avoid any misreading from mechanical oscillation. It is worth noting that the minimum recorded value from sensor activation is an outlier. In future studies, the possibility of adding a personalized threshold for every subject could be assessed.

For every position sensor activation percentage, a correlation analysis with the weight and foot size of the volunteers was performed. Analysis suggests that sensor activation is only moderately impacted by the weight of volunteers, and foot size of volunteers has a low impact on sensor activation. In Table 2, correlation values for different positions analyzed on the mat are shown.

To calculate the height reached by the user during the vertical jump, when the subject jumps and there is no contact on the mat, the system counts the elapsed time until the subject lands on the mat again (flight time), and with the calculated time the flight-time formula is used [3,8,9,14,16] to predict the height reached. This formula is defined as: Height = g∆t²/8, where g is the constant value of gravity force g=9.81 m/s² and Δt is the flight time obtained by the system. Once the height of the vertical jump is obtained, this value is wirelessly sent via Bluetooth to the monitoring device selected by the health care professional.

Two different experiments were performed. The purpose of the first experiment, in which 38 volunteers participated, was to validate the reliability of the proposed system. For the second experiment, the objective was to compare the effects of different sampling frequencies when calculating the height reached on the jumps, and 15 volunteers participated. The protocol used for each experiment is the same. For the first experiment, data are directly processed by the microcontroller and the predicted value is sent to the selected monitoring station. In the second experiment, raw data are obtained to perform an offline downsampling to analyze the effects of different sampling frequencies on the predicted result.

Researchers asked for assistance from a sports and fitness center to recruit volunteers who attended the center regularly for physical training. Researchers visited this center with all the necessary equipment for the implementation of the protocols, and installed it in an area specified by the managers of the center. No specific physical attributes were required from the volunteers, as these characteristics should not affect the performance of the system. Researchers approached people at the center, explained the purpose of the study, and politely asked for their collaboration on the protocols if they were available at any given moment. Before starting any trial, volunteers were asked if they had any kind of injury that could affect their physical integrity when performing the protocol, and if so, the trials would not proceed. Every volunteer gave their written consent for the performance of the proposed protocol. The countermovement jump (CMJ) and countermovement jump with arm swing (CMJAS) techniques were selected for this protocol. These jumping techniques are commonly used as a measure to assess the overall force and explosive power of the lower body muscles on a person [26], and it is considered as the most reliable jumping test for this purpose [27]. By adding an arm swing to the CMJ, with the proper technique, the height reached by the person is increased around one-third and up to two-thirds [28-30], which increases the dynamic range of data obtained.

In the proposed protocol, volunteers were asked to stand on a marker placed on the center of the mat and perform 3 medium-to-maximal effort CMJs, with their hands fixed at the waist, with 5 to 10 seconds rest between trials. This technique is depicted in Figure 5. After these jumps, the volunteers were asked to perform CMJAS this time, and following the same scheme. This technique is depicted in Figure 6. As a reference system, all trials were recorded on video with a high-speed camera (120 fps). The camera was placed 1.3 m away from the mat, perpendicular to the sagittal plane of the volunteer and 20 cm above the ground, held by a tripod. The setup for this protocol is depicted in Figure 7.

To measure height reached by the subject with the video reference, the takeoff and landing frames were selected manually like in the studies of Balsalobre-Fernandez et al [11,22], and height was calculated by using the elapsed time between the frames using the flight-time formula.

For the first experiment, a total of 228 jumps (114 CMJs and 114 CMJASs) were performed for each, the proposed system and the video reference. An example of the recorded jumps is shown in Figure 8.

To analyze the proposed system performance, mean relative error (MRE) and mean absolute error (MAE) were calculated for the overall jump trials and for each technique, CMJ and CMJAS. The MRE obtained from all 228 trials was 1.98%. For CMJ and CMJAS, relative errors were 2.17% and 1.78%, respectively. MAE obtained from all jump trials was 0.38 cm, and for CMJ and CMJAS, the errors obtained were 0.34 cm and 0.42 cm, respectively. These results are summarized in Table 3.

Correlation and Bland-Altman analyses were performed from data obtained and are shown in Figure 9 and Figure 10, respectively. Correlation analysis shows a coefficient of determination of R²=.996. These analyses demonstrate that the proposed system not only has a high correlation, but it shows that the difference of the two paired measurements is really low, which means that both methods produce systematically the same results.

In Figure 11, the normalized MAE and MRE are shown for different ranges of jump heights reached. By analyzing the different ranges of height reached by the volunteers, which are <10 cm, 10 to 20 cm, 20 to 30 cm, and >30 cm, MREs obtained were 2.38%, 2.07%, 1.90%, and 1.54%, respectively. MAE obtained were 0.18 cm, 0.31 cm, 0.46 cm, and 0.50 cm, respectively. From this data, no significant difference can be found. However, it can be noticed that MAE increases as jump height increases, while MRE decreases.

Figure 12 shows the charts with distribution of the heights reached by the volunteers when performing the jump trials. For CMJ, no volunteer was able to surpass the 30 cm height. However, by adding the arm swing, 22% of the volunteers surpassed the 30 cm height. Also, for CMJAS trials, 47% of the subjects reached a height ranging from 20 to 30 cm, compared with CMJ, in which only 31% of the subjects reached this height.

In this experiment, the effects of different sampling frequencies were analyzed. Raw data from the system was obtained for a total of 90 jumps (45 CMJs and 45 CMJASs). An offline emulation of different sampling frequencies was performed through downsampling of this raw data. This means samples are removed to emulate a slower sampling frequency. With this method, and with the base sampling period of 5 ms from the system, 200 Hz, 100 Hz, 66.6 Hz, 50 Hz, 40 Hz, 33.3 Hz, 28.5 Hz, 25 Hz, 22.2 Hz, and 20 Hz frequencies were emulated.

Similar to the first experiment, the error was calculated using the high-speed camera as reference. For this analysis, only MRE was obtained for each sampling frequency to assess which frequencies are able to maintain a relative error below 5%. Results show that sampling frequencies of 200 Hz, 100 Hz, and 66.6 Hz have similar performance, with relative errors of 1.88%, 2.22%, and 2.88%, respectively. However, the maximum error among the 90 trials increases considerably between these frequencies, with maximum errors of 5.27%, 7.02%, and 8.25% for each respective frequency. Sampling frequencies of 50 Hz, 40 Hz, and 33.3 Hz also show good performance regarding the relative error, which is maintained below 5% for the 3 cases, but the maximum relative error found in these 3 frequencies is considerably higher than the found in the previous set.

In Table 4, MRE and maximum and minimum relative errors found among trials for the different sampling frequencies are shown. With slower sampling frequencies, MRE increases exponentially as shown in Figure 13, which suggests that sampling frequencies equal to or below 28.5 Hz are not reliable enough to maintain MRE below 5%. Also, sampling frequencies slower than 50 Hz and 33.3 Hz show maximum relative error among trials higher than 10% and 20%, respectively.

Table 5 shows how MRE is distributed in different ranges. Only 200 Hz and 100 Hz sampling frequencies are able to maintain 95% of their results within 5% of relative error. Also, sampling frequencies slower than 50 Hz considerably increase the percentage of relative errors found above 5%. These results suggest that sampling frequencies of 200 Hz and 100 Hz are the most reliable, frequencies of 66.6 Hz and 50 Hz have an acceptable performance, and the remaining sampling frequencies are unreliable for this specific application.

When MRE is obtained from different jump heights (≤10 cm, 10 to 20 cm, 20 to 30 cm, and >30 cm) at each sampling frequency, the relevance of a proper sampling frequency when calculating height reached for small jumps (<20 cm) is observed. When using sampling frequencies slower than 50 Hz, MRE obtained from these small jumps is always higher than 5%, and for the slowest sampling frequency, MRE reaches a value of 21.50% for jump heights smaller than 10 cm. For higher jump heights, an increase in MRE (>5%) is noticeable for sampling frequencies slower than 40 Hz, reaching a value of up to 9.15% for the slowest sampling frequency. A summary of these results is shown in Table 6.

The vertical jump is a test commonly used by health care professionals to assess strength in the lower limb muscles of a subject. Although this test is widely used for strength assessment among athletes, relevant information can be obtained from people with no relevant sports background.

An important point to highlight about the system developed in this study is its low price. The total for components used in construction is approximately US $40. In comparison with commercially available devices, this developed system is significantly more affordable. Among the devices commonly used on medical and sports fields to measure vertical jump height are the vertical jump test mat (Gill Athletics) [31], Just Jump system (Perform Better) [10,32], Vertec device (Gill Athletics) [10,33], electronic vertical jump tester (Gill Athletics) [34], Optojump testing (Perform Better) [12,35], and bilateral force plate (Hawkin Dynamics) [18,36]. Our proposed system will have to pass through different standards and certifications (like ISO standards [37]) before it can be considered as a standard medical device. Table 7 shows a comparison of prices between commercially available devices and the system proposed here. Prices of the commercially available devices are listed as found at the moment of writing this article.

Throughout data capturing in both experiments, some important points can be highlighted. Despite the advantages that the proposed system and reference device offer, both have an inherent error due to their sampling frequency (more specifically due to their sampling period). The proposed system has a sampling frequency of 200 Hz, and thus the sampling period is 5 ms. Likewise, the reference device has a sampling frequency of 120 Hz and a sampling period of 8.3 ms. This means that every sampling period each device updates its readings, which implies an uncertainty of the sampling period between data updates. In other words, there is an inherent uncertainty in the system during the takeoff and landing phases of the jump, time span that is used to calculate height reached. From both phases, the proposed system has a total uncertainty of 10 ms, while the reference device has a total uncertainty of 16.6 ms. This inherent error is characteristic of electronic devices and directly related to their sampling frequency. Nonelectronic methods for jump height measuring lack of this inherent error, but as stated before, these methods tend to overestimate obtained measurements and are less precise.

Regarding the high-speed camera used as a reference device, when the recorded videos were analyzed, the ease of selecting the correct frames depended on the correct technique execution of the volunteer: taking off from both forefeet at the same time during the takeoff phase and landing with both forefeet at the same time during the landing phase. This was the ideal technique execution. On the other hand, some volunteers either took off or landed with only one forefoot and not with the same foot in some occasions. In such cases, it was harder to select the takeoff and landing frames. This is difficult for volunteers to control without long-term training in the proper technique.

On the proposed protocol, the inclusion of two different jump techniques proved to be useful in order to increase the dynamic range of the data. The difference between the CMJ and CMJAS was significant. The addition of an arm swing increased jump height an average of 44.84% in the first experiment and 34.86% in the second experiment.

One of the main limitations of the developed system was its sampling frequency. Although the microcontroller used had a high CPU frequency, the sampling frequency was limited because of the number of operations needed for a full scan of the mat (16 rows and 16 columns, a scan of 256 individual cells) and number of operations this implies. Another limitation was the total sensing area of the system of 30×30 cm. Although no volunteer reported discomfort, the total area limits the stance of volunteers; in addition, the landing phase of every jump trial must be performed in a controlled manner, so the volunteer lands inside this area.

These limitations can be solved in future versions of the mat. The design of the mat can be modified to increase its total sensing area and the size of each row and column, so in this way with fewer number of rows and columns the same sensing area could be achieved, thus increasing the sampling frequency of the system. However, this would diminish the resolution of the system.

In this study, a novel low-cost system for measurement of the jump height is proposed. Two experiments were performed—one to validate the system and the other to assess the effects of different sampling frequencies.

When evaluating the performance of the proposed system in the first experiment, results show that with the proposed sampling frequency of 200 Hz relative error for all of the 228 jump trials is maintained below 5%. In the second experiment, with sampling frequencies of 200 Hz and 100 Hz, relative error is maintained below 5% for 98.89% and 94.44% of the jump trials, respectively.

The flight-time formula is a widely used, validated method to calculate height reached during vertical jumps. A high-speed camera as reference device has been used in related studies along with the flight-time formula, proving to be a reliable tool. Our first experiment showed through correlation and Bland-Altman analyses that the proposed system and a high-speed camera reference device produced systematically similar results when calculating jump height.

Our second experiment concluded that 200 Hz and 100 Hz sampling frequencies have similar performance, and both frequencies are reliable when calculating jump height using the flight-time formula. This implies that if access to hardware capable of processing data at 200 Hz were limited, hardware capable of processing data to at least 100 Hz could offer similar results. However, if higher sampling frequencies are available, they should be used.

These results demonstrate that the proposed system is as reliable as a commercially available device, and the selected sampling frequency of 200 Hz is reliable for obtaining relative errors below 5% for at least 95% of the jump trials. The proposed system offers an alternative for health care professionals to use a mobile monitoring station of their choice, and its price is more affordable than commercially available devices.