CN106767815A - Weighted least-squares indoor positioning algorithms based on the range finding of phase difference Euclidean distance - Google Patents

Abstract

The invention discloses a weighted least squares indoor positioning algorithm based on phase difference Euclidean distance measurement, including: arranging and positioning RFID readers and reference tags; using the phase difference received by the readers to estimate the distance between the readers and the tags , the ranging error caused by multipath effect and Gaussian white noise is equivalent to a Gaussian distribution, and the mean and variance of the deviation between the estimated distance and the actual distance between the reference tag and each reader constitute the position parameter and scale of the Gaussian distribution parameter Parameters; distance estimation between the reference tag and the tag to be positioned; the reciprocal of the variance of the distance estimation error between the tag to be positioned and the reader and the reference tag is used as the weighting factor, and the weighted least squares algorithm is used to solve the positioning problem. The invention has the characteristics of high precision.

Description

Weighted Least Squares Indoor Positioning Algorithm Based on Phase Difference Euclidean Distance Ranging

technical field

The invention relates to an indoor positioning problem.

Background technique

Positioning technology has brought great convenience to people's lives. In recent years, with the rapid development of the Internet of Things, people's demand for positioning has become higher and higher, and the application of indoor positioning technology has become more extensive. Satellite-based positioning technology and mobile cellular network-based positioning technology are greatly affected by buildings. In scenes where buildings such as schools, warehouses, and shopping malls are relatively concentrated, the positioning accuracy will be greatly reduced, which cannot meet the high-precision positioning requirements.

In indoor positioning, electromagnetic waves will reflect when encountering the ground, ceiling, walls, obstacles, etc. during transmission, resulting in multipath effects, which lead to changes in the energy, phase, time and other information of the signals received by the receiver , which seriously interferes with the positioning results.

In the current positioning technology, there are mainly infrared positioning technology, ultrasonic indoor positioning technology, Bluetooth indoor positioning technology, WIFI indoor positioning technology, ZigBee indoor positioning technology, computer vision positioning technology, ultra-wideband indoor positioning technology, UHF RFID indoor positioning technology, etc. . Among them, the RFID-based positioning technology has the advantages of low cost, high precision, and strong real-time performance, and does not need to establish a fingerprint database in advance, and the workload of later maintenance is relatively small.

Contents of the invention

The purpose of the present invention is to provide an indoor positioning algorithm with relatively small maintenance workload and high precision. The technical scheme is as follows:

A weighted least squares indoor positioning algorithm based on phase difference Euclidean distance ranging, comprising the following steps:

1) Arrange the positioning scene: arrange at least three RFID readers in different positions of the scene to be positioned, and lay reference tags;

2) Estimation of the distance between the reader and the tag to be located: the phase difference received by the reader is used to estimate the distance between the reader and the tag, and the ranging error caused by multipath effect and Gaussian white noise is equivalent to a Gaussian distribution, and the reference tag The mean and variance of the deviation between the estimated distance and the actual distance with each reader constitute the position parameter and scale parameter of the Gaussian distribution parameter;

3) Estimation of the distance between the reference tag and the tag to be located: Construct the phase difference matrix of the tag, fit the actual distance between the reference tags and the Euclidean distance of the phase difference, and solve the undetermined coefficient a of d _ij = a E _ij + b and b, where d _ij is the actual distance between the i-th reference label and the j-th reference label, E _ij is the phase difference Euclidean distance between the i-th reference label and the j-th reference label; Effect, phase difference Euclidean distance fitting and Gaussian white noise cause the ranging error is equivalent to a Gaussian distribution, the mean value of the deviation between the estimated distance and the actual distance between any reference tag and other reference tags by linear fitting and the variance constitute the position parameter and scale parameter of the Gaussian distribution parameter;

4) Taking the reciprocal of the variance of the distance estimation error between the tag to be positioned and the reader and the reference tag as the weighting factor, the weighted least squares algorithm is used to solve the positioning problem.

The present invention can alleviate the influence of multipath effect and Gaussian white noise on the positioning results in indoor positioning, and does not need to establish a fingerprint library, nor need to know the specific conditions of the environment in advance, and the distance estimation between the reference tag and the tag to be positioned uses the phase difference Euclidean distance fitting, the distance estimation error caused by multipath effect, Gaussian white noise, and phase difference Euclidean distance fitting is equivalent to Gaussian distribution, and then the weighted least squares is used to solve the positioning problem to improve the positioning accuracy.

Description of drawings

FIG. 1 shows a schematic diagram of a positioning scenario in the present invention.

Figure 2 shows the reader distance estimation error curve.

Figure 3 shows the reference tag distance estimation error curve.

Fig. 4 shows a comparison chart of positioning performance.

detailed description

In order to verify the effectiveness of the proposed algorithm, the present invention has carried out experimental simulation in matlab. Among them, the multipath channel model adopts a statistical channel model, and the maximum multipath number of the signal received by the reader is changed from 3 to 10 in turn, and the positioning is carried out in a 10×10m ² belt positioning area. The specific application in this implementation example is as follows:

1. Arrange the positioning scene. Four readers are placed at the four corners of the area to be located, and nine reference tags are laid equidistantly on the ground, as shown in Figure 1.

2. Estimation of the distance between the reader and the tag to be located. Using the phase difference received by the reader to estimate the distance between the reader and the tag, the ranging error caused by the multipath effect and Gaussian white noise is equivalent to a Gaussian distribution, and the estimated distance between the reference tag and each reader is the same as the actual The mean and variance of the deviation between distances constitute the location and scale parameters of the Gaussian distribution parameters.

3. Estimating the distance between the reference tag and the tag to be located. Construct the phase difference matrix of the tag, and the phase difference Euclidean distance between tag i and tag j is The actual distance between the reference tags and the Euclidean distance of the phase difference are fitted, and the undetermined coefficients a and b of d _ij =a·E _ij +b are obtained. The ranging error caused by multipath effect, phase difference Euclidean distance fitting, and Gaussian white noise is equivalent to a Gaussian distribution, and the estimated distance between any reference tag and other reference tags through linear fitting and the actual distance The mean and variance of the deviation constitute the location and scale parameters of the Gaussian distribution parameters.

4. Verify the feasibility of equating the distance estimation error to a Gaussian distribution. When the maximum number of multipaths is 7, the probability density curve of the distance estimation error between the reader and the reference tag is close to the Gaussian distribution curve calculated by using the position information and phase difference information of the reference tag, as shown in Figure 2 and Figure 3 , it is feasible to equate the distance estimation error to a Gaussian distribution.

5. Consider the reader and the reference tag as reference nodes, and there are N reference nodes in total. Through steps 2 and 3, the position parameter λ _i and the scale parameter σ _i of the Gaussian distribution parameters of the distance estimation from the reference node can be calculated, and The distance between reference nodes is estimated to be d _i , i=1,...,N. then there is

The formula derivation can get the following formula:

WAθ=Wb

in,

By calculating the above formula, the coordinate θ=( ^AT WA) ^{-1 AT} Wb of the tag to be located can be obtained.

Claims (1)

1. A weighted least squares indoor positioning algorithm based on phase difference Euclidean distance ranging, comprising the following steps: 1) Arrange the positioning scene: arrange at least three RFID readers in different positions of the scene to be positioned, and lay reference tags; 2) Estimation of the distance between the reader and the tag to be located: the phase difference received by the reader is used to estimate the distance between the reader and the tag, and the ranging error caused by multipath effect and Gaussian white noise is equivalent to a Gaussian distribution, and the reference tag The mean and variance of the deviation between the estimated distance and the actual distance with each reader constitute the position parameter and scale parameter of the Gaussian distribution parameter; 3) Estimation of the distance between the reference tag and the tag to be located: Construct the phase difference matrix of the tag, fit the actual distance between the reference tags and the Euclidean distance of the phase difference, and solve the undetermined coefficient a of d _ij = a E _ij + b and b, where d _ij is the actual distance between the i-th reference label and the j-th reference label, E _ij is the phase difference Euclidean distance between the i-th reference label and the j-th reference label; Effect, phase difference Euclidean distance fitting and Gaussian white noise cause the ranging error is equivalent to a Gaussian distribution, the mean value of the deviation between the estimated distance and the actual distance between any reference tag and other reference tags by linear fitting and the variance constitute the position parameter and scale parameter of the Gaussian distribution parameter; 4) Taking the reciprocal of the variance of the distance estimation error between the tag to be positioned and the reader and the reference tag as the weighting factor, the weighted least squares algorithm is used to solve the positioning problem.