Design and Characterization of a Wearable Inertial Measurement Unit

1. Introduction

The use of inertial measurement units (IMU) as wearable sensors is continuously expanding in various domains, including healthcare [1] [2], sports [3], rehabilitation [4], and human computer interaction [5]. The improvement and innovation in sensor technology is a key requisite to such expansion.

Each specific application of inertial measurement units (IMUs) is characterized by unique operational demands, leading to diverse usage modalities under a wide array of conditions. These units are affixed to various segments of the human body, and the signals of interest may include distinct subsets of accelerometers and gyroscopes, as well as different spatial orientations of the device. In some applications, such as energy expenditure estimation, these signals are sampled over long periods of time with signals of interest at low frequencies, ranging from 3 to 15 days at between 20 Hz and 100 Hz. Others, such as sports analysis, require sampling for just a few minutes with signals at frequencies closer to 1 kHz [6].

Because of this variability of needs, there is a wide and growing offer of devices of this type on the market, usually with closed characteristics suitable for a specific type of monitoring problem [7].

Our interest lies in developing a general-purpose, configurable wearable device capable of capturing both high-frequency signals for precise, short-term monitoring and low-frequency signals for extended monitoring. This device aims to optimize energy consumption and storage capacity, essential for enhancing its operational efficiency and usability in various monitoring contexts. Additionally, we intend for this device to serve as an affordable alternative to gold-standard systems such as the Xsens, making advanced monitoring technologies more accessible while maintaining a high level of accuracy and reliability.

This requires precise control of the hardware, as well as rigorous characterization of the device’s performance, so that it can be optimized while maintaining the accuracy and robustness that will be required for its use in applications.

In this paper the first iteration of the design of such wearable sensor is presented, with emphasis in its evaluation and characterization [8][9][10]. The device was assembled and then analyzed in several aspects: power consumption, sampling performance and error characterization.

The results show a good response and put on the spotlight the most critical optimizations needed to improve the device to reach the goal of a smart general-use unit for human motion monitoring.

2. Materials and Methods

After a series of preliminary tests, a sensor capable of satisfying the best consumption/performance ratio in the context described above was selected. The optimization of components and smaller hardware resources was also started, seeking to increase the density of components on the PCB, by means of 0402 resistors and capacitors, suppressing unnecessary sockets, etc.

2.1. Description of the sensor

The LSM6DSL IMU sensor from STMicroelectronics was selected [11]. This choice is motivated by the elimination of the magnetometer component, its low power consumption, and its specific performance as a sensor for use in wearables, as shown in Table 1 for the main characteristics of the sensor.

2.2. Description of the Microcontroller

The selected control unit is the STM32L051[12] low power microcontroller from the same manufacturer as the sensor. The characteristics of this unit meet our requirements for the integrated peripherals minimizing the consumption. It is also available with a pinless package and 7 mm wide, which together with the elimination of the external clock optimizes the space on the PCB, as detailed in Table 2 for the main characteristics of the microcontroller.

2.3. Description of the Device Design

The device design consists of two PCBs placed on both sides of the battery and connected by a flex cable as can be seen in Figure 1. On the main side most of the system components are located on the other side only the SD card socket and the contacts for the socket. This saves space and miniaturizes the entire assembly.

For battery management, the circuit utilizes the STNS01PUR integrated chip, which combines a battery management system (BMS) for safe charging with a 3.1V LDO voltage regulator. This chip provides overcharge, over-discharge, and overcurrent protection to prevent the battery from being damaged under fault conditions. Additionally, it features a charger enable input to stop the charging process when battery overtemperature is detected by external circuitry.

When shutdown mode is activated, the battery power consumption is minimized to less than 500 nA, maximizing battery life during shelf time or shipping. The battery used is a 220mAh 402030 LiPo with an integrated NTC thermistor.

To simplify the device’s operation and eliminate the need for push buttons, we have opted to utilize the tilt function of the IMU accelerometer. The test parking functionality (sync SD) is activated by shaking the sensor when it is tilted beyond a specific threshold of 4g. This feature is employed to enhance the device’s functionality. Additionally, a low-power RGB LED is used to indicate different modes and sensor states. It achieves this through a combination of its three colors, and patterns of continuous or intermittent flashing, as well as fading in and out.

2.4. Test Procedures

This section details the test procedures used to validate and assess the proposed system’s performance. We systematically evaluate the solution’s accuracy, reliability, and efficiency, highlighting its potential in high data capture rate scenarios.

Before obtaining any result, the IMU box alignment matrix is calculated to ensure accurate orientation of the device axes relative to the box axes within the device. The experiment begins by aligning each box axis with gravity as a consistent reference. This alignment is done by placing the device in the end effector of a UR3 robot (Figure 2. The theoretical acceleration matrix A represents ideal outputs under perfect alignment, while the measured matrix B records actual outputs given the current device orientation. The alignment matrix R is derived as

$$R_{3\times 3}=A_{3\times m}{\left(B_{m\times 3}^T\right)}^{-1}$$

(1)

This misalignment was quantitatively assessed and corrected using an alignment matrix. As depicted in Figure 3, the original signal exhibited noticeable discrepancies when compared to the corrected signal. After applying the calibration matrix, the corrected signal demonstrates a significant improvement, closely matching the intended orientation and minimizing the observed deviations.

2.4.1. Sampling Frequency

In evaluating the LSM6DSL and STM32L051K8 system, we focused on the constraints of the SPI communication protocol. Using a digital analyzer, we scrutinized the SPI signals between the sensor, microcontroller, and SD card memory. We specifically adjusted the sensor’s sampling frequency at various rates to identify the point at which the SPI buffer becomes saturated.

The sensor has been precisely configured to operate within a measurement range of ±4g for acceleration and 250 degrees per second (dps) for angular velocity.

2.4.2. Power Analysis

A systematic approach was employed by integrating a 0.1 $\Omega$ shunt resistor for precise current measurement. Additionally, a FLIR E60 camera was utilized to analyze temperature variations, enhancing the assessment of thermal dynamics within the system. This setup allowed for the monitoring of charging efficiency and thermal performance under various operational conditions and modes. The documentation and analysis of energy consumption across different states provide a comprehensive understanding of the system’s energy dynamics, facilitating phase optimization.

2.4.3. Standard Deviation

The standard deviation (2) is a statistical measure that quantifies data dispersion and, within the scope of this study, enables the evaluation of consistency and precision of measurements along each axis. The method employed to calculate this parameter involved the sensor collecting data over a 10-minute duration. The sensor was situated on a stable, vibration-isolated table, Figure 2.

$$s=\sqrt{{\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^N{(x_i-\overline{x})}^2}$$

(2)

2.4.4. Drift

Drift refers to any systematic change or undesired variation in sensor measurements over time, occurring independently of external changes in operating conditions. To characterize drift, the sensor was placed in a stable, anti-vibration table for 24 hours. Subsequently, a linear regression analysis was applied to estimate the drift along each axis (x, y, and z).

2.4.5. Fixed Bias

The fixed bias represents a consistent error in sensor measurements that is inherent due to its systematic nature. To neutralize this error, measurements from opposite directions are summed, which effectively doubles the fixed bias for each sensor type (3). Samples were collected over 150 seconds by positioning the device at opposite angles for accelerometer readings along each axis, and by applying reverse angular velocities for each axis during the gyroscope evaluation using a robot arm, as illustrated in Figure 2.

$$Bias={\displaystyle \frac{1}{2}}[s_x^{+}+s_x^{-},s_y^{+}+s_y^{-},s_z^{+}+s_z^{-}]$$

(3)

2.4.6. Scale Factor

The scale factor measures how the sensor responds to specific measurements within its range. It is calculated by subtracting the averages of two measurements to eliminate fixed bias effects and then doubling the sensor output (4). For accelerometers, the specific reference measurement is local gravity, and for gyroscopes, it is the rotational speed of the device.

$$Scal{e}_{\mathrm{acc}}={\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{s_{ref}}}[s_x^{+}-s_x^{-},s_y^{+}-s_y^{-},s_z^{+}-s_z^{-}]$$

(4)

2.4.7. Power Spectral Density

Following [10], noise characteristics were analyzed using power spectral density. In this analysis, the sensor was kept at rest for ninety minutes during two separate tests. Power spectral density (PSD) quantifies the intensity of unwanted signals across different frequencies, providing insights into the sensor’s response to environmental variations and electronic interferences. This comprehensive analysis is crucial for understanding the sensor’s operational fidelity under real-world conditions.

2.4.8. Allan Deviation

The Allan deviation test was also conducted as described in [10]. The sensor was kept at rest for ninety minutes during two separate tests. The Allan deviation assesses the stability of the sensor’s measurements over time, identifying the types of noise that affect the sensor. This detailed examination is essential for determining the long-term reliability and accuracy of the sensor in various operational scenarios.