# Smartphone-Based Traveled Distance Estimation Using Individual Walking Patterns for Indoor Localization

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Outdoor walking patterns are learned and then applied to indoor localization. To learn the individual user’s walking patterns, the trajectory with a GPS error was corrected for the user, and along with the IMU sensor signal was mapped on the available GPS area using the user’s own smartphone. Indeed, our proposed approach is more effective in terms of the device, user, and walking pattern diversities compared to conventional manually-designed feature extraction.
- (2)
- Estimation of the average moving speed for segmented IMU sensor signal frames. In the case of conventional PDR, the traveled distance is estimated by calculating the step count and stride length using the handcrafted features of the IMU signal. However, we proposed a scheme to estimate the traveled distance by calculating the average moving speed and duration of the signal frame.
- (3)
- Combination of multiscaling for automatic pre-processing at different time scales and CNNs for nonlinear feature extraction and RNNs for temporal information along the walking patterns. Multi-scaling makes the overall trend for different time series input signals. Several stacked convolutional operations create feature vectors from the input signal automatically, and a recurrent neural network model deals with the sequence problems.
- (4)
- End-to-end time series classification model without any handcraft feature extractions as well as requiring any signal or application specific analysis. Many of the existing methods are time-consuming and labor-intensive for feature extraction and classification, and these are limited in their domain-specific application. However, our proposed framework is a general-purpose approach, and it can be easily applied to more kinds of time-series signal classification, regression, and forecasting.

## 2. Related Works

#### 2.1. Indoor Localization

#### 2.2. Deep Learning for Time-Series Sensory Signal Analysis

## 3. The Proposed System Design

#### 3.1. Automatic Dataset Collection Using the Corrected Pedestrian Trajectory with Kalman Filter

_{t}denotes the corrected GPS position x, y at time t, which are transformed into the longitude and latitude into the universal transverse mercator (UTM) coordinate system, respectively. Δd

_{t}and s

_{t}are the displacement and the velocity computed using positions at time t and t − 1, respectively. In addition, s

_{t}is assigned to the label of the IMU sensor signal measured from t − 1 to t. The above process is repeated every second when walking outdoors where GPS is available, and the automatically generated dataset is used for learning.

#### 3.2. Multiscale and Multiple 1D-CNN for Feature Extraction

_{i}is the sample value at time index i, s is a scaling factor, and N denotes the number of samples in each segmented signal frame. The time-series signal x is divided into a non-overlapped window length s (i.e., the scaling factor), and then, window j’s data points are consecutively averaged. We can construct a multi-scaled signal ${}_{s}x=\{{}_{s}x_{1},\cdots ,{}_{s}x_{j},\cdots ,{}_{s}x_{n/s}\}$.

^{l−}

^{1}denotes the number of kernel filters in layer l − 1. ${}_{s}y_{i}^{l}$ denotes the output of max pooling layer l, as well as the input of the next convolutional layer l + 1. Consequently, pairs of convolutional and pooling layers reconstruct a feature vector as the input of the above recurrent neural network model. Additional details of the backpropagation by minimizing the cost function are available in Lecun et al. [39].

#### 3.3. Hierarchical Multiscale Recurrent Neural Networks

_{t},

_{s}m

_{t}, and h

_{t}

_{−s}, the output is h

_{t}and h

_{t+s}for time t. Both gates are similarly computed as in the following equation:

_{x}, U

_{h}, and W

_{m}denote the learnable parameters that linearly combine the input vector x

_{t}, previous hidden state output vector h

_{t}

_{−s}, and additional multiscaled input

_{s}m

_{t}, respectively, b is a bias, superscripts z and r mean that the corresponding parameter belongs to the update gate or the reset gate, and the activation function σ is a sigmoid. The difference of the basic GRU is that the scaling factor s determines whether the recurrent path is activated or not.

_{t}is a set of reset gates, $\circ $ is element-wise multiplication, and tanh is used as an activation function. The candidate activation $\tilde{h}$

_{t}is calculated by the current state W

_{x}x

_{t}, W

_{ms}m

_{t}, and previous hidden state Uh

_{t}

_{−s}, but it depends on the reset gate r

_{t}to activate the previous hidden state. The activation function of the reset gate is a sigmoid, σ(x) $\in $ [0, 1]. If the reset gate value is 0, the previously computed state is forgotten, if it is 1, it allows it to maintain a previously computed state. The current state information is reflected, regardless of the reset gate.

_{t}of the GRU at time t is computed as follows:

_{t}

_{−s}is the previous activation and $\tilde{{h}_{t}}$ is the candidate activation of the current state, and the update gate z

_{t}determines how much it updates each component. The update gate also uses the sigmoid; if z

_{t}is 0, all of the previous activation is forgotten, and only $\tilde{h}$

_{t}is activated, if it is 1, the previous activation h

_{t}

_{−s}is determined as the output of GRU.

## 4. Experimental Results

#### 4.1. Experimental Setup

#### 4.2. Performance Evaluation

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An overview of our indoor localization system using a proposed outdoor walking pattern learning scheme. (

**a**) Inertial measurement unit (IMU) signal and velocity mapping using global position service (GPS)-based user trajectory by walking pattern at outdoor. The collected dataset is used as training data to the following proposed deep learning model; (

**b**) Hybrid CNN–RNN deep learning model. The nonlinear features of the training data were automatically extracted using the multiple convolutional layers with activation and pooling layers; (

**c**) The RNN uses the extracted feature vector at each time step as an input, and learns using signal patterns and labeled velocities; (

**d**) The pedestrian’s average velocity at each time step and the cumulative traveled distance using the learned deep learning model parameters are estimated when moved indoors.

**Figure 2.**The proposed dataset collection scheme for pedestrian walking patterns in real-time, automatically. The blue dots are the raw GPS positions and the red dots are the corrected GPS positions with a Kalman filter. The moving speed is obtained by the displacement of the current position at t and previous position at t − 1, and it is assigned to a segmented IMU signal every 1 s (i.e., the GPS data update rate is 1 Hz) corresponding to the label directly.

**Figure 3.**The proposed multiscale and multiple CNN scheme to extract features. Even if the scaling factor is different, the size of converted signals is same. The multi-scaled signals are fed into each CNN, and then each feature map is generated.

**Figure 4.**Our proposed enhanced gated recurrent unit (GRU) cell. The new components are displayed in dot-line. m is the feature vector of the multiscaled (s) signal at time t, and also, it is the same as the feature vector extracted from the last corresponding CNN layer by Equation (3). The output activation to the recurrent path is determined by the scaling factor s.

**Figure 5.**Our proposed hybrid multiscale convolutional and recurrent neural network model to train and estimate the moving speed for segmented and multiscaled sensory signal. The transformed signals with different timescales are fed into a corresponding CNN to extract the feature vector, and then, each feature vector is fed into the corresponding GRU cell as an additional input,

_{s}m

_{t}. Only the feature vector x

_{t}(s = 1) is fed into the first GRU layer of the stacked RNNs as the input, and h

_{t}is used for the input of the upper GRU layer. The recurrent activation at each GRU layer is determined by the scaling factor of the additional input

_{s}m

_{t}. Finally, the probability distribution for the target moving velocity is computed by Softmax.

**Figure 6.**Confusion matrix with normalization for classification results of Table 3. The number of samples predicted for corresponding class is presented in the parentheses. (

**a**) Represents the result of CNN; (

**b**) shows the result of GRU; (

**c**) is the result of basic hybrid CNN and GRU model; (

**d**) represents the result of our proposed model.

**Table 1.**Simplified Hybrid Single-Scale CNN–Gated Recurrent Unit (GRU) Model Structure and Parameters.

Structure | Input (I) | Filter | Depth | Stride | Output (O) | Number of Parameters |
---|---|---|---|---|---|---|

Conv1 + Relu | 200 × 1 × 3 | 4 × 1 | 64 | 1 | 197 × 1 × 64 | (4 × 1 × 3 + 1) × 64 = 832 |

Max Pooling (dropout 0.2) | 197 × 1 × 64 | 2 × 1 | 98 × 1 × 64 | |||

Conv2 + Relu | 98 × 1 × 64 | 4 × 1 | 64 | 1 | 95 × 1 × 64 | (4 × 1 × 64 + 1) × 64 = 16,448 |

Max Pooling (dropout 0.2) | 95 × 1 × 64 | 2 × 1 | 47 × 1 × 64 | |||

Conv3 + Relu | 47 × 1 × 64 | 4 × 1 | 64 | 1 | 44 × 1 × 64 | (4 × 1 × 64 + 1) × 64 = 16,448 |

GRU | 44 × 1 × 64 | 128 | 2 × 3(I^{2} + I × O + I) = 49,758,720 | |||

Output Classes | 128 | 5 | 128 × 5 = 640 | |||

Overall | 49,793,088 |

Type | Distance (m)/Mean ± Std | ||||
---|---|---|---|---|---|

25 m | 50 m | 75 m | 100 m | Average | |

Handheld | 1.53 ± 0.45 | 0.83 ± 0.27 | 1.29 ± 0.22 | 2.44 ± 0.56 | 1.52 |

Swing | 2.55 ± 0.49 | 2.25 ± 0.20 | 1.23 ± 0.28 | 1.94 ± 0.32 | 1.99 |

2.28 ± 0.82 | 2.88 ± 0.49 | 1.64 ± 0.68 | 2.05 ± 0.88 | 1.96 | |

Mix | 2.57 ± 0.55 | 0.87 ± 0.26 | 1.26 ± 0.48 | 1.61 ± 0.45 | 1.58 |

Average | 1.79 m | 1.28 m | 1.50 m | 2.08 m | 1.66 m |

Models | Evaluation Parameters | ||||
---|---|---|---|---|---|

Distance Error (%) | Accuracy | Precision | Recall | F − 1 Score | |

ANN | 6.466 | 0.668 | 0.564 | 0.536 | 0.538 |

CNN | 3.599 | 0.878 | 0.852 | 0.848 | 0.87 |

Vanilla RNN | 5.676 | 0.714 | 0.643 | 0.633 | 0.629 |

LSTM | 2.441 | 0.904 | 0.895 | 0.888 | 0.887 |

GRU | 2.379 | 0.903 | 0.890 | 0.885 | 0.885 |

CNN + GRU | 1.860 | 0.925 | 0.915 | 0.913 | 0.912 |

Multiscale CNN + GRU with classification (Proposed) | 1.278 | 0.949 | 0.943 | 0.942 | 0.942 |

Multiscale CNN + GRU with regression | 1.572 | - |

Types | Subject 1 | Subject 2 | Subject 3 | Subject 4 | Subject 5 | Subject 6 | Subject 7 | Subject 8 | Subject 9 |
---|---|---|---|---|---|---|---|---|---|

Smartphone | Samsung Galaxy Note 7 | Samsung Galaxy S8 | LG V30 | Samsung Galaxy S7 | LG G6 | LG V30 | Samsung Galaxy Note 7 | Samsung Galaxy S8+ | Samsung Galaxy S7 |

Dataset configuration for training | 14.4 h, 41 km | 11.1 h, 34 km | 10.1 h, 31 km | 4.0 h, 22 km | 4.9 h, 16 km | 4.3 h, 14 km | 2.2 h, 10 km | 2.4 h, 7 km | 1.3 h, 3.6 km |

Pedestrian properties | 181 cm, 85 kg, 38 age, male | 175 cm, 68 kg, 30 age, male | 179 cm, 78 kg 30 age, male | 173 cm, 75 kg, 28 age, male | 163 cm, 53 kg, 24 age, female | 177 cm, 79 kg, 35 age, male | 172 cm, 70 kg, 27 age, male | 160 cm, 55 kg, 21 age, female | 161 cm, 48 kg, 28 age, female |

Models | Subject 1 | Subject 2 | Subject 3 | Subject 4 | Subject 5 | Subject 6 | Subject 7 | Subject 8 | Subject 9 | Average | |
---|---|---|---|---|---|---|---|---|---|---|---|

Proposed Method | Handheld | 1.12 ± 0.14 | 1.01 ± 0.34 | 1.66 ± 0.49 | 2.02 ± 0.33 | 0.89 ± 0.07 | 1.51 ± 0.17 | 1.42 ± 0.14 | 1.98 ± 0.38 | 3.02 ± 0.75 | 1.63 m |

Swing | 1.05 ± 0.27 | 1.16 ± 0.29 | 1.03 ± 0.15 | 1.99 ± 0.24 | 1.12 ± 0.37 | 1.60 ± 0.40 | 1.45 ± 0.61 | 2.63 ± 0.63 | 3.55 ± 0.64 | 1.74 m | |

0.78 ± 0.07 | 0.65 ± 0.15 | 0.87 ± 0.21 | 1.18 ± 0.19 | 1.04 ± 0.21 | 2.37 ± 0.27 | 1.40 ± 0.41 | 2.73 ± 0.35 | 3.42 ± 0.67 | 1.60 m | ||

Weinberg [12] | Handheld | 12.7 ± 0.74 | 13.8 ± 0.29 | 8.12 ± 1.15 | 12.4 ± 0.67 | 12.3 ± 1.36 | 8.73 ± 1.57 | 4.27 ± 2.71 | 3.67 ± 0.86 | 3.95 ± 0.97 | 8.90 m |

Swing | 25.26 ± 3.78 | 22.16 ± 4.14 | 29.58 ± 2.70 | 27.05 ± 2.01 | 20.46 ± 2.16 | 25.12 ± 2.21 | 20.88 ± 5.39 | 17.44 ± 3.12 | 16.64 ± 3.17 | 22.73 m | |

16.20 ± 0.95 | 18.23 ± 2.09 | 20.30 ± 1.94 | 17.02 ± 2.21 | 25.91 ± 3.29 | 18.18 ± 4.92 | 13.75 ± 2.70 | 12.37 ± 0.94 | 14.20 ± 1.58 | 17.35 m | ||

Ho et al. [11] | Handheld | 6.30 ± 3.82 | 3.01 ± 3.81 | 4.49 ± 3.00 | 3.48 ± 1.61 | 3.18 ± 1.88 | 3.46 ± 1.22 | 2.43 ± 2.55 | 6.39 ± 3.46 | 4.93 ± 4.25 | 4.19 m |

Swing | 13.73 ± 2.66 | 18.26 ± 3.40 | 21.65 ± 3.84 | 17.65 ± 3.61 | 20.26 ± 2.62 | 22.14 ± 1.79 | 18.67 ± 3.22 | 20.57 ± 3.71 | 16.39 ± 2.58 | 18.81 m | |

17.37 ± 3.89 | 12.63 ± 5.15 | 14.11 ± 1.48 | 15.13 ± 2.19 | 16.35 ± 2.18 | 15.72 ± 5.74 | 10.82 ± 1.07 | 13.63 ± 2.22 | 10.33 ± 2.26 | 14.01 m | ||

Huang et al. [23] | Handheld | - | - | - | - | - | - | - | - | - | - |

Swing | 3.24 ± 1.10 | 4.22 ± 2.27 | 11.39 ± 1.90 | 3.38 ± 3.00 | 16.03 ± 6.14 | 15.31 ± 6.14 | 7.25 ± 4.23 | 12.21 ± 3.90 | 4.24 ± 1.81 | 8.58 m | |

- | - | - | - | - | - | - | - | - | - | ||

Xing et al. [35] | Handheld | 2.50 ± 0.52 | 2.75 ± 0.26 | 3.19 ± 0.70 | 3.61 ± 1.68 | 4.28 ± 0.97 | 5.93 ± 0.40 | 3.98 ± 2.13 | 5.53 ± 0.94 | 5.76 ± 1.06 | 4.17 m |

Swing | 4.17 ± 0.95 | 3.94 ± 1.92 | 5.93 ± 0.38 | 4.08 ± 0.41 | 5.69 ± 2.17 | 6.13 ± 0.68 | 7.54 ± 0.81 | 6.57 ± 1.00 | 7.48 ± 0.66 | 5.73 m | |

5.21 ± 0.98 | 4.94 ± 0.97 | 7.64 ± 1.11 | 6.42 ± 1.76 | 7.14 ± 1.15 | 8.02 ± 1.62 | 8.83 ± 0.43 | 9.29 ± 2.52 | 8.28 ± 1.12 | 7.31 m |

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## Share and Cite

**MDPI and ACS Style**

Kang, J.; Lee, J.; Eom, D.-S.
Smartphone-Based Traveled Distance Estimation Using Individual Walking Patterns for Indoor Localization. *Sensors* **2018**, *18*, 3149.
https://doi.org/10.3390/s18093149

**AMA Style**

Kang J, Lee J, Eom D-S.
Smartphone-Based Traveled Distance Estimation Using Individual Walking Patterns for Indoor Localization. *Sensors*. 2018; 18(9):3149.
https://doi.org/10.3390/s18093149

**Chicago/Turabian Style**

Kang, Jiheon, Joonbeom Lee, and Doo-Seop Eom.
2018. "Smartphone-Based Traveled Distance Estimation Using Individual Walking Patterns for Indoor Localization" *Sensors* 18, no. 9: 3149.
https://doi.org/10.3390/s18093149