Step Length Estimation Method Research Articles

A step length estimation method based on frequency domain feature analysis and gait recognition for pedestrian dead reckoning

Purpose Step length is a key factor for pedestrian dead reckoning (PDR), which affects positioning accuracy and reliability. Traditional methods are difficult to handle step length estimation of dynamic gait, which have larger error and are not adapted to real walking. This paper aims to propose a step length estimation method based on frequency domain feature analysis and gait recognition for PDR, which considers the effects of real-time gait. Design/methodology/approach The new step length estimation method transformed the acceleration of pedestrians from time domain to frequency domain, and gait characteristics of pedestrians were obtained and matched with different walking speeds. Findings Many experiments are conducted and compared with Weinberg and Kim models, and the results show that the average errors of the new method were improved by about 2 meters to 5 meters. It also shows that the proposed method has strong stability and device robustness and meets the accuracy requirements of positioning. Originality/value A sliding window strategy used in fast Fourier transform is proposed to implement frequency domain analysis of the acceleration, and a fast adaptive gait recognition mechanism is proposed to identify gait of pedestrians.

Multi-Information Fusion Indoor Localization Using Smartphones

Accurate indoor localization estimation has important social and commercial values, such as indoor location services and pedestrian retention times. Acoustic-based methods can achieve high localization accuracies in specific scenarios with special equipment; however, it is a challenge to obtain accurate localization with general equipment in indoor environments. To solve this problem, we propose a novel fusion CHAN and the improved pedestrian dead reckoning (PDR) indoor localization system (CHAN-IPDR-ILS). In this system, we propose a step length estimation method that adds the previous two steps for extracting more accurate information to estimate the current step length. The maximum influence factor is set for the previous two steps to ensure the importance of the current step length. We also propose a heading direction correction method to mitigate the errors in sensor data. Finally, pedestrian localization is achieved using a motion model with acoustic estimation and dynamic improved PDR estimation. In the fusion localization, the threshold and confidence level of the distance between estimation base-acoustic and improved PDR estimation are set to mitigate accidental and cumulative errors. The experiments were performed at trial sites with different users, devices, and scenarios, and experimental results demonstrate that the proposed method can achieve a higher accuracy compared with the state-of-the-art methods. The proposed fusion localization system manages equipment heterogeneity and provides generality and flexibility with different devices and scenarios at a low cost.

Conditional Generative Adversarial Network-Based Regression Approach for Walking Distance Estimation Using Waist-Mounted Inertial Sensors

This paper introduces a novel regression approach based on deep learning for estimating the walking distance using inertial sensors attached to the pedestrian’s waist. Walking step length can be estimated by using supervised learning. However, supervised learning commonly requires a large amount of labeled training data to achieve better performance. To tackle this issue, we propose the walking step length estimation method based on conditional generative adversarial network (CGAN) used as a regression model. The CGAN-based regression model consists of a generator model for a step length regression task and a discriminator model for a classification task. Step segmentation is performed to extract acceleration amplitude data into step segments. These data are applied as additional input for both generator and discriminator. The generator model aims to generate walking step length as a label, while the discriminator model aims to classify an input label as either real or generated. Then, the step length prediction model using the CGAN-based regression approach is applied to calculate the walking distance. Two experiments are performed to evaluate the performance of the proposed method, where test walking paths include an 80 m straight corridor and a rectangular on the football field of about 1282 m. The results show that the proposed method using small labeled datasets with 120 to 300 samples achieves estimation accuracy with an average error of 0.77% for straight paths and 0.88% for rectangular paths.

An improved PDR system with accurate heading and step length estimation using handheld smartphone

AbstractPedestrian dead reckoning (PDR) is widely used in handheld indoor positioning systems. However, low-cost inertial sensors built into smartphones provide poor-quality measurements, resulting in cumulative error which consists of heading estimation error caused by gyroscope and step length estimation error caused by an accelerometer. Learning more motion features through limited measurements is important to improve positioning accuracy. This paper proposes an improved PDR system using smartphone sensors. Using gyroscope, two motion patterns, walking straight or turning, can be recognised based on dynamic time warp (DTW) and thus improve heading estimation from an extended Kalman filter (EKF). Joint quasi-static field (JQSF) detection is used to avoid bad magnetic measurements due to magnetic disturbances in an indoor environment. In terms of periodicity of angular rate while walking, peak–valley angular velocity detection and zero-cross detection is combined to detect steps. A step-length estimation method based on deep belief network (DBN) is proposed. Experimental results demonstrate that the proposed PDR system can achieve more accurate indoor positioning.

Walking Step Length Estimation Using Waist-Mounted Inertial Sensors With Known Total Walking Distance

This paper presents a new constrained optimization-based smoothing algorithm for walking step length estimation using waist-mounted inertial sensors, where the total walking distance is known. The walking trajectory is estimated by double integrating acceleration. Due to sensor noises, the walking step length estimation accuracy degrades as the walking distance becomes longer. To tackle this problem, we introduce a known distance straight-line walking trajectory constraint and a constant speed constraint to the smoothing algorithm. These constraints reduce the walking step estimation accuracy degradation even for long walking distance. Two experiments are conducted to evaluate the pedestrian trajectory and walking step length estimation accuracy. The accuracy of a 20 m walking trajectory estimation has been investigated in the first experiment. This experiment compares the estimated position and velocity with Lidar-based references. The second experiment is to demonstrate the usefulness of the proposed walking step length estimation method. The result shows that the average of mean relative errors is 0.6801% for three different walking speed levels. The proposed method can be applied to generate training data for walking step length estimation without requiring spatial infrastructure.

Exact line search method for using the L1-norm misfit function in full waveform inversion

Full waveform inversion (FWI) is a non-linear inverse problem that can be sensitive to noise. The tolerance of the noise-interference characteristics depends on the types of misfit functions. To date, different misfit functions, such as the least-squares norm (L2), the least-absolute-value norm (L1), and combinations of the two (e.g., the Huber and hybrid criteria), have been applied to FWI. The L2 norm is highly sensitive to non-Gaussian errors in the data and gives rise to high-amplitude artifacts in reconstructed models. For non-Gaussian noise data, the L1 norm and the Huber and hybrid criteria always reliably reconstruct models. However, the Huber and hybrid criteria require tedious error investigations to estimate their threshold criterion. Thus, the L1 norm is adopted here to improve the anti-noise ability of the FWI. The step length is closely related to the misfit function, and an optimal step-length estimation method can rapidly make the FWI algorithm reach the global minimum, with a reduced number of iterations and fewer extra forward modeling simulations during each iteration. The step length can usually be obtained using the exact or inexact line search method. Generally, the exact line search method is faster than the inexact one. Therefore, we derived an exact line search method for the L1 norm in the FWI process. Its effectiveness was tested using noise-free data from Overthrust and the SEG/EAGE salt models. The results demonstrate that this method can recover high-resolution velocity models with low computational costs. Numerical tests using the synthetic Overthrust model contaminated by strong noise were used to further validate the robustness of this exact line search method.

Research of step-length estimation methods for full waveform inversion in time domain

ABSTRACTFull waveform inversion (FWI) is a powerful tool for reconstructing high-resolution subsurface parameters estimated by iteratively minimising the difference between calculated and observed data. Step-length estimation is a key step in the successful implementation of the FWI algorithm. An optimal step-length value rapidly causes the FWI algorithm to reach the global minimum with reduced iterations and fewer extra forward modelling simulations during each iteration. Step-length can typically be calculated using an inexact or an exact line-search method. The backtracking line-search method (BLSM) is a typical inexact method. Initial methods of guessing the step-length and evaluation conditions determine the efficiency of a BLSM scheme. Here, we propose a quadratic extrapolation value as the initial guess in a BLSM scheme, and then compare it with other initial-guess approaches by using the first Wolfe condition to evaluate step-length values. Exact line-search methods include a parabolic fitting search method through three points (PFSM-3), a parabolic fitting search method through two points (PFSM-2) and the analytical step-length method (ASLM). To find optimal and stable step-length estimation methods for FWI, we compare four step-length estimation methods: BLSM, PFSM-3, PFSM-2 and ASLM. Numerical examples using synthetic data demonstrate that quadratic extrapolation values perform better than first-order change and adaptive values in the BLSM scheme, in terms of resolution of the reconstructed model and computational costs. Of the four step-length estimation methods, ASLM and BLSM are both efficient for noise-free data, and robust ASLM is more efficient for noisy data. However, PFSM-2 and PFSM-3 are less efficient because of low accuracy and high computational cost.

Accurate Step Length Estimation for Pedestrian Dead Reckoning Localization Using Stacked Autoencoders

Pedestrian dead reckoning (PDR) is a popular indoor localization method due to its independence of additional infrastructures and the wide availability of smart devices. Step length estimation is a key component of PDR, which has an important influence on the performance of PDR. Existing step length estimation models suffer from various limitations such as requiring knowledge of user’s height, lack of consideration of varying phone carrying ways, and dependence on spatial constraints. To solve these problems, we propose a deep learning-based step length estimation model, which can adapt to different phone carrying ways and does not require individual stature information and spatial constraints. Experimental results show that the proposed method outperforms existing popular step length estimation methods.

A Novel Pedestrian Dead Reckoning Algorithm for Multi-Mode Recognition Based on Smartphones

With the rapid development of smartphone technology, pedestrian navigation based on built-in inertial sensors in smartphones shows great application prospects. Currently, most smartphone-based pedestrian dead reckoning (PDR) algorithms normally require a user to hold the phone in a fixed mode and, thus, need to correct the gyroscope heading with inputs from other sensors, which restricts the viability of pedestrian navigation significantly. In this paper, in order to improve the accuracy of the traditional step detection and step length estimation method for different users, a state transition-based step detection method and a step length estimation method using a neural network are proposed. In order to decrease the heading errors and inertial sensor errors in multi-mode system, a multi-mode intelligent recognition method based on a neural network was constructed. On this basis, we propose a heading correction method based on zero angular velocity and an overall correction method based on lateral velocity limitation (LV). Experimental results show that the maximum positioning errors obtained by the proposed algorithm are about 0.9% of the total path length. The proposed novel PDR algorithm dramatically enhances the user experience and, thus, has high value in real applications.

Step Length Estimation Methods Based on Inertial Sensors: A Review

Inertial sensors are included in most of the current smart devices and many researchers have identified their ability to be used for analyzing different parameters of human behavior. Among them, the pedestrian’s step length provides very useful information for different applications, such as pedestrian dead reckoning positioning or gait analysis. During the last three decades, many step length estimation methods using inertial sensors have been proposed; however, there is no specific review work that reflects the current state of the art. In this paper, we will conduct a systematic and complete review that covers the whole workflow of tasks involved in the design, test, and evaluation of step length estimation methods based on inertial sensors. The main conclusion drawn from this review is that the lack of public data sets and standard methodologies to guide testing and evaluation makes it difficult to compare the different methods in a fair and robust way. Some reflections on how to move forward on this direction have been presented.

Personal Dead Reckoning Using IMU Mounted on Upper Torso and Inverted Pendulum Model

There has been an increasing demand for infrastructureless localization. Current approaches involving inertial measurement unit (IMU) generally utilize step detection and step counting to estimate the displacement. However, the accuracy is affected, because the step sizes are neglected. Some groups have proposed algorithms that involve placing the IMU on the foot to estimate the step size, but users have commented that it affects their walking. Hence, this paper presents a new method to estimate both the forward displacement and orientation with the IMU placed at the upper torso. Placing IMU at the upper torso to estimate horizontal displacement has been challenging, as the accuracy of the inertial sensors is greatly handicapped by the notorious integration drift when performing integration in the travel direction with the lack of opportunity for zero velocity update. Thus, a novel method is proposed in this paper by exploiting the vertical component of the accelerometer reading. An inverted pendulum model is proposed with a step detector and a step length estimation method. The system is implemented, and two sets of experiments are conducted to demonstrate the capability. The experiment sets include straight lines and rectangular shape path, and in each set, four step sizes of small, normal, large, and mixture are conducted for each test and each test is performed four times. The experimental results show an average displacement error of 1% for straight line paths and 2% for the rectangular paths.

A Knowledge-Based Step Length Estimation Method Based on Fuzzy Logic and Multi-Sensor Fusion Algorithms for a Pedestrian Dead Reckoning System

The demand for pedestrian navigation has increased along with the rapid progress in mobile and wearable devices. This study develops an accurate and usable Step Length Estimation (SLE) method for a Pedestrian Dead Reckoning (PDR) system with features including a wide range of step lengths, a self-contained system, and real-time computing, based on the multi-sensor fusion and Fuzzy Logic (FL) algorithms. The wide-range SLE developed in this study was achieved by using a knowledge-based method to model the walking patterns of the user. The input variables of the FL are step strength and frequency, and the output is the estimated step length. Moreover, a waist-mounted sensor module has been developed using low-cost inertial sensors. Since low-cost sensors suffer from various errors, a calibration procedure has been utilized to improve accuracy. The proposed PDR scheme in this study demonstrates its ability to be implemented on waist-mounted devices in real time and is suitable for the indoor and outdoor environments considered in this study without the need for map information or any pre-installed infrastructure. The experiment results show that the maximum distance error was within 1.2% of 116.51 m in an indoor environment and was 1.78% of 385.2 m in an outdoor environment.

Time-domain multiscale full-waveform inversion using the rapid expansion method and efficient step-length estimation

Full-waveform inversion (FWI) is rapidly becoming a standard tool for high-resolution velocity estimation. However, the application of this method is usually limited to low frequencies due to the high computational cost of the wavefield propagation and the inversion scheme. To mitigate this problem, we have developed a rapid expansion method (REM) for numerical wavefield extrapolation inside the FWI workflow. This method approximated the partial time derivative of the wave equation using Chebyshev polynomials instead of the conventional finite-difference (FD) approximation. This allowed the REM to accurately propagate wavefields with bigger time steps, thus improving the computational efficiency of FWI. We have compared high-frequency FWI results using REM and the traditional FD approximation of the time derivative to illustrate the ability of REM to remain stable and free of numerical dispersion noise even with large grid and time samplings. In addition, we studied a step-length estimation scheme with the objective of avoiding an extra forward wavefield propagation during the line search at each FWI iteration. In this scheme, we estimated the step-length value based on prior iterations and validated this value using the Wolfe conditions. If the value was accepted, then the forward modeling was availed in the next iteration and no extra propagation was necessary. We tried seven different step-length estimation methods, from which we highlighted the adaptive Barzilai-Borwein method when combined with the steepest-descent inversion scheme, and the unitary step length for the L-BFGS algorithm. Through synthetic numerical results, we showed how this scheme could achieve convergence, while keeping the number of extra forward modelings way below the number of FWI iterations.

Adapted step length estimators for patients with Parkinson's disease using a lateral belt worn accelerometer.

Parkinson's disease (PD) is a neurodegenerative disease that predominantly alters patients' motor performance. Reduced step length and inability of step are important symptoms associated with PD. Assessing patients' motor state monitoring step length helps to detect periods in which patients suffer lack of medication effect. Evaluate the adaption of existing step length estimation methods based on accelerometer sensors to a new position on left lateral side of waist in 28 PD patients. In this paper, a user-friendly position, the lateral side of the waist, is selected to place a tri-axial accelerometer. A newly developed step detection algorithm - Sliding Window Averaging Technique (SWAT) is evaluated in detecting steps using signals from this location. The detected steps are then used to estimate step length using four proposed correction factors for Zijlstra's, Gonzalez's and Weinberg's methods that were originally developed for the signals from lower back. Results obtained from 28 PD patients are discussed and the effects of calibrating in each motor state are compared. A generic correction factor is also proposed and compared with the best method to use instead of individual calibration. Despite variable gait speed and different motor state, SWAT achieved overall accuracy of 96.76% in step detection. Among the different step length estimators, the Zijlstra method performs better with multiplying individual correction factors that consider left and right step length separately providing average error of 0.033 m. Zijlstra's method with individual correction factor that considers left and right step length separately and obtained from during ON state of a PD patients provide most accurate estimation among the others. As training session is during ON state, data from induced OFF state to train the methods are not required. A generic correction factor is also proposed to apply with Zijlstra's method to avoid individual calibration process.

A Pedestrian Dead Reckoning System Integrating Low - Cost MEMS Inertial Sensors and GPS Receiver

The body-mounted inertial systems for pedestrian navigation do not require any preinstalled facilities and can run autonomously. The advantages over other technologies make it especially attractive for the applications such as first responders, military and consumer markets. The hardware platform integrating the low-cost, low-power and small-size MEMS (micro-electro-mechanical systems) inertial sensors and GPS (global positioning system) receiver is proposed. When the satellite signals are available, the location of the pedestrian is directly obtained from the GPS receiver. The inertial sensors are the complement of the GPS receiver in places where the GPS signals are not available, such as indoors, urban canyons and places under dense foliages. The height tracking is achieved by the barometer. The proposed PDR (pedestrian dead reckoning) algorithm is real-timely implemented in the platform. The simple but effective step detection and step length estimation method are realized to reduce the computation and memory requirements on the microprocessor. A complementary filter is proposed to fuse the data from the accelerometer, gyroscope and digital compass for decreasing the heading error, which is the main error source in positioning. The reliability and accuracy of the proposed system is verified by field pedestrian walking tests in outdoors and indoors. The positioning error is less than 4% of the total traveled distance. The results indicate that the pedestrian dead reckoning system is able to provide satisfactory tracking performance.

Design of a Wireless Assisted Pedestrian Dead Reckoning System—The NavMote Experience

In this paper, we combine inertial sensing and sensor network technology to create a pedestrian dead reckoning system. The core of the system is a lightweight sensor-and-wireless-embedded device called NavMote that is carried by a pedestrian. The NavMote gathers information about pedestrian motion from an integrated magnetic compass and accelerometers. When the NavMote comes within range of a sensor network (composed of NetMotes), it downloads the compressed data to the network. The network relays the data via a RelayMote to an information center where the data are processed into an estimate of the pedestrian trajectory based on a dead reckoning algorithm. System details including the NavMote hardware/software, sensor network middleware services, and the dead reckoning algorithm are provided. In particular, simple but effective step detection and step length estimation methods are implemented in order to reduce computation, memory, and communication requirements on the Motes. Static and dynamic calibrations of the compass data are crucial to compensate the heading errors. The dead reckoning performance is further enhanced by wireless telemetry and map matching. Extensive testing results show that satisfactory tracking performance with relatively long operational time is achieved. The paper also serves as a brief survey on pedestrian navigation systems, sensors, and techniques.

Step length problem for trimming curve approximation in tessellating trimmed surfaces

A trimmed parametric surface is mainly composed of a surface together with trimming curves lying in D, the parametric space of the surface. By investigating the interrelation between surface tessellation and trimming curve approximation, we point out some problems on trimming curve approximation in existing trimmed surface tessellation algorithms. Counter examples are presented to show that a valid approximation of trimming curves in D together with the refinement imposed by surface tessellation does not necessarily generate a valid linear approximation in 3D space. To assure the 3D derivation tolerance, we propose two novel step-length estimation methods such that a piecewise linear interpolant of the trimming curve based on the proposed step lengths will result in a valid linear approximation in 3D space. The first method exploits the triangle inequality and takes the derivation tolerance in 3D space into account to compute the effective step length. Our second method is based on segmenting the trimming curve into subcurves first and then approximates each subcurve according to the derivation tolerance in 3D space. Moreover, several empirical tests are given to demonstrate the correctness of our step length estimations.

Convergence Conditions for Ascent Methods

Convergence Conditions for Ascent Methods