# Stochastic Cooperative Decision Approach for Studying the Symmetric Behavior of People in Wireless Indoor Location Systems

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- Proximity detection or connectivity-based is one of the simplest positioning methods to implement. It provides symbolic relative location information.
- Triangulation uses the geometric properties of triangles to determine the target location [10]. There are two kinds of techniques: (1) techniques based on the measurement of the propagation-time system and RSS-based and received signal phase methods; and (2) techniques based on the angle of arrival of that the mobile signal is coming from.
- Scene analysis is based on the theory of pattern recognition [11], which combines an electronic map with location information to obtain the real position.

## 2. Related Work

## 3. Wireless Indoor Location System

#### 3.1. Wireless Infrastructure

#### 3.2. Node Description

## 4. Studying the Transition Symmetry

_{ij}, denotes the number of transitions observed from location l

_{i}to l

_{j}. It is not possible to have a transition from l

_{i}to li, thus the values of the main diagonal are zero.

## 5. Stochastic Approach for Cooperative Location Estimation

#### 5.1. Introduction

#### 5.2. Stochastic Approach

_{1}, …, l

_{8}. We are interested in the study of movement from one location to another. Thus, we denote as l’ the previous location from where the user is coming.

_{i}to l

_{j}is very similar to transitions from l

_{j}to li; therefore, p(l’|l) ≈ p(l|l’). We can use this fact to better estimate p(l’|l). We assume that p(l’|l) = p(l|l’), and define p(l’, l) as the probability to go from l’ to l or go from l to l’. Using this assumption, Equation (4) can be reformulated as:

#### 5.3. Inductive Training

_{i}, is represented as (l

_{i}, l’

_{i}, u

_{i}, h

_{i}, d

_{i}), where i can be from 1 to t. Several alternatives have been proposed in the literature to estimate p(l’, u, h, d |l) from T: the histogram method [32,33], the Bayesian method [34], or the kernel method [32,35]. The Bayesian method is used in this paper.

## 6. Experimental Results

#### 6.1. Time Spent in Each Location

#### 6.2. Evaluation of the Location Estimation

## 7. Conclusions

_{i}to l

_{j}approximates the number of users that go from l

_{j}to l

_{i}.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Spending time average in each location. (

**a**) Comparison for 10 users for a morning; (

**b**) As a function of the studied time.

**Figure 7.**Percentage of correct predictions (

**a**) using the initial Equation (5); (

**b**) using Equation (6); (

**c**) using Equation (7); (

**d**) using Equation (8).

Parameter | Description | Parameter | Description |
---|---|---|---|

l | location | l^{’} | previous location |

u | user | h | hour of day |

d | day of week | t | number of training samples |

T | set of training data | T_{i} | training sample i; i ∈ {1,…,t}; T_{i} = (l_{i}, l’_{i}, p_{i}, h_{i}, d_{i}) |

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**MDPI and ACS Style**

Tomás, J.; Garcia-Pineda, M.; Cánovas, A.; Lloret, J.
Stochastic Cooperative Decision Approach for Studying the Symmetric Behavior of People in Wireless Indoor Location Systems. *Symmetry* **2016**, *8*, 61.
https://doi.org/10.3390/sym8070061

**AMA Style**

Tomás J, Garcia-Pineda M, Cánovas A, Lloret J.
Stochastic Cooperative Decision Approach for Studying the Symmetric Behavior of People in Wireless Indoor Location Systems. *Symmetry*. 2016; 8(7):61.
https://doi.org/10.3390/sym8070061

**Chicago/Turabian Style**

Tomás, Jesús, Miguel Garcia-Pineda, Alejandro Cánovas, and Jaime Lloret.
2016. "Stochastic Cooperative Decision Approach for Studying the Symmetric Behavior of People in Wireless Indoor Location Systems" *Symmetry* 8, no. 7: 61.
https://doi.org/10.3390/sym8070061