CN107205268A - A kind of 3-D positioning method based on radio communication base station - Google Patents

Abstract

The invention discloses a kind of 3-D positioning method based on radio communication base station, the time difference (obtaining corresponding TDOA data) according to signal from mobile phone terminal to two different base stations calculates distance, then solves positioning equation group.The present invention is tested using measured data to this localization method.Experiment test shows that the method can realize preferable positioning precision, has good inhibiting effect to NLOS, synchronous error and noise jamming.

Description

A 3D Positioning Method Based on Wireless Communication Base Station

technical field

The invention relates to the communication field, in particular to a three-dimensional positioning method based on a wireless communication base station.

Background technique

Due to the vigorous development of wireless communication networks and mobile Internet, providing services based on geographic location information (abbreviated as LBS) has become one of the businesses with the most market potential. At present, the means to achieve precise positioning include GPS positioning, WiFi positioning, wireless communication base station positioning, etc. Although GPS positioning has high precision, it has two defects: one is that it cannot solve indoor positioning, and the other is that it is expensive; the coverage of WiFi positioning is limited, and the working frequency band of WiFi signals is susceptible to interference. Therefore, positioning using a wireless communication base station based on an operator becomes the choice of the present invention, which can not only perform accurate positioning, but also avoid the above-mentioned problems. Modern commercial communication base stations can be used to determine the position coordinates of the terminal (user's mobile phone) in three-dimensional space, that is, the three-dimensional positioning problem. However, the positioning methods of existing communication base stations also have the following problems. The timing of the base station and the timing of the mobile phone terminal cannot be accurately synchronized, which affects the positioning accuracy; the impact of non-line-of-sight propagation (NLOS) on the positioning accuracy; A problem where the received signal strength fluctuates violently due to noise interference and continues to affect positioning.

Contents of the invention

In view of the above technical problems, the present invention designs and develops a three-dimensional positioning method based on a wireless communication base station that has fast convergence speed and is robust to interference and noise.

The technical scheme provided by the invention is:

A three-dimensional positioning method based on a wireless communication base station, comprising:

Step 1. Assuming that the distance difference between the mobile terminal and the first base station and the second base station is di, 1, use the Kalman smoothing filter algorithm to smooth and filter all the measured values of each group, and then take the mean value of the estimated values in the stationary phase As the di,1 value after filter optimization;

Step 2. Calculate the estimated position of the terminal:

Assuming that the distance between a mobile terminal and the i-th base station is di, then:

Assuming that the distance difference between the mobile terminal and the first base station and the i-th base station is d _i,1 , the time difference between the signals sent by these two base stations arriving at the mobile terminal is Δt _i,1 , Δt _i,1 =|t _i -t ₁ |, then d _{i, 1} = c×Δt _{i, 1} , c is the propagation speed of electromagnetic waves in space;

Then: d _i,1 =d _i ² -d ₁ ² =(xx _i ) ² +(yy _i ) ² +(zz _i ) ² -(xx ₁ ) ² -(yy ₁ ) ² -(zz ₁ ) ² ;

Let X _i,1 =xx _i , Y _i,1 =yy _i , Zi _,1 =zz _i , then the above formula can be simplified as:

where K _i = x _i ² +y _i ² + z _i ² ;

When the number of base stations N= ₄ , according to the value of d1, the estimated value of the position of the mobile terminal is:

Preferably, in the described three-dimensional positioning method based on the wireless communication base station, the specific process of the step 1 is:

During the positioning period, keep the position of the terminal unchanged, and obtain the observed value at multiple times d _{i, 1} ; during the measurement process, the real value is interfered by additive noise n(k), assuming that the noise at any two moments is independent of each other, According to the Kalman smoothing filter theory, the state estimation of the system is established, and the state equation and parameter equation of the system are set as:

X(k)=X(k-1),

Z(k)=X(k)+n(k),

Among them, X(k) represents the true value of d _{i , 1 at time k, Z(k) is the observed value of d i, 1} at time k, and the best estimate of X(k) is given by the Kalman filter equation:

predict:

State estimation:

The filter gain is: K(k)=P(k,k-1)[P(k,k-1)+σ ² ] ^-1 ,

The predicted error covariance is: P(k,k-1)=P(k-1),

The estimated error covariance is: P(k)=[1-K(k)]P(k,k-1),

given initial value and P(0), from the observed value of d _{i, 1} at time k to calculate the value, the estimate of the starting state is: The calculation starts from the observation value of the third d _i,1 .

Preferably, the described three-dimensional positioning method based on the wireless communication base station also includes:

Step 3. Use the average positioning error evaluation formula to evaluate the positioning accuracy:

Among them, RMSE represents the mean square error of positioning; M represents the number of mobile terminals; Indicates the three-dimensional coordinates calculated by the kth mobile terminal in a certain scene; (x _k , y _k , z _k ) indicates the actual three-dimensional coordinates of the kth mobile terminal in a certain scene.

A three-dimensional positioning method based on a wireless communication base station, comprising:

Step 1. Assuming that the distance difference between the mobile terminal and the first base station and the second base station is d _{i, 1} , the Kalman smoothing filter algorithm is used to smooth and filter all the measured values of each group, and then take the estimated value of the stationary stage The mean value is used as the value of d _{i, 1} after filtering optimization;

Step 2. Calculate the estimated position of the terminal:

Suppose the distance between a mobile terminal and the i-th base station is d _i , then:

Assuming that the distance difference between the mobile terminal and the first base station and the i-th base station is d _i,1 , the time difference between the signals sent by these two base stations arriving at the mobile terminal is Δt _i,1 , Δt _i,1 =|t _i -t ₁ |, then d _{i, 1} = c×Δt _{i, 1} , c is the propagation speed of electromagnetic waves in space;

Then: d _i,1 =d _i ² -d ₁ ² =(xx _i ) ² +(yy _i ) ² +(zz _i ) ² -(xx ₁ ) ² -(yy ₁ ) ² -(zz ₁ ) ² ;

Let X _i,1 =xx _i , Y _i,1 =yy _i , z _i,1 =zz _i , then the above formula can be simplified as:

where K _i = x _i ² +y _i ² + z _i ² ;

When the number of base stations is N≥5, the weighted least squares method is used to calculate the estimated position of the mobile terminal using redundant data. The specific process includes:

(1) First put the initial nonlinear equations Transformed into a system of linear equations, using the weighted least squares method to obtain the first initial solution z _a :

make: is an unknown vector, where z _p =[x,y,z] ^T , then establish a linear equation with TDOA measurement noise: Ψ=hG _a z _a ;

in,

z _a value corresponding to the actual position of the mobile terminal;

Assuming that the elements of z _a are independent of each other, the result of the weighted least squares estimation of z _a is:

Among them, φ is the covariance matrix of the error vector ψ, φ=E[ψψ ^T ]=c ² BQB,

Q is the covariance matrix of TDOA measurements,

according to obtain;

(2) Use the estimated coordinates obtained for the first time and the known constraints such as additional variables to perform the second WLS estimation to obtain improved estimated coordinates:

First estimate the covariance matrix of z _a , under the condition of given additive noise:

in, Then there are:

make Then there are:

The vector z _a is a random vector whose mean is the actual value, and each element of z _a is expressed as:

z _a,1 =x ⁰ +e ₁ , z _a,2 =y ⁰ +e ₂ , z _a,3 =z ⁰ +e ₃ , z _a,4 =d ⁰ +e ₄ , where e ₁ ,e ₂ , e ₃ , e ₄ are the estimation error of z _a ; then establish the following linear equations:

Among them, ψ' is the error vector of z _a , Then the solution of the unknown vector z _a ' containing the terminal position is obtained as:

Among them, φ' ^-1 is the covariance matrix of the estimation error,

Finally, the three-dimensional position expression of the terminal is obtained:

Preferably, in the described three-dimensional positioning method based on the wireless communication base station, the specific process of the step 1 is:

During the positioning period, keep the position of the terminal unchanged, and obtain the observed value at multiple times d _{i, 1} ; during the measurement process, the real value is interfered by additive noise n(k), assuming that the noise at any two moments is independent of each other, According to the Kalman smoothing filter theory, the state estimation of the system is established, and the state equation and parameter equation of the system are set as:

X(k)=X(k-1),

Z(k)=X(k)+n(k),

Among them, X(k) represents the true value of d _{i , 1 at time k, Z(k) is the observed value of d i, 1} at time k, and the best estimate of X(k) is given by the Kalman filter equation:

predict:

State estimation:

The filter gain is: K(k)=P(k,k-1)[P(k,k-1)+σ ² ] ^-1 ,

The predicted error covariance is: P(k,k-1)=P(k-1),

The estimated error covariance is: P(k)=[1-K(k)]P(k,k-1),

given initial value and P(0), from the observed value of d _{i, 1} at time k to calculate the value, the estimate of the starting state is: The calculation starts from the observation value of the third d _i,1 .

Preferably, the described three-dimensional positioning method based on the wireless communication base station also includes:

Step 3. Use the average positioning error evaluation formula to evaluate the positioning accuracy:

Among them, RMSE represents the mean square error of positioning; M represents the number of mobile terminals; Indicates the three-dimensional coordinates calculated by the kth mobile terminal in a certain scene; (x _k , y _k , z _k ) indicates the actual three-dimensional coordinates of the kth mobile terminal in a certain scene.

The three-dimensional positioning method based on the wireless communication base station described in the present invention is based on the TDOA ranging principle and uses as few base stations as possible to complete the positioning of the terminal equipment. The designed algorithm has the characteristics of fast convergence speed and robustness to interference and noise. . This positioning method is especially suitable for the following places: urban areas with many high-rise buildings, inside buildings, underground parking lots, etc.

The three-dimensional positioning method based on the wireless communication base station of the present invention solves the problem that GPS cannot perform indoor positioning; solves the problem that WiFi positioning coverage is limited and the working frequency band is easily interfered; solves the problem that the timing of the base station and the timing of the mobile phone terminal cannot be accurately synchronized Thus affecting the positioning accuracy; solving the impact of non-line-of-sight propagation (NLOS) on positioning accuracy; solving the problem that the radio signal is disturbed by noise during the propagation process and the received signal strength fluctuates violently and continues to affect positioning.

Description of drawings

FIG. 1 is a schematic diagram of a three-dimensional positioning method based on a wireless communication base station according to the present invention.

Fig. 2 is a comparison diagram of positioning accuracy of different numbers of base stations according to the present invention.

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings, so that those skilled in the art can implement it with reference to the description.

As shown in Figure 1, the present invention designs a three-dimensional positioning method based on a wireless communication base station. Afterwards, the present invention uses the measured data to conduct experiments on the positioning method. Experimental tests show that this method can achieve better positioning accuracy, and has a better suppression effect on NLOS, synchronization error and noise interference.

The three-dimensional positioning method based on the wireless communication base station described in the present invention is based on the TDOA ranging principle and uses as few base stations as possible to complete the positioning of the terminal equipment. The designed algorithm has the characteristics of fast convergence speed and robustness to interference and noise. . This positioning method is especially suitable for the following places: urban areas with many high-rise buildings, inside buildings, underground parking lots, etc. This is because these application scenarios are dense in both the number of base stations and the number of mobile phones, which can provide sufficient positioning data for base station positioning.

The factors that affect the accuracy of the three-dimensional positioning of the base station are: (1), the time synchronization problem between the base station and the mobile phone; (2), the noise of the electromagnetic environment affects the accuracy of the measurement data; (3), the time caused by non-line-of-sight (NLOS) delay. Among the three influencing factors, NLOS has the greatest impact on the ranging error, and for indoor positioning, NLOS is an inevitable factor.

The invention solves the problem that GPS cannot perform indoor positioning; solves the problem that WiFi positioning coverage is limited and the working frequency band is easily interfered; The impact of distance propagation (NLOS) on positioning accuracy; (because consulting relevant information shows that the impact of NLOS on positioning accuracy is the most common and largest, so this method focuses on solving this problem); solves the radio signal in the propagation process The problem that the received signal strength fluctuates violently due to noise interference continues to affect positioning.

The core of the three-dimensional positioning method is to calculate the distance according to the time difference of the signal from the mobile terminal to two different base stations (to obtain the corresponding TDOA data), and then solve the positioning equations. Since the equations are nonlinear, the double least squares (WLS) method is used to solve the positioning equations. However, due to the influence of NLOS and environmental noise, the performance of the measurement error increasing algorithm will be degraded.

Therefore, the present invention takes the following two steps to solve the above-mentioned problem: the first step, adopts the Kalman filter algorithm to carry out smoothing filtering process to all d _{i of each group, 1} measurement value (assuming that the mobile phone terminal arrives at the first base station and the first base station The distance difference is d _i , :), and then take the mean value of the estimated value in the stationary stage as the optimized d _{i, 1} value after filtering. In the second step, the estimated value of the position of the terminal is calculated by using the optimized value of d _i,1 .

Assuming that a mobile terminal (MS) arrives at the The distance between base stations is d _i , then:

Assuming that the distance difference between the terminal and the first base station and the i-th base station is d _{i, 1} , the time difference between the signals sent by these two base stations arriving at the terminal is Δt _{i, 1} (Δt _{i, 1} =|t _i -t ₁ | ), then d _i,1 ,=c×Δt _i,1 . (c is the propagation speed of electromagnetic waves in space, generally 3×10 ⁸ m/s).

Then: d _i,1 =d _i ² -d ₁ ² =(xx _i ) ² +(yy _i ) ² +(zz _i ) ² -(xx ₁ ) ² -(yy ₁ ) ² -(zz ₁ ) ² (2)

Let X _i,1 =xx _i , Y _i,1 =yy _i , Zi _,1 =zz _i , then the above formula can be simplified as:

where K _i = x _i ² +y _i ² + z _i ² ;

When the number of base stations N= ₄ , according to the value of d1, the estimated value of the position of the mobile terminal is:

When the number of base stations N≥5, the weighted least square method (WLS) can be used to make full use of redundant data to obtain a better terminal position estimation value.

In the actual three-dimensional positioning, the TDOA data (TDOA, Time Difference Of Arrival, time difference of arrival. In this method, the TDOA data measured by the present invention is Δt _{i, 1.} ) is very likely to include the information measured under the NLOS environment, Therefore, the present invention should first perform Kalman smoothing filter processing on the relevant data to obtain a more accurate distance value, thereby improving the positioning accuracy:

During positioning, the position of the terminal remains unchanged, and the value of d _i,1 is obtained multiple times. During the measurement process, the real value is disturbed by additive noise n(k). Assuming that the noise at any two moments is independent of each other, according to the Kalman filter theory, the system state estimation is established. The state equation and parameter equation of the system are respectively:

X(k)=X(k-1) (5) Z(k)=X(k)+n(k) (6)

Among them, X(k) represents the true value of d _{i , 1 at time k, Z(k) is the observed value of d i, 1} at time k, and the best estimate of X(k) can be given by the Kalman filter equation:

Further predictions:

State estimation:

The filter gain is: K(k)=P(k,k-1)[P(k,k-1)+σ ² ] ^-1 (9)

The predicted error covariance is: P(k,k-1)=P(k-1) (10)

The estimated error covariance is: P(k)=[1-K(k)]P(k,k-1) (11)

In summary, as long as the initial value is given and P(0), the observed value at k time can be calculated from the k time value. The estimate for the starting state is: The calculation starts from the observation value of the third d _i,1 .

The optimized values of d _i,1 are obtained through the above Kalman filtering, and the present invention can use these values to calculate a more accurate position estimation of the terminal.

When the number of base stations N≥5, the present invention can use the weighted least square method (WLS) to make full use of redundant data to obtain a better terminal position estimate, and the process is as follows:

(1) First convert the initial nonlinear equations (3) into linear equations, and use WLS to obtain the first initial solution; (2), use the estimated coordinates obtained for the first time and known constraints such as additional variables to carry out 2nd WLS estimate, resulting in improved estimated coordinates.

make: is an unknown vector, where z _p =[x,y,z] ^T , then a linear equation with TDOA measurement noise can be established: Ψ=hG _a z _a (12)

in,

is the z _a value corresponding to the actual position of the terminal. When solving nonlinear equations, it is assumed that the elements of z _a are independent of each other, and the result of the weighted least squares estimation of z _a is:

where φ is the covariance matrix of the error vector ψ. Check relevant information: φ＝E[ψψ ^T ]＝c ² BQB,

Q is the covariance matrix of TDOA measurements.

can be based on Get it. The present invention can obtain the preliminary estimation result of the terminal position through the formula (13), but this result is an estimated value calculated under the premise that each element in z _a is independent of each other, in fact d in z _a is the same as (x, y, z) related. Replacing the covariance matrix φ of the error vector with Q approximation will bring some errors. In order to further obtain more accurate positioning coordinate values, the present invention performs the second step of estimation. First estimate the covariance matrix of z _a , under the condition of additive noise given in the title:

because So according to formula (12):

make Then there are:

The vector z _a is a random vector whose mean is the actual value, so each element of z _a can be expressed as:

z _a,1 =x ⁰ +e ₁ , z _a,2 =y ⁰ +e ₂ , z _a,3 =z ⁰ +e ₃ , z _a,4 =d ⁰ +e ₄ , where e ₁ ,e ₂ , e ₃ , e ₄ are the estimated errors of z _a . Then establish the following linear equations:

Among them, ψ' is the error vector of z _a ,

Similar to the derivation when the number of base stations is N=4, the present invention can obtain the solution of the unknown vector z _a ' containing the terminal position as:

Among them, φ' ^-1 is the covariance matrix of the estimation error,

Finally, the three-dimensional position expression of the terminal is obtained:

At this time, the present invention can determine the precise location of the terminal according to the prior information.

Finally, in this positioning method, the present invention uses the average positioning error to evaluate the positioning accuracy of the above model:

Among them, RMSE represents the mean square error of positioning; M represents the number of terminals; The three-dimensional coordinates of the kth terminal in a certain scene calculated according to the positioning method; (x _k , y _k , z _k ) represent the actual three-dimensional coordinates of the kth terminal in a certain scene.

In practice, the present invention measures and calculates 20 sets of TDOA data (each set of TDOA data corresponds to a different geographic location), uses the above-mentioned positioning method to utilize any 5 sets of data and any 9 sets of data for positioning, and compares each Calculate the error RMSE of each positioning from the actual value of each geographic location, and get Table 1 and Table 2.

Table 1 Positioning error table based on 5 base stations

It can be seen from the above table that this positioning method has high positioning accuracy for mobile terminals, and the average positioning error is ≤10 meters, which basically meets the daily positioning requirements.

The following table is the error table of using 9 different base stations to locate the mobile terminal.

Table 2 Positioning error table based on 9 base stations

It can be seen from the above table that this positioning method has high positioning accuracy for mobile terminals, and the average positioning error is ≤10 meters, which meets the daily positioning requirements.

In addition, the present invention first selects 5 base stations to perform positioning analysis on the mobile terminal. Please refer to Figure 2. It turns out that when the number of base stations is 5, the RMSE deviation of positioning is relatively large. From 5 base stations, the positioning accuracy increases rapidly with the increase of the number of base stations, and the number of base stations ≥ 9 does not change much. Although the embodiment of the present invention has been disclosed as above, it is not limited to the use listed in the specification and implementation, it can be applied to various fields suitable for the present invention, and it can be easily understood by those skilled in the art Therefore, the invention is not limited to the specific details and examples shown and described herein without departing from the general concept defined by the claims and their equivalents.

Claims (6)

1. A three-dimensional positioning method based on a wireless communication base station, characterized in that, comprising: Step 1. Assuming that the distance difference between the mobile terminal and the first base station and the second base station is d _{i, 1} , the Kalman smoothing filter algorithm is used to smooth and filter all the measured values of each group, and then take the estimated value of the stationary stage The mean value is used as the value of d _{i, 1} after filtering optimization; Step 2. Calculate the estimated position of the terminal: Suppose the distance between a mobile terminal and the i-th base station is d _i , then: <mrow> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> Assuming that the distance difference between the mobile terminal and the first base station and the i-th base station is d _i,1 , the time difference between the signals sent by these two base stations arriving at the mobile terminal is Δt _i,1 , Δt _i,1 =|t _i -t ₁ |, then d _{i, 1} = c×Δt _{i, 1} , c is the propagation speed of electromagnetic waves in space; Then: d _i,1 =d _i ² -d ₁ ² =(xx _i ) ² +(yy _i ) ² +(zz _i ) ² -(xx ₁ ) ² -(yy ₁ ) ² -(zz ₁ ) ² ; Let X _i,1 =xx _i , Y _i,1 =yy _i , Zi _,1 =zz _i , then the above formula can be simplified as: <mrow> <msup> <msub> <mi>d</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msup> <msub> <mi>d</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mn>2</mn> <mo>&amp;lsqb;</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfenced open = "{" close = "}"> <mtable> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>;</mo> </mrow> where K _i = x _i ² +y _i ² + z _i ² ; When the number of base stations N= ₄ , according to the value of d1, the estimated value of the position of the mobile terminal is: <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>Y</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>Z</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>Y</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>Z</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>Y</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>Z</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>&amp;times;</mo> <mrow> <mo>{</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>d</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>d</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>d</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>K</mi> <mn>4</mn> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mrow> 2. the three-dimensional positioning method based on wireless communication base station as claimed in claim 1, is characterized in that, the specific process of described step 1 is: During the positioning period, keep the position of the terminal unchanged, and obtain the observed value at multiple times d _{i, 1} ; during the measurement process, the real value is interfered by additive noise n(k), assuming that the noise at any two moments is independent of each other, According to the Kalman smoothing filter theory, the state estimation of the system is established, and the state equation and parameter equation of the system are set as: X(k)=X(k-1), Z(k)=X(k)+n(k), Among them, X(k) represents the true value of d _{i , 1 at time k, Z(k) is the observed value of d i, 1} at time k, and the best estimate of X(k) is given by the Kalman filter equation: predict: State estimation: The filter gain is: K(k)=P(k,k-1)[P(k,k-1)+σ ² ] ^-1 , The predicted error covariance is: P(k,k-1)=P(k-1), The estimated error covariance is: P(k)=[1-K(k)]P(k,k-1), given initial value and P(0), from the observed value of d _{i, 1} at time k to calculate the value, the estimate of the starting state is: The calculation starts from the observation value of the third d _i,1 . 3. The three-dimensional positioning method based on wireless communication base station as claimed in claim 1, is characterized in that, also comprises: Step 3. Use the average positioning error evaluation formula to evaluate the positioning accuracy: <mrow> <mi>R</mi> <mi>M</mi> <mi>S</mi> <mi>E</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>,</mo> </mrow> Among them, RMSE represents the mean square error of positioning; M represents the number of mobile terminals; Indicates the three-dimensional coordinates calculated by the kth mobile terminal in a certain scene; (x _k , y _k , z _k ) indicates the actual three-dimensional coordinates of the kth mobile terminal in a certain scene. 4. A three-dimensional positioning method based on a wireless communication base station, characterized in that, comprising: Step 1. Assuming that the distance difference between the mobile terminal and the first base station and the second base station is d _{i, 1} , the Kalman smoothing filter algorithm is used to smooth and filter all the measured values of each group, and then take the estimated value of the stationary stage The mean value is used as the value of d _{i, 1} after filtering optimization; Step 2. Calculate the estimated position of the terminal: Suppose the distance between a mobile terminal and the i-th base station is d _i , then: <mrow> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> Assuming that the distance difference between the mobile terminal and the first base station and the i-th base station is d _i,1 , the time difference between the signals sent by these two base stations arriving at the mobile terminal is Δt _i,1 , Δt _i,1 =|t _i -t ₁ |, then d _{i, 1} = c×Δt _{i, 1} , c is the propagation speed of electromagnetic waves in space; Then: d _i,1 =d _i ² -d ₁ ² =(xx _i ) ² +(yy _i ) ² +(zz _i ) ² -(xx ₁ ) ² -(yy ₁ ) ² -(zz ₁ ) ² ; Let X _i,1 =xx _i , Y _i,1 =yy _i , Zi _,1 =zz _i , then the above formula can be simplified as: <mrow> <msup> <msub> <mi>d</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msup> <msub> <mi>d</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mn>2</mn> <mo>&amp;lsqb;</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Z</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfenced open = "{" close = "}"> <mtable> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>;</mo> </mrow> where K _i = x _i ² +y _i ² + z _i ² ; When the number of base stations is N≥5, the weighted least squares method is used to calculate the estimated position of the mobile terminal using redundant data. The specific process includes: (1) First put the initial nonlinear equations Transformed into a system of linear equations, using the weighted least squares method to obtain the first initial solution z _a : make: is an unknown vector, where z _p =[x,y,z] ^T , then establish a linear equation with TDOA measurement noise: Ψ=hG _a z _a ; in, z _a value corresponding to the actual position of the mobile terminal; Assuming that the elements of z _a are independent of each other, the result of the weighted least squares estimation of z _a is: Among them, φ is the covariance matrix of the error vector ψ, φ=E[ψψ ^T ]=c ² BQB, Q is the covariance matrix of TDOA measurements, according to obtain; (2) Use the estimated coordinates obtained for the first time and the known constraints such as additional variables to perform the second WLS estimation to obtain improved estimated coordinates: First estimate the covariance matrix of z _a , under the condition of given additive noise: h=h ⁰ +Δh, in, Then there are: make Then there are: <mrow> <msub> <mi>&amp;Delta;z</mi> <mi>a</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>G</mi> <mi>a</mi> <mi>T</mi> </msubsup> <msup> <mi>&amp;psi;</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>G</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>G</mi> <mi>a</mi> <mi>T</mi> </msubsup> <msup> <mi>&amp;psi;</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>B</mi> <mi>n</mi> <mo>,</mo> <mi>cov</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Delta;z</mi> <mi>a</mi> </msub> <msubsup> <mi>&amp;Delta;z</mi> <mi>a</mi> <mi>T</mi> </msubsup> <mo>&amp;rsqb;</mo> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>G</mi> <mi>a</mi> <mrow> <mn>0</mn> <mi>T</mi> </mrow> </msubsup> <msup> <mi>&amp;psi;</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>G</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> </mrow> The vector z _a is a random vector whose mean is the actual value, and each element of z _a is expressed as: z _a,1 =x ⁰ +e ₁ , z _a,2 =y ⁰ +e ₂ , z _a,3 =z ⁰ +e ₃ , z _a,4 =d ⁰ +e ₄ , where e ₁ ,e ₂ , e ₃ , e ₄ are the estimation error of z _a ; then establish the following linear equations: <mrow> <msup> <mi>&amp;psi;</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <msup> <mi>h</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msubsup> <mi>G</mi> <mi>a</mi> <mo>&amp;prime;</mo> </msubsup> <msup> <msubsup> <mi>z</mi> <mi>a</mi> <mo>&amp;prime;</mo> </msubsup> <mn>0</mn> </msup> <mo>;</mo> </mrow> Among them, ψ' is the error vector of z _a , Then the solution of the unknown vector z _a ' containing the terminal position is obtained as: Among them, φ' ^-1 is the covariance matrix of the estimation error, <mrow> <msup> <mi>&amp;psi;</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <msup> <mi>h</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msubsup> <mi>G</mi> <mi>a</mi> <mo>&amp;prime;</mo> </msubsup> <msup> <msubsup> <mi>z</mi> <mi>a</mi> <mo>&amp;prime;</mo> </msubsup> <mn>0</mn> </msup> <mo>,</mo> <msup> <mi>&amp;phi;</mi> <mrow> <mo>&amp;prime;</mo> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <msup> <mi>&amp;psi;</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>&amp;psi;</mi> <mrow> <mo>&amp;prime;</mo> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;rsqb;</mo> <mo>=</mo> <mn>4</mn> <msup> <mi>B</mi> <mo>&amp;prime;</mo> </msup> <mi>cov</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>B</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msup> <mi>B</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>{</mo> <msup> <mi>x</mi> <mn>0</mn> </msup> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msup> <mi>y</mi> <mn>0</mn> </msup> <mo>-</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>,</mo> <msup> <mi>z</mi> <mn>0</mn> </msup> <mo>-</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>,</mo> <msubsup> <mi>d</mi> <mn>1</mn> <mn>0</mn> </msubsup> <mo>}</mo> <mo>,</mo> </mrow> Finally, the three-dimensional position expression of the terminal is obtained: <mrow> <msub> <mi>z</mi> <mi>p</mi> </msub> <mo>=</mo> <mo>&amp;PlusMinus;</mo> <msqrt> <msubsup> <mi>z</mi> <mi>a</mi> <mo>&amp;prime;</mo> </msubsup> </msqrt> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mn>1</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> 5. the three-dimensional positioning method based on wireless communication base station as claimed in claim 1, is characterized in that, the specific process of described step 1 is: During the positioning period, keep the position of the terminal unchanged, and obtain the observed values at multiple times d _{i, 1} ; during the measurement process, the real value is interfered by additive noise n(k), assuming that the noises at any two moments are independent of each other, According to the Kalman smoothing filter theory, the state estimation of the system is established, and the state equation and parameter equation of the system are set as: X(k)=X(k-1), Z(k)=X(k)+n(k), Among them, X(k) represents the true value of d _{i , 1 at time k, Z(k) is the observed value of d i, 1} at time k, and the best estimate of X(k) is given by the Kalman filter equation: predict: State estimation: The filter gain is: K(k)=P(k,k-1)[P(k,k-1)+σ ² ] ^-1 , The predicted error covariance is: P(k,k-1)=P(k-1), The estimated error covariance is: P(k)=[1-K(k)]P(k,k-1), given initial value and P(0), from the observed value of d _{i, 1} at time k to calculate the value, the estimate of the starting state is: The calculation starts from the observation value of the third d _i,1 . 6. The three-dimensional positioning method based on wireless communication base stations as claimed in claim 1, further comprising: Step 3. Use the average positioning error evaluation formula to evaluate the positioning accuracy: <mrow> <mi>R</mi> <mi>M</mi> <mi>S</mi> <mi>E</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>,</mo> </mrow> Among them, RMSE represents the mean square error of positioning; M represents the number of mobile terminals; Indicates the three-dimensional coordinates calculated by the kth mobile terminal in a certain scene; (x _k , y _k , z _k ) indicates the actual three-dimensional coordinates of the kth mobile terminal in a certain scene.