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

Three-dimensional positioning method based on wireless communication base station

Technical Field

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

Background

Due to the rapid development of wireless communication networks and mobile internet, providing services based on geographical location information (abbreviated as LBS) has become one of the most market potential services. At present, means for realizing accurate positioning include GPS positioning, WiFi positioning, wireless communication base station positioning and the like. Although the GPS positioning has high accuracy, there are 2 defects: firstly, indoor positioning cannot be solved, and secondly, the cost is expensive; coverage of WiFi positioning is limited and the operating band of WiFi signals is susceptible to interference. Therefore, positioning using the wireless communication base station based on the operator becomes an option of the present invention, which not only can perform accurate positioning, but also can avoid the above problems. Modern commercial communication base stations can be used to determine the position coordinates of a terminal (the user's handset) in three-dimensional space, i.e. three-dimensional positioning problems. However, the existing positioning method of the communication base station also has the following problems that the timing of the base station and the timing of the mobile phone terminal cannot be accurately synchronized, thereby influencing the positioning accuracy; the impact of non line of sight (NLOS) on positioning accuracy; the radio signal is interfered by noise in the process of propagation, so that the strong fluctuation of the received signal strength continuously influences the positioning.

Disclosure of Invention

Aiming at the technical problems, the invention designs and develops a three-dimensional positioning method based on a wireless communication base station, which has high convergence rate and robustness on interference and noise.

The technical scheme provided by the invention is as follows:

a three-dimensional positioning method based on a wireless communication base station comprises the following steps:

step one, assuming that the distance difference from the mobile phone terminal to the first base station and the first base station is di, 1, adopting a Kalman smoothing filter algorithm to carry out smoothing filter processing on all measured values of each group, and then taking the average value of the estimated values in the stationary stage as the di, 1 value after filter optimization;

step two, calculating a position estimation value of the terminal:

assuming that the distance from a mobile terminal to the ith base station is di:

suppose that the distance difference from the mobile terminal to the first base station and the ith base station is d_i，1The time difference of the signals from the two base stations arriving at the mobile terminal is delta t_i，1，Δt_i，1＝|t_i-t₁I, then d_i，1＝c×Δt_i，1C is the propagation speed of the electromagnetic wave in space;

then, there are: d_i，1＝d_i ²-d₁ ²＝(x-x_i)²+(y-y_i)²+(z-z_i)²-(x-x₁)²-(y-y₁)²-(z-z₁)²；

Let X_i，1＝x-x_i，Y_i，1＝y-y_i，Z_i，1＝z-z_iThen the above equation can be simplified as:

wherein K_i＝x_i ²+y_i ²+z_i ²；

When the number of base stations N is 4, according to d₁The position estimation value of the mobile terminal is:

preferably, in the three-dimensional positioning method based on a wireless communication base station, a specific process of the first step is as follows:

during positioning, keeping the position of the terminal unchanged, obtaining for a plurality of times d_i，1The observed value of (a); in the measurement process, the true value is interfered by additive noise n (k), the noise at any two moments is assumed to be independent, the system state estimation is established according to the Kalman smoothing filtering theory, and the state equation and the parameter equation of the system are respectively set as follows:

X(k)＝X(k-1)，

Z(k)＝X(k)+n(k)，

wherein X (k) represents the k time d_i，1Z (k) is the k time d_i，1The best estimate of x (k) is given by the kalman filter equation:

and (3) prediction:

and (3) state estimation:

the filter gain is: k (k) ═ P (k, k-1) [ P (k, k-1) + σ²]^-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),

giving an initial valueAnd P (0) from d at time k_i，1By calculation of the k-time from the observed valuesThe value, the initial state estimate, is:from 3 rd d_i，1The observed value of (a) is calculated.

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

thirdly, evaluating the positioning precision by using an average positioning error evaluation formula:

wherein RMSE represents the mean square error of the positioning; m represents the number of the mobile terminals;representing the three-dimensional coordinate calculated by the kth mobile terminal in a certain scene; (x)_k,y_k,z_k) Representing the actual three-dimensional coordinates of the kth mobile terminal in a scene.

A three-dimensional positioning method based on a wireless communication base station comprises the following steps:

step one, assuming that the distance difference from the mobile phone terminal to the first base station and the second base station is d_i，1Smoothing all the measured values of each group by adopting a Kalman smoothing filtering algorithmFiltering, and taking the average value of the estimated values of the stationary stage as d after filtering optimization_i，1A value;

step two, calculating a position estimation value of the terminal:

suppose a mobile terminal is a distance d from the ith base station_iAnd then:

suppose that the distance difference from the mobile terminal to the first base station and the ith base station is d_i，1The time difference of the signals from the two base stations arriving at the mobile terminal is delta t_i，1，Δt_i，1＝|t_i-t₁I, then d_i，1＝c×Δt_i，1C is the propagation speed of the electromagnetic wave in space;

then, there are: d_i，1＝d_i ²-d₁ ²＝(x-x_i)²+(y-y_i)²+(z-z_i)²-(x-x₁)²-(y-y₁)²-(z-z₁)²；

Let X_i，1＝x-x_i，Y_i，1＝y-y_i，z_i，1＝z-z_iThen the above equation can be simplified as:

wherein K_i＝x_i ²+y_i ²+z_i ²；

When the number N of the base stations is more than or equal to 5, the position estimation value of the mobile terminal is calculated by using the redundant data by using a weighted least square method, and the specific process comprises the following steps:

(1) firstly, the initial nonlinear equation is processedGroup ofConverting into linear equation system, and obtaining the first initial solution z by using weighted least square method_a：

Order:is an unknown vector, wherein z_p＝[x,y,z]^TThen, a linear equation is established for the presence of TDOA measurement noise: Ψ -h-G_az_a；

Wherein,

z corresponding to the actual position of the mobile terminal_aA value;

suppose z_aEach element being independent of the other, z_aThe result of the weighted least squares estimation of (c) is:

where phi is the covariance matrix of the error vector psi, phi ═ E [ psi^T]＝c²BQB，

Q is the covariance matrix of the TDOA measurements,

according toObtaining;

(2) and performing WLS estimation for the 2 nd time by using the estimated coordinates obtained for the first time and known constraint conditions such as additional variables, so as to obtain improved estimated coordinates:

first estimate z_aUnder the given additive noise condition:

wherein,then there are:

order toThen there are:

vector z_aIs a random vector with the mean value as the actual value, z_aThe elements are represented as:

z_a,1＝x⁰+e₁,z_a,2＝y⁰+e₂,z_a,3＝z⁰+e₃,z_a,4＝d⁰+e₄wherein e is₁,e₂,e₃,e₄Is z_aThe estimation error of (2); further, the following linear equation set is established:

wherein ψ' is z_aThe error vector of (a) is calculated,an unknown vector z containing the terminal position is obtained_aThe solution of' is:

wherein phi'^-1In order to estimate the covariance matrix of the error,

finally, obtaining a three-dimensional position expression of the terminal:

preferably, in the three-dimensional positioning method based on a wireless communication base station, a specific process of the first step is as follows:

during positioning, keeping the position of the terminal unchanged, obtaining for a plurality of times d_i，1The observed value of (a); in the measurement process, the true value is interfered by additive noise n (k), the noise at any two moments is assumed to be independent, the system state estimation is established according to the Kalman smoothing filtering theory, and the state equation and the parameter equation of the system are respectively set as follows:

X(k)＝X(k-1)，

Z(k)＝X(k)+n(k)，

wherein X (k) represents the k time d_i，1Z (k) is the k time d_i，1The best estimate of x (k) is given by the kalman filter equation:

and (3) prediction:

and (3) state estimation:

the filter gain is: k (k) ═ P (k, k-1) [ P (k, k-1) + σ²]^-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),

giving an initial valueAnd P (0) from d at time k_i，1By calculation of the k-time from the observed valuesThe value, the initial state estimate, is:from 3 rd d_i，1The observed value of (a) is calculated.

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

thirdly, evaluating the positioning precision by using an average positioning error evaluation formula:

wherein RMSE represents the mean square error of the positioning; m represents the number of the mobile terminals;indicating the kth mobile terminal calculation in a sceneThe three-dimensional coordinates are obtained; (x)_k,y_k,z_k) Representing the actual three-dimensional coordinates of the kth mobile terminal in a scene.

The three-dimensional positioning method based on the wireless communication base station completes the positioning of the terminal equipment by using as few base stations as possible based on the TDOA ranging principle, and the designed algorithm has the characteristics of high convergence speed, robustness to interference and noise and the like. The positioning method is particularly suitable for the following places: urban areas where high buildings stand, inside buildings, underground parking lots and the like.

The three-dimensional positioning method based on the wireless communication base station solves the problem that the GPS cannot perform indoor positioning; the problems that the WiFi positioning coverage range is limited and the working frequency band is easily interfered are solved; the problem that the positioning precision is influenced because the timing of the base station and the timing of the mobile phone terminal cannot be accurately synchronized is solved; the influence of non line of sight (NLOS) on the positioning precision is solved; the problem that the positioning is continuously influenced by the severe fluctuation of the received signal strength caused by the interference of noise in the transmission process of the radio signal is solved.

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 diagram illustrating the positioning accuracy comparison of different numbers of base stations according to the present invention.

Detailed Description

The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.

As shown in fig. 1, the present invention designs a three-dimensional positioning method based on a wireless communication base station. Then, the invention uses the measured data to carry out the experiment on the positioning method. Experimental tests show that the method can achieve good positioning accuracy and has good inhibition effect on NLOS, synchronization errors and noise interference.

The three-dimensional positioning method based on the wireless communication base station completes the positioning of the terminal equipment by using as few base stations as possible based on the TDOA ranging principle, and the designed algorithm has the characteristics of high convergence speed, robustness to interference and noise and the like. The positioning method is particularly suitable for the following places: urban areas where high buildings stand, inside buildings, underground parking lots and the like. This is because these application scenarios, whether the number of base stations or the number of mobile phones, are dense, can provide sufficient positioning data for positioning the base stations.

Factors influencing the accuracy of three-dimensional positioning of a base station include: (1) time synchronization of the base station and the mobile phone; (2) the noise of the electromagnetic environment influences the accuracy of the measured data; (3) non line of sight (NLOS) induced latency. Of these 3 influencing factors, the influence of NLOS on the ranging error is the largest, and NLOS is an unavoidable factor for indoor positioning.

The invention solves the problem that the GPS can not carry out indoor positioning; the problems that the WiFi positioning coverage range is limited and the working frequency band is easily interfered are solved; the problem that the positioning precision is influenced because the timing of the base station and the timing of the mobile phone terminal cannot be accurately synchronized is solved; the influence of non line of sight (NLOS) on the positioning precision is solved; (because the influence of NLOS on the positioning accuracy is most common and greatest by looking up relevant data, the method mainly solves the problem); the problem that the positioning is continuously influenced by the severe fluctuation of the received signal strength caused by the interference of noise in the transmission process of the radio signal is solved.

The core of the three-dimensional positioning method is to calculate the distance according to the time difference (obtaining corresponding TDOA data) between a signal and two different base stations from a mobile phone terminal, and then solve a positioning equation set. Because the system of equations is non-linear, a two-fold least squares (WLS) method is used to solve for the deformation of the system of equations in the localization. However, the performance of the measurement error increase algorithm is degraded due to the NLOS and the influence of the environmental noise.

Therefore, the present invention takes the following 2 steps to solve the above problems: firstly, adopting Kalman filtering algorithm to process all d of each group_i，1The measured values are smoothed (assuming that the distance difference between the mobile terminal and the first and 1 st base stations is d_i,: ) Then taking the mean value of the estimated values of the stationary phase as d after the filter optimization_i，1The value is obtained. Second step, using optimized d_i，1And calculating the position estimation value of the terminal.

Suppose a certain mobile terminal (MS) goes toDistance of base station is d_iAnd then:

suppose that the difference in the distance from the terminal to the first base station and the ith base station is d_i，1The time difference of the arrival of the signals from the two base stations at the terminal is Δ t_i，1(Δt_i，1＝|t_i-t₁I), then d)_i，1,＝c×Δt_i，1(c is the propagation velocity of electromagnetic wave in space, generally 3 × 10⁸m/s)。

Then, there are: d_i，1＝d_i ²-d₁ ²＝(x-x_i)²+(y-y_i)²+(z-z_i)²-(x-x₁)²-(y-y₁)²-(z-z₁)²(2)

Let X_i，1＝x-x_i，Y_i，1＝y-y_i，Z_i，1＝z-z_iThen the above equation can be simplified as:

wherein K_i＝x_i ²+y_i ²+z_i ²；

When the number of base stations N is 4, according to d₁The position estimation value of the mobile terminal is:

when the number N of the base stations is more than or equal to 5, a weighted least square method (WLS) can be used for fully utilizing redundant data to obtain a better terminal position estimation value.

TDOA data (Time Difference of arrival, Difference of arrival) measured in the present invention in actual three-dimensional localization_i，1. ) Therefore, the present invention should first perform kalman smoothing filtering on the relevant data to obtain a more accurate distance value, thereby improving the positioning accuracy:

during the positioning, the position of the terminal is not changed, and d is obtained for a plurality of times_i，1The value of (c). In the measurement process, the true value is interfered by additive noise n (k), the noise at any two moments is assumed to be independent, the state estimation of the system is established according to the Kalman filtering theory, and the state equation and the parameter equation of the system are respectively set as follows:

X(k)＝X(k-1) (5)Z(k)＝X(k)+n(k) (6)

wherein X (k) represents the k time d_i，1Z (k) is the k time d_i，1The best estimate of x (k) can be given by the Kalman filter equation:

it is further predicted that:

and (3) state estimation:

the filter gain is: k (k) ═ P (k, k-1) [ P (k, k-1) + σ²]^-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)

To sum up, as long as the initial value is givenAnd P (0), the observed value at the k time can be used to calculate the k timeThe value is obtained. The initial state estimate is:from 3 rd d_i，1The observed value of (a) is calculated.

Obtaining optimized d through the Kalman filtering_i，1The present invention can use these values to calculate a more accurate position estimate for the terminal.

When the number N of the base stations is more than or equal to 5, the invention can use a weighted least square method (WLS) to fully utilize redundant data to obtain a better terminal position estimation value, and the processing process is as follows:

(1) firstly, converting an initial nonlinear equation set (3) into a linear equation set, and obtaining a first initial solution by adopting a WLS (wafer level system); (2) and performing WLS estimation for the 2 nd time by using the estimated coordinates obtained for the first time and known constraint conditions such as additional variables, so as to obtain improved estimated coordinates.

Order:is an unknown vector, wherein z_p＝[x,y,z]^TThen a linear equation can be established for the presence of TDOA measurement noise: Ψ -h-G_az_a(12)

Wherein,

z corresponding to the actual position of the terminal_aThe value is obtained. In solving the non-linear equation, assume z_aEach element being independent of the other, z_aThe result of the weighted least squares estimation of (c) is:

where phi is the covariance matrix of the error vector psi. Looking up related data to know: phi ═ E [ psi-^T]＝c²BQB，

Q is the covariance matrix of the TDOA measurements.

Can be based onAnd (6) obtaining. The invention can obtain the initial estimation result of the terminal position by the formula (13), but the result is in z_aThe estimated value calculated on the premise that each element in the group is independent of each other, z_aD in (2) is related to (x, y, z). Replacing the covariance matrix of the error vector with the Q approximation introduces some errors,in order to further obtain more accurate positioning coordinate values, the method carries out the second step of estimation. First estimate z_aUnder the condition of additive noise given by the title:

because of the fact thatTherefore, according to the formula (12):

order toThen there are:

vector z_aIs a random vector whose mean is the actual value, hence z_aThe elements may be represented as:

z_a,1＝x⁰+e₁,z_a,2＝y⁰+e₂,z_a,3＝z⁰+e₃,z_a,4＝d⁰+e₄wherein e is₁,e₂,e₃,e₄Is z_aThe estimation error of (2). Further, the following linear equation set is established:

wherein ψ' is z_aThe error vector of (a) is calculated,

similar to the derivation when the number of base stations N is 4, the present invention can obtain the unknown vector z containing the terminal position_aThe solution of' is:

wherein phi'^-1In order to estimate the covariance matrix of the error,

finally, obtaining a three-dimensional position expression of the terminal:

at this time, the present invention can determine the accurate position of the terminal according to the prior information.

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

wherein RMSE represents the mean square error of the positioning; m represents the number of terminals;calculating a three-dimensional coordinate of a kth terminal in a certain scene according to the positioning method; (x)_k,y_k,z_k) Representing the actual three-dimensional coordinates of the kth terminal in a scene.

In practice, the present invention measures and calculates 20 sets of TDOA data (each set of TDOA data corresponds to a different geographical location), uses any 5 sets of data and any 9 sets of data to perform positioning using the above-mentioned positioning method, and compares the actual values of each geographical location to calculate the error RMSE of each positioning, resulting in tables 1 and 2.

Table 1 positioning error table based on 5 base stations

As can be seen from the above table, the positioning method has high positioning accuracy for the mobile phone terminal, the average positioning error is less than or equal to 10 meters, and the daily positioning requirements are basically met.

The following table is an error table for positioning the mobile phone terminal by using 9 different base stations.

Table 2 positioning error table based on 9 base stations

As can be seen from the above table, the positioning method has high positioning accuracy for the mobile phone terminal, the average positioning error is less than or equal to 10 meters, and the daily positioning requirement is met.

In addition, the invention selects 5 base stations optionally to carry out positioning analysis on the mobile phone terminal. Referring to fig. 2, it is found that the RMSE deviation of the positioning is large when the number of the base stations is 5, the positioning accuracy increases rapidly with the increase of the number of the base stations from 5 base stations, and the variation is not large after the number of the base stations is greater than or equal to 9. While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims (6)

1. A three-dimensional positioning method based on a wireless communication base station is characterized by comprising the following steps:

step one, assuming that the distance difference from the mobile phone terminal to the first base station and the second base station is d_i，1Smoothing filtering all the measured values in each group by Kalman smoothing filtering algorithm, and taking the average value of the estimated values in the stationary stage as d after filtering optimization_i，1A value;

step two, calculating a position estimation value of the terminal:

assuming a mobile terminal to the ith base stationDistance is d_iAnd 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>

suppose that the distance difference from the mobile terminal to the first base station and the ith base station is d_i，1The time difference of the signals from the two base stations arriving at the mobile terminal is delta t_i，1，Δt_i，1＝|t_i-t₁I, then d_i，1＝c×Δt_i，1C is the propagation speed of the electromagnetic wave in space;

then, there are: d_i，1＝d_i ²-d₁ ²＝(x-x_i)²+(y-y_i)²+(z-z_i)²-(x-x₁)²-(y-y₁)²-(z-z₁)²；

Let X_i，1＝x-x_i，Y_i，1＝y-y_i，Z_i，1＝z-z_iThen the above equation 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>

wherein K_i＝x_i ²+y_i ²+z_i ²；

When the number of base stations N is 4, according to d₁The position estimation value 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 stations as claimed in claim 1, wherein the specific process of the step one is as follows:

during positioning, keeping the position of the terminal unchanged, obtaining for a plurality of times d_i，1The observed value of (a); in the measurement process, the true value is interfered by additive noise n (k), the noise at any two moments is assumed to be independent, the system state estimation is established according to the Kalman smoothing filtering theory, and the state equation and the parameter equation of the system are respectively set as follows:

X(k)＝X(k-1)，

Z(k)＝X(k)+n(k)，

wherein X (k) represents the k time d_i，1Z (k) is the k time d_i，1The best estimate of x (k) is given by the kalman filter equation:

and (3) prediction:

and (3) state estimation:

the filter gain is: k (k) ═ P (k, k-1) [ P (k, k-1) + σ²]^-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),

giving an initial valueAnd P (0) from d at time k_i，1By calculation of the k-time from the observed valuesThe value, the initial state estimate, is:from 3 rd d_i，1The observed value of (a) is calculated.

3. The three-dimensional positioning method based on wireless communication base station as claimed in claim 1, further comprising:

thirdly, evaluating the positioning precision by using an average positioning error evaluation formula:

<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>

wherein RMSE represents the mean square error of the positioning; m represents the number of the mobile terminals;representing the three-dimensional coordinate calculated by the kth mobile terminal in a certain scene; (x)_k,y_k,z_k) Representing the actual three-dimensional coordinates of the kth mobile terminal in a scene.

4. A three-dimensional positioning method based on a wireless communication base station is characterized by comprising the following steps:

step one, assuming that the distance difference from the mobile phone terminal to the first base station and the second base station is d_i，1Smoothing filtering all the measured values in each group by Kalman smoothing filtering algorithm, and taking the average value of the estimated values in the stationary stage as d after filtering optimization_i，1A value;

step two, calculating a position estimation value of the terminal:

suppose a mobile terminal is a distance d from the ith base station_iAnd 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>

suppose that the distance difference from the mobile terminal to the first base station and the ith base station is d_i，1The time difference of the signals from the two base stations arriving at the mobile terminal is delta t_i，1，Δt_i，1＝|t_i-t₁I, then d_i，1＝c×Δt_i，1C is the propagation speed of the electromagnetic wave in space;

then, there are: d_i，1＝d_i ²-d₁ ²＝(x-x_i)²+(y-y_i)²+(z-z_i)²-(x-x₁)²-(y-y₁)²-(z-z₁)²；

Let X_i，1＝x-x_i，Y_i，1＝y-y_i，Z_i，1＝z-z_iThen the above equation 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>

wherein K_i＝x_i ²+y_i ²+z_i ²；

When the number N of the base stations is more than or equal to 5, the position estimation value of the mobile terminal is calculated by using the redundant data by using a weighted least square method, and the specific process comprises the following steps:

(1) firstly, the initial nonlinear equation system is processedConverting into linear equation system, and obtaining the first initial solution z by using weighted least square method_a：

Order:is an unknown vector, wherein z_p＝[x,y,z]^TThen, a linear equation is established for the presence of TDOA measurement noise: Ψ -h-G_az_a；

Wherein,

z corresponding to the actual position of the mobile terminal_aA value;

suppose z_aEach element being independent of the other, z_aThe result of the weighted least squares estimation of (c) is:

where phi is the covariance matrix of the error vector psi, phi ═ E [ psi^T]＝c²BQB，

Q is the covariance matrix of the TDOA measurements,

according toObtaining;

(2) and performing WLS estimation for the 2 nd time by using the estimated coordinates obtained for the first time and known constraint conditions such as additional variables, so as to obtain improved estimated coordinates:

first estimate z_aUnder the given additive noise condition:

h＝h⁰+Δh，

wherein,then there are:

order toThen 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>

vector z_aIs a random vector with the mean value as the actual value, z_aThe elements are represented as:

z_a,1＝x⁰+e₁,z_a,2＝y⁰+e₂,z_a,3＝z⁰+e₃,z_a,4＝d⁰+e₄wherein e is₁,e₂,e₃,e₄Is z_aThe estimation error of (2); further, the following linear equation set is established:

<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>

wherein ψ' is z_aThe error vector of (a) is calculated,

an unknown vector z containing the terminal position is obtained_aThe solution of' is:

wherein phi'^-1In order to estimate the covariance matrix of the 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, obtaining a three-dimensional position expression of the terminal:

<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 stations as claimed in claim 1, wherein the specific process of the step one is as follows:

holding the terminal during positioningIs obtained a plurality of times d_i，1The observed value of (a); in the measurement process, the true value is interfered by additive noise n (k), the noise at any two moments is assumed to be independent, the system state estimation is established according to the Kalman smoothing filtering theory, and the state equation and the parameter equation of the system are respectively set as follows:

X(k)＝X(k-1)，

Z(k)＝X(k)+n(k)，

wherein X (k) represents the k time d_i，1Z (k) is the k time d_i，1The best estimate of x (k) is given by the kalman filter equation:

and (3) prediction:

and (3) state estimation:

the filter gain is: k (k) ═ P (k, k-1) [ P (k, k-1) + σ²]^-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),

giving an initial valueAnd P (0) from d at time k_i，1By calculation of the k-time from the observed valuesThe value, the initial state estimate, is:from 3 rd d_i，1The observed value of (a) is calculated.

6. The three-dimensional positioning method based on wireless communication base station as claimed in claim 1, further comprising:

thirdly, evaluating the positioning precision by using an average positioning error evaluation formula:

<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>

wherein RMSE represents the mean square error of the positioning; m represents the number of the mobile terminals;representing the three-dimensional coordinate calculated by the kth mobile terminal in a certain scene;(x_k,y_k,z_k) Representing the actual three-dimensional coordinates of the kth mobile terminal in a scene.