Occupancy inference using infrastructure elements in indoor environment: a multi-sensor data fusion

Abstract

Gathering occupancy information in indoor environments has gained extensive research interest due to its potential use in energy savings, user comfort and degree of automation. Occupancy information has become a decisive element in many automation systems, such as smart homes and offices, where energy demand is directly linked to user occupancy. However, there is a trade-off between energy consumption and user comfort, thus requiring fine-grained and reliable occupancy information. In this context, this paper presents a multi-modal occupancy inference system to infer the occupancy status of a large Lab or an office setting. Many past works have used different sensors to infer the occupancy of a room. However, we believe that this work is the first of its kind that uses non-intrusive infrastructure-based sensing modalities, such as WiFi and Bluetooth, and fuses them using Dempster–Shafer evidence theory to obtain accurate occupancy information. The system is tested in a graduate student Lab, and the experimental results show that the proposed method provides substantially high accuracy (87.69%) as compared to any single sensing modality. We also establish through empirical studies that the proposed system gives optimal results when the mass assignments are calculated over three to six days on our datasets.

Appendices

Appendix

Dempster–Shafer evidence theory

Dempster–Shafer evidence theory (DSET) computes the probability of the hypothesis which is supported by the available knowledge or evidence (which might be insufficient or contradicting) (Parsons 1994).

1.1 Frame of discernment

In DSET proposition, the basic hypotheses are called frame of discernment $\theta$ (Chen et al. 2014) and it is a collection of mutually exclusive and exhaustive possibilities or hypotheses and all the hypothesis components are not further divisible. The set of all subsets of $\theta$ given by its power set 2$^{\theta }$. As an illustration, if set $\theta$ = {absent, present} then the hypothesis set $\Theta$ includes all the 2$^{\theta }$ possibilities i.e. 2$^{\theta }$ = {$\varnothing$, {absent}, {present}, {absent, present}} where $\varnothing$ is defined as null set (Pratama et al. 2018).

1.2 Probability mass assignment

The system assigns ‘belief’ to the possible hypothesis $\theta$ based on the observed ‘evidence’ (E) from individual sensing elements. The belief assignment from each sensor is called the PMA (m$_{i}$), and it provides a value between 0 and 1 to each hypothesis (Parsons 1994), such that:

• the PMA of the null set $\varnothing$ is zero i.e., belief cannot be assigned to an empty or null hypothesis that is, m($\varnothing$) = 0, and

• the belief of the hypothesis A is described as the summation of every single evidence E$_{k}$ as shown in Equation (1) (Jiang et al. 2017).

  $$\begin{aligned} {Belief_i}(A) = \sum _{E_k \subseteq A} {m_i}({E_k}) \end{aligned}$$

  (1)

1.3 Dempster–Shafer rule of combination

The output of the fusion process considers the most significant value after combining compatible PMAs. Based on the beliefs of multiple sensing elements, the combined belief evaluated with the help of Eq. (2).

$$\begin{aligned} {Belief}(A) = {m_1}\oplus {m_2} \end{aligned}$$

(2)

Now if, $A,B,C\subseteq \theta$ and $m_1(B)\;m_2(C)\;$ are the PMAs of $\theta$ such that$A\subseteq \theta \ne \varnothing$. Thus the combined belief of a given hypothesis A is defined as $m_1\oplus \;m_2and\;\varnothing$ is defined as null set. Here, the numerator in Eq. (3) represents the combined evidence given by the sets B and C. The disagreement among the evidence sources is characterized by the conflict factor K as given in Eq. (4).

Here,

$$\begin{aligned} \begin{aligned} m_1 \oplus m_2 (A) = \frac{\sum _{B \cap C =A} m_1{(B)} m_2{(C)}}{1-K} \end{aligned} \end{aligned}$$

(3)

and

$$\begin{aligned} K = {\sum _{B \cap C =\phi } m_1{(B)} m_2{(C)}} \end{aligned}$$

(4)