Sensor Data Simulation for Anomaly Detection of the Elderly Living Alone

TL;DR

A novel sensor data simulator that can model appropriately the long-term transitions and correlations between anomalies that exist in reality and simulates well day-to-day variations of real data is proposed.

Abstract

With the increase of the number of elderly people living alone around the world, there is a growing demand for sensor-based detection of anomalous behaviors. Although smart homes with ambient sensors could be useful for detecting such anomalies, there is a problem of lack of sufficient real data for developing detection algorithms. For coping with this problem, several sensor data simulators have been proposed, but they have not been able to model appropriately the long-term transitions and correlations between anomalies that exist in reality. In this paper, therefore, we propose a novel sensor data simulator that can model these factors in generation of sensor data. Anomalies considered in this study were classified into three types of \textit{state anomalies}, \textit{activity anomalies}, and \textit{moving anomalies}. The simulator produces 10 years data in 100 min. including six anomalies, two for each type. Numerical evaluations show that this simulator is superior to the past simulators in the sense that it simulates well day-to-day variations of real data.

Figures (11)

• Figure 1: The proposed simulator consisting of four component simulators and a sensor data collector (each surrounded by lines).
• Figure 2: Floor plan and sensor arrangement. The unit of length is a meter. There are chair (C), cupboard (CB), dining table (DT), kitchen stove (KS), refrigerator (RF), trash box (T), wardrobe (WR), washing machine (WM) and water closet (WC). Colors and symbols distinguish kinds of sensors; blue for flow COST sensors, yellow for power COST sensors, gray for PR sensors, and red for PIR sensors.
• Figure 3: Activity scheduling of a day. (1) Fundamental, (2) necessary, and (3) random activities are detemrined in the order. Their start times, durations and other statistics are determined by probabilistic models: a normal distribution $N(\mu, \sigma^2)$ with mean $\mu$ and variance $\sigma^2$, a Poisson distribution $Poi(\lambda)$ with mean $\lambda$, an uniform distribution $U(R)$ with remainder time range $R$ that is not filled yet, and a distribution $p(S_R)$ of occurrence probabilities over random activities $S_R$.
• Figure 4: Generation of a walking trajectory from an activity sequence. A walking trajectory between $\bm{a}_k$ and $\bm{a}_{k+1}$ is $W_{\bm{a}_k, \bm{a}_{k+1}} = \left((t_1, l_1), (t_2, l_2), \ldots, (t_N, l_N)\right)$, where $l_1 = a_{k, l}$ and $l_N = a_{k+1, l}$. The trajectory is obtained by connecting body centers in the movement almost straight while avoiding furniture. Body centers are determined in short and smooth connected steps with a specified stride length.
• Figure 5: A graphical model of anomalies. For example, MMSE score in $t$th month $M_t$ is generated according to the previous value $M_{t-1}$ and the noise $\sigma_{t}$. Random variables $\alpha_t$ and $\beta_t$ denote the parameters of state anomaly and activity anomaly, respectively (Table \ref{['tab:six_implemented_anomalies']}). They are conditioned by $M_t$ and condition the parameters ($\theta_t$ and $I_t$) of activities and walking trajectory, respectively.