Surrogate Modelling for Oxygen Uptake Prediction Using LSTM Neural Network.

Oxygen uptake (V˙O2) is an important metric in any exercise test including walking and running. It can be measured using portable spirometers or metabolic analyzers. Those devices are, however, not suitable for constant use by consumers due to their costs, difficulty of operation and their intervening in the physical integrity of their users. Therefore, it is important to develop approaches for the indirect estimation of V˙O2-based measurements of motion parameters, heart rate data and application-specific measurements from consumer-grade sensors. Typically, these approaches are based on linear regression models or neural networks. This study investigates how motion data contribute to V˙O2 estimation accuracy during unconstrained running and walking. The results suggest that a long short term memory (LSTM) neural network can predict oxygen consumption with an accuracy of 2.49 mL/min/kg (95% limits of agreement) based only on speed, speed change, cadence and vertical oscillation measurements from an inertial navigation system combined with a Global Positioning System (INS/GPS) device developed by our group, worn on the torso. Combining motion data and heart rate data can significantly improve the V˙O2 estimation resulting in approximately 1.7-1.9 times smaller prediction errors than using only motion or heart rate data.

Indirect Estimation of Vertical Ground Reaction Force from a Body-Mounted INS/GPS Using Machine Learning.

Vertical ground reaction force (vGRF) can be measured by force plates or instrumented treadmills, but their application is limited to indoor environments. Insoles remove this restriction but suffer from low durability (several hundred hours). Therefore, interest in the indirect estimation of vGRF using inertial measurement units and machine learning techniques has increased. This paper presents a methodology for indirectly estimating vGRF and other features used in gait analysis from measurements of a wearable GPS-aided inertial navigation system (INS/GPS) device. A set of 27 features was extracted from the INS/GPS data. Feature analysis showed that six of these features suffice to provide precise estimates of 11 different gait parameters. Bagged ensembles of regression trees were then trained and used for predicting gait parameters for a dataset from the test subject from whom the training data were collected and for a dataset from a subject for whom no training data were available. The prediction accuracies for the latter were significantly worse than for the first subject but still sufficiently good. K-nearest neighbor (KNN) and long short-term memory (LSTM) neural networks were then used for predicting vGRF and ground contact times. The KNN yielded a lower normalized root mean square error than the neural network for vGRF predictions but cannot detect new patterns in force curves.

A Novel KGP Algorithm for Improving INS/GPS Integrated Navigation Positioning Accuracy.

The fusion of multi-source sensor data is an effective method for improving the accuracy of vehicle navigation. The generalization abilities of neural-network-based inertial devices and GPS integrated navigation systems weaken as the nonlinearity in the system increases, resulting in decreased positioning accuracy. Therefore, a KF-GDBT-PSO (Kalman Filter-Gradient Boosting Decision Tree-Particle Swarm Optimization, KGP) data fusion method was proposed in this work. This method establishes an Inertial Navigation System (INS) error compensation model by integrating Kalman Filter (KF) and Gradient Boosting Decision Tree (GBDT). To improve the prediction accuracy of the GBDT, we optimized the learning algorithm and the fitness parameter using Particle Swarm Optimization (PSO). When the GPS signal was stable, the KGP method was used to solve the nonlinearity issue between the vehicle feature and positioning data. When the GPS signal was unstable, the training model was used to correct the positioning error for the INS, thereby improving the positioning accuracy and continuity. The experimental results show that our method increased the positioning accuracy by 28.20-59.89% compared with the multi-layer perceptual neural network and random forest regression.

Continuous Analysis of Running Mechanics by Means of an Integrated INS/GPS Device.

This paper describes a single body-mounted sensor that integrates accelerometers, gyroscopes, compasses, barometers, a GPS receiver, and a methodology to process the data for biomechanical studies. The sensor and its data processing system can accurately compute the speed, acceleration, angular velocity, and angular orientation at an output rate of 400 Hz and has the ability to collect large volumes of ecologically-valid data. The system also segments steps and computes metrics for each step. We analyzed the sensitivity of these metrics to changing the start time of the gait cycle. Along with traditional metrics, such as cadence, speed, step length, and vertical oscillation, this system estimates ground contact time and ground reaction forces using machine learning techniques. This equipment is less expensive and cumbersome than the currently used alternatives: Optical tracking systems, in-shoe pressure measurement systems, and force plates. Another advantage, compared to existing methods, is that natural movement is not impeded at the expense of measurement accuracy. The proposed technology could be applied to different sports and activities, including walking, running, motion disorder diagnosis, and geriatric studies. In this paper, we present the results of tests in which the system performed real-time estimation of some parameters of walking and running which are relevant to biomechanical research. Contact time and ground reaction forces computed by the neural network were found to be as accurate as those obtained by an in-shoe pressure measurement system.

A RLS-SVM Aided Fusion Methodology for INS during GPS Outages.

In order to maintain a relatively high accuracy of navigation performance during global positioning system (GPS) outages, a novel robust least squares support vector machine (LS-SVM)-aided fusion methodology is explored to provide the pseudo-GPS position information for the inertial navigation system (INS). The relationship between the yaw, specific force, velocity, and the position increment is modeled. Rather than share the same weight in the traditional LS-SVM, the proposed algorithm allocates various weights for different data, which makes the system immune to the outliers. Field test data was collected to evaluate the proposed algorithm. The comparison results indicate that the proposed algorithm can effectively provide position corrections for standalone INS during the 300 s GPS outage, which outperforms the traditional LS-SVM method. Historical information is also involved to better represent the vehicle dynamics.

INS/GNSS Tightly-Coupled Integration Using Quaternion-Based AUPF for USV.

This paper addresses the problem of integration of Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) for the purpose of developing a low-cost, robust and highly accurate navigation system for unmanned surface vehicles (USVs). A tightly-coupled integration approach is one of the most promising architectures to fuse the GNSS data with INS measurements. However, the resulting system and measurement models turn out to be nonlinear, and the sensor stochastic measurement errors are non-Gaussian and distributed in a practical system. Particle filter (PF), one of the most theoretical attractive non-linear/non-Gaussian estimation methods, is becoming more and more attractive in navigation applications. However, the large computation burden limits its practical usage. For the purpose of reducing the computational burden without degrading the system estimation accuracy, a quaternion-based adaptive unscented particle filter (AUPF), which combines the adaptive unscented Kalman filter (AUKF) with PF, has been proposed in this paper. The unscented Kalman filter (UKF) is used in the algorithm to improve the proposal distribution and generate a posterior estimates, which specify the PF importance density function for generating particles more intelligently. In addition, the computational complexity of the filter is reduced with the avoidance of the re-sampling step. Furthermore, a residual-based covariance matching technique is used to adapt the measurement error covariance. A trajectory simulator based on a dynamic model of USV is used to test the proposed algorithm. Results show that quaternion-based AUPF can significantly improve the overall navigation accuracy and reliability.

A derivative UKF for tightly coupled INS/GPS integrated navigation.

The tightly coupled INS/GPS integration introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange measurements. The extended Kalman filter (EKF) is a typical method to address the nonlinearity by linearizing the pseudorange measurements. However, the linearization may cause large modeling error or even degraded navigation solution. To solve this problem, this paper constructs a nonlinear measurement equation by including the second-order term in the Taylor series of the pseudorange measurements. Nevertheless, when using the unscented Kalman filter (UKF) to the INS/GPS integration for navigation estimation, it causes a great amount of redundant computation in the prediction process due to the linear feature of system state equation, especially for the case with system state vector in much higher dimension than measurement vector. To overcome this drawback in computational burden, this paper further develops a derivative UKF based on the constructed nonlinear measurement equation. The derivative UKF adopts the concise form of the original Kalman filter (KF) to the prediction process and employs the unscented transformation technique to the update process. Theoretical analysis and simulation results demonstrate that the derivative UKF can achieve higher accuracy with a much smaller computational cost in comparison with the traditional UKF.

Tightly coupled low cost 3D RISS/GPS integration using a mixture particle filter for vehicular navigation.

Satellite navigation systems such as the global positioning system (GPS) are currently the most common technique used for land vehicle positioning. However, in GPS-denied environments, there is an interruption in the positioning information. Low-cost micro-electro mechanical system (MEMS)-based inertial sensors can be integrated with GPS and enhance the performance in denied GPS environments. The traditional technique for this integration problem is Kalman filtering (KF). Due to the inherent errors of low-cost MEMS inertial sensors and their large stochastic drifts, KF, with its linearized models, has limited capabilities in providing accurate positioning. Particle filtering (PF) was recently suggested as a nonlinear filtering technique to accommodate for arbitrary inertial sensor characteristics, motion dynamics and noise distributions. An enhanced version of PF called the Mixture PF is utilized in this study to perform tightly coupled integration of a three dimensional (3D) reduced inertial sensors system (RISS) with GPS. In this work, the RISS consists of one single-axis gyroscope and a two-axis accelerometer used together with the vehicle's odometer to obtain 3D navigation states. These sensors are then integrated with GPS in a tightly coupled scheme. In loosely-coupled integration, at least four satellites are needed to provide acceptable GPS position and velocity updates for the integration filter. The advantage of the tightly-coupled integration is that it can provide GPS measurement update(s) even when the number of visible satellites is three or lower, thereby improving the operation of the navigation system in environments with partial blockages by providing continuous aiding to the inertial sensors even during limited GPS satellite availability. To effectively exploit the capabilities of PF, advanced modeling for the stochastic drift of the vertically aligned gyroscope is used. In order to benefit from measurement updates for such drift, which are loosely-coupled updates, a hybrid loosely/tightly coupled solution is proposed. This solution is suitable for downtown environments because of the long natural outages or degradation of GPS. The performance of the proposed 3D Navigation solution using Mixture PF for 3D RISS/GPS integration is examined by road test trajectories in a land vehicle and compared to the KF counterpart.