Step Length Estimation Methods based on Inertial Sensors A Review.pdf-资料库

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors Journal JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 1 Step Length Estimation Methods based on Inertial Sensors: A Review Luis E. D´ıez, Alfonso Bahillo, Jon Otegui and Timothy Otim Abstract—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 work, 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 datasets and standard methodologies to guide the 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. Index Terms—Step Length Estimation, Walking Speed Estima- tion, Inertial Sensor, Pedestrian Dead Reckoning, Gait Analysis I. INTRODUCTION T HANKS to the development of micro electro-mechanical systems (MEMS) technology, inertial sensors have be- come smaller, lighter and cheaper, and they are now included in many of the current smart devices. This presents many opportunities for measuring, detecting, estimating and classi- fying different parameters of human behavior and locomotion. Among them, the step length estimation (SLE) has attracted the attention of many researchers because of the possibility of using this information in a variety of applications, such as sport activity monitoring, human gait analysis, energy consumption assessment, or prediction of human health status [1]. One of the most important applications of SLE is pedestrian positioning. On the one hand, because of the potential of this end application and, on the other hand, because pedestrian positioning demands the highest requirements of the SLE methods. Let’s develop these two ideas in more detail: • Inertial pedestrian dead reckoning (PDR) is a positioning technique whose main strength is that no additional Manuscript received on March 28, 2018 This work has been supported in part by the Spanish Ministry of Economy and Competitiveness under the ESPHIA project (TIN2014-56042-JIN), in part by the Basque Department of Education under the BLUE project (ref. PI 2016 0010), and in part by the Research Training Grants Programme of the University of Deusto L. E. D´ıez, A. Bahillo and T. Otim are with Faculty of Engineering, University of Deusto, Av. Universidades, 24, 48007, Bilbao, Spain, e-mail: {luis.enrique.diez, alfonso.bahillo, otim.timothy}@deusto.es. J. Otegui is with DeustoTech-Fundaci´on Deusto, Deusto Foundation, Uni- versity of Deusto, Av. Universidades, 24, 48007, Bilbao, Spain, e-mail: jon.otegui@deusto.es. infrastructure needs to be installed in the environment. It only requires the inertial sensors (namely, accelerometers and gyroscopes) that are carried by the pedestrian. The strapdown inertial navigation system (INS) mechaniza- tion is the standard implementation of inertial PDR but, because of the signiﬁcant errors of MEMS sensors, the position error grows cubically in time. To reduce this drift, it is posible to apply zero-velocity updates (ZUPTs) when the foot is stationary on the ground, making the position error linear with the number of steps [2][3]. However, this correction requires that the sensor is mounted on the foot, which may mean a limitation of usability. A step-and-heading system (SHS) is an alternative method of implementing a PDR system and it is based on the integration of the displacement vectors associated to each step. For obtaining those displacement vectors, a SHS is composed of three main sub-algorithms: step detection, step length estimation (SLE), and step heading estimation [4]. Therefore, although the step heading estimation is currently the sub-algorithm whose performance is the most limiting for positioning purposes, the SLE is also one of the basic parts. One advantage of the SHS implementation is that its position error is also proportional to the number of steps (similar to the INS with ZUPT implementation) but without the restriction of using only foot-mounted sensors. Therefore, SHS, and SLE methods as one of its main parts, are essential for the development of pedestrian positioning systems that are based on wearable devices, which are considered as key devices for implementing real and practical seamless Location Based Services (LBS). • The accuracy requirements for SLE methods is more demanding for positioning purposes than for other appli- cations. For example, a 1% estimation error after traveling 8 kilometers (i.e., 80 meters) makes little difference if the purpose of the application is to monitor a person’s activity level, for instance. On the contrary, that same 80 meters error could mean missing the room in which a person is and, depending on the ﬁnal LBS, this could be unacceptable. There are many proposals for SLE methods which are based on different models and assumptions and which are tested and evaluated in various ways. This indicates that SLE is still in its research stage and that there is no existing gold standard solution. However, in the scientiﬁc literature there are not speciﬁc surveys that review the state of the art of this topic. Only a few general positioning surveys [4]–[6] and new SLE 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors Journal JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 2 Left stride Right step Left step Right stride speed estimation methods, and they found that most of them were oriented towards clinical experimentation and foot-mounted inertial sensors were commonly used [14]. • Only works in which the importance of the SLE is not reduced by the use of additional sources of information were included, such as map matching or the fusion with other absolute positioning technologies. Fig. 1. Strides are deﬁned by the positions of two consecutive footfalls of the same foot, while the steps are deﬁned by the positions of opposite feet. B. Article Selection method proposals [7]–[11] include a short and basic review. Therefore, it would be advisable to carry out a deep and systematic review of the SLE methods, including a description of all of the phases of their workﬂow (design, implementation, testing and validation). This would give us a complete view of the state of the art of this ﬁeld, it will identify the unsolved problems and it will outline the future trends. This has been both the aim and the contribution of this work. A. Scope of the Review To make this review tractable, the following set of criteria were established, delimiting the scope of the review: • The target activity is walking, although some reviewed articles have also dealt with running. • Strides are deﬁned by the positions of two consecutive footfalls of the same foot, while the steps are deﬁned by the positions of opposite feet (see Fig. 1). When walking straight, the stride lengths of both feet are equal to each other and equal to the sum of the last two steps. However, this does not happen when turning, as the foot further from the center of rotation travels a greater distance than the other foot. Additionally, different step length deﬁnitions can produce different results [12]. This is something that applications which integrate stride or step lengths must take into account. For this review, both step and stride length estimation methods were considered and no further distinction has been made. • Only works in which one sensor unit is used were included. Naturally, the use of multiple sensors provides more information but it also makes the system more complex, so it will be assumed that the user only carries one smart device at a time. • Works with a foot-mounted inertial sensor were not included because it is considered that an implementation based on INS and ZUPT is the best option when the inertial sensor is on that body location, since no training or calibration is needed. However, we are aware that there exists statistical learning based SLE methods for foot- mounted inertial sensors that obtain good results, such as in Hannink et al. [13]. • Works that estimate the walking speed were also in- cluded, as long as the estimation is provided at a rate that is valid for positioning purposes. Although walking speed estimation is quite common in gait analysis applica- tions, they do not usually have the same requirements as positioning. For example, Yang and Li surveyed walking Inspired by the procedure followed by Yang and Li in their survey [14], we searched in the following three popular electronic engines/databases in the ﬁelds of engineering and biomechanics: PubMed, ISI Web of Knowledge and IEEE Xplore. The search was made on the ﬁrst week of May 2018 and the searched keyword string was “(assessment OR estimation OR calculation OR computation OR measurement) AND (inertial sensor OR accelerometer OR gyroscope OR inertial measurement unit) AND (speed OR velocity OR step length OR stride velocity OR stride length) AND (walking)” for appearance in the title (ISI Web of Knowledge) or in any ﬁeld (PubMed and IEEE Xplore). The results were then reﬁned by selecting only those works that were published from 1990 onwards. Initially, 987 references were obtained. The title and the abstract of each article was read carefully to exclude any duplicates and works that did not ﬁt in the deﬁned scope. A total of 49 works were ultimately included, as follows: [7]– [11], [15]–[58]. C. Structure of the Review The structure of the rest of this paper is as follows. Sec- tion II describes the deﬁnition of the a priori questions that we tried to answer during the literature review. The results of the review are described in sections III, V, IV and VI. Section VII presents a series of reﬂections on the availability of standards and public datasets in this area, whose current lack is considered to be a barrier to progress in this ﬁeld. Finally, the conclusions and some recommendations for future work are given in section VIII. II. DEFINING THE REVIEW QUESTIONS To make a complete and systematic review of the state of the art of a given ﬁeld, it is advisable to identify in advance the questions, concepts, or criteria on which the focus will be placed when reviewing the selected literature. In this work, to make this identiﬁcation as exhaustive as possible, a hypothetical workﬂow to design and validate a new SLE method was deﬁned, as can be seen in Fig. 2. Reﬂecting on each of the tasks that make up this workﬂow, we have identiﬁed the questions that we will try to answer during the review of the selected literature. Positioning was selected as the possible target application because it imposes high performance requirements on the SLE method. 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors Journal JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 3 SLE Method Design Prior Step Length Knowledge SLE Method System Characteristics Scope and Use Cases SLE Method Testing SLE Method Evaluation Fig. 2. Hypothetical workﬂow that could be followed during the design, testing, and evaluation of a new SLE method that is part of a higher level system. It can be seen that deﬁnition of use cases can affect all phases: design, test and evaluation. The dotted arrows mean that, after a SLE method is evaluated, it can be decided to loop back iteratively for improving its performance. A. SLE Method Design The design of an SLE method will be the result of a certain compromise between the characteristics of the system in which the SLE method will be included, the use cases to be addressed and the previously available knowledge on the behavior of the step length. The review questions that may arise in each of these individual areas will be presented below, without analyzing the possible inter-dependencies between them. 1) Prior Step Length Knowledge: To design an SLE method, it is necessary to have certain knowledge about the process that will be estimated. The following questions may arise from this task: • What knowledge or observations are used as a basis for the different SLE methods? • What ﬁelds do they come from? • Do they come from proven and recent sources? (E.g. journals, conferences, books, etc.) 2) System Characteristics: Most of the system character- istics that can be involved in the SLE method’s design are related to the hardware used, so the following questions arise: • What types of sensors are used? Accelerometers? Gyro- scopes? Others? • What are the technical characteristics of the sensors? For example, what are the number of axes, sampling rate, measuring range? 3) Scope and Use Cases: Given the great variability in users, activities and conﬁgurations, it is common that systems that deal with human activities are designed for a limited number of use cases. The following questions can be stated: • Where on the body is the sensor unit placed? • What are the target users’ characteristics? Will age or anatomical restrictions be used? Will only healthy people be used or will people with gait pathologies be included? • What kind of movements and activities are contemplated? • In which scenarios will the system be used? Indoors or outdoors? Leveled or with slopes? Stairs? As can be seen in Fig. 2, the deﬁnition of the use cases can inﬂuence both the experimentation and evaluation processes, since they all have to be aligned. 4) SLE Method: The combination of the prior knowledge about step length, the system characteristics and the use cases will lead to the design or choice of a particular SLE method, which can be described from different criteria: • What types of SLE methods exist? What kind of model or assumption is each type of SLE method based on? • How many input parameters does each type of SLE method need? Of what kind? And, how are these inputs obtained? • Is it necessary a calibration of the SLE method for each speciﬁc user? If so, will it be an ofﬂine or an online calibration? B. SLE Method Testing Once a SLE method has been implemented, it must be tested to validate its operation. This experimentation process can be described according to different parameters, as follows: • Are the experimentation’s trials aligned with the use cases deﬁned by the scope? • Is the test data sufﬁcient in volume and variability? • What information source is taken as a reference or ground truth? C. SLE Method Evaluation The aim of the evaluation is to extract enough information from the data obtained during the experimentation to decide whether the performance of the SLE method is valid or to loop back iteratively to improve it. For this purpose, the evaluation can be broken down into several phases: the deﬁnition of the performance metrics, the calculation of the value of these metrics and the decision about the validity of the SLE method by comparing its performance with some predeﬁned thresholds or other SLE methods’ performances. Thus, the following questions arise: • What different performance metrics are commonly used? • Assuming that the estimation error is the most common performance metric, what deﬁnitions of estimation error are commonly used? • Since experimentation only provide a sample of the performance of the SLE method, how is the process of estimating the SLE error? What descriptive statistics are commonly used to describe the SLE error? • What is the performance of the different SLE methods of the state of the art? Is it possible to compare them from the reported SLE errors? 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors Journal JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 4 D. Results of the review The following sections will present the results obtained after reviewing the selected literature through the points of view deﬁned by the identiﬁed review questions. To do this, the workﬂow shown in Fig. 2 will be followed downwards: • Section III. Prior Knowledge about Step Length • Section IV. Step Length Estimation Methods • Section V. System, Use Cases and Experimentation: All aspects related to the characteristics of the ﬁnal system, the deﬁnition of the use cases and the experimentation will be grouped in the same section, because all of them must be aligned. • Section VI. SLE Methods Evaluation III. PRIOR KNOWLEDGE ABOUT STEP LENGTH It is possible to design SLE methods using simple ideas, such as the relationship between the stride length, the user’s leg length, and the opening angle of the leg during each stride. However, most of the SLE methods are based on not so evident patterns that have been observed thanks to the study of the human gait over many years, especially in the ﬁeld of biomechanics. A. Displacement of the Pelvis During Human Walking Given that the Center of Mass (COM) of the body lies within the pelvis, it is very interesting to know the trajectories of that part of the body during locomotion. To study the ﬂuctuations of the potential and kinetic energies of the body during walking, Cavagna et al. proposed a model in which the COM rotates as an inverted pendulum over the stance foot during the single support phase, followed by a forward horizontal displacement during the double support phase; that is, when both feet are on the ground [59]. Later, Zijlstra et al. used this model to study how the spatio-temporal gait parameters affect the pelvis’ displacement and they derived a geometrical expression that relates the vertical displacement of the pelvis, the leg’s length and the step length [60]. This geometrical expression has been used many times by different SLE method proposals. Later works have proposed improvements of Cavagna’s inverted pendulum model, such as the use of a percentage of the foot length for the longitudinal displacement during the double-stance phase or more complex models that also take into consideration the rotation of the pelvis and the ﬂexion of the ankle and the knee [61]–[64]. B. Spatio-temporal Gait Parameters The human gait has been analyzed in depth for many years. Spatio-temporal parameters, such as step length, step frequency, walking speed or gait asymmetry, are used as one of the main tools to describe gait operation and to detect anomalies. The behaviour of the step length, as one of these spatio-temporal parameters, has been studied in relation to different parameters, such as its variation over time, between alternative footsteps, age or gender [65]. One topic that has attracted a lot of interest is the relation- ship between walking speed, step length and step rate. A faster walking speed implies an increase in both the step rate and the step length, but each person implements that mechanism in a different way. The works of Kuo [66], and Bertram and Ruina [67] proposed a model for this relationship and they suggested that it is due to an optimization strategy, in which each person optimizes an underlying objective function that has a minimum at the preferred gait. However, works such as Sun et al. have shown that this relationship is also affected by other external factors, such as the slope of the terrain [68]. C. The Arms During the Gait Usually, biomechanical studies of human gait tend to focus on the role of the lower limbs and the trunk, so the upper limbs have been little studied. Swinging is the natural motion of the arms when walking with the hands free, and it is well-known that it is synchronized with the opposite side’s foot. That is, the most advanced position of the left hand coincides with the right footstep, and vice versa. However, little is known about how and why this swinging is generated. The survey by Meyns et al. collected the existing knowledge about this topic, indicating that one of the possible functions of arm swinging is to reduce energy consumption by compensating the angular moment that is produced in the trunk by the legs during each stride [69]. IV. STEP LENGTH ESTIMATION METHODS Methods for computing the step length can be divided in two main classes: the ﬁrst are direct methods, based on the integration of the accelerations; and the second are indirect methods, which use a model to compute the step length. For the latter, there is a large variety of proposals that can be di- vided again according to whether they are based on geometric models or if they use statistical methods of prediction. Next, each type of method will be described in more detail. This is supported by table I, which presents the main characteristics of the indirect methods, and Fig. 3, which shows the distribution of the reviewed references over the main body locations. In addition, the different types of calibration that are usually applied to SLE methods to adjust their performance to the characteristics of each user and/or scenario will be described. A. Integration Methods The double integration of the acceleration in the forward direction is the best method in theory to compute the length of the steps because it is not based on any model or assump- tion and it does not require training stages or user speciﬁc calibration. However, as for any INS, the non-negligible bias and noise of the MEMS accelerometers and gyroscopes make the distance error grow boundless cubically in time. Several assumptions and heuristics have been used to reduce this error rate. However, the ﬁrst difﬁculty of these methods is how to obtain the acceleration in the forward direction from the sen- sor’s measurements. Because each part of the body moves in 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors Journal JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 5 Any place where step frequency can be sensed: [8], [15], [18], [28], [33], [41], [47], [48], [50] Head: [9], [11], [44], [56] Handheld/Wrist-worn coupled to COM: [8], [9], [11], [33], [37], [39]–[41], [47], [48], [57] COM: [7], [17]–[20], [22]–[25], [28], [30], [36]–[38], [44], [49], [51] Front Pocket/Thigh: [10], [16], [29], [37], [40], [43], [46]–[48] Shank: [31], [32] Chest: [26], [40] Back Pocket: [40], [47] Handheld/Wrist-worn swinging: [8], [9], [11], [35], [37], [39], [41], [45], [48], [50],[52], [55], [57} Ankle: [21], [51] Fig. 3. Distribution of the different body locations of the SLE methods from the reviewed references. The SLE methods that only depend on the step frequency can be used on any body location in which that feature is sensed. For those SLE methods, the body location on which they were tested in the original reference is also indicated. different directions during walking, it is not easy to constantly maintain a sensor parallel to the direction of travel. It is, therefore, necessary to continuously know the orientation of the sensor, which will involve the use of several accelerometers and gyroscopes to transform the sensors accelerations into the navigation reference system. Of course, this process is also not error-free. Li and Yang proposed mounting a 2-axis accelerometer and a 1-axis gyroscope on the lateral side of the mid-shank [31], [32]. Both the segmentation into strides and the transformation of the accelerations into the navigation frame are obtained by using the angle obtained by integrating the gyroscope’s angular rate. They use the vertical position of the shank to divide the stride segments and they assume that the initial velocity in that moment is zero. After integration, they also assume that the net acceleration during one stride was zero to correct the error of the accelerometers. K¨ose et al. proposed a system that requires a 3-axis ac- celerometer and a 2-axis gyroscope that are placed on one side of the pelvis [7]. They are able to detect and differentiate the steps of each foot by using wavelet decomposition. They then compute the length of each step using a combination of direct and reverse integrations of high-pass ﬁltered accelerations. The fact that only these two works have been found and that both are focused on gait analysis, where the environment is usually more controlled and the time of use is shorter than in positioning applications, highlights that these integration techniques are less suitable for positioning than ZUPT for foot- mounted sensors. B. Biomechanical Models Due to the mechanical nature of the human body, it is possible to deﬁne analytical expressions of the step length based on geometrical relations between some dimensions, angles, and displacements of different parts of the body. The advantage of using biomechanical models is that it allows a good understanding of the relationships on which the es- timation of the step length is built. However, due to the complexity of the human body and the great variability of people and scenarios, these models are usually simpliﬁcations and approximations that require calibration phases to adjust their performance to each speciﬁc user and walking pace. Miyazaki used a simple geometric model in which he estimated the stride length using the leg length and the opening angle during the stride [16]. To measure this angle, he used a 1- axis gyroscope mounted on the thigh. Miyazaki found that the error in the estimation of this model depends on the walking speed, so he introduced an adaptive correction parameter to address this issue. Several SLE method proposals have emerged from the relationship between the vertical displacement of the pelvis and step length, as described in section III-A: Using the inverted COM pendulum model, Zijlstra and Hof derived [20] the geometric expression (1) that relates the step length, the length of the user’s leg (L), and the vertical displacement of the COM during the stance phase (H), which is obtained by 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors Journal JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 6 double integration of the high-pass ﬁltered vertical acceleration of a sensor placed on the low back. However, they found that this model tends to underestimate the step length and that a calibration parameter is needed to adjust the performance to each user. SL = 2p2LH − H 2 (1) Alvarez and Gonzalez proposed several modiﬁcations of Zijlstra’s model, such as the use of heuristics to reduce the integration drift error in [22] or the inclusion of the length of the user’s foot as a predictor of the forward displacement during the double-stance phase in [25]. There are also works that are based on the same biome- chanical observation but which propose empirically simpliﬁed expressions to avoid the integration: Weinberg proposed in [19] the expression (2), which is proportional to the amplitude of the vertical acceleration during a step. Later, Scarlett proposed an alternative expression that also took into account the dispersion of the vertical acceleration during the step, looking for a better adaptation to different users [24]. Neither expression contained a parameter related to the user’s physical characteristics and, therefore, they need to be calibrated for each user and each walking pace. SL = K 4pAmax − Amin (2) In an attempt to simplify the calibration process at different paces, Mikov et al. substituted the calibration parameter in Weinberg’s expression by the time duration of the step [40]. In a more general way, Zhu et al. substituted this with a linear regression model of the step frequency and the acceleration variance during a step [44]. More complex biomechanical models have also been used, such as in Hu et al., where the authors used a pelvic displace- ment model that takes into account the knee and ankle ﬂexion during the stance phase, which is often known as rolling-feet. They derived a dynamic model of the pelvis and they estimated the walking speed using an unscented Kalman ﬁlter [38]. Although the inverted pendulum model offers simplicity and acceptable performance, it usually requires the accelerometers to be as close to the COM as possible. Recently, Jiang et al. proposed a geometric model in which they estimated the COM’s vertical displacement from a wrist-worn sensor during arm swinging [55]. They used some assumptions about the synchronization between the vertical movements of the trunk and the hand, which have not been referenced or demonstrated. However, this is a novel proposal that reﬂects the potential of using knowledge about the body’s mechanical structure. Also for a wrist-worn sensor, Bertstchi et al. proposed a walking speed estimation method that is based on a biomechanical explanation of the purpose of the arm swinging; that is, the compensation of the torque generated by the legs in the trunk. They claimed that walking speed is proportional to both the step frequency and to this torque, which they modeled as a non-linear function whose expression is not described because the patent is pending [45]. C. Statistical Regression Methods Statistical regression methods seek to estimate the relation- ships among variables, which is useful for predicting the value of a variable that is difﬁcult to obtain from the values of other variables that are easier to measure. These latter variables are known as features or predictors. As seen in section III-B, there is a clear relationship between step frequency and step length, and also with other variables. Therefore, they can be used as predictors of the step length and, thanks to the periodicity of human gait and the mechanical nature of the human body, some of them can be measured from different body locations, and by using different techniques and sensors. This ﬂexibility is one of the main reasons to use statistical models for SLE. The features used in the SLE methods of the reviewed articles can be observed in table I. The task of estimating the relationship between the variables of interest is usually known as training. The data and the model estimation techniques used during this task will affect the accuracy and the generalizability of the subsequent estimation of the step length. There are two types of model estimation techniques: parametric and non-parametric. Parametric techniques assume an a priori type of model. Generally, they are simple models with a low number of predictors, which can provide a certain insight about the real relationship. However, if the selected a priori model is very different from the real one, then the prediction accuracy will be low. The simplest and most commonly used parametric technique is the linear regression (or ordinary least squares). It is assumed that step length is a linear combination of the features, using as ﬁtting criteria the minimization of the quadratic error. Many works use this technique with the step frequency as the only feature ([15], [28], [33], [50]), or they also add the variance of the acceleration over a step ([17], [23], [36], [39]), or a greater number of features, such as Fasel et al. [57]. Although the step frequency is the most common predictor, there are works that are based on other features. For example, Diaz et al. proposed to use an inertial sensor mounted on the thigh and they built a linear regression model using the amplitude of the variation of the leg’s pitch as the only predictor [10], [43]. The linearity criterion refers to the parameters that ﬁt the model and it does not refer to the predictors. Consequently, it is also common to ﬁnd proposals that use transformed versions of the features and/or products of several features. in which the linear model In general, using more predictors helps to get better pre- dictions but there is a higher risk of overﬁtting the model to the training data. To reduce this, Zihajehzadeh et al. used the Lasso regression, is ﬁtted by minimizing a penalized version of the least squares loss function [51], [52]. This makes it possible to include a large number of features into the training, but the model is ﬁtted by using only a selection of them. Some proposals have used non-linear models. For example, the logistic regression used in [47], or system identiﬁcation techniques, such as Fast Orthogonal Search (FOS) used in [9], [11], in which the feature selection is made from a set that also includes values of features of previous taken steps. Fuzzy inference systems 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 Journal TABLE I PROPOSED SLE INDIRECT METHODS IN THE REVIEWED LITERATURE AND THE MAIN FEATURES THAT THEY USE. 7 SLE Method References Features Gait parameters User Signal SF VD ANG H L W σ2 acc △ FFT Biomechanical [55] [38] [20] [22], [25] [19] [24] [40] [44] [16] [45] [57] Linear regression [8], [41], [48] [17], [23], [35], [36], [39] [15], [18], [28], [33], [50] Lasso regression Logistic regression FOS FIS GPR RLS ANN Empirical [10], [43] [51], [52] [47] [9], [11] [49] [46] [30] [51], [52], [56] [37] [26] [21] [29] 4 6 2 3 1 3 2 3 2 6 5 2 2 1 1 50 1 14 2 2 6144 50 61 5 1 3 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Other features Hand’s vertical displacement Hand’s forward displacement User’s arm length User’s pelvis width Rolling-foot radius to leg length ratio Navigation frame accelerations User’s foot length Mean, max, min of vertical acceleration Navigation frame accelerations Variation of altitude in the terrain Mean of acceleration norm [48] uses square root of step freq. [35] also square and product of features [18] quadratic model X Temporal statistics of acceleration Delayed versions and all inter-products Area of acceleration norm X X X Temporal statistics of acceleration Energy Mean absolute acceleration Mean absolute acceleration Acronyms: step frequency (SF); vertical displacement of the COM (VD); angular amplitude of the leg (ANG); users’ height (H), leg length (L) and weight (W); moving variance of the acceleration (σ2 acc); range of the acceleration (△); FFT coefﬁcients of the acceleration (FFT); fast orthogonal search (FOS); fuzzy inference system (FIS); Gaussian process regression (GPR); regularized least squares (RLS); artiﬁcial neural networks (ANN). (FIS) could also be considered as a parametric method because they allow us to build a prediction method in the cases where the model is vaguely known, or fuzzy deﬁned. The works of Li et al. [46] and Lai et al. [49] used this approach. Non-parametric techniques do not assume an a priori model and are ﬁtted to the training data in a ﬂexible way. In gen- eral, they achieve better prediction accuracy than parametric techniques but they require larger training datasets, need more features, are more prone to overﬁtting, and they provide less information about the actual relationship. In the revised literature, we have found works that have used non-parametric methods such as Gaussian process regression (GPR) in [30], [51], [52], [56], Regularized least squares (RLS) in [37] and artiﬁcial neural networks (ANN) in [26]. Non-parametric methods can include works that propose expressions obtained by empirical manual ﬁtting, such as the works of Kim et al. [21] or Bylemans et al. [29]. D. Calibration Procedures All SLE methods, except those based on direct integration, require the execution of a calibration procedure to adjust the accuracy of the SLE. Three main types have been identiﬁed, as will be described in the following subsections. 1) Universal Calibration: This refers to the training phase that is typical of the SLE methods based on statistical re- gression. This type of calibration is very convenient for the end users because they do not need to participate in the training phase and, therefore, they can start using the SLE method immediately. At most, they will have to inform some parameters about their anatomy, such as the height. However, the accuracy of the SLE method will also depend on its generalizability. As mentioned in section IV-C, this is affected by both the model estimation technique and the training data. 2) Ofﬂine Individual Calibration: This type of calibration is common in SLE methods based on biomechanical models, since it is necessary to previously adjust certain parameters of the model to the characteristics of each user in order to improve the accuracy. These procedures usually consist of walking a known distance and then adjusting a scaling parameter to improve the estimation result. Although this is a simple task, this is not always convenient for the ﬁnal user. For instance, some SLE methods, such as the one proposed 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2857502, IEEE Sensors Journal JOURNAL OF XXXX, VOL. XX, NO. XX, MMMM 2018 8 by Scarlett [24], requires each user to perform that calibration procedure for each different walking pace. Qian et al. proposed a more comfortable procedure in which the optical ﬂow captured by the camera of a smartphone is used to compute the traveled distance and to automatically perform the individual calibration [42]. 3) Online Individual Calibration: This type of calibration attempts to combine the advantages of the two previous types of calibration. A universally calibrated regression model is progressively modiﬁed, as long as the SLE method is used, to ﬁnd a better ﬁt to the characteristics of the active user. GNSSs are usually used as the necessary source of ground truth. In this way, when walking outdoors, it is possible to adjust the SLE method so that, when entering a zone without GNSS coverage, the SLE method will yield a better accuracy than using the initial universal calibration. Several authors have proposed different iterative techniques for implementing online calibration, such as the Extended Kalman Filter [35], [41], an adaptive Kalman Filter [17], and recursive least squares [8]. In a similar way to the training phase in statistical learning, these recursive methods need to process sufﬁciently varied data to estimate the closest model for the user and to avoid obtaining just a local optimization. This could happen, for instance, if the calibration is performed using data from a small range of walking speeds. V. SYSTEM, USE CASES AND EXPERIMENTATION A. Sensor Mounting Point As can be observed in Fig. 3, several SLE methods are available for many parts of the body. The ﬁrst proposed SLE methods were designed for mounting the sensor in just one possible body location, preferably involving as little change of orientation as possible. Therefore, the pelvis and the low back were the ﬁrst places chosen. In the case of gait analysis applications, because the experimentation is usually carried out in a controlled environment, other body locations such as thigh or shank were also proposed. In both cases, these body locations are ideal for SLE methods based on biomechanical models. Many researchers have begun to use smartphones for SLE. This has led to the design and validation of SLE methods for the body locations where smartphones are usually car- ried, including the possibility that the device may change its position and orientation during the estimation process. In the experimentation, only a limited number of places where the smartphone can be carried are usually considered. The most common places are in the trouser pocket, handheld (in several poses), or inside a bag [8], [11], [37]. Finally, the recent appearance of wearable devices, such as smartwatches or smartglasses, has again generated the opportunity to design SLE methods for speciﬁc body locations because it can be assumed that the wearable device will not change its mounting point [45], [52], [55]–[57]. B. Characteristics of the Sensors Accelerometers are the most commonly used inertial sensor for SLE, either alone or with gyroscopes. Miyazaki’s proposal is the only one that has been found that estimates the step length using only a gyroscope [16]. Regarding other types of sensors, Fasel et al. also included a barometer to measure changes in the terrain’s altitude and added that information into the SLE [57]. The number of axes of the sensors should be differentiated between those available in the sensor unit and those that are actually used for SLE. The latter depends on both the type of SLE method and the body location where the sensor is mounted. Works that use only accelerometers usually choose 3-axis accelerometers and they compute the norm of the vector composed by the measurements of the three axes. This signal has the advantage of being immune to the change of the sensor’s orientation. If the sensor is placed in a body position where its orientation is almost constant, then it is possible to dispense with some of the axes. This is the case of some trunk-mounted SLE methods that process only the vertical axis [18], [19], [24]. Regarding the SLE methods using both accelerometers and gyroscopes, it is common that both sensors have three axes because they are necessary for continuously estimating the sensor unit’s three dimensional orientation and, later, transforming the sensor’s accelerations to the navigation reference frame. In some cases, when it is known that the motion of interest occurs only in one plane, it is possible to use fewer measuring axes, as Yang and Li [31], [32], who only used a 2-axis accelerometer and a 1-axis gyroscope for measuring the swinging of the shank. The measuring range and sampling rate are also important characteristics of inertial sensors. Both values have to be suitable for the dynamic range of motion to be measured. Regarding the measuring range, although many authors do not indicate this value in their works, values between ±2g and ±16g have been found for accelerometers, the lowest is the most common, and 150°/s, 300°/s and 1000°/s is used for the gyroscopes’ measuring range. It should be noted that the larger measuring ranges were found in works with wrist- worn sensors [39], [45], [57], which is one of the body areas that experiences greater range of motion during walking. For the sampling rate, the reported values range from 10Hz to 200Hz, and 100Hz is the most used value. A person’s step rate does not usually exceed 3Hz, so a 10Hz sampling rate may be enough to sample the signals. It is common that both the accelerometers and gyroscopes work at the same rate. C. User Typology Most of the reviewed works present a good user gender balance in the experimentation. However, their scope is limited mainly to young people, excluding children and the elderly. It is also common to include in the experimentation only users without gait pathologies. Some exceptions are found in Miyazaki [16], in which tests were performed on patients with above knee prostheses or hemiplegia, and in Duong et al., whose work was speciﬁcally designed for people that needed a walker to move around [54]. For the physical description of the users included in the experimentation, some works describe their physical characteristics, such as their height or weight, but they are never values too far from the average and it is 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Step Length Estimation Methods based on Inertial Sensors A Review.pdf

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