Multiple Inertial Measurement Units Research Articles

Multiple and Gyro-Free Inertial Datasets

An inertial navigation system (INS) utilizes three orthogonal accelerometers and gyroscopes to determine platform position, velocity, and orientation. There are countless applications for INS, including robotics, autonomous platforms, and the internet of things. Recent research explores the integration of data-driven methods with INS, highlighting significant innovations, improving accuracy and efficiency. Despite the growing interest in this field and the availability of INS datasets, no datasets are available for gyro-free INS (GFINS) and multiple inertial measurement unit (MIMU) architectures. To fill this gap and to stimulate further research in this field, we designed and recorded GFINS and MIMU datasets using 54 inertial sensors grouped in nine inertial measurement units. These sensors can be used to define and evaluate different types of MIMU and GFINS architectures. The inertial sensors were arranged in three different sensor configurations and mounted on a mobile robot, a passenger car and a turntable. In total, the dataset contains 45 hours of inertial data and corresponding ground truth trajectories. The data is freely accessible through our figshare repository.

Auto-Correlation and Channel Attention Enhanced Deep Graph Convolution Networks for Gait Phase Prediction Based on Multi-IMU System

Gait phase prediction is important in controlling assistive robotic devices such as exoskeletons, where the control unit must differentiate between gait phases to provide the necessary assistance when the user is wearing the exoskeleton. To achieve the objective of precisely identifying the gait phase of users for the accurate control of the exoskeleton, this study proposes Auto-Correlation and Channel Attention enhanced Deep Graph Convolutional Networks (ACCA-DGCN) for gait phase prediction, and a gait phase prediction model based on multiple inertial measurement units (IMUs) and skeleton graph was established, in order to fully utilize the dependency among joints, and enhance accuracy and reliability of gait phase prediction. First, a human lower limb gait data acquisition equipment was developed, and the gait data of human walking were collected. The skeleton graph of the human lower limb was constructed through the natural connection relationship of joints in the human skeleton. After that, the ACCA-DGCN-based gait phase prediction model was constructed by using the gait data of human walking. Auto-Correlation (AC) and Efficient Channel Attention (ECA) were introduced to effectively capture periodic features of gait data and focus on the channels with high contributions to gait phase prediction. Finally, the effect of the window size on the performance of the ACCA-DGCN model was explored, and the proposed algorithm was compared with the other five deep learning algorithms: CNN, RNN, TCN, LSTM, and DGCN. The experimental results show that the average accuracy of gait phase prediction model based on ACCA-DGCN reaches up to 92.26% and 97.21% in user-independent and user-dependent experiments, respectively, which is superior to the other five algorithms. This study provides a new method for gait phase prediction, which is useful for improving the control of exoskeleton robots.

Error Compensation Method for Pedestrian Navigation System Based on Low-Cost Inertial Sensor Array.

In the pedestrian navigation system, researchers have reduced measurement errors and improved system navigation performance by fusing measurements from multiple low-cost inertial measurement unit (IMU) arrays. Unfortunately, the current data fusion methods for inertial sensor arrays ignore the system error compensation of individual IMUs and the correction of position information in the zero-velocity interval. Therefore, these methods cannot effectively reduce errors and improve accuracy. An error compensation method for pedestrian navigation systems based on a low-cost array of IMUs is proposed in this paper. The calibration method for multiple location-free IMUs is improved by using a sliding variance detector to segment the angular velocity magnitude into stationary and motion intervals, and each IMU is calibrated independently. Compensation is then applied to the velocity residuals in the zero-velocity interval after zero-velocity update (ZUPT). The experimental results show a significant improvement in the average noise performance of the calibrated IMU array, with a 3.01-fold increase in static noise performance. In the closed-loop walking experiment, the average horizontal position error of a single calibrated IMU is reduced by 27.52% compared to the uncalibrated IMU, while the calibrated IMU array shows a 2.98-fold reduction in average horizontal position error compared to a single calibrated IMU. After compensating for residual velocity, the average horizontal position error of a single IMU is reduced by 0.73 m, while that of the IMU array is reduced by 64.52%.

Sensor location influences the associations between IMU and motion capture measurements of impact landing in healthy male and female runners at multiple running speeds

ABSTRACT This study investigated the relationships between inertial measurement unit (IMU) acceleration at multiple body locations and 3D motion capture impact landing measures in runners. Thirty healthy runners ran on an instrumented treadmill at five running speeds (9–17 km/h) during 3D motion capture. Axial and resultant acceleration were collected from IMUs at the distal and proximal tibia, distal femur and sacrum. Relationships between peak acceleration from each IMU location and patellofemoral joint (PFJ) peak force and loading rate, impact peak and instantaneous vertical loading rate (IVLR) were investigated using linear mixed models. Acceleration was positively related to IVLR at all lower limb locations (p < 0.01). Models predicted a 1.9–3.2 g peak acceleration change at the tibia and distal femur, corresponding with a 10% IVLR change. Impact peak was positively related to acceleration at the distal femur only (p < 0.01). PFJ peak force was positively related to acceleration at the distal (p = 0.03) and proximal tibia (p = 0.03). PFJ loading rate was positively related to the tibia and femur acceleration in males only (p < 0.01). These findings suggest multiple IMU lower limb locations are viable for measuring peak acceleration during running as a meaningful indicator of IVLR.

Prediction of Spasticity through Upper Limb Active Range of Motion in Stroke Survivors: A Generalized Estimating Equation Model.

We aim to study the association between spasticity and active range of motion (ROM) during four repetitive functional tasks such as cone stacking (CS), fast flexion-extension (FFE), fast ball squeezing (FBS), and slow ball squeezing (SBS), and predicted spasticity models. An experimental study with control and stroke groups was conducted in a Medical Center. A total of sixty-four participants, including healthy control (n = 22; average age (years) = 54.68 ± 9.63; male/female = 12/10) and chronic stroke survivors (n = 42; average age = 56.83 ± 11.74; male/female = 32/10) were recruited. We employed a previously developed smart glove device mounted with multiple inertial measurement unit (IMU) sensors on the upper limbs of healthy and chronic stroke individuals. The recorded ROMs were used to predict subjective spasticity through generalized estimating equations (GEE) for the affected side. The models have significant (p ≤ 0.05 *) prediction of spasticity for the elbow, thumb, index, middle, ring, and little fingers. Overall, during SBS and FFE activities, the maximum number of upper limb joints attained the greater average ROMs. For large joints, the elbow during CS and the wrist during FFE have the highest average ROMs, but smaller joints and the wrist have covered the highest average ROMs during FFE, FBS, and SBS activities. Thus, it is concluded that CS can be used for spasticity assessment of the elbow, FFE for the wrist, and SBS, FFE, and FBS activities for the thumb and finger joints in chronic stroke survivors.

Machine learning based canine posture estimation using inertial data.

The aim of this study was to design a new canine posture estimation system specifically for working dogs. The system was composed of Inertial Measurement Units (IMUs) that are commercially available, and a supervised learning algorithm which was developed for different behaviours. Three IMUs, each containing a 3-axis accelerometer, gyroscope, and magnetometer, were attached to the dogs' chest, back, and neck. To build and test the model, data were collected during a video-recorded behaviour test where the trainee assistance dogs performed static postures (standing, sitting, lying down) and dynamic activities (walking, body shake). Advanced feature extraction techniques were employed for the first time in this field, including statistical, temporal, and spectral methods. The most important features for posture prediction were chosen using Select K Best with ANOVA F-value. The individual contributions of each IMU, sensor, and feature type were analysed using Select K Best scores and Random Forest feature importance. Results showed that the back and chest IMUs were more important than the neck IMU, and the accelerometers were more important than the gyroscopes. The addition of IMUs to the chest and back of dog harnesses is recommended to improve performance. Additionally, statistical and temporal feature domains were more important than spectral feature domains. Three novel cascade arrangements of Random Forest and Isolation Forest were fitted to the dataset. The best classifier achieved an f1-macro of 0.83 and an f1-weighted of 0.90 for the prediction of the five postures, demonstrating a better performance than previous studies. These results were attributed to the data collection methodology (number of subjects and observations, multiple IMUs, use of common working dog breeds) and novel machine learning techniques (advanced feature extraction, feature selection and modelling arrangements) employed. The dataset and code used are publicly available on Mendeley Data and GitHub, respectively.

A MULTI-IMU BASED SELF-CONTAINED PEDESTRIAN NAVIGATION ALGORITHM

Abstract. The demand for navigation and positioning is increasing in various fields nowadays. Although Global Navigation Satellite Systems (GNSS) are currently the most widely used high-accuracy positioning method, their operation rests on signal transmission and reception, which is prone to interference from obstacles such as high-rise buildings, thereby limiting indoor navigation. In addition, in highly dynamic scenarios, the low update rate of the signal cannot track detailed motions. In this case, Inertial Measurement Units (IMUs) play an important role in serving as a complementary component. However, a single high-accuracy IMU is financially prohibitive. On the other hand, the lack of accuracy and stability limits the application of low-cost IMU in navigation. One way to improve the performance of low-cost IMU is to fuse multiple IMUs. This study focuses on the development of pedestrian navigation using multi-sensor integration of low-cost IMUs and magnetometers exploring different integration techniques to compare their performance. The Pedestrian Dead Reckoning (PDR) algorithm is a technique used to estimate the relative motion of pedestrian, which is a commonly used technology for indoor pedestrian navigation. This study use PDR with multi-sensor integration of low-cost IMUs to reduce the position error of pedestrian navigation to within one meter, with the aim of establishing a high-precision, reliable, and low-cost pedestrian navigation algorithm.

A robust walking detection algorithm using a single foot-worn inertial sensor: validation in real-life settings.

Walking activity and gait parameters are considered among the most relevant mobility-related parameters. Currently, gait assessments have been mainly analyzed in laboratory or hospital settings, which only partially reflect usual performance (i.e., real world behavior). In this study, we aim to validate a robust walking detection algorithm using a single foot-worn inertial measurement unit (IMU) in real-life settings. We used a challenging dataset including 18 individuals performing free-living activities. A multi-sensor wearable system including pressure insoles, multiple IMUs, and infrared distance sensors (INDIP) was used as reference. Accurate walking detection was obtained, with sensitivity and specificity of 98 and 91% respectively. As robust walking detection is needed for ambulatory monitoring to complete the processing pipeline from raw recorded data to walking/mobility outcomes, a validated algorithm would pave the way for assessing patient performance and gait quality in real-world conditions.

Attention‐based sensor fusion for emotion recognition from human motion by combining convolutional neural network and weighted kernel support vector machine and using inertial measurement unit signals

AbstractThe remarkable development of human–computer interactions has created an urgent need for machines to be able to recognise human emotions. Human motions play a key role in emphasising and conveying emotions to meet the complexity of daily application scenarios, such as medical rehabilitation and social education. Therefore, this paper aims to explore hidden emotional states from human motions. Accordingly, we proposed a novel approach for emotion recognition using multiple inertial measurement unit (IMU) sensors worn on different body parts. First, the mapping relationship between emotion and human motion was established through fuzzy comprehensive evaluation, and data were collected for six emotional states: sleepy, bored, excited, tense, angry, and distressed. Second, the preprocessed data were used as input in a lightweight convolutional neural network to extract discriminative features. Third, an attention‐based sensor fusion module was developed to obtain the importance scores of each IMU sensor for generating a fused feature representation. In the recognition phase, we constructed a weighted kernel support vector machine (SVM) model with an auxiliary fuzzy function to improve the weight calculation method of kernel functions in a multiple kernel SVM. Finally, the results obtained are compared with those of similar state‐of‐the‐art studies, the proposed method showed a higher accuracy (99.02%) for the six emotional states mentioned above. These findings may promote the development of social robots with non‐verbal emotional communication capabilities.

An Optimal Fusion Method of Multiple Inertial Measurement Units Based on Measurement Noise Variance Estimation

At present, most inertial systems generally only contain a single inertial measurement unit (IMU). Considering the low cost and low accuracy of the micro-electromechanical system (MEMS)-IMU, it has attracted much attention to fuse multiple IMUs to improve the accuracy and robustness of the system. In this article, two online noise variance estimators based on second-order-mutual-difference (SOMD) algorithm are proposed for two redundant measurements and multiple redundant measurements, respectively. In addition, the unbiasedness and consistency of the estimators are proved. Using the proposed noise variance estimators, measurement noise variances of each sensor can be estimated in real time when multiple IMUs exist. Based on the estimated noise variance of each sensor, the weighted least squares (WLS) estimation method is used to generate the optimal virtual IMU (VIMU) in the observation domain. Finally, comparative simulations and the real-world experiment were conducted to evaluate the proposed online noise estimation algorithm. The simulation results demonstrate its superiority compared with other noise variance estimation methods, and the real-world experiment results show the effectiveness of the IMU fusion method based on the proposed noise variance estimation algorithm.

A scoping review on recent trends in wearable sensors to analyze gait in people with stroke: From sensor placement to validation against gold-standard equipment.

The purpose of the review is to evaluate wearable sensor placement, their impact and validation of wearable sensors on analyzing gait, primarily the postural instability in people with stroke. Databases, namely PubMed, Cochrane, SpringerLink, and IEEE Xplore were searched to identify related articles published since January 2005. The authors have selected the articles by considering patient characteristics, intervention details, and outcome measurements by following the priorly set inclusion and exclusion criteria. From a total of 1077 articles, 142 were included in this study and classified into functional fields, namely postural stability (PS) assessments, physical activity monitoring (PA), gait pattern classification (GPC), and foot drop correction (FDC). The review covers the types of wearable sensors, their placement, and their performance in terms of reliability and validity. When employing a single wearable sensor, the pelvis and foot were the most used locations for detecting gait asymmetry and kinetic parameters, respectively. Multiple Inertial Measurement Units placed at different body parts were effectively used to estimate postural stability and gait pattern. This review article has compared results of placement of sensors at different locations helping researchers and clinicians to identify the best possible placement for sensors to measure specific kinematic and kinetic parameters in persons with stroke.

A novel positioning method of anti-punching drilling robot based on the fusion of multi-IMUs and visual image

Anti-punching drilling robot (APDR) is the key equipment for underground rock burst relief in coal mine and the accurate position and attitude determination is the basis and premise for realizing unmanned pressure relief operation. In this paper, a novel positioning method of APDR based on spatial array inertial measurement units (IMUs) and visual image is proposed. Firstly, the spatial array layout of multiple IMUs is displayed creatively, and the data fusion model and the posture calculation process of spatial array IMUs are constructed. The superiority of proposed spatial array IMUs is verified through the motion trajectory simulation analysis and mobile carrier simulation experiments. Then, an image enhancement method (SSR-AF) is designed to overcome the problems of atomization, glare, uneven illumination and noise interference in coal mine images, so as to improve the accuracy of image feature extraction and matching. Accordingly, the positioning estimation model based on continuous frame images is established. Furthermore, the fusion positioning process of APDR is presented by using the loose coupling mode based on Kalman filtering algorithm. The position and attitude monitoring experimental platform of APDR is built in a simulated coal mine tunnel. The experimental results indicate that the calculation errors of displacement and attitude based on the proposed fusion positioning method is superior to the competing methods, which meet the actual positioning requirements, and verify the feasibility and practicability of the proposed positioning method for APDR.

Classification of static postures with wearable sensors mounted on loose clothing

Inertial Measurement Units (IMUs) are a potential way to monitor the mobility of people outside clinical or laboratory settings at an acceptable cost. To increase accuracy, multiple IMUs can be used. By embedding multiple sensors into everyday clothing, it is possible to simplify having to put on individual sensors, ensuring sensors are correctly located and oriented. This research demonstrates how clothing-mounted IMU readings can be used to identify 4 common postures: standing, sitting, lying down and sitting on the floor. Data were collected from 5 healthy adults, with each providing 1–4 days of data with approximately 5 h each day. Each day, participants performed a fixed set of activities that were video-recorded to provide a ground truth. This is an analysis of accelerometry data from 3 sensors incorporated into right trouser-leg at the waist, thigh and ankle. Data were classified as static/ dynamic activities using a K-nearest neighbour (KNN) algorithm. For static activities, the inclination angles of the three sensors were estimated and used to train a second KNN classifier. For this highly-selected dataset (60000–70000 data points/posture), the static postures were classified with 100% accuracy, illustrating the potential for clothing-mounted sensors to be used in posture classification.

Depth-Imaging for Gait Analysis on a Treadmill in Older Adults at Risk of Falling.

Accidental falls are a major health issue in older people. One significant and potentially modifiable risk factor is reduced gait stability. Clinicians do not have sophisticated kinematic options to measure this risk factor with simple and affordable systems. Depth-imaging with AI-pose estimation can be used for gait analysis in young healthy adults. However, is it applicable for measuring gait in older adults at a risk of falling? In this methodological comparison 59 older adults with and without a history of falls walked on a treadmill while their gait pattern was recorded with multiple inertial measurement units and with an Azure Kinect depth-camera. Spatiotemporal gait parameters of both systems were compared for convergent validity and with a Bland-Altman plot. Correlation between systems for stride length (r=.992, [Formula: see text]) and stride time (r=0.914, [Formula: see text]) was high. Bland-Altman plots revealed a moderate agreement in stride length (-0.74 ± 3.68 cm; [-7.96 cm to 6.47 cm]) and stride time (-3.7±54 ms; [-109 ms to 102 ms]). Gait parameters in older adults with and without a history of falls can be measured with inertial measurement units and Azure Kinect cameras. Affordable and small depth-cameras agree with IMUs for gait analysis in older adults with and without an increased risk of falling. However, tolerable accuracy is limited to the average over multiple steps of spatiotemporal parameters derived from the initial foot contact. Clinical Translation Statement- Gait parameters in older adults with and without a history of falls can be measured with inertial measurement units and Azure Kinect. Affordable and small depth-cameras, developed for various purposes in research and industry, agree with IMUs in clinical gait analysis in older adults with and without an increased risk of falling. However, tolerable accuracy to assess function or monitor changes in gait is limited to the average over multiple steps of spatiotemporal parameters derived from the initial foot contact.

Best Axes Composition extended: Multiple gyroscopes and accelerometers data fusion to reduce systematic error

Multiple rigidly attached Inertial Measurement Unit (IMU) sensors provide a richer flow of data compared to a single IMU. State-of-the-art methods follow a probabilistic model of IMU measurements based on the random nature of errors combined under a Bayesian framework. However, affordable low-grade IMUs, in addition, suffer from systematic errors due to their imperfections not covered by their corresponding probabilistic model. In this paper, we propose a method, the Best Axes Composition (BAC) of combining Multiple IMU (MIMU) sensors data for accurate 3D-pose estimation that takes into account both random and systematic errors by dynamically choosing the best IMU axes from the set of all available axes. We evaluate our approach on our MIMU visual–inertial sensor and compare the performance of the method with a purely probabilistic state-of-the-art approach of MIMU data fusion. We show that BAC outperforms the latter and achieves up to 20% accuracy improvement for both orientation and position estimation in open loop, but needs proper treatment to keep the obtained gain.

Evaluation of Motion Segment Size as a New Sensor-based Functional Outcome Measure in Stroke Rehabilitation.

ObjectiveTo evaluate a novel parameter, motion segment size (MSS), in stroke patients with upper limb impairment and validate its clinical applicability by correlating results with a standard clinical task-based functional evaluation tool.MethodsIn this cross-sectional study, patients with hemiplegia and healthy controls equipped with multiple inertial measurement unit (IMU) sensors performed Action Research Arm Test (ARAT) and activities of daily living (ADL) tasks. Acceleration of the wrist and Euler angles of each upper limb segment were measured. The average and maximum MSS, accumulated motion, total performance time, and average motion speed (AMS) were extracted for analysis.ResultsData from nine patients and 10 controls showed that the average MSS of forearm supination/pronation and elbow flexion/extension during full ARAT tasks showed a significant difference between patients and controls and a significant correlation with ARAT scores.ConclusionsWe suggest that MSS may provide clinically relevant information regarding upper limb functional status in stroke patients.

Upper Limbs Extension and Flexion Angles Calculation and Visualization Using Two Wearable Inertial Measurement Units

Human motion analysis is widely used in many fields such as physical reha-bilitation, athlete training, health status diagnosis and others. Upper limb’s movement analysis is important because we need our hands to conduct daily works such as driving, eating and others. But the existed equipment can only be used to analyse the upper limb’s movement by trained personnel such as physicians or therapists. Besides, the existed system that used the cable wire for data transmission was limited their workspace to detect the upper limb motion. The objective of this research is to develop a system using multiple Inertial Measurement Units (IMU) to analyse the upper limb motion that can transfer data by using Bluetooth Low Energy (BLE) and develop a program to visualize the motion. In this research, a system had developed to measure the upper limb angle using wearable sensors. The wearable sensor we used is an Inertial Measurement Unit (IMU) which is Intel CurieNano to measure the upper limb angle. Intel CurieNano combines accelerometer and gyroscope was used as a sensor. The data from accelerometer and gyroscope were combined using the Complementary filter to get the joint angle. The IMU is connected to a program Python and the data is sent from IMU to the program through BLE. The program displayed the data and visualized the motion. The IMU is used to measure some certain angles such as 10º, 30º, 60º and 90º, and the correlation coefficient is 0.9967 with goniometer. The upper limb’s angle is measured using the system and compared the data with goniometer for determining the accuracy of the system. This system can achieve 95% of accuracy compared to goniometer.

Multiple inertial measurement unit combination and location for recognizing general, fatigue, and simulated-fatigue gait

BackgroundMuscle fatigue of the lower limbs results in dynamic imbalance and gait instability, increasing the risk of falling. However, people might slow walk without physical muscle fatigue due to mental fatigue. Wearable inertial measurement units (IMU) and machine learning approaches have been well employed for recognizing human activities. Research questionThe study aims to use a machine learning technique to recognize the data collected from IMUs for physically fatigued or slow-walking gaits. Second, the study aims to reveal the location or the number of IMUs can have the best performance. MethodsSixteen healthy adults with six IMUs attached to their heels, toes, sacrum, and head participated in the experiment. On the first day, the participants were instructed to walk along a hallway before and after the fatigue protocol as the Pre- and Post-fatigue gait. On the second day, the participants were instructed to walk along a hallway following the beat of their fatigue gait cadence measured on the first day as the simulated cadence (SC) gait. Gait cycles of each condition were segmented as the inputs of the Long Short-Term Memory (LSTM) model for recognization. ResultsThe result revealed that the LSTM model could recognize the gait of simulated cadence with the highest accuracy among these three gaits. For the signal body part, the highest accuracy was 93.20 % observed at the IMUs of toes. For the best combination, the IMUs of toes and sacrum achieved the highest accuracy of 95.71 %. SignificanceThe machine learning technique of LSTM with one or more IMUs can recognize the gait under normal, physical fatigue, or simulated cadence without muscle fatigue. Our model and approach would be expected to provide conditional warning in multiple fields, such as industrial safety for potential applications.

Enhancing navigation integrity for Urban Air Mobility with redundant inertial sensors

Urban Air Mobility (UAM) uses highly automated air vehicles to offer safe and efficient low-altitude urban air transportation services, for which ensuring navigation safety (measured by integrity) is an essential precondition. UAM vehicles can navigate themselves using Global Navigation Satellite Systems (GNSS)/Inertial Measurement Unit (IMU) tightly coupled systems. However, these systems are vulnerable to IMU failures aside from GNSS faults, given that UAM vehicles will use low-cost IMUs. IMU faults can severely degrade navigation integrity, thereby threatening UAM operational safety and increasing the difficulty of urban air traffic management. This issue can be mitigated by employing redundant IMUs. Civil aircraft use consistency checks among multiple high-performance Inertial Navigation Systems (INSs) to enhance navigation integrity. But this approach is not suitable for low-cost IMUs because of fast error accumulation. In response, this work proposes a new approach to enhance navigation integrity for UAM by integrating multiple IMUs with GNSS. In this approach, multiple IMUs and GNSS are tightly coupled by a centralized Kalman filter, and the corresponding integrity monitoring algorithm is developed to (a) detect the faults in GNSS and/or IMUs and (b) evaluate the probabilistic upper bounds on navigation errors, namely protection levels. Simulations are conducted to demonstrate the proposed method and to present sensitivity analyses, and the results suggest the effectiveness of the new approach. This method is beneficial to improving UAM operational safety and can potentially be applied to civil aircraft in the future.

Extrinsic Calibration of Multiple Inertial Sensors From Arbitrary Trajectories

We present a method of extrinsic calibration for a system of multiple inertial measurement units (IMUs) that estimates the relative pose of each IMU on a rigid body using only measurements from the IMUs themselves, without the need to prescribe the trajectory. Our method is based on solving a nonlinear least-squares problem that penalizes inconsistency between measurements from pairs of IMUs. We validate our method with experiments both in simulation and in hardware. In particular, we show that it meets or exceeds the performance—in terms of error, success rate, and computation time—of an existing, state-of-the-art method that does not rely only on IMU measurements and instead requires the use of a camera and a fiducial marker. We also show that the performance of our method is largely insensitive to the choice of trajectory along which IMU measurements are collected.