Varying Step Length Estimation Using Nonlinear System Identification (2013)

Step length estimation is one of the most important aspects of pedestrian navigation solutions especially in pedestrian dead reckoning (PDR). Using absolute navigation systems, such as Global Navigation Satellite System (GNSS), has proved to be insufficient for indoor navigation or when navigating in urban canyons due to multipath or signal blockage. This opened the gate widely 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 (accelerometers and gyroscopes) are commonly used for tracking human movements such as step detection, step length estimation, and consequently estimation of distance traveled.

The step length of pedestrians was estimated in many former research works with noticeable approximation. Step length estimation of a pedestrian is used in several applications such as PDR or measuring the distance travelled by the user. The easiest and most trivial assumption (but not accurate) is that the step length is a constant value regardless the pedestrian characteristics like height, weight, and gender, or motion dynamics (such as for example walking or running speed and acceleration). Some methods require the placement of inertial sensors in certain locations the user’s body (such as, foot, waist or chest … etc.) in order to calculate a varying step length. This makes these methods hard to apply for a variety of applications except those supporting the location for which the method was built.

Some known methods for step length estimation may be categorized roughly into two main groups, namely methods based biomechanical models and methods based empirical relationships. One main drawback of using the biomechanical models is that it is user-dependent since for these methods to work properly, one must find the best scale constant for each specific user. The same problem again appears in the empirical relationships, where there is one or more parameter which requires calibration and customization for each user. As such, these methods are practically not appealing. 

Some prior work that may fall under the empirical category noticed that the speed of a moving pedestrian can affect his step length, for example when a person walks faster he tends to increase the length of his step, also his motion style and dynamics are affected by his increased speed. A related parameter is that the step frequency affects the step length. This type of methods is in general more suitable than other methods for various applications even without need for special mounting of the inertial sensors the body or special mounting in a certain location. In some prior work it was assumed that the step length has a linear relation with the step frequency, where step frequency indicates how many steps are detected per second. The results of this method as is are not satisfactory for applications that requires accurate varying step length estimation as the frequency of step is not the only parameter that can affect the step length. Therefore another technique was used assuming the step length has a linear relation with both the 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 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 requires to be trained with different walking or running speeds, which is not guaranteed and most probably will not happen in a natural real-life trajectory during GNSS availability for online training. This issue is solved by using offline training and the step length estimation is better than online training implementations. The main drawback in the last 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 nonlinear. This problem is also more severe when the step length estimation is intended for both walking and running, not just walking with different speeds. 

This paper introduces a new method for varying step length estimation for on activities, such as walking and running, using nonlinear system identification. The method assumes a nonlinear relation between step length and different parameters that represent human motion dynamics such as step frequency, acceleration variance during step, acceleration peak value during step, peak to peak acceleration value during step, among others. Two phases are required for accurate estimation of varying step length using the proposed method. The first phase is a model building phase where a nonlinear model is built offline by a nonlinear system identification technique; the nonlinear system identification technique is fed by different parameters that represent human motion dynamics by different people with different characteristics such as weights, heights, genders, etc. The second phase is the usage phase in which the nonlinear model is used directly with any user to estimate a varying step length that can vary nonlinearly with human motion dynamics. Fast Orthogonal Search (FOS) is chosen as the nonlinear 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 from the FOS-built nonlinear model and the linear regression model from literature were compared several foot trajectories collected by different people with different speeds to clarify the advantage of using a nonlinear model in step length estimation. Also PDR results using both models were compared.

The presented results demonstrate that the step length estimated from the nonlinear model are more accurate than the one estimated from linear regression model in all the speeds which clearly indicates that the nonlinear model is more capable of solving the varying step length problem for foot motion without the need of linear approximations.