An Algorithm for Detecting the Minimal Sample Frequency for Tracking a Preset Motion Scenario

Published Online August 2020 in MECS

Modern inertial sensors manufactured using MEMS (Micro-Electro-Mechanical Systems) technology have numerous advantages, including small size, light weight and low power consumption, which makes them wearable. Moreover, such sensors are self-containing, i.e., one does not need any external tools for tracking the position and attitude of an object supplied with such sensors, both indoors and outdoors. The latter property coupled with the possibility to embed MEMS inertial sensors into clothes and footwear gives rise to a variety of applications, primarily in human motion capture systems. Constant tracking motions and position of aging or convalescent people in their natural living environment helps understand the cause of many diseases and thus provides valuable information for medical diagnosis and/or feedback on the treatment efficacy. Among the common neurological problems that affect human motor functions are Parkinson disease, multiple sclerosis, stroke, traumatic brain injury, and spinal cord injuries [1]. If a patient is supposed to perform exercises on their own, a human motion capture system can replace surveillance from medical personnel. Fall detection systems are another popular research subject, since they can mitigate the fall consequences by reporting a fall straightaway after it occurred and calling for immediate medical help. Inertial sensors are helpful in analysis of sport activities for performance assessment and injury prevention [2]. Another vast application area relates to classification of an employee’s movements as correct or incorrect. A lot of recent research results have been published on gait analysis and classification of human activities. Besides, human motion capture is used in humanmachine interaction, user authentication [3], robotics and telemedicine [4]. The appearance of MEMS inertial sensors became a decent means to overcome the inherent limitations of other motion capture systems – optical, structured light, acoustic, magnetic and mechanical ones. Commercial optical systems such as Vicon or Optotrack are considered to be the gold standard in human motion capture due to their high accuracy. The benefits of inertial sensors are corroborated by the variety of commercially available IMUs and IMU-based systems manufactured by Invensense and Microstrain (the USA), Trivisio (Germany), and XSens (The Netherlands) [5].

However, MEMS inertial sensors have their limitations [6]. Most researchers focus on filtering algorithms to process noisy measurements. However, the performance of any filtering algorithm is highly dependent on the discretization time, especially for non-linear filtering problems. That is why the selection of sensors with a suitable sample frequency is of key importance, since it will be extremely difficult to extract meaningful information out of seldom and faulty sensor readings. Surprisingly, the problem is not paid the attention it actually deserves. Our aim is to develop an algorithm for calculation of the minimal sample frequency suitable for tracking a specific rotational motion. The algorithm would help the embedded software engineer choose the right gyroscope when designing a motion tracking system from scratch.

2.    Related Work

A lot has been published on tracking human motion. One can distinguish several main research directions. A large research area concerns usage of smartphones for recognition of their owners’ basic daily activities. Modern smartphones are supplied with various sensors such as 3D accelerometers and magnetometers, compasses, proximity sensors, GPS, digital cameras and microphones. Such equipment coupled with the total ubiquity of smartphones make the latter useful for scientific and clinical research, for instance in healthcare and physical activity monitoring. Ref. [7] studied the applicability of smartphones for clinical motion research. The authors showed that smartphones could be used to assess range of motion and joint angle measurement for postural and gait control. They benchmarked performance of different smartphone sensors against an Xsens product. Ref. [8] proposed a human fall monitoring system comprised by a portable sensor unit including a 3D accelerometer, a 3D gyroscope and a 3D magnetometer and a cell phone. However, with cell phones, researchers face the following problems. Firstly, movement of a phone depends on where it is placed on the owner’s body. Secondly, people carry their cell phones in different orientations, thus the gravity affects accelerometer readings differently. Thirdly, the variety of hardware models and operating systems cause challenges to activity recognition. Finally, energy-efficiency is always an issue with cell phones. Hence, the main research topics in this field are light methods for user-, orientation- and hardware-independent activity recognition.

Smartphones are not an option in industrial context, where occasional misclassifications of human activities are intolerable. Thus a plenty of specially designed devices appeared. In contrast to smartphones, such devices can afford more complicated recognition algorithms because they are not that restricted in battery consumption and computational complexity. One of the main research topics in this case is the required amount and location of sensors and suitable recognition methods depending on complexity, periodicity, and dynamicity of activities to be analyzed. In [9] a human body motion tracking system was introduced. Ref. [10] proposed a small-sized cheap-to-manufacture measurement system suitable for spatial orientation of the foot, detection of gait cycle phases, assessment of motor activity, etc. The system implements algorithms for determination of the orientation of objects within three-dimensional space using an integrated triaxial MEMS system, magnetometer, and Madgwick’s AHRS sensor fusion algorithm. Ref. [11] evaluated the accuracy of postural human motion tracking based on miniature inertial sensors. Ref. [1] demonstrated that wearable inertial sensors can be used to develop metrics for objective measurements of tremor and dyskinesia in individuals suffering from Parkinson’s disease, whereas the authors of [12] developed an inertial ambulatory monitoring system that provides a complete motor assessment of tremor, bradykinesia, and hypokinesia. Ref [13] presented a novel interactive method for recognizing handwritten words using inertial sensors included into smartwatches.

Ref. [14] introduced three strategies to measure motions of classical cross-country skiing, ski mountaineering, alpine ski racing and outdoor walking over long distances (several kilometers). These strategies found an articulate implementation in a system for alpine ski racing, which is highly dynamic, i.e., characterized by fast direction changes, high speeds and the absence of static or slow phases. The proposed methods rely only on inertial sensors and magnetometers. Nevertheless, they provide position, attitude and speed information with an accuracy close to the “gold standards”. For each activity specific biomechanical constraints and movement dynamics were exploited. The authors emphasize the role of the sample frequency. They pinpoint two error types for signal sampling: signal losses caused by an insufficiently high sampling frequency and inadequate low-pass filters at analogue-to-digital conversion. Signal losses are especially likely to occur for rapidly changing movements such as foot movements during gait. The IMU’s sampling frequency used in [14] was 500 Hz, which the authors found to be sufficient for their gyroscopes to measure all movements accurately. Ref. [15] discussed fusion of GNSS with data from inertial and magnetic sensors in order to analyze performance in alpine ski racing. The authors sampled magnetometer data at 125 Hz and data from 3D accelerometers and gyroscopes at 500 Hz. The same sample frequencies were used in the experimental setup of [16]. In their experiments two inertial sensors were attached to the right shank and thigh of a skier. Ref. [17], among other valuable dissertation results, discusses the influence of accelerometer sample frequency on the recognition rate when classifying different swimming styles (two different sensor locations were considered). Besides, in order to reduce battery consumption, the researcher exploits the characteristics of long-term activities: if one was cycling for a while, it is most likely that the same person will be still cycling at the next moment. In his thesis [17] Pekka Siirtola took an original 50 Hz, formed 5 Hz, 10 Hz and 25 Hz signals by picking each 10th, 5th or 2nd point correspondingly and recorded the recognition rate of three periodic activities – freestyle, breaststroke and backstroke swimming – for each sample frequency. He revealed that the recognition rate did not suffer much from the sample frequency reduction. The role of the underlying hardware is proven by the results obtained by the same author. The recognition rate of five typical human activities (walking, running, cycling, driving a car and idling) turned out to be slightly higher for a Symbian smartphone than for an Android smartphone.

According to [18], a sample frequency 100 Hz is enough for capturing active human motion in sufficient detail. Ref. [19] presented an implementation of a system for 3D attitude measurement and estimation using a magnetic and inertial measurement unit and a Kalman-filter based sensor fusion algorithm. They stated the used sample frequency 200 Hz. The researchers benchmarked their results against traditional optical motion capture systems. Ref. [20] investigated the impact of the amount, location and type of inertial sensors on the accuracy of activity and posture recognition. The authors used Xsens-MTx sensors, each equipped with a 3-axis accelerometer, 3D gyroscope and 3D magnetometer, with the sampling frequency 6 Hz. According to [21] and [22] sampling frequencies exceeding 50 Hz should be used. However, in [23] experiments at the frequency of 2 Hz proved to be successful – eleven activities were distinguished with the average recognition rate of 85%.

Ref. [24] studied the influence of different sampling rates on the recognition accuracy of ten daily activities. The research results prove that the reduction of sampling frequency from 100 Hz to 5 Hz affects different activities in a different way. The worst effect was observed for a walking activity. Ref. [25] introduced a system that utilizes a wearable device and an effective quaternion algorithm for timely fall detection. The system distinguishes a fall from normal everyday activities and alarms the caregivers. In accordance with [25] 100 Hz is a proper sample frequency for human fall detection. However, [26] sampled signals of inertial sensors at 10 Hz. The reason was that the authors made their fall detection system upon a combination of inertial sensors and a location system Ubisense. The latter has a limited sample rate and the authors preferred to synchronize all the readings. Wireless IMUs were used in [27] in combination with the Kinect sensor whose sampling frequency is too low for capturing fast movements (25–35 Hz) and cannot be controlled by the user. Such a combination was used for skeleton tracking. Ref. [28] studied fall detection using a smartwatch. Accelerometer data were obtained at 50 Hz.

Ref. [29] deals with a choice of a MEMS accelerometer suitable for a specific application. However, the author does not take into account a motion scenario to be captured. Ref. [30] studied the applicability of some IMUs for tracking specific motion kinds. The issues stem from the fact that the static and dynamic accuracy of an IMU dictate whether or not the IMU is suitable for a specific application, and the manufacturer of an inertial sensor often does not specify for which motions their dynamic accuracy specification is valid.

Ref. [31] is one of the fundamental works related to the subject of inertial sensors. The authors mentioned that high sample frequencies are required for capturing high-frequency signals but did not investigated the issue on their own.