# Nonlinear Analysis of Built-in Sensor in Smart Device under the Condition of Voice Actuating
## 1 Introduction  
Nowadays, the high-performance chips largely enhance the real-time computation of the modern smart device. Moreover, a smart device also enables rich interactive experiences while extending the functions by using various built-in sensors, such as the accelerometer and the gyroscope.  
Built-in sensors in the smart device are kinds of microelectromechanical systems that capture the subtle changes of light, heat, and temperature. For instance, a tiny embedded accelerometer in a smartphone has the capability to detect instantaneous acceleration magnitude on three coordinate axes. Researchers also attempt to acquire accurate velocity and direction of the smart device from these instantaneous acceleration magnitudes in order to identify the motion state of a human target including walking up, running and tumbling [1].  
Recently, researchers found that built-in sensors in a smart device could output response when they receive voice as actuating signals [2, 3]. Based on this feature, built-in sensors gradually replace microphone to realize voice control in various application scenarios. At present, the voice-activated communication between user and smart device increasingly becomes a brand-new interactive pattern. For instance, Siri in iOS system and Google Now in Android system [4, 5] are two successful voice interactive platforms in mobile devices. Generally, these two systems would receive the specific voice commands and transform them into instructions to control a smart device to complete multiple real-time tasks by using a built-in microphone. Meanwhile, the microphone has to be kept in working condition to give immediate feedback to users. This significant energy consumption mode undoubtedly becomes a challenge in the battery-powered smart device. Therefore, a low-power built-in sensor is considered to become a viable alternative to resolve the conflict between high-energy consumption and real-time monitoring of speech signal [6, 7].  
Due to its hardware structure constraint, the output signal of a built-in sensor usually appears strong non-linear [8]. Therefore, on the basis of non-linear dynamics chaotic theory, we attempt to reveal the chaotic features of output signal of the built-in accelerometer when the smart device receives voice commands. We also try to develop a suitable mathematical model to express the nonlinearproperties of built-in accelerometer for realizing accurate output signal prediction, characteristics extraction, and pattern recognition.  
The main contributions of this paper are as follow:  
1. We attempt to apply nonlinear dynamics and chaotic theory to built-in sensor signal analysis.
2. We calculate the optimal delay time and proper correlation dimension, and then we reveal the nonlinear properties of built-in accelerometer in the smart device by reconstructing the attractors.  
The remaining parts of the paper are arranged as follows:  
In Section 2, we illustrate the feasibility of built-in accelerometer in smart-device. In Section 3, the optimal delay time and proper correlation dimension are calculated. In addition, the attractors are also reconstructed. We present the results of experiments in Section 4. We also try to show the results of nonlinear mapping between microphone and accelerometer in Section 5. The conclusions and subsequent research directions are finally presented in Section 6.