Motion Estimation Using Sensors

Motion Estimation Using Sensors

Lakshmi Areekath Vellore Institute of Technology

Abstract

Linear displacement estimation of a mobile device is useful in various real time applications, such as inertial navigation systems, video surveillance, video encoding etc. Present state of the art techniques perform the global motion estimation using image processing techniques, which requires complex computations and more power consumption.

Here, an attempt has been made to estimate the linear displacement of a mobile device using the in- built sensors. The in-built 3-axis accelerometer of mobile devices is employed to determine the linear displacement. Three different methods are used to convert acceleration to displacement. From the results we conclude that the in-built sensors can be used for linear displacement estimation of mobile devices.

1. Introduction

   The recent advancement in the field of MEMS technology has led to a rapid growth in the inclusion of sensors in mobile devices. These devices consume only a fraction of the power used by the device and function in the background at all times. This has led to the development of applications that use the sensor readings.

   Among the sensors the most widely used in mobile devices is the 3-axis accelerometer. The accelerometer is a hardware sensor that measures the acceleration force in m/s2 that is applied to a device on all three physical axes (x (lateral), y (longitudinal), and z (vertical) axes.), including the force of gravity [2]. It is considered reliable for motion detection and consumes about 10 times less power than the other motion sensors.

   In this paper we present three different approaches to determine displacement from accelerometer data. Unlike the previous experiments in which the accelerometer sensor is fixed on the device, here we use the in-built accelerometer in the Smartphone. The three approaches gives insight regarding the various degrees of accuracy that can be achieved through changes in the algorithm. Of the methods presented the first two have been dealt with in literature, while the third is a new step in the direction of motion estimation using accelerometer data alone.

   The next section deals with the error sources associated with the conversion of accelerometer data into displacement data. Section 3 deals with the related work in this area, section 4 with the various methods adopted, section 5 with the results and discussion, followed by the conclusion.

2. Error sources

   The accelerometer senses all kinds of acceleration. Its output consists not only of the desired motion data but also of other sources of acceleration. Thus the accelerometer data is generally noisy and requires a great deal of preprocessing before it is used. The two primary sources of noise in the received signal are irregular sampling rates and the noise inherent in discrete physical sampling of a continuous function [1]. The filtering out of noise is a difficult process esp. since it may result in loss of trajectory information. However the small amount of noise in the data can lead to severe

   drift in the derived displacement on double integration.

3. Related work

   Related Work on Sensors-Assisted Applications: Some sensor-based work has been done in the areas of vehicle movement detection and computer vision. For example, the European patent application EP1921867 presented the idea of employing vehicle motion information provided by various sensors to improve coding efficiency of the video encoder [12]. The authors of [13] proposed a method for deploying mobile device cameras and inertial sensors for autonomous vehicle motion estimation. However, [12], [13] focused on detecting vehicle movement and vehicle-mounted mobile device cameras.

4. Adopted methods

   Data acquisition consists of both the displacement and sensor data simultaneously of a mobile device. The displacement data is collected using image processing technique and sensor data using the Android APIs. The acquisition is performed after calibration of the device. Due to the implementation of the Android framework, its sampling mechanism is generally irregular.To regularize sampled values, the holes in the signal were interpolated via a process called data linearization

   1. Time domain approach

      According to the Laws of Physics, displacement, s, is obtained from the acceleration by

      T

      S = a(t) dt dt (1) 0

      Since the signals are in digital domain, the integration is replaced by summation. To remove the low amplitude error from the acceleration signal, the mean from the signal. The signal is

      cumulatively summed once to get velocity. The mean of this signal is subtracted again from itself and cumulatively summed again to get the displacement. The mean value is subtracted again from the resultant signal. The drift in the plot is removed by subtracting the trend component from it.

   2. Frequency domain approach

      The mean is removed from the acceleration data. The Fast Fourier Transform of this data is determined. The integration is performed by dividing each element by the square of magnitude of the frequency band. The Inverse Fourier Transform of the resultant data is determined. The result is scaled.

   3. Statistical approach using neural network

      An artificial neural network is a mathematical model that consists of an interconnected group of artificial neurons. Neural network processes information using a connectionist approach to computation of input data. The neural network sometimes acts as an adaptive system that changes its structure during a learning phase. They are used to model complex relationships between inputs and outputs or to find patterns in data. Here the Levenberg-Marquardt Back Propagation algorithm [8], [9] is used to determine the relationship between the collected accelerometer and displacement data. The accelerometer data is divided into blocks of ten data each and these act as the input and the displacement data act as target values.

5. Results

   On performing data processing in Matlab 2009b it is observed that the MSE values in the case of time and frequency domain approaches are 1.6602 m and 0.4869 m respectively. However in the statistical approach the MSE is 0.0000000535917 m and the regression value R is 0.999999999. These results can be attributed to the robustness of the NN model.

   Figure 1. Results of time domain approach

   actual displacement(m)

   actual displacement(m)

   0.5

   0.4

   0.3

   0.2

   0.1

   0 100 200 300 400 500 600 700

   time(ms)

   computed displacement(m)

   computed displacement(m)

   0.5

   0

   -0.5

   -1

   0 100 200 300 400 500 600 700

   time(ms)

   Figure 2. Results of frequency domain approach

6. Conclusion

   The various approaches to displacement estimation resulted in different levels of accuracy. In the first two approaches the noise in the accelerometer data was converted into drift leading to larger error in the resultant signal. These methods are suited for trajectory or position estimation in Inertial Navigation Systems (INS). As regards to the third method

   using Neural Networks, the performance index of 0.0000000535917 MSE indicates high performance of the proposed model. Also this method achieves automatic synchronization of the sensor and displacement data unlike previous attempts that focused on manual synchronization. The practical implementation that uses in-built sensors is cost effective and consumes less power. n addition to all this since the sensor used is a basic accelerometer sensor, it can be implemented on a wide range of mobile devices. Currently the proposed model is tested for only a single device and along the z-axis. As further work, the data collection module can be extended to other devices and larger datasets to arrive at a more robust linear displacement estimation model.

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