# S-PDR: SBAUPT-Based Pedestrian Dead Reckoning Algorithm for Free-Moving Handheld Devices
## 2 Related Work
### Step-Length Estimation  
The final subsystem of a PDR is the step length estimation. There are mainly two approaches regarding this point: The first is using an average step length per user, and the second is to estimate the step length on the go. Studies from [24,78] show a relationship between the pedestrian physical features, frequency of steps, and their step length. It is found that the step length is directly proportional to the step frequency and with the user's leg length and height. Other studies include the age and gender of the pedestrian as more factors for computing the step length. In its simplest form, step length can be estimated by applying position mechanization for the in-step accelerations [79], but it requires means of bias and drift correction. In the approach of using a foot-mounted IMU this is feasible as a ZUPT would help estimate the errors in velocity and compensate for the position error. In the case of a handheld device, applying ZUPT is not feasible as the device does not experience a zero-velocity period. Various step length models have been proposed for step length estimation and they rely on the relation between the step length and step characteristics of the user. Acceleration-based step length estimation techniques refrain from the integration of the accelerations as it imposes an error that is large relative to the step size. Instead, they employ models that utilize some of the step characteristics such as average acceleration in the step, maximum and minimum accelerations, and include a user-specific parameter that is usually based on the user's physical features [80, 81, 82]. Another famous approach is the frequency-based step length estimation model, where the step is estimated as a function of the frequency of steps taken. Many models exist that use a different underlying relationship between the step frequency and the step length, whereas in some cases the relation is assumed to be linear [83, 84], and user information such as height can be used to make it more adaptive [85]. In other cases, the relation is assumed to be quadratic [86]. A more informed model can use the step frequency in combination with the acceleration variances, or a combination of average, maximum, and minimum accelerations, and user-specific information such as leg length [87, 88]. In all cases, these methods require user-specific information to be able to estimate the step and would usually perform well in strapdown mode. More complex models that use machine learning and avoid the use of predetermined user-specific parameters have been tested, where the step length is computed based on artificial intelligence machine learning algorithms, feature extraction, classifiers, and alternative sensors. Some of the approaches are based on--but not limited to--long short-term memory (LSTM) [89], autoencoders [90], back propagation neural network (BP-NN) [91], DT- and ANN-based classification [92], adaptive step length parameters [93], adaptive parameters based on classifiers [94, 95], and optical flow from camera [96]. Different studies for step length estimation have been carried out that mainly rely on physical features of the user such as leg length or height, or factors related to their walking behavior such as their step frequency, acceleration variance, average walking velocity, and the sway angles. The problem when using any of these models is that it needs to be trained individually per each user to obtain the user-specific estimator parameters. For models relying on physical features, the more information provided about the pedestrian the more accurate they could get. On the other hand, the use of step frequency and variance in acceleration measurements provide very promising results, but they also require a lot of preprocessing and filtering in order to obtain the signal representing only the walking motion of the pedestrian. Usual PDR approaches suffer from the problem of restricting the user activity where there is an assumption made about the motion mode and/or use case of the navigation device.