CN107389068B - TDOA-based binary search positioning method - Google Patents

TDOA-based binary search positioning method Download PDF

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CN107389068B
CN107389068B CN201710591898.8A CN201710591898A CN107389068B CN 107389068 B CN107389068 B CN 107389068B CN 201710591898 A CN201710591898 A CN 201710591898A CN 107389068 B CN107389068 B CN 107389068B
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CN107389068A (en
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陈昱衡
陈香
张旭
曹帅
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University of Science and Technology of China USTC
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G01C21/206—Instruments for performing navigational calculations specially adapted for indoor navigation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/26—Position of receiver fixed by co-ordinating a plurality of position lines defined by path-difference measurements

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Abstract

The invention discloses a TDOA-based binary search positioning method, which gives accurate estimation to an estimated position through the steps of coordinate conversion, binary search and the like, compensates a two-dimensional positioning error through a height compensation method under the condition of height difference, and ensures the positioning precision. The method has small calculation amount, is convenient for the research and development of a subsequent real-time system, and can be widely used for estimating the position of the mobile terminal.

Description

TDOA-based binary search positioning method
Technical Field
The invention relates to the field of indoor positioning, in particular to a TDOA-based binary search positioning method.
Background
With the development of internet technology and communication technology, the importance of location information is continuously highlighted, and the positioning problem caused by the importance of location information is widely concerned by people. At present, technologies such as GPS can accurately complete outdoor positioning. However, as society develops, the number of large buildings (such as shopping malls) increases, and thus the demand for indoor positioning increases, but the GPS cannot perform accurate positioning indoors, which requires an accurate indoor positioning technology. The current technologies for indoor positioning are based on RF, optics, geomagnetism, audio and the like, and no matter which positioning technology is adopted, the indoor positioning method mainly comprises the following steps: fingerprinting, direction angle based, Time Difference of Arrival (TDOA), and Time of Arrival (TOA), where fingerprinting requires the establishment and maintenance of a fingerprint library prior to location, which requires a large amount of work and the method is less accurate; orientation angle based positioning methods often require higher hardware costs; TDOA and TOA can achieve high accuracy indoor positioning, but TOA requires more stringent clock synchronization conditions than do the two.
The existing TDOA-based positioning method mainly includes a Chan algorithm, a Taylor algorithm, and the like, wherein the Chan algorithm calculates coordinates when the difference between the estimated distance difference and the theoretical distance difference is minimum according to a least square principle, however, in real application, certain errors may occur in TDOA data, and the estimated position obtained by the Chan algorithm under the condition is poor in stability and large in calculation amount. The Taylor algorithm needs an initial value, the initial value is obtained by multiple times of calculation and averaging through the Chan algorithm, then the estimated position can be obtained, the calculation amount of the algorithm is large, and the algorithm has a great relation with the initial value selection. The TDOA-based binary search positioning method can estimate the position more stably, has small calculation amount and is easy for subsequent transplantation.
In indoor positioning, two-dimensional position estimation can satisfy most of the demands. However, in an actual indoor positioning arrangement, the base station may be placed on a wall surface, a ceiling, or the like, so that a height difference exists between a plane formed by the base station and a horizontal plane where the target is located, and the height difference affects positioning accuracy. Three-dimensional positioning is currently commonly used to solve this problem, but this increases the amount of computation.
Disclosure of Invention
The invention aims to provide a TDOA-based binary search positioning method, which can quickly and accurately acquire a target two-dimensional coordinate and has small calculation amount.
The purpose of the invention is realized by the following technical scheme:
a binary search positioning method based on TDOA comprises the following steps:
acquiring TDOA information;
judging whether a height difference exists between a plane formed by the receiving points and a horizontal plane where the target is located or not, and determining according to the height of each point;
case 1: if the height difference does not exist, calculating the distance difference according to the TDOA information, performing primary estimation on the target position by using a binary search algorithm according to any two distance differences, screening the primarily estimated target position according to the average values and standard deviations of all the primarily estimated target positions, and updating the average value and the standard deviation until the standard deviation meets the requirement, wherein the position of the average value is the final target position;
case 2: if the height difference exists, the original distance difference is calculated by using the TDOA information, the estimated position of the target point is preliminarily estimated by using any two original distance differences and adopting a binary search algorithm, the difference value of the height difference and the distance difference without the height difference is calculated at the estimated position, then the corresponding difference value is subtracted from the original distance difference, the distance difference is updated, and then the positioning is finished by combining the updated distance difference with the condition 1.
The acquiring the TDOA information comprises the following steps:
transmitting a signal source by a target, and receiving time differences of the signal source by receiving points at different positions;
or, the signal source is transmitted by each receiving point, and the target receives the time difference of the signal sources of different base stations.
The specific process of obtaining the target final position in case 1 is as follows:
assuming that there are three receiving points, namely a target point P and A, B, C, and a plane formed by the three receiving points is parallel to a horizontal plane where the target point P is located; the target point P transmits an audio signal, the audio signal is received by a microphone at A, B, C three receiving points, and the arrival time of the signal is judged by a related detection algorithm; calculating the time difference delta t1 between the point A and the point B and the time difference delta t2 between the point B and the point C, and then recording R1 as the distance difference between the distance from the target position P to the receiving point A and the distance from the target position P to the receiving point B; let R2 be the distance difference between the distance from the target position point P to the receiving point B and the distance from the target position point P to the receiving point C, and C be the speed of sound, then:
Figure BDA0001354943590000021
then, preliminarily estimating the target position by using a binary search positioning method, wherein the steps are as follows:
a. and (3) coordinate conversion: suppose (x)A,yA)、(xB,yB)、(xC,yC) Coordinates of reception point A, B, C are respectively shifted to origin (0, 0) by translation, and then rotated counterclockwise by an angle θ around reception point a in accordance with the following equation so that coordinates of reception points B and C become (x'B,0)、(x′C,y′C)；
Figure BDA0001354943590000033
b. Judging whether the distance difference R1 is equal to 0 or not, if so, locating the target position in a perpendicular bisector between the receiving points A and B to obtain target position coordinates (x'B2, 0); otherwise, estimating that the target position is located on a hyperbolic curve, taking the receiving points A and B as focuses of the hyperbolic curve, and continuing the next step;
c. initializing the ordinate of the point P1 and the ordinate of the point P2, enabling the ordinate of the point P1 and the ordinate of the point P2 to be respectively corresponding to the ordinate of the point B and the point C, calculating the abscissa of the point P1 and the point P2 according to the following formula, and calculating according to x'BPositive and negative of (2) determine the positive and negative of the origin, and ensure that the absolute value of the abscissa is less than x'BAbsolute value of (d); then taking the median value of the ordinate of the P1 point and the ordinate of the P2 point as the abscissa of the P point, and substituting the following formula to obtain the ordinate of the point P:
Figure BDA0001354943590000031
wherein a ═ 0.5 ═ R1, c ═ 0.5 ^ x'B，b2＝c2-a2P1A | - | | P1B | | ═ R1, | | P2A | - | | | P2B | | | - | R1, P1A, P1B, P2A, P2B are the distance from the point P1 to the receiving point a, the distance from the point P1 to the receiving point B, the distance from the point P2 to the receiving point a, and the distance from the point P1 to the receiving point B, respectively;
d. calculating the following two formulas, and updating the point P1 or the point P2 according to the calculation result:
Figure BDA0001354943590000032
wherein, P1C, PB, PC, and P2C are the distance from point P1 to receiving point C, the distance from point P to receiving point B, the distance from point P to receiving point C, and the distance from point P2 to receiving point C, respectively;
if the first equation is greater than 0, fixing the point P2, and moving the point P1 to the point P; if the second equation is greater than 0, fix point P1, move point P2 to point P;
e. repeating the step d until | | | P1P2| | | < δ, wherein δ is a set value, the ordinate of the estimated position obtained preliminarily at this time is the midpoint of the P1 point and the P2 point, the abscissa is calculated by the formula in the step c, so that a target position coordinate is obtained, then the coordinate is converted according to the principle of the step a, and the converted coordinate is the preliminarily estimated target position and is marked as pos 1;
repeating the steps a to e to obtain n preliminarily estimated target positions, and then calculating a mean value and a standard deviation;
if the standard deviation is larger than the threshold value, excluding the positions of the n preliminary estimated target positions which are farthest away from the mean position, and recalculating the mean value and the standard deviation from the rest target positions; and repeating the process continuously until the standard deviation meets the requirement, wherein the positions of the residual target position mean values are the target final positions.
The specific process of obtaining the target final position in case 2 is as follows:
calculating original distance difference information based on the TDOA information, wherein a distance difference between a distance from the point of the target position P to the receiving point a and a distance from the point of the target position P to the receiving point B is denoted as R1'; the distance difference between the distance from the point of the target position P to the receiving point B and the distance from the point of the target position P to the receiving point C is recorded as R2';
secondly, obtaining a preliminary positioning result (x ', y') by using the distance differences R1 'and R2' in combination with the steps a-e in the case 1;
then, the difference between the height difference h and the distance difference without height difference at (x ', y') is calculated by the following formula, and is recorded as Δ R1, Δ R2:
Figure BDA0001354943590000041
re-update distance difference:
Figure BDA0001354943590000042
finally, the target final position is calculated from the updated distance differences R1 "and R2" in case 1 manner.
According to the technical scheme provided by the invention, the estimated position is accurately estimated through the steps of coordinate conversion, binary search and the like, and for the condition of height difference, a two-dimensional positioning error is made up through a height compensation method, so that the positioning accuracy is ensured. The method has small calculation amount, is convenient for the research and development of a subsequent real-time system, and can be widely used for estimating the position of the mobile terminal.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
FIG. 1 is a flowchart of a TDOA-based binary search positioning method according to an embodiment of the present invention;
FIG. 2 is a model diagram of a binary search positioning method according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a final result obtained by weighted average of multiple estimated positions according to an embodiment of the present invention
Fig. 4 is a schematic view of height compensation positioning according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a flowchart of a TDOA-based binary search positioning method according to an embodiment of the present invention. As shown in fig. 1, it mainly includes the following steps:
and step 11, obtaining the TDOA information.
In the embodiment of the present invention, the TDOA information may be obtained in the following two ways: transmitting a signal source by a target, and receiving time differences of the signal source by receiving points at different positions; or, the signal source is transmitted by each receiving point, and the target receives the time difference of the signal sources of different base stations.
For example, a TDOA-based binary search location method can be provided assuming audio as a location means. As shown in fig. 2, the target point P transmits an audio signal, receives the audio signal through a microphone at A, B, C three points (taking a rectangle as an example), determines the arrival time of the signal through a correlation detection algorithm, and calculates the time difference Δ t1 between the arrival at point a and the arrival at point B and the time difference Δ t2 between the arrival at point B and the arrival at point C, and let R1 be the distance difference between the distance from the target point P to the receiving point a and the distance from the target point P to the receiving point B; r2 is the distance difference between the distance from the target position P to the receiving point B and the distance from the target position P to the receiving point C, and C is the speed of sound, then there are:
Figure BDA0001354943590000051
in addition, in the embodiment of the invention, the plane formed by the three receiving points is parallel to the horizontal plane of the target.
And step 12, judging whether a height difference exists between the plane formed by the receiving points and the horizontal plane where the target is located.
In the embodiment of the invention, calculation is carried out according to two conditions of whether the height difference exists or not; in case 1, if there is no height difference, the process proceeds to step 13; in case 2, the height difference is present, and the process proceeds to step 14.
And step 13, calculating distance differences according to the TDOA information, performing initial estimation on the target position by using a binary search algorithm according to any two distance differences, screening the initially estimated target position according to the average values and standard deviations of all the initially estimated target positions, and updating the average values and the standard deviations until the standard deviations meet requirements, wherein the position of the average value is the final target position.
The scene of this step is still shown in fig. 2, and there are A, B, C receiving points in total, and the plane formed by the three receiving points is parallel to the horizontal plane of the target.
The manner of calculating the distance differences R1 and R2 based on the TDOA information is given above; for convenience of subsequent description, the embodiment of the invention further provides a geometric method for calculating the distance differences R1 and R2; the method comprises the following specific steps:
let (x, y) be the coordinates of the target position P point, (x)A,yA)、(xB,yB)、(xC,yC) The coordinates of the receiving point A, B, C, respectively, according to the distance difference formula:
Figure BDA0001354943590000061
wherein, R1 is the distance difference between the distance from the target position P to the receiving point a and the distance from the target position P to the receiving point B; r2 is the difference between the distance from the point of the target position P to the receiving point B and the distance from the point of the target position P to the receiving point C.
Then, preliminarily estimating the target position by using a binary search positioning method, wherein the steps are as follows:
a. and (3) coordinate conversion: reception point a is moved to the origin (0, 0) by translation, and then rotated counterclockwise by an angle θ around reception point a as follows, so that the coordinates of reception points B and C become (x'B,0)、(x′C,y′C)。
Figure BDA0001354943590000062
b. Judging whether the distance difference R1 is equal to 0 or not, if so, locating the target position in a perpendicular bisector between the receiving points A and B to obtain target position coordinates (x'B2, 0) (also needs to be subjected to coordinate conversion into a preliminarily estimated target position in the manner described in the step e); otherwise, the target position is estimated to be located on a hyperbolic curve, the hyperbolic curve takes the receiving points A and B as focuses, and the next step is continued.
c. Initializing the ordinate of the point P1 and the ordinate of the point P2, enabling the ordinate of the point P1 and the ordinate of the point P2 to be respectively corresponding to the ordinate of the point B and the point C, calculating the abscissa of the point P1 and the point P2 according to the following formula, and calculating according to x'BThe positive and negative of the evolution is determined,ensure absolute value of abscissa less than x'BAbsolute value of (d); then taking the median value of the ordinate of the P1 point and the ordinate of the P2 point as the abscissa of the P point, and substituting the following formula to obtain the ordinate of the point P:
Figure BDA0001354943590000063
wherein a ═ 0.5 ═ R1, c ═ 0.5 ^ x'B，b2＝c2-a2And | | | P1A | - | | P1B | | | ═ R1, | | P2A | - | | | P2B | | | -R1, P1A, P1B, P2A, P2B are the distance from point P1 to receiving point a, the distance from point P1 to receiving point B, the distance from point P2 to receiving point a, and the distance from point P1 to receiving point B, respectively.
For example, the ordinate (i.e. y) of P1 and P2 are known, and by substituting the above equations, two x values can be solved, and the coordinates of P1 and P2 can be obtained. Then, by substituting the median of the two x values into the above formula, one y can be solved, and the coordinates of the point P are obtained.
d. Calculating the following two formulas, and updating the point P1 or the point P2 according to the calculation result:
Figure BDA0001354943590000071
wherein, P1C, PB, PC, and P2C are the distance from point P1 to receiving point C, the distance from point P to receiving point B, the distance from point P to receiving point C, and the distance from point P2 to receiving point C, respectively;
if the first equation is greater than 0, fixing the point P2, and moving the point P1 to the point P; if the second equation is greater than 0, fix point P1, move point P2 to point P;
e. and d, repeating the step d until | | | P1P2| | | < δ, wherein δ is a set value, the ordinate of the estimated position is obtained preliminarily at this time and is the midpoint of the P1 point and the P2 point, the abscissa is calculated by the formula in the step c, so that a target position coordinate is obtained, then the coordinate is converted according to the principle of the step a, and the converted coordinate is the preliminarily estimated target position and is marked as pos 1.
Repeating the steps a-e to obtain n preliminarily estimated target positions, and then calculating the mean value and the standard deviation. The calculated target position is calculated on the basis of the fixed distance difference R1, and by using a similar method, the calculated target position pos2 at the time of the fixed distance difference R2 can be obtained; similarly, the target position pos3 can be calculated by fixing the distance from the target position point P to the reception point a, the distance difference R3 from the distance from the target position point P to the reception point C, and the like. Based on such a principle, n preliminary estimated target positions can be finally obtained, and the mean and standard deviation thereof are calculated.
As shown in fig. 3, if the standard deviation is greater than the threshold, excluding the n preliminarily estimated target positions from the position of the mean, and recalculating the mean and standard deviation from the remaining target positions; and repeating the process continuously until the standard deviation meets the requirement, wherein the positions of the residual target position mean values are the target final positions.
Those skilled in the art will appreciate that the threshold and the setting referred to herein can be set according to actual conditions, and at the same time, the standard deviation satisfies the requirement, or the standard deviation reaches a smaller value (preset value)
Step 14, obtaining the original distance difference information through TDOA information (speed of sound time difference), but there is a high influence, and the position is estimated directly according to the previous step 13, and there is a large error, so the height compensation method is adopted. The method comprises the following specific steps: calculating original distance difference information by using TDOA information, preliminarily estimating an estimated position P4 of a target point by using any two original distance differences and adopting a binary search algorithm (namely steps a to e in step 13), calculating a difference value of the height difference and the distance difference without the height difference at a point P4, subtracting the difference value from the original distance difference to fulfill the aim of updating the distance difference, then finishing positioning by combining a new distance difference with a case 1, and finally finishing final positioning by iteration according to the process.
In the embodiment of the present invention, when there is a height difference, the original distance difference information is calculated using the TDOA information as well, and as shown in the above equation (1), in order to distinguish from the case 1, the distance difference between the distance from the point P of the target position to the receiving point a and the distance from the point P of the target position to the receiving point B in the case 2 is denoted as R1'; the difference between the distance from the point of the target position P to the reception point B and the distance from the point of the target position P to the reception point C is denoted as R2'.
Of course, the distance differences R1 'and R2' can also be described by a geometric method, as shown in fig. 4, in consideration of the height difference existing on the basis of the case 1, the target positioning accuracy is further improved by the height compensation method as shown in the following formula (2):
Figure BDA0001354943590000081
wherein h is a height difference, is a known value or floats within a certain range.
Next, using the distance differences R1 'and R2' in combination with steps a-e of case 1, a preliminary positioning result P4(x ', y') is obtained. Simply speaking, R1 'and R2' replace R1 and R2 in steps a to e, and step e obtains the target position after coordinate transformation, i.e. the preliminary positioning result P4(x ', y').
Then, the difference between the height difference h and the distance difference without height difference at (x ', y') is calculated by the following formula, and is recorded as Δ R1, Δ R2:
Figure BDA0001354943590000082
re-update distance difference:
Figure BDA0001354943590000083
and finally, completing position estimation again by adopting a case 1 mode according to the updated distance differences R1 'and R2', and iterating after obtaining the position estimation, wherein the iteration process is as follows: and (4) calculating the delta R1 and the delta R2 again at the current estimated position, updating the original distance difference information again according to the formula (3), and repeating iteration for multiple times to obtain a final detection point.
Once fixed one in the iterative process, the position is not changed, that is, two estimated positions can be obtained according to R1 "and R2", namely fixed R1 "and fixed R2". When there are more receiving points, at least three receiving points can get two distance differences.
According to the scheme of the embodiment of the invention, the estimated position is accurately estimated through the steps of coordinate conversion, binary search and the like, and for the condition of height difference, a two-dimensional positioning error is made up through a height compensation method, so that the positioning accuracy is ensured. The method has small calculation amount, is convenient for the research and development of a subsequent real-time system, and can be widely used for the estimation of the mobile terminal.
Through the above description of the embodiments, it is clear to those skilled in the art that the above embodiments can be implemented by software, and can also be implemented by software plus a necessary general hardware platform. With this understanding, the technical solutions of the embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a usb disk, a removable hard disk, etc.), and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods according to the embodiments of the present invention.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (4)

1. A binary search positioning method based on TDOA is characterized by comprising the following steps:
acquiring TDOA information;
judging whether a height difference exists between a plane formed by the receiving points and a horizontal plane where the target is located or not, and determining according to the height of each point;
case 1: if the height difference does not exist, calculating the distance difference according to the TDOA information, performing primary estimation on the target position by using a binary search algorithm according to any two distance differences, screening the primarily estimated target position according to the average values and standard deviations of all the primarily estimated target positions, and updating the average value and the standard deviation until the standard deviation meets the requirement, wherein the position of the average value is the final target position;
case 2: if the height difference exists, the original distance difference is calculated by using the TDOA information, the estimated position of the target point is preliminarily estimated by using any two original distance differences and adopting a binary search algorithm, the difference value of the height difference and the distance difference without the height difference is calculated at the estimated position, then the corresponding difference value is subtracted from the original distance difference, the distance difference is updated, and then the positioning is finished by combining the updated distance difference with the condition 1.
2. A TDOA-based binary search location method according to claim 1, wherein said obtaining TDOA information comprises:
transmitting a signal source by a target, and receiving time differences of the signal source by receiving points at different positions;
or, the signal source is transmitted by each receiving point, and the target receives the time difference of the signal sources of different base stations.
3. A TDOA-based binary search positioning method as recited in claim 1, wherein the specific procedure for obtaining the final position of the target in case 1 is as follows:
assuming that there are three receiving points, namely a target point P and A, B, C, and a plane formed by the three receiving points is parallel to a horizontal plane where the target point P is located; the target point P transmits an audio signal, the audio signal is received by a microphone at A, B, C three receiving points, and the arrival time of the signal is judged by a related detection algorithm; calculating the time difference delta t1 between the point A and the point B and the time difference delta t2 between the point B and the point C, and then recording R1 as the distance difference between the distance from the target position P to the receiving point A and the distance from the target position P to the receiving point B; let R2 be the distance difference between the distance from the target position point P to the receiving point B and the distance from the target position point P to the receiving point C, and C be the speed of sound, then:
R1＝c·Δt1
R2＝c·Δt2；
then, preliminarily estimating the target position by using a binary search positioning method, wherein the steps are as follows:
a. and (3) coordinate conversion: suppose (x)A,yA)、(xB,yB)、(xC,yC) Coordinates of reception point A, B, C are respectively shifted to origin (0, 0) by translation, and then rotated counterclockwise by an angle θ around reception point a in accordance with the following equation so that coordinates of reception points B and C become (x'B,0)、(x′C,y′C)；
Figure FDA0001354943580000021
b. Judging whether the distance difference R1 is equal to 0 or not, if so, locating the target position in a perpendicular bisector between the receiving points A and B to obtain target position coordinates (x'B2, 0); otherwise, estimating that the target position is located on a hyperbolic curve, taking the receiving points A and B as focuses of the hyperbolic curve, and continuing the next step;
c. initializing the ordinate of the point P1 and the ordinate of the point P2, enabling the ordinate of the point P1 and the ordinate of the point P2 to be respectively corresponding to the ordinate of the point B and the point C, calculating the abscissa of the point P1 and the point P2 according to the following formula, and calculating according to x'BPositive and negative of (2) determine the positive and negative of the origin, and ensure that the absolute value of the abscissa is less than x'BAbsolute value of (d); then taking the median value of the ordinate of the P1 point and the ordinate of the P2 point as the abscissa of the P point, and substituting the following formula to obtain the ordinate of the point P:
Figure FDA0001354943580000022
wherein a ═ 0.5 ═ R1, c ═ 0.5 ^ x'B，b2＝c2-a2P1A | - | | P1B | | ═ R1, | | P2A | - | | | P2B | | | - | R1, P1A, P1B, P2A, P2B are the distance from the point P1 to the receiving point a, the distance from the point P1 to the receiving point B, the distance from the point P2 to the receiving point a, and the distance from the point P1 to the receiving point B, respectively;
d. calculating the following two formulas, and updating the point P1 or the point P2 according to the calculation result:
Figure FDA0001354943580000023
wherein, P1C, PB, PC, and P2C are the distance from point P1 to receiving point C, the distance from point P to receiving point B, the distance from point P to receiving point C, and the distance from point P2 to receiving point C, respectively;
if the first equation is greater than 0, fixing the point P2, and moving the point P1 to the point P; if the second equation is greater than 0, fix point P1, move point P2 to point P;
e. repeating the step d until | | | P1P2| | | < δ, wherein δ is a set value, the ordinate of the estimated position obtained preliminarily at this time is the midpoint of the P1 point and the P2 point, the abscissa is calculated by the formula in the step c, so that a target position coordinate is obtained, then the coordinate is converted according to the principle of the step a, and the converted coordinate is the preliminarily estimated target position and is marked as pos 1;
repeating the steps a to e to obtain n preliminarily estimated target positions, and then calculating a mean value and a standard deviation;
if the standard deviation is larger than the threshold value, excluding the positions of the n preliminary estimated target positions which are farthest away from the mean position, and recalculating the mean value and the standard deviation from the rest target positions; and repeating the process continuously until the standard deviation meets the requirement, wherein the positions of the residual target position mean values are the target final positions.
4. A TDOA-based binary search positioning method according to claim 3, wherein said specific procedure for obtaining the final position of the target in case 2 is as follows:
calculating original distance difference information based on the TDOA information, wherein a distance difference between a distance from the point of the target position P to the receiving point a and a distance from the point of the target position P to the receiving point B is denoted as R1'; the distance difference between the distance from the point of the target position P to the receiving point B and the distance from the point of the target position P to the receiving point C is recorded as R2';
secondly, obtaining a preliminary positioning result (x ', y') by using the distance differences R1 'and R2' in combination with the steps a-e in the case 1;
then, the difference between the height difference h and the distance difference without height difference at (x ', y') is calculated by the following formula, and is recorded as Δ R1, Δ R2:
Figure FDA0001354943580000031
re-update distance difference:
Figure FDA0001354943580000032
finally, the target final position is calculated from the updated distance differences R1 "and R2" in case 1 manner.
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