SIGNAL SOURCE POSITION ESTIMATION IN 2D SPACE BASED ON TDOA INFORMATION USING SOLUTION SPACE REDUCTION, ASYMPTOTIC APPROACH, AND HYPERBOLIC VERTICES TUNING

• Main Author: Awaludin, Iwan
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/57028
• Institution: Institut Teknologi Bandung

The estimation of the position of the signal source is a real-world application that has been researched for a long time. Time Difference of Arrival is one of the most popular quantified information for position estimation. This model does not require time synchronization between the signal source and the signal capture sensors. Simply synchronize time between sensors and compare signal arrival times across sensor pairs. From the results of the different arrival times of the signal in the sensor pair, points that have the potential to be the position of the signal source will be obtained. These points will form a hyperbolic curve when certain conditions are met. The intersection of two hyperbolic curves becomes the estimated position of the signal source. Hyperbola can be expressed as a non-linear mathematical equation. The search for the intersection of two hyperbolic curves must be solved by finding the intersection of non-linear mathematical equations. This work is laborious to do analytically. The analytical method will make a mathematical formula of the phenomenon of concern. But the mathematical formula is only an approximation of the actual conditions. The mathematical formula will use a variable that has a correlation between the dependent and independent variables. Meanwhile, in the real world there are many factors that affect the dependent variable, but only some of these factors are represented by the independent variable. As a result, under certain conditions the mathematical formula that has been built does not model the system of concern. Therefore, several studies have developed iterative and non-iterative estimation algorithms to solve this TDOA problem. Iterative algorithms such as Newton-Rhapson or Taylor require precise initialization and large computational resources. This happens because of the lack of reference space for the solution search. Initialization plays an important role because there is a possibility that the iteration direction moves to the wrong location because there are other hyperbola intersections that are closer. While the solution search space is too wide, the number of iterations that must be limited may not guarantee the achievement of convergence in the searched position. The non-iterative algorithm has a special place in position estimation applications because of its ease of implementation. The Maximum Likelihood Estimator or Hyperbolic Positioning Algorithm algorithm has become a reference for developing and implementing real-world position estimation. The disadvantage of non-iterative algorithms, such as the Maximum Likelihood Estimator and Hyperbolic Positioning Algorithm, is that the error requirements must be small. Therefore, for the case of position estimation with a very far sensor distance, such as the Geospatial Positioning System, this algorithm can work well. Apart from that, from the mathematical formula there are conditions that will cause a critical area. This area will be found if the matrix in the formula is a singular matrix or if there is a zero denominator. Other algorithms that use the asymptotic approach are constrained by the validity of the hyperbola equation. Hyperbola is valid between 0 <TDOA <sensor distance to the median point. Meanwhile, the TDOA measurement results allow values outside this range. As a result, the asymptotic algorithm or other algorithms that use the hyperbolic approach are invalid. The proposed algorithm comprises three steps, namely: 1) Solution Space Reduction; 2) Asymptotic Approach; 3) Tuning of hyperbolic vertex. The first step will be to limit the search space to cross-sectional sections of multiple planes. The second step is to approach the non-linear equation to be linear regarding the hyperbolic equation requirements. The third step is to improve the estimation by tuning hyperbolic curve vertex to approximate the real hyperbola. Solution Space Reduction will divide the Cartesian Plane into eight symmetrical areas. For this reason, four sensors are topologically arranged according to a symmetrical shape on each axis with the same distance from the origin. By measuring TDOA, the appearance of the areas according to the TDOA value will be obtained. The area with the most occurrences will be the potential place where the signal source is located. Determining the area will help in choosing which the equation of the asymptote lines to be used and to be eliminated. The asymptotic approach basically estimates the position of the signal source using a system of linear equations. TDOA measurement results outside the validity of hyperbole will be represented by a linear equation line. For example, if the measured result is zero then the equation for the perpendicular to the major axis will be used. If greater than or equal to the maximum limit of TDOA then the equation line of the major axis will be used. Meanwhile, the TDOA measurement result between zero and its maximum limit can be represented by a hyperbole curve. For the hyperbolic equation to find the intersection with the major axis line and the perpendicular line to the major axis, the linear equation that approximates the hyperbola curve will be used. This equation is an asymptotic approach that converts the hyperbolic equation into an asymptotic line equation. The intersection of the linear equation lines as an estimate of the position of the signal source can easily be found using the Least Square Method. Each hyperbola has two asymptotic line equations. In other studies, the selection of the asymptote lines is done by looking for the intersection of the most congregated lines. Meanwhile, in this study the selection of the asymptote line used is based on the TDOA value, the gradient of the line, and the resulting area of the Solution Space Reduction. Tuning of hyperbolic vertices is carried out to improve the estimation performance. In the selected estimation system, the error will be carried over in the TDOA measurement. As a result, the vertex of the hyperbola curve will be shifted from the true value. The correction is expected by shifting the vertex back from the measurement results closer to the actual vertex. Therefore, by tuning the vertex of the hyperbola curve, it is expected that the performance will increase. Hyperbolic curve vertex tuning will add or subtract a small value in a limited range to the vertex value. Because of the tuning of the vertices of the hyperbola curve, the linear equation lines will be rotated and their intersections with other linear equations will change. The tuning process is an iterative process. The stopping criteria will be based on the average distance of the intersection of the estimated position or the maximum limit of tuning. Simulations and experiments were carried out with case studies of sound and moving sources. As a performance comparison, the Hyperbolic Positioning Algorithm is taken because this algorithm uses an exact solution as a way of calculating estimates and uses the same number of sensors. From the simulation results obtained MAPE performance of 2%, while from the experiment obtained an MAPE performance of 9%. The proposed algorithm has the potential to be a good estimator.