Quantified Living Habits Using RTI Based Target Footprint Data

Abstract

Providing personalized healthcare for elders is more and more necessary in aging society. It is the premise to quantify their living habits properly. In this paper, a classification algorithm is used to transform footprints of elder into daily activities by combining point of interest. A concept of activity matrix and vector is proposed to quantify daily life, and then a clustering algorithm based on similarity is put forward to realize abnormal behaviors recognition. Finally, a experiment is given to illustrate the effectiveness of the proposed methods.

Appendices

Appendix 1: Radio Tomographic Imaging (RTI): Loss Model

A wireless sensor network with objects using radio frequency (RF) nodes is shown in Fig. 10a. In RF sensor network, the received signal strength (RSS) ${y_i}(t)$ of link i at time t is described as [8]

$$\begin{aligned} \ {y_i}(t) = {P_i} - {L_i} - {S_i}(t) - {F_i}(t) - {n_i}(t) \end{aligned}$$

(8)

where ${P_i}$ is transmitted power, ${S_i}$ is shadowing loss due to objects who attenuate the signal, ${F_i}(t)$ is fading loss that occurs from constructive and destructive interference of narrowband signals in multipath environment, ${L_i}$ is static losses due to distance, antenna patterns, etc. ${n_i}(t)$ is measurement noise, and the unit is decibels.

Fig. 10

RTI model

The shadowing loss ${S_i}(t)$ can be approximated as a sum of attenuation that occurs in each voxel. Since the contribution of each voxel to the attenuation of a link is different for each link, a weighting is applied. it is described as

$$\begin{aligned} \ {S_i}(t) = \sum \limits _{j = 1}^N {{w_{ij}}{x_j}(t)} \end{aligned}$$

(9)

where ${{x_j}(t)}$ is the attenuation occuring in voxel j at time t, and ${w_{ij}}$ is the weighting of pixel j for link i

Imaging only the changing attenuation simplifies the problem, since all static losses can be removed over time. The change in RSS $\varDelta {y_i}$ from time $t_a$ to $t_b$ is

$$\begin{aligned} \ \varDelta {y_i} = \sum \limits _{j = 1}^N {{w_{ij}}\varDelta {x_j} + \varDelta {N_i}} \end{aligned}$$

(10)

where $\varDelta {N_i}$ is the grouping noise, it is defined as

$$\begin{aligned} \varDelta {N_i} = {F_i}({t_b}) - {F_i}({t_a}) + {n_i}({t_b}) - {n_i}({t_a}) \end{aligned}$$

and $\varDelta {x_j}$ is the difference in attenuation at pixel j from time $t_a$ to $t_b$, it is defined as

$$\begin{aligned} \varDelta {x_j} = {x_j}({t_b}) - {x_j}({t_a}) \end{aligned}$$

Considering all links in the network, the system of RSS equations can be described in matrix form as

$$\begin{aligned} \ \varDelta \mathbf{{y}} = \mathbf{{W}}\varDelta \mathbf{{x}} + \mathbf{{n}} \end{aligned}$$

(11)

where

$$\begin{aligned} \varDelta \mathbf{{y}} = {[\varDelta {y_1},\varDelta {y_2} \cdots \varDelta {y_M}]^T} \end{aligned}$$

$$\begin{aligned} \varDelta \mathbf{{x}} = {[\varDelta {x_1},\varDelta {x_2} \cdots \varDelta {x_N}]^T} \end{aligned}$$

$$\begin{aligned} \mathbf{{n}} = {[{n_1},{n_2} \cdots {n_M}]^T} \end{aligned}$$

$$\begin{aligned} {\left[ \mathbf{{W}} \right] _{i,j}} = {w_{i,j}} \end{aligned}$$

Appendix 2: Radio Tomographic Imaging (RTI): Weight Model

An ellipsoid with foci at each node location can be used as a model to determine the weighting for each link in the network [9]. The model is shown in Fig. 10b.

If a particular voxel falls outside the ellipsoid, the weighting for that voxel is set to zero, if a particular voxel is within the ellipsoid, its weighting is set to be inversely proportional to the square root of the link distance. The model is described as [10]

$$\begin{aligned} \ {w_{ij}} = \frac{1}{{\sqrt{d} }}{} {} \left\{ \begin{array}{l} 1 \quad \mathrm{{if}} \quad d_{ij}^t + d_{ij}^r < d + \lambda \\ 0 \quad \mathrm{{otherwise}} \end{array} \right. \end{aligned}$$

(12)

where d is the distance between the two nodes, $d_{ij}^t$ and $d_{ij}^r$ are the distances from the center of voxel j to the two node locations for link i, and $\lambda$ is a tunable parameter describing the width of the ellipse.