Research On Gaussian Mixture Model Based Location Estimation Algorithms For WSN

In wireless sensor networks, sensor's location information is the prerequisite of many wireless sensor applications such as environment monitoring, data collecting, target tracking, etc. Thus, localization for wireless sensor is one of the hot topics in wireless sensor networks. The simplest solution for network localization is to equip every wireless node with a GPS (global positioning system) device. However, a GPS device is unavailable with the most wireless node due to considerations on either cost or the GPS satellite signal reception limitations. Therefore, researchers provide a set of in-network localization algorithms for the practical reason. This paper analysed the existing localization solustions, and found that there are some problems as follow.First, among those localization algorithms, comparing with the algorithms based on AOA(Angle of Arrival), TOA(Time of Arrival), and TDOA(Time Difference of Arrival), the RSS(Received Signal Strength) based algorithms do not require extra devices, and the RSS measurement is easily available and least expensive to derive from transceivers. However, because the RF(Radio Frequency) signal is influenced by the complicated environment condition, the localization results of RSS based algorithms are usually less accurate. Therefore, extensive research was carried out on designing robust RSS based localization algorithms using probabilistic models and calibration enhancements.Second, most of the existing localization algorithms suppose that the beacon nodes are fixed. In order to ensure the localization accuracy, the algorithms require enough number of beacon nodes and the distribution of those beacon nodes is expect to be uniform. However, the cost of the beacon node is far more than that of the general node. Therefore, there is a tradeoff between location accuracy and the cost of the localization system. In order to solve this problem, researchers provide movable beacon node, which can save the cost and ensure the localization accuracy at the same time. Because one movable beacon node can instead numbers of fixed node.In addition, many existing localization algorithms suppose that the number of sensor is known, and the ID of the signal's sender is known. However, in real wireless network environment, we usually cannot forecast the number of the sensor, or the sender's ID from the received signal.To solve these above problems, this paper proposes three localization algorithms. In order to save the localization cost, these three algorithms use the RSS measurement. And with the purpose of improving the localization accuracy, all of them are probabilistic algorithms based on Gaussian Mixture Model. Two of them are Offline LEGMM (location estimation based on Gaussian mixture model), and the other is Online LEGMM. The two Offline LEGMM are IGrid-LEGMM (Iterative Grid Location estimation based on Gaussian mixture model) and Grid-EM-LEGMM (Grid and Expectation Maximization Location estimation based on Gaussian mixture model, Grid-EM-LEGMM).Offline LEGMM algorithm and Online LEGMM algorithm are based on the same mathematical models, but differ in the amount of data that they rely on. The Offline LEGMM algorithm depends on the complete set of data, while the Online LEGMM algorithm depends on only a part of the time series, and incrementally builds the whole picture of the sensor locations.All of the three algorithms require only a single mobile GPS-equipped node with minimum system knowledge to collect RSS information. By the"minimum knowledge"assumption, we mean that it does not require informative clues, such as the number of wireless sensors or their identifiers, in order to localize the sensors. Instead, all of the three algorithms derive sensor positions and their number based on the RSS data collected by the GPS-equipped sensor while it roams in the wireless sensor fields. Each of the data points is connoted with the corresponding GPS locations. The GPS-equipped mobile sensor is called the RSS-collector.In the three algorithms, we model the RSS values as Gaussian random variables coming from unknown number of signal sources, and use maximum likelihood estimation methods to derive the number and locations of these sources. To each of the localization algorithms, we use two kind of experiments (simulation and real test-bed experiment) to verify the validity and accuracy of the proposed localization algorithms. We introduce our localization algorithms as follows.1. IGrid-LEGMM combines the path loss model, Gaussian mixture model, and Bayesian information criterion together. IGrid-LEGMM first divides the location area into grids, and estimates the rough locations of the sensors using a grid-search method and the maximum likelihood estimation, which is called Grid-LEGMM. IGrid-LEGMM iteratively executes Grid-LEGMM with shrinking the location area and the grid's size, and refines the accuracy of the localization results. The validity and accuracy of IGrid-LEGMM algorithm are evaluated by both simulations and real testbed experiments.2. Grid-EM-LEGMM improves IGrid-LEGMM, and it has two steps as follow. First, it uses Grid-LEGMM to estimates the number and rough locations of the sensors; Second, Grid-EM-LEGMM improves the location estimation accuracy using an EM (expectation maximization) method to refine the results of Grid-LEGMM, which is called EM-LGMM. The results of simulations and real testbed experiments show that the Grid-EM-LEGMM algorithm can produce reasonable location and number estimates of wireless sensors.3. Online LEGMM can localize the sensors while the RSS collector is moving and collecting data. It depends on only a part of the data series, and incrementally builds the whole picture of the sensor locations. Online LEGMM is an iterative algorithm. It groups the collected RSS data series into different groups as different inputs of each round for location estimations. In each round, the Online LEGMM consists of three different steps. First, search the likely wireless sensor locations on a grid structure using Grid-LEGMM. Second, refine the wireless sensors'locations using the EM-method. Finally, use a credit-based mechanism to revise and reinforce the estimation on the number and locations of the wireless sensors, which is called Credit-LEGMM, so that the spurious sensor can be removed. The performance of online localization algorithms are evaluated using simulations and real testbed experiments. And we compared the online localization algorithm and the Grid-EM-LEGMM algorithm using the Cramer-Rao lower bound.Our challenge and solutions on all of the three localization approaches in this paper are based on three aspects:1) all of them are based on GMM;2) all of them use a single RSS collector and only the RSS measurements to derive the wireless sensors' locations,3) all of them do not assume but derive the number of wireless sensors.