Step length estimation is one of the most important aspects of pedestrian navigation solutions especially in pedestrian dead reckoning (PDR). For indoor navigation or urban environments that experience multipath and signal blockages, the use of absolute navigation systems such as Global Navigation Satellite System (GNSS), have proven to be insufficient. This has opened the door for sensors-based navigation systems to develop, especially after the development of low-cost micro-electro-mechanical systems (MEMS) sensors. In addition to inertial navigation and dead-reckoning, inertial sensors such as accelerometers and gyroscopes are commonly used for tracking human movements such as step detection, step length estimation, and consequent estimation of distance traveled. In former research, pedestrian step length was able to be estimated with noticeable approximation. These estimations can be used in several applications such as PDR or measuring the distance travelled by the user. The easiest and most inaccurate assumption is that step length is a constant value regardless of the pedestrian’s characteristics such as height, weight, and gender, or motion dynamics such as walking vs. sprinting. In order to calculate a varying step length, some methods require inertial sensors to be placed on the user’s body, such as on the waist, chest, foot, etc. This results in these methods being difficult to apply to a variety of applications, except those supporting the location for which the method was designed.

There are roughly two main categories of known methods for step length estimation, biomechanical models and methods based on empirical relationships. The main drawback of using biomechanical models is that it is user dependent. For these methods to work properly, one must find the best scale constant for each specific user. The same problem appears in the empirical relationships, where there is one or more parameters that requires calibration and customization for each user. As such, these methods are not practical or appealing. Prior work done under the empirical category found that the speed of a moving pedestrian can affect their step length. For example, when a person walks faster, they tend to increase the length of their step, and their motion style and dynamics are affected by their increased speed. A related parameter is that the step frequency also affects the step length. This type of method is generally more suitable than other methods for various applications, even without the need for special mounting of the inertial sensors on the body or special mounting in a certain location. In prior studies it was assumed that step length has a linear relation with step frequency, where step frequency indicates how many steps are detected per second. The results of this method are not satisfactory for applications that require accurate varying step length estimation, as the frequency of step is not the only parameter that can affect step length. Therefore, another technique was used assuming the step length has a linear relation with both step frequency and the acceleration variance in a step, where acceleration variance is the variance of the acceleration measured by the accelerometers during one step period. The parameters of the linear model are obtained either by online training when a GNSS signal is available or by offline training before the model is used by the user. The main drawback of online training is that the model needs to be trained with different walking or running speeds, which is not guaranteed and most likely will not happen in a natural real-life trajectory during GNSS availability for online training. This issue is solved by using the offline training and the step length estimation is better than online training implementations. The main issue with the afore-mentioned approach is the assumption of linear relation, which neglects the effect of some motion dynamics and speeds that differ among users and can cause the relation to be non-linear. This issue is also amplified when the step length estimation is intended for both walking and running, not just walking at varying speeds.

This paper introduces a new method for varying step length estimation for “on foot” activities, such as walking and running, using non-linear system identification. The method assumes a non-linear relation between step length and different parameters that represent human motion dynamics such as step frequency, acceleration variance, acceleration peak value, peak to peak acceleration value, etc. Using the proposed method, two phases are required for accurate estimation of varying step length. The first phase is a model building phase where a non-linear model is built offline by a non-linear system identification technique. This non-linear system identification technique is fed by different parameters that represent human motion dynamics by people with varying characteristics such as weight, height, gender, etc. The second phase is the usage phase in which the non-linear model is used directly with any user to estimate a varying step length that can vary non-linearly with human motion dynamics. Fast Orthogonal Search (FOS) is the chosen non-linear system identification technique for implementing the proposed method. For the sake of comparison, an implementation for the method from literature that assumed the step length has a linear relation with step length and acceleration variance, is made using linear regression to calculate the linear relation parameters. The results were compared on several foot trajectories collected by different users with varying speeds from the FOS-built nonlinear model and the linear regression model from literature. This was done to clarify the advantage of using a non-linear model in step length estimation. PDR results using both models were also used in this comparison. The presented results demonstrate that the step length estimated from the non-linear model are more accurate than the one estimated from linear regression model in all the speeds. This clearly indicates that the non-linear model is more capable of solving the varying step length problem for on foot motion without the need of linear approximations.

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