Improvement of Location Algorithm in Wireless Networks

: In order to improve the accuracy of wireless network positioning, the triangulation method of wireless network positioning technology is proposed, which is based on the linear least square fitting method. It makes the observed value and the fitting value very close, effectively solves the problem of significant contradiction between the fitting result and the observed value in the principle of least square method, and can realize the accurate measurement of geographic information by wireless network positioning technology.


Introduction
In geographic information measurement, accurate location technology is very important. At present, the most widely used Positioning technology at home and abroad is GPS (Global Positioning System). However, there are also some problems in the practical application of GPS technology. For example, when working in places with occlusion (indoor, tunnel, etc.) or strong interference sources (under strong magnetic environment, under high voltage line, etc.), GPS positioning technology will have certain blind spots and cannot provide high-precision positioning services. Thus wireless network location technology is applied.
The most common application of wireless network positioning technology is the positioning measurement of coal mines. Since coal mines are usually underground, it is difficult to obtain satellite signals. The movement of personnel and equipment in limited space also makes the acquisition of signals more difficult. The wireless network positioning system can solve this problem.
Wireless sensors receive satellite measurements, measure the user's position, and obtain positioning information. Based on the detected network data, the position of the mobile terminal is measured. Then the actual distance is determined by the Signal Strength detected by the mobile terminal box receiver. The specific location of the mobile terminal can be accurately determined by the measured data.

Principles of Wireless Network Positioning
The application of wireless network positioning technology follows the law of technology development, and usually triangulation is used to solve the positioning technology in wireless network according to the principle of least square. Wireless network positioning device is the main part of mobile node and the reference node, and the difference between the two nodes reference node does not participate in the process of positioning is calculated, and the mobile node can be performed within the node control freedom of movement, when the mobile node RSSI signal from the received within the scope of the reference node, according to the measured values accurately find the position. First of all, data-intensive calculation should be carried out, that is, after calculating the parameter data of the relevant computer node position, the information should be transmitted to the central data collection point to calculate the node position, and finally the calculated data of the node position should be transmitted to the original node. Due to certain defects in the measurement method of this node, the traffic required in the process of calculation will increase continuously along with the number of nodes, which is not conducive to the expansion of its application scope and more suitable for small networks and situations with fewer nodes [1,2].
Engine positioning as an important part of the wireless network positioning technology, its technical principle is relatively simple, as a three-dimensional coordinate system needs to have 3-5 reference node, so as to determine the distance between the coordinate points, just according to the principle of minimum square method by means of triangulation, using computer to aerial triangulation. For example, a relatively simple positioning system is mainly composed of 1 positioning node and 3 reference nodes. This measurement method is also a relatively common positioning method, which finds the coordinate position by the distance between different points. However, the calculated value may not match the actual distance, and the fitting result is significantly inconsistent with the observed value. In this paper, the least square method is used to fit the observed data into a straight line, which effectively solves the contradiction between the two and improves the measurement accuracy.

Principle of Least Square Method
In two observations, there is always a quantity with higher accuracy, which can be used to represent the observation with higher accuracy, assuming that it has no error, and all the errors are summed up as the error of y . The function relation of x and y is expressed as follows: is some parameter that needs to be determined experimentally. By observing each set , we can find a point on the plane ( y x, ).If there is no measurement error, the data points will be arranged accurately on the theoretical curve. As long as m group of measured values is selected and substituted into Eq. (1), the following equations can be obtained [3] ( ) In the formula above, Then the probability density of i y is [4]: , Because each measurement is independent of each other, So the likelihood function the observed value of ( ) Take the maximum value of likelihood function L to estimate parameter C: When the function minimizes, the distribution of y is not limited to a normal distribution, Formula (5) is called the least square rule. If it has a normal distribution, the maximum likelihood method is consistent with the least square method. Let the weight factor be The least square method is used to estimate the parameters, The weighted sum of squares of the deviation of each measured value y is the minimum.wei can get [5]: So we get the system of equations: Solve the equations (7) , There is a significant contradiction between the fitting results and the observed values.

Linear Least Squares Fitting
In order to solve the above contradiction, the method of linear least squares fitting can be adopted. Let the equation of the line between x and y be: x is the exact value, The resulting error is related to the observed value i y . In this way, the least square method can be used to fit a line.

Estimation of Line Parameters
When the least square method is used to estimate parameters, the weighted sum of the i y deviation of the observed value is required to be the minimum. For the line fitting of the observation values of the same accuracy, formula (5) can be obtained [6]: If a (representing 1 0 , a a ) takes the minimum as the best estimate of the parameter, then the sum of squares of the deviation of i y is also the minimum. According to Eq. (11), the following equation can be obtained:

Deviation of Fitting Results
As the estimated values of line parameters 0 a and 1 a are calculated based on the observation data points with errors, there is inevitably certain deviation. Since the observed data points do not fall on the fitting line accurately, there is also a certain deviation between the observed value i y and the fitted line i ŷ .

Correlation Coefficient and Its Significance Test
When fitting the observed data point ( ) ρ is used to judge if it is not clear how close the linear relationship between x and y is. Instead, the correlation coefficient can be expressed as: where x and y are the arithmetic mean values of x and y respectively, and [ ] (1) When 0 > r , the slope of the line is positive, indicating a positive correlation; (2) When 0 < r , the slope of the line is negative, indicating a negative correlation; , then there is no correlation between x and y . The closer r is to ±1, the closer the linear relationship between them is.

Discussion and Conclusion
Aiming at the application of wireless network positioning technology in actual measurement, this paper analyzes the limitations of positioning technology, wireless sensor network and RSSI positioning method in actual application process, and theoretically analyzes that the calculated value may not match the actual distance. There is a significant contradiction between the fitting results and the observed values. An improvement is proposed to the original algorithm. Through data analysis, about 68.3% of all distributed observation data points can fall within the range between the two expected lines, so as to accurately determine the specific location of the mobile terminal.
To sum up, the development of positioning technology is bound to be more advanced and more accurate, so that wireless positioning technology can be well combined with wireless sensor network, and the accuracy and coverage will be greatly improved.
Funding Statement: This paper has no funding.

Conflicts of Interest:
The authors declare that they have no conflicts of interest to report regarding the present study.