Foot-mounted Inertial Navigation Research Articles

A Novel Minimum Distance Constraint Method Enhanced Dual-Foot-Mounted Inertial Navigation System for Pedestrian Positioning

Foot-mounted inertial navigation system (Foot-INS) with the zero velocity update (ZUPT) has become one of the indispensable technical means in professional pedestrian positioning fields due to the advantages of self-constraint and immune to environmental factors. The dual-Foot-INS can provide more excellent autonomous positioning performance than a single-Foot-INS because it utilizes more opportunities for zero velocity correction and additional distance constraint information. However, the classical dual-Foot-INS does not fully exploit the distance constraint potential for positioning improvement. In this paper, we proposed a novel minimum distance constraint (MDC) method that achieves higher positioning accuracy than the traditional dual-Foot-INS methods. To obtain an accurate and consistent state estimation under the nonlinear distance constraint problem, we propose an iterative distance constraint (IDC) algorithm. The IDC is transformed into an approximate linear constraint model, and an alternative estimate is obtained by the estimation projection method. To solve the problem that the distance constraint moment in the traditional method is affected by the recursive foot positions, we propose a more reasonable and reliable minimum distance moment detection (MDMD) method. The proposed MDMD method maximizes the positioning performance improvement of the dual-foot pedestrian system. Two rigorous experimental tests with a long walking trajectory without turn-around and close-loop were conducted to verify the effectiveness of the proposed method, the positioning error of the proposed method is reduced by 83.5% and 62.9% compared to the classical ZUPT and minimum distance constraint methods, respectively.

Cooperative Localization of Firefighters Based on Relative Ranging Constraints of UWB and Autonomous Navigation

There are many demands for the cooperative localization (CL) of multiple people, such as firefighter rescue. The classical foot-mounted inertial navigation based on zero velocity update (ZUPT) suffers from accumulating error due to the low-cost inertial sensor, and the pre-placed anchors in the ultra-wideband (UWB) system limit the application in an unknown environment. In this study, a group of sensors including the inertial measurement unit (IMU), magnetometer, barometer, and UWB sensor is used. Through the different characteristics of sensors and the position relationship between people, a cooperative localization system using an extended Kalman filter for three-dimensional firefighter tracking is proposed. Ranging information between firefighters from UWB is utilized, and couplings introduced by relative measurement are estimated. Two experiments are designed to verify the proposed algorithm in building and forest environments. Compared with the results of single-person inertial navigation, the average positioning precision of the algorithm in the building and forest is, respectively, improved by 38.93% and 79.01%. This approach successfully suppresses the divergence of positioning errors, and fixed UWB anchors are not needed.

A Novel Adaptive Zero Velocity Detection Algorithm Based on Improved General Likelihood Ratio Test Detector

The zero-velocity update (ZUPT) method is an effective technique, which has been widely used in low-cost foot-mounted inertial navigation systems. It can mitigate the accumulated error by using the fact that, when the foot is stationary, the velocity should be zero. However, it is hard to detect the zero-velocity phases (ZVPs) correctly in various motion modes. To deal with this problem, a novel adaptive zero velocity detection algorithm based on an improved general likelihood ratio test (IGLRT) detector is proposed. The prior knowledge of the proposed IGLRT detector is the minima output value of inertial sensors, which is determined by an improved peak-valley detection method, while the prior knowledge of the traditional general likelihood ratio test (GLRT) method is based on the hypothesis that, when the foot is stationary, the magnitude of angular rates is zero, and the magnitude of accelerometers is equal to the magnitude of gravitation. Also, an adaptive method is proposed to enhance the robustness of the IGLRT, where the thresholds of IGLRT can be adjusted adaptively according to the amplitude of accelerometers. Field tests show that the proposed algorithm performs better than conventional and state-of-the-art approaches in mixed motion modes.

IOAM: A Novel Sensor Fusion-Based Wearable for Localization and Mapping

With the development of indoor location-based services (ILBS), the dual foot-mounted inertial navigation system (DF-INS) has been extensively used in many fields involving monitoring and direction-finding. It is a widespread ILBS implementation with considerable application potential in various areas such as firefighting and home care. However, the existing DF-INS is limited by a high inaccuracy rate due to the highly dynamic and non-stable stride length thresholds. The system also provides less clear and significant information visualization of a person’s position and the surrounding map. This study proposes a novel wearable-foot IOAM-inertial odometry and mapping to address the aforementioned issues. First, the person’s gait analysis is computed using the zero-velocity update (ZUPT) method with data fusion from ultrasound sensors placed on the inner side of the shoes. This study introduces a dynamic minimum centroid distance (MCD) algorithm to improve the existing extended Kalman filter (EKF) by limiting the stride length to a minimum range, significantly reducing the bias in data fusion. Then, a dual trajectory fusion (DTF) method is proposed to combine the left- and right-foot trajectories into a single center body of mass (CBoM) trajectory using ZUPT clustering and fusion weight computation. Next, ultrasound-type mapping is introduced to reconstruct the surrounding occupancy grid map (S-OGM) using the sphere projection method. The CBoM trajectory and S-OGM results were simultaneously visualized to provide comprehensive localization and mapping information. The results indicate a significant improvement with a lower root mean square error (RMSE = 1.2 m) than the existing methods.

Pedestrian Positioning Based on Dual Inertial Sensors and Foot Geometric Constraints

Foot-mounted inertial navigation with zero velocity update (ZUPT) is commonly used in pedestrian positioning. To suppress the accumulating position error owing to the low-cost inertial sensor, classical dual-foot pedestrian navigation method provides the compensation using the two feet's relative step length, whose values can be set an upper bound constraint or measured by ranging sensors. However, it suffers from low improvement and poor wearability. In this study, the two sensors are distributed on the toe and ankle of the same leg. The sensor-to-sensor position is unchangeable with the lower limb segments. This makes the uncoupled two subsystems be related. Through gait analysis, the step is divided into the stance and swing phases. For each phase, positions, velocities, and the related characteristics of the toe and the ankle are analyzed and modeled, respectively. A Kalman filter is constructed to fuse the position and velocity observations according to the geometric constraints and the foot vector. The Mahony filter by fusing the inertial sensor and magnetometer is adopted for the attitude improvement. Several experiments at low and high walking velocities on the plane and upstairs are carried out to verify the proposed method. The results show that compared with the conventional single-inertial measurement unit (IMU) ZUPT and dual-IMU two-foot constraint methods, the position and heading errors have been well suppressed.

Pedestrian Trajectory Estimation Based on Foot-Mounted Inertial Navigation System for Multistory Buildings in Postprocessing Mode

Acquiring accurate and reliable pedestrian trajectories is essential for providing indoor location-based services. Although a foot-mounted inertial navigation system (Foot-INS) can acquire pedestrian trajectories in multistory buildings, it will inevitably encounter heading divergence because the constraint information is not always valid. Therefore, we proposed an accurate and convenient postprocessing indoor pedestrian positioning system (IPPS) to acquire pedestrian trajectories in multistory buildings such as shopping malls. Based on the hypotheses that the start and end points of the pedestrian trajectories on a single floor were closed, and the horizontal position of the closing point on each floor was identical. Therefore, in the single floor of multistory buildings, we use the closing point to control the trajectory drift error caused by the Foot-INS, and use a smoothing algorithm to reasonably distribute the drift error to the entire trajectory. Heading divergence is unavoidable with the Foot-INS, result in the pedestrian trajectories acquired on different floors were rotationally offset. Because pedestrian trajectories can epitomize the building orientation and provide an opportunity to align those trajectories on multistory buildings, an algorithm was proposed to match the trajectories acquired on different floors. A hybrid simulation experiment was conducted using an accurate reference object to evaluate the positioning performance of the proposed IPPS. The effectiveness of acquiring pedestrian trajectories was also confirmed by various experimental tests in a large shopping mall. The study findings suggest that the proposed IPPS is self-contained, low cost, and has the potential for large-scale applications.

PEDESTRIAN INERTIAL NAVIGATION ALGORITHM BASED ON SCENE RECOGNITION

Abstract. As indoor location-based services become increasingly essential to people's daily life, it is necessary to build a stable and accurate indoor pedestrian positioning system. The foot-mounted inertial navigation system can provide a short-term robust solution but suffer from error accumulation over time. To alleviate this issue, this paper proposes a pedestrian inertial navigation algorithm based on scene recognition to reduce the heading drift. Based on the hypothesis that corridors in buildings are generally narrow and straight and pedestrians have a high probability to walk in straight lines in corridors, we use a scene recognition model to assist foot-mounted INS. When the scene recognition model determines that the pedestrian is walking in a corridor, a straight-line constraint will be implemented to reduce the heading drift and improve the observability of the vertical gyroscope bias. Experiments show that the algorithm can effectively improve the navigation performance and the observability of vertical gyroscope bias when the sensor biases are significant.

A Pedestrian Indoor Navigation System Using Deep-Learning-Aided Cellular Signals and ZUPT-Aided Foot-Mounted IMUs

A signal-sensor-based indoor pedestrian navigation system is developed. The proposed system: 1) utilizes a foot-mounted inertial navigation system (INS), in which the accumulated errors are mitigated via a zero velocity update (ZUPT) approach; 2) exploits opportunistically cellular long-term evolution (LTE) signals in a deep neural network (DNN)-based synthetic aperture navigation (SAN) framework, in which the pedestrian’s motion is utilized to suppress multipath-induced errors. The proposed DNN-SAN-LTE-ZUPT-INS (DUALS) indoor pedestrian navigation system utilizes the complementary the desirable characteristics of both subsystems, coupled via two architectures: (a) loosely-coupled and (b) tightly-coupled. This paper designs and assesses both architectures experimentally in an indoor environment. The experimental study demonstrates a pedestrian traversing a trajectory of 600 m in 14 minutes, including a stationary period, straight segments, up/down the stairs, and riding in an elevator, while receiving signals from 4 LTE base stations (also known as evolved node Bs (eNodeBs)). The proposed tightly-coupled DUALS system exhibited a three-dimensional (3-D) position root mean-squared error (RMSE) of 1.34 m, outperforming the loosely-coupled DUALS, ZUPT-aided INS, and LTE-DNN-SAN, which achieved a position RMSE of 1.38, 1.49, and 1.97 m, respectively.

A Robust Visual-Aided Inertial Navigation Algorithm for Pedestrians

Real-time and robust state estimation for pedestrians is a challenging problem under the satellite denial environment. The zero-velocity-aided foot-mounted inertial navigation system, with the shortcomings of unobservable heading, error accumulation, and poorly adaptable parameters, is a conventional method to estimate the pose relative to a known origin. Visual and inertial fusion is a popular technology for state estimation over the past decades, but it cannot make full use of the movement characteristics of pedestrians. In this paper, we propose a novel visual-aided inertial navigation algorithm for pedestrians, which improves the robustness in the dynamic environment and for multi-motion pedestrians. The algorithm proposed combines the zero-velocity-aided INS with visual odometry to obtain more accurate pose estimation in various environments. And then, the parameters of INS have adjusted adaptively via taking errors between fusion estimation and INS outputs as observers in the factor graphs. We evaluate the performance of our system with real-world experiments. Results are compared with other algorithms to show that the absolute trajectory accuracy in the algorithm proposed has been greatly improved, especially in the dynamic scene and multi-motions trials.

F²IMU-R: Pedestrian Navigation by Low-Cost Foot-Mounted Dual IMUs and Interfoot Ranging

Foot-mounted inertial sensors become popular in many indoor or GPS-denied applications, including but not limited to medical monitoring, gait analysis, soldier, and first responder positioning. However, the foot-mounted inertial navigation relies largely on the aid of zero velocity update (ZUPT) and has encountered inherent problems, such as heading drift. This article implements a pedestrian navigation system based on dual foot-mounted low-cost inertial measurement units (IMUs) and interfoot ultrasonic ranging. The observability analysis of the system is performed to investigate the roles of the ZUPT measurement and the foot-to-foot ranging measurement in improving the state estimability. A Kalman-based estimation algorithm is mechanized in the Earth frame, rather than in the common navigation frame, which is found to be effective in depressing the linearization error in Kalman filtering. An ellipsoid constraint in the Earth frame is also proposed to further restrict the height drift. Simulation and real field experiments show that the proposed method has better robustness and positioning accuracy (about 0.1%–0.2% traveled distance) than the traditional pedestrian navigation schemes do.

A Reconstruction Filter for Saturated Accelerometer Signals Due to Insufficient FSR in Foot-Mounted Inertial Navigation System

In pedestrian inertial navigation, one possible placement of Inertial Measurement Units (IMUs) is on a footwear. This placement allows to limit the accumulation of navigation errors due to the bias drift of inertial sensors and is generally a preferable placement of sensors to achieve the highest precision of pedestrian inertial navigation. However, inertial sensors mounted on footwear experience significantly higher accelerations and angular velocities (10s of g and 1000s of deg/sec) during regular pedestrian activities than during more conventional navigation tasks, which could exceed Full Scale Range (FSR) of many commercial-off-the-shelf IMUs, therefore degrading accuracy of pedestrian navigation systems. This paper proposes a reconstruction filter to mitigate localization error in pedestrian navigation due to insufficient FSR of inertial sensors. The proposed reconstruction filter approximates immeasurable accelerometer’s signals with a triangular function and estimates the size of the triangles using a Gaussian Process (GP) regression. To evaluate performance of pedestrian navigation systems enhanced by the proposed reconstruction filter, we conducted two series of indoor pedestrian navigation experiments with a VectorNav VN-200 IMU and an Analog Device ADIS16497-3 IMU, which have accelerometer’s FSR of ±16 g and ±40 g, respectively. In the first series of experiments, forces experienced by the foot-mounted IMUs did not exceed the FSRs of the sensors, while in the second series, the forces surpassed the FSR of the VN-200 IMU and saturated the accelerometer’s readings. The saturated accelerometer’s readings reduced the accuracy of estimated positions using the VN-200 by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${1.34}\times $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${3.37}\times $ </tex-math></inline-formula> along horizontal and vertical directions. When applying our proposed reconstruction filter to the saturated accelerometer’s measurements, the navigation accuracy along horizontal and vertical directions was increased by 5% and 50%, respectively, as compared to using unreconstructed signals.

The Improved Constraint Methods for Foot-Mounted Pedestrian Three-Dimensional Inertial Navigation

The foot-mounted pedestrian navigation system (PNS) that uses microelectromechanical systems (MEMS) inertial measurement units (IMUs) to track the person’s position. However errors accumulate over time during inertial navigation solutions, which affects the positioning precision. In this paper, a multicondition zero velocity detector is used to detect the stance phase of gait. Then the errors are corrected in the stance phase and the swing phase, respectively, through the Kalman filter. When pedestrians are going up and down the stairs, the divergence of height will reduce the accuracy of three-dimensional positioning. In this paper, an accelerometer and a barometer are used to obtain altitude variation, and after that the stair condition detection (SCD) algorithm is proposed to correct the height of Kalman filter output and detect the walking state of pedestrians. Through theoretical research and field experiments, these algorithms are studied carefully. The results of the experiment show that the algorithm proposed in this paper can effectively eliminate errors and achieve more accurate positioning.

Contrastive Learning of Zero-Velocity Detection for Pedestrian Inertial Navigation

Robust and accurate zero-velocity detection can improve the performance of zero-velocity-aided foot-mounted inertial navigation system. To ensure the accuracy of zero-velocity detection, we propose a novel detector based on contrastive learning. This detector roughly eliminates the inertial data that must not be the zero-velocity event in advance, to reduce the computation cost. Then the detector uses the remaining inertial data to detect the zero-velocity event via a trained contrastive neural network. The contrastive neural network uses the triplet network and is trained by comparing with the anchor data which consists of the known static inertial data from the period of initial alignment. The classifier will finally determine whether the output of the triplet network is the zero-velocity event. Two experiments were conducted to evaluate this novel detector, showing that it can adaptively and accurately detect the zero-velocity event. The horizontal position errors of the two experiments are respectively 1.33m over a 953m outdoor path with walking and 3.74m over a 1143m indoor/outdoor path with combined motion of low dynamic and high dynamic.

Learning of Zero-Velocity Detection for Inertial Pedestrian Navigation

The detection of zero-velocity states is the vital prerequisite for zero-velocity update in the foot-mounted inertial pedestrian navigation system. The previous zero-velocity detector determines zero-velocity states by comparing measured inertial data with a calibrated threshold. The calibration of the threshold is inconvenient for this kind of the zero-velocity detector because the threshold is variable corresponding to different people and locomotion. The best threshold needs to be tuned corresponding to different situations. In essence, the detection of zero-velocity states is a binary classification problem. As the success of deep learning in in image classification and speech recognition, it is possible to design an adaptive zero-velocity detector based on it. A Siamese network is designed to learn the metric of distinguish zero-velocity states. This method can adaptively get the most likely correct results without threshold tuning. Experiments are conducted and results show that the matching degree is about 96.31% and the navigation accuracy can reach within 4m in 20min.

A Simple Positioning System for Large-Scale Indoor Patrol Inspection Using Foot-Mounted INS, QR Code Control Points, and Smartphone

A reliable and practical personnel positioning system is necessary for large-scale indoor patrol inspection. In this study, we designed a personnel positioning system that entails the implementation of a foot-mounted inertial module, a smartphone, and pre-determined sparse QR code points. Foot-mounted inertial navigation system (Foot-INS) is self-contained system that send real-time dead-reckoning positions to a smartphone via a built-in Bluetooth module. When the inspector arrives at a planned control point area marked by the QR code, the smartphone actively scans the QR code and obtains the three-dimensional (3D) coordinates of the control point. Then, a newly developed data fusion algorithm performs real-time and post-processing fusion of the relative foot position and 3D QR code control point coordinate data. The proposed algorithm was implemented on an Android smartphone and was evaluated by extensive experiments in an indoor office building and an outdoor open-sky area. The experimental results confirmed the effectiveness and feasibility of the proposed personnel positioning system. The designed system was proven to be decent, robust, and not susceptible to environmental changes. It is also low-cost, has low power consumption, is easy to operate, and is compatible with common smartphones. Moreover, the proposed personnel positioning system provides a practical application pattern of the Foot-INS.

Исследование состоятельности расширенного фильтра Калмана в задаче навигации пешехода с БИНС, закрепленными на стопах

The paper focuses on pedestrian navigation with foot-mounted strapdown inertial navigation systems (SINS). Zero velocity updates (ZUPT) during the stance phase are commonly applied in such systems to improve the accuracy. Zero velocity data are processed by the extended Kalman filter (EKF). Zero velocity condition is written in two forms: in reference and body frames. The first form traditional for pedestrian navigation is shown to provide an inconsistent EKF. The second form provides a correct ZUPT algorithm, which is naturally written in so-called dynamic errors. The analyzed algorithm for data fusion from two SINS is based on the bound on foot-to-foot distance. It is shown how EKF inconsistency can be manifested, and how it can be avoided by proceeding back to dynamic errors. The results are obtained analytically using observability theory and covariance analysis.

An Adaptive Zero-Velocity Interval Detector Using Instep-Mounted Inertial Measurement Unit

The zero-velocity update (ZUPT) technique plays a key role in foot-mounted inertial navigation system, which can minimize the drift errors of low-cost inertial measurement unit (IMU) by resetting the velocity to zero when the foot is stationary. However, it is difficult to detect the zero-velocity interval (ZVI) in mixed locomotion patterns. This article presents a novel ZVI detector based on adaptive simulated energy consumption (SEC) curve. It can identify the ZVIs of various locomotion patterns, such as normal walking, fast walking, running, going upstairs, and downstairs. The SEC curve is generated based on the signal processing approach using the interlaced peak property of the IMU-measured angular rate and acceleration waveforms. Another benefit of the proposed method is that the IMU can be mounted on the instep without restrictions of orientation and position, which improves flexibility and convenience. Experiment results show that the proposed algorithm performs better than three other widely used methods in mixed gait patterns.

Lower Limb Model Based Inertial Indoor Pedestrian Navigation System for Walking and Running

Foot-mounted inertial navigation systems are suitable in GNSS denied environment for special tasks such as fire rescue, soldier, etc. These tasks are often accompanied by vigorous movements such as running and jumping, which is a challenge for the Zero Velocity Update (ZUPT) based inertial navigation system. As the speed increases, the inertial sensor drift increases, while the zero-velocity interval shortens, making the gait detection more difficult and resulting in a limited error correction. And as the motion intensifies, the stability of the system decreases. A multi-node inertial pedestrian navigation system based on the lower limb model constraint is proposed in this paper. Our first contribution in this paper is studying a simplified adaptive zero-bias estimation algorithm. The changes in velocity and angular velocity between two steps are used to estimate and compensate for the drift of accelerometers and gyroscopes. Our second contribution is proposing a novel gait segmentation method by lower limb motion statistics feature. A hybrid detection model of dual IMU is conducted to improve the accuracy of gait recognition. After that, the maximum distance inequality constraint is studied to correct the position error when the still phase is not available in vigorous movement. The final contribution is studying the chi-square fault detection method to improve the stability of KF. Multiple experiments prove that the proposed multi-node inertial pedestrian navigation system is effective in dealing with various challenging in walking, running, and hybrid motion pedestrian inertial navigation problems which could achieve less than 0.3% average distance error.

Fifteen Years of Progress at Zero Velocity: A Review

Fifteen years have passed since the publication of Foxlin's seminal paper “Pedestrian tracking with shoe-mounted inertial sensors”. In addition to popularizing the zero-velocity update, Foxlin also hinted that the optimal parameter tuning of the zero-velocity detector is dependent on, for example, the user's gait speed. As demonstrated by the recent influx of related studies, the question of how to properly design a robust zero-velocity detector is still an open research question. In this review, we first recount the history of foot-mounted inertial navigation and characterize the main sources of error, thereby motivating the need for a robust solution. Following this, we systematically analyze current approaches to robust zero-velocity detection, while categorizing public code and data. The article concludes with a discussion on commercialization along with guidance for future research.

Machine Learning-Based Zero-Velocity Detection for Inertial Pedestrian Navigation

Zero velocity update is a common and efficient approach to bound the accumulated error growth for foot-mounted inertial navigation system. Thus a robust zero velocity detector (ZVD) for all kinds of locomotion is needed for high accuracy pedestrian navigation systems. In this paper, we investigate two machine learning-based ZVDs: Histogram-based Gradient Boosting (HGB) and Random Forest (RF), aiming at adapting to different motion types while reducing the computation costs compared to the deep learning-based detectors. A complete data pre-processing procedure, including a feature engineering study and data augmentation techniques, is proposed. A motion classifier based on HGB is used to distinguish “single support” and “double float” motions. This concept is different from the traditional locomotion classification (walking, running, stair climbing) since it merges similar motions into the same class. The proposed ZVDs are evaluated with inertial data collected by two subjects over a 1.8 km indoor/outdoor path with different motions and speeds. The results show that without huge training dataset, these two machine learning-based ZVDs achieve better performances (55 cm positioning accuracy) and lower computational costs than the two deep learning-based Long Short-Term Memory methods (1.21 m positioning accuracy).