CN109870672B - Positioning algorithm based on anchor node differential time synchronization and Taylor cooperation - Google Patents

Positioning algorithm based on anchor node differential time synchronization and Taylor cooperation Download PDF

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CN109870672B
CN109870672B CN201910104100.1A CN201910104100A CN109870672B CN 109870672 B CN109870672 B CN 109870672B CN 201910104100 A CN201910104100 A CN 201910104100A CN 109870672 B CN109870672 B CN 109870672B
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赵甜甜
郑正奇
华程
董大南
余超
张裕
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East China Normal University
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Abstract

The invention discloses a positioning algorithm based on anchor node differential time synchronization and Taylor cooperation, which is characterized in that pseudo-range differences between labels and all slave base stations and pseudo-range differences among all slave base stations are calculated, corresponding pseudo-range correction is carried out by utilizing a covariance matrix of an observed value and known position coordinates of not less than four slave base stations, an initial coordinate of the label is obtained by adopting a method of solving a linear equation set, and a final accurate positioning coordinate of the label is obtained by a Taylor recursion algorithm. Compared with the prior art, the method has higher and more stable positioning accuracy, reduces the calculation load, the production cost and the volume of a mobile terminal, does not need to additionally lay a large amount of hardware equipment or change the existing hardware equipment, is realized by completely depending on a software form, is easy to popularize, and has greater advantages and commercial prospect in an indoor positioning application environment which mainly manages multiple users by using manager application.

Description

Positioning algorithm based on anchor node differential time synchronization and Taylor cooperation
Technical Field
The invention relates to the technical field of positioning navigation, in particular to a positioning algorithm based on anchor node differential time synchronization and Taylor cooperation.
Background
The key technical research and industrialization of indoor positioning and the accompanying position service industry are more and more concerned by society, the development of space technology enables the outdoor Satellite Navigation positioning technology based on GNSS (global Navigation Satellite system) to be developed vigorously, the centimeter-level or even millimeter-level positioning accuracy is achieved, the popular application of position service is driven, and the daily life of people is greatly facilitated. Outdoor positioning technology has matured, while development of indoor positioning technology and corresponding location services, which account for 80% of human lives, lags behind outdoor positioning. Indoor positioning is difficult to simply transplant the existing mature outdoor positioning technology due to the reasons of large application difference, high environment complexity, serious error source interference, equipment cost limitation and the like.
At present, indoor positioning does not have a well-recognized mature key technology which occupies overwhelming advantages, and various technical schemes are respectively researched and developed. These technologies can be roughly classified into fading localization according to signal strength, such as fingerprint analysis of Wi-Fi, infrared, visual optics, geomagnetism, bluetooth, ZigBee, and the like; positioning according to arrival time of signals, such as A-GPS, pseudolite, ultrasound, UWB and the like, and self-positioning according to integral or dead reckoning, such as inertial sensors, RFID and the like. In the high-precision indoor positioning field, the strength attenuation positioning and the autonomous positioning all meet the bottleneck in meter-level precision, and are difficult to break through. The uncertainty of the empirical relationship between the intensity attenuation and the distance, the susceptibility to the indoor environment, and the non-linear increase of the accumulated error over time due to the time integration required for autonomous positioning are one of the main causes of the bottleneck, which is the weakness of the positioning technology itself. The multi-source fusion positioning is a development trend, the positioning accuracy can be further improved, but the foundation of the multi-source fusion positioning comes from the accuracy improvement and the stability enhancement of various positioning technologies. On the other hand, the intensive research on the signal arrival indoor positioning technology can also provide a single technical support for breaking through the bottleneck. The high accuracy of GNSS positioning is based on the accurate determination of the arrival time of the satellite signals, time being one of the seven basic physical quantities, the measurement accuracy of a time unit reaching the level of 10-15 seconds, so that the unit meter of the length of the other basic physical quantity is instead defined by the distance travelled by the light in the time interval of 1/299792458 seconds in vacuum. The time synchronization of the signal transmitting end and each receiving end is the key for realizing high-precision positioning, and the positioning precision within meter level can be realized only when the time synchronization of the radio wave observation in the time is required to reach within 3 nanoseconds.
Disclosure of Invention
The invention aims to design a positioning algorithm based on anchor node differential time synchronization and Taylor cooperation aiming at the defects of the prior art, adopts a method for realizing fixed end time synchronization by using a correction number, so as to eliminate system errors of clock error, hardware delay, cable delay and the like of a transmitting end and a receiving end, realize high-precision positioning, and utilize the synchronous node to realize and mark the difference between optical fiber propagation and mechanical time delay between the fixed nodes and store it in the background server, further promote the positioning accuracy and reliability, reduce the calculation load of the mobile terminal (label), production cost and volume, need not to lay a large amount of hardware equipment additionally, need not to change the existing hardware equipment, totally rely on the software form to realize, easy to popularize, the method has great advantages and business prospects in an indoor positioning application environment which mainly manages multiple users by using manager application.
The purpose of the invention is realized as follows: a positioning algorithm based on anchor node differential time synchronization and Taylor cooperation is characterized in that pseudo-range differences between labels and all slave base stations and pseudo-range differences between all slave base stations are calculated, corresponding pseudo-range correction is carried out by utilizing a covariance matrix of an observed value and known position coordinates of not less than four slave base stations, a method of solving a linear equation set is adopted to obtain initial coordinates of the labels, and the final accurate positioning of the labels is solved by a Taylor recursion algorithm, and the specific calculation comprises the following steps:
calculating the arrival time difference of the label to each base station, thereby calculating the relative geometric distance between the mobile label and the base station, and correcting the pseudo-range error
a. Solving the anchor node A by the following formula (1)iTime difference with the synchronization node S
Figure BDA0001966249770000021
Figure BDA0001966249770000031
Wherein:
Figure BDA0001966249770000032
is an anchor node AiDistance from the synchronization node S;
Figure BDA0001966249770000033
is an anchor node AiFiber length to local engine; tau isSThe clock difference of the clock of the synchronous node S at the moment of transmitting the signal;
Figure BDA0001966249770000034
is an anchor node AiThe clock difference itself at the moment it receives the signal.
b. For two anchor nodes A2And A1The time difference with the synchronization node S is calculated as a pseudo-range difference by the following equation (4)
Figure BDA0001966249770000035
Represents:
Figure BDA0001966249770000036
wherein:
Figure BDA0001966249770000037
is an anchor node AiAnd A1Receiving a pseudo-range difference (which is a direct observation) corresponding to the time difference of the tag T signal;
Figure BDA0001966249770000038
is an anchor node AiAnd A1Pseudo-range corrections (pre-calibrated) corresponding to fiber propagation and hardware delay; the first item to the right of the equal sign contains the coordinates of the tag T to be solved.
c. Assuming that the errors of the pseudo-ranges observed by the respective anchor nodes are independent of each other, the errors and the pseudo-ranges are expressed by the following equation (5):
Figure BDA0001966249770000039
wherein: rho0Is a reference distance; sigma0Is the observation error corresponding to the reference distance.
d. Since the pseudorange observations of the single differences are correlated, the covariance matrix is represented by the following equation (6):
Figure BDA00019662497700000310
(II) calculating the initial coordinates of the tag by using a linear equation set on the basis of the pseudo-range error correction value
a. The anchor node A is calculated by the following formula (7)iAnd synchronization node S:
Figure BDA00019662497700000311
b. anchor node A1For the reference node, the above equation (7) is transformed and the above equation (4) is substituted to obtain the following linear equation system of equation (8):
Figure BDA0001966249770000041
c. all anchor nodes are set at the same height, i.e.
Figure BDA0001966249770000042
And is defined as follows:
Figure BDA0001966249770000043
Figure BDA0001966249770000044
d. the linear equation system of the above equation (8) is formed by a matrix of the following equation (9):
PT＝(AC-1A)-1ATC-1(Δρ+λ)； (9)
wherein: A. λ are known quantities; the delta rho is an observation matrix after propagation delay correction, and the coordinate sum of the label can be calculated
Figure BDA0001966249770000045
And substituting the same into the above formula (7) to obtain
Figure BDA0001966249770000046
(III) substituting the calculation result into an improved Taylor algorithm to obtain the positioning coordinate value of the label
a. An anchor node A obtained by the above formula (7)iAnd anchor node A1The distance difference between the mobile tag T and the mobile tag T is expressed by the following equation (10)
Figure BDA0001966249770000047
The first order Taylor expansion is performed to obtain the following formula (11):
Figure BDA0001966249770000048
Figure BDA0001966249770000049
b. as defined below:
Figure BDA0001966249770000051
Figure BDA0001966249770000052
c. the expression (11) is expressed in a matrix form by the following expression (12):
ΔPT＝(HTC-1H)-1HTC-1ΔρT。 (12)
d. repeating the above steps for recursion, and adding delta P to the initial positioning result of the anchor node algorithm when the value of the above equation (12) is less than a preset threshold valueTAnd the coordinate value corrected for the Taylor is the positioning coordinate of the label.
Compared with the prior art, the method has higher and more stable positioning accuracy, greatly reduces the calculation load, the production cost and the volume of a mobile terminal (label), does not need to additionally lay a large amount of hardware equipment, does not need to change the existing hardware equipment, is realized completely depending on a software form, is easy to popularize, and has greater advantages and commercial prospects in an indoor positioning application environment which mainly manages multiple users by using manager application.
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FIG. 1 is a schematic diagram of a positioning system of the present invention;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a comparison of the results of the present invention compared to conventional positioning algorithms and experimental platforms.
Detailed Description
The invention calculates the pseudo-range difference of the label to each slave base station and the pseudo-range difference between the slave base stations, uses the covariance matrix of the observed value and the known position coordinates of at least four slave base stations to carry out corresponding pseudo-range correction, adopts the method of solving the linear equation set to obtain the initial coordinate of the label, and uses the Taylor recursive algorithm to solve the final accurate positioning of the label, and the specific calculation comprises the following steps:
calculating the arrival time difference of the label to each base station, thereby calculating the relative geometric distance between the mobile label and the base station, and correcting the pseudo-range error
a. Solving the anchor node A by the following formula (1)iTime difference with the synchronizing node S
Figure BDA0001966249770000061
Figure BDA0001966249770000062
Wherein:
Figure BDA0001966249770000063
is an anchor node AiDistance from the synchronization node S;
Figure BDA0001966249770000064
is an anchor node AiFiber length to local engine; tau.SThe clock difference of the clock of the synchronous node S at the moment of transmitting the signal;
Figure BDA0001966249770000065
is an anchor node AiThe clock difference itself at the moment it receives the signal.
b. For two anchor nodes A of the same transmitting signal2And A1The difference between the measured travel times may be represented by the pseudo-range form represented by the following equation (2):
Figure BDA0001966249770000066
anchor node A2And A1The difference in measurement is for the same frame signal sent by the synchronization node S, so the clock difference term of the transmitting terminal is eliminated,
Figure BDA0001966249770000067
is an anchor node A2And A1The difference of clock differences of the anchor nodes is actually the clock difference of the local engine clock receiving time difference (usually less than 1000 ns) between the two anchor nodes because the same clock of the local engine is shared by the anchor nodes when receiving the synchronous node S signal. Within such a short time interval, the clock error of the local engine can be approximately expressed as a clock error drift rate (considered as a constant)
Figure BDA0001966249770000068
And propagation time, the clock error drift rate of the local engine is typically less than 100ppm,
Figure BDA0001966249770000069
can be omitted. Therefore, the above equation (2) can be simplified to a pseudo range form of the following equation (3):
Figure BDA00019662497700000610
c. defining:
Figure BDA00019662497700000611
indicating the anchor node a to be surveyed2And A1Pseudo-range differences corresponding to differences in fiber and hardware propagation delays; the first term on the right of the equation is an observed quantity, the second term is a known quantity, a plurality of synchronous node observations with known positions are generally selected to weaken the influence of random errors, and the propagation delay difference between anchor nodes is estimated by least square fitting.
d. The pseudo range error between each base station and the main base station is corrected by correcting the tag, and the pseudo range form of the following equation (4) can be obtained by converting equation (3):
Figure BDA0001966249770000071
wherein:
Figure BDA0001966249770000072
for uncorrected anchor node AiAnd A1Receiving pseudo-range difference corresponding to the time difference of the tag T signal, wherein the pseudo-range difference is a direct observed quantity;
Figure BDA0001966249770000073
is an anchor node AiAnd A1Pseudo range correction corresponding to optical fiber propagation and hardware delay is calibrated in advance; the first entry to the right of the equal sign contains the coordinates of the unknown tag T to be solved.
e. The variance of the travel time error of the tag to each base station is unknown, the observation equation is not strictly synchronous observation, and the clock drift degrees of each base station are also unequal, so a reasonable covariance matrix of the observed value must be selected in order to solve the parameter to be estimated. Assuming that the pseudo-range errors observed by each anchor node are independent of each other, and the errors are proportional to the distance of the pseudo-range, the pseudo-range error can be expressed by the following equation (5):
Figure BDA0001966249770000074
wherein: rho0Is a reference distance; sigma0Is the observation error corresponding to the reference distance. The pseudorange observations of the single differences are correlated, and their covariance matrix can be represented by the following equation (6):
Figure BDA0001966249770000075
(II) calculating the initial coordinates of the tag by using a linear equation set on the basis of the pseudo-range error correction value
a. Anchor node AiAnd the synchronization node S can be represented by the following equation (7):
Figure BDA0001966249770000076
b. anchor node A1For the reference node, the above equation (7) is transformed, and the equation (4) is substituted to obtain the following linear equation system of equation (8):
Figure BDA0001966249770000077
c. based on the pseudorange error correction value, the initial coordinates of the tag are calculated using the linear equation set of the above equation (8).
d. All anchor nodes are connected on the premise of not influencing the conclusionAre all arranged at the same height, i.e.
Figure BDA0001966249770000081
And defines:
Figure BDA0001966249770000082
Figure BDA0001966249770000083
in summary, a matrix form of the following equation (9) is obtained:
PT＝(AC-1A)-1ATC-1(Δρ+λ)； (9)
wherein: A. λ are known quantities; the delta rho is an observation matrix after propagation delay correction, and the coordinate sum of the mobile tag can be calculated
Figure BDA0001966249770000084
And substituting the compound into the above formula (7) to obtain
Figure BDA0001966249770000085
d. Substituting the calculation result into the improved Taylor algorithm to obtain a more accurate and stable positioning result, and obtaining the anchor node A represented by the following formula (10) by the formula (7)iAnd anchor node A1The difference in geometric distance from the moving tag T:
Figure BDA0001966249770000086
e. applying the above equation (10) to the estimated position of the mobile tag
Figure BDA0001966249770000087
To perform first-order taylor expansion (ignoring second-order and above components), a differential form represented by the following expression (11) is obtained:
Figure BDA0001966249770000088
f. defining:
Figure BDA0001966249770000091
Figure BDA0001966249770000092
g. the expression (11) is expressed in a matrix form of the following expression (12):
ΔPT＝(HTC-1H)-1HTC-1ΔρT； (12)
repeating the steps for recursion, and when the value in the formula (12) is smaller than a preset threshold value, adding the initial positioning result of the anchor node algorithm to obtain the coordinate value corrected by Taylor. And obtaining the final accurate positioning coordinate of the label based on the anchor node differential time synchronization and Taylor cooperative positioning algorithm.
The present invention will be described in further detail with reference to specific examples.
Example 1
Referring to fig. 1, the present invention adopts a positioning system with a positioning base station and tag 5, an exchange 2 and a background server 1, wherein the positioning base station is composed of a master base station 31 and a plurality of slave base stations 32, the positioning base station transmits data back to the background server 1 through optical fibers and is powered by poe (power Over ethernet). The switch 2 is used for transmitting a plurality of tag positioning packets received from the base stations 32 and a synchronization packet of the main base station 31 to the background server 1, and the background server 1 has the functions of base station synchronization, data packet analysis, pseudo range correction value storage, information of each slave base station 32, tag 5 position solution calculation and the like.
Referring to fig. 2, the tag (location) in the present invention is used to send a location packet, and the sync node (anchor node or calibrated known location) is a mobile tag that uses a laser range finder to determine the actual coordinates, and stores the actual coordinates to the background server. Before the positioning system works normally, the synchronous node sends a positioning packet, and each slave base station receives the positioning packet and the synchronous packet of the master base station and then sends the positioning packet and the synchronous packet to the background server through the switch. And the background server calculates the distance difference between each slave base station and the main base station from the mobile tag through calculating the arrival time difference. Since the real coordinates of the synchronization node are known, the real value of the distance difference between the synchronization node (anchor node) and each slave base station and the master base station can be obtained by using the following equation (5):
Figure BDA0001966249770000101
the covariance matrix of the observed values can be determined by the following equation (6):
Figure BDA0001966249770000102
finally, the following formula (3) is used:
Figure BDA0001966249770000103
and obtaining and storing the corresponding pseudo-range compensation difference. To obtain a more accurate covariance matrix of pseudorange corrections and observations, a number of synchronization nodes (anchor nodes) are selected. When the positioning system works normally, the mobile tags send positioning packets containing positioning information, and each slave base station receives the positioning packets of each mobile tag and the synchronous packets of the master base station and then sends the positioning packets and the synchronous packets to the background server through the switch. The background server calculates a data packet, calculates the distance difference between each base station and the main base station through the arrival time difference, and then utilizes the following formula (9):
PT＝(AC-1A)-1ATC-1(Δρ+λ)； (9)
obtaining the initial coordinates of the mobile tag, and then substituting the initial coordinates into the following formula (12) to obtain more accurate positioning coordinates of the tag:
ΔPT＝(HTC-1H)-1HTC-1ΔρT。 (12)
referring to fig. 3, by comparing the results of the conventional positioning algorithm and the experimental platform, it can be seen that the positioning effect based on the anchor node differential time synchronization and the "Taylor" cooperation is better, and the positioning accuracy is higher and more stable. The method has the advantages that the difference between optical fiber propagation and mechanical time delay between fixed nodes is calibrated in advance by utilizing a synchronous node (anchor node), and is stored in a server at the background, and then the pseudo-range calculation result of an unknown positioning label is subjected to error correction, so that indoor positioning is realized under the condition of simply and effectively considering time errors, the positioning precision and the stability are improved, and the positioning precision is greatly superior to that in the prior art.
The invention has been described in further detail in order to avoid limiting the scope of the invention, and it is intended that all such equivalent embodiments be included within the scope of the following claims.

Claims (1)

1. A positioning algorithm based on anchor node differential time synchronization and Taylor cooperation is characterized in that pseudo-range differences between labels and all slave base stations and pseudo-range differences among all slave base stations are calculated, corresponding pseudo-range correction is carried out by utilizing a covariance matrix of an observed value and known position coordinates of not less than four slave base stations, an initial coordinate of the label is obtained by adopting a method of solving a linear equation set, and the final accurate positioning of the label is solved by a Taylor recursion algorithm, and the specific calculation comprises the following steps:
(I) calculating the time difference of arrival of the tag at each base station, thereby calculating the relative geometric distance between the mobile tag and the base station, and correcting the pseudo-range error
a. Solving the anchor node A by the following formula (1)iTime difference with the synchronizing node S
Figure FDA0003646424390000011
Figure FDA0003646424390000012
Wherein:
Figure FDA0003646424390000013
is an anchor node AiDistance from the synchronization node S;
Figure FDA0003646424390000014
is an anchor node AiFiber length to local engine; tau isSThe clock difference of the clock of the synchronous node S at the moment of transmitting the signal;
Figure FDA0003646424390000015
is an anchor node AiThe clock difference itself at the moment it receives the signal;
b. for two anchor nodes AiAnd A1The time difference with the synchronization node S is a pseudo-range difference calculated by the following equation (4)
Figure FDA0003646424390000016
Represents:
Figure FDA0003646424390000017
wherein:
Figure FDA0003646424390000018
is an anchor node AiAnd A1Receiving a pseudo-range difference corresponding to the time difference of the tag T signal;
Figure FDA0003646424390000019
is an anchor node AiAnd A1Performing pseudo-range correction corresponding to the fiber propagation and hardware delay; the first item on the right side of the equal sign contains the coordinate of the tag T to be solved;
c. assuming that the errors of the pseudo ranges observed by the anchor nodes are independent of each other, the errors and the pseudo ranges are expressed by the following equation (5):
Figure FDA00036464243900000110
wherein: rho0Is a reference distance; sigma0The observation error corresponding to the reference distance;
d. since the pseudorange observations of the single differences are correlated, the covariance matrix is then represented by the following equation (6):
Figure FDA0003646424390000021
(II) calculating the initial coordinates of the tag by using a linear equation set on the basis of the pseudo-range error correction value
a. The anchor node A is calculated by the following formula (7)iAnd the geometric distance between the synchronization nodes S:
Figure FDA0003646424390000022
b. anchor node A1For the reference node, the above equation (7) is transformed, and the above equation (4) is substituted to obtain the linear equation system of the following equation (8):
Figure FDA0003646424390000023
c. all anchor nodes are set at the same height, i.e.
Figure FDA0003646424390000024
And is defined as follows:
Figure FDA0003646424390000025
Figure FDA0003646424390000026
d. the linear equation system of the above equation (8) is formed by a matrix of the following equation (9):
PT＝(ATC-1A)-1ATC-1(Δρ+λ)； (9)
wherein: A. lambda is a known quantity; the delta rho is an observation matrix after propagation delay correction, and the coordinate sum of the label can be calculated
Figure FDA0003646424390000027
And substituting the compound into the above formula (7) to obtain
Figure FDA0003646424390000028
And (III) substituting the calculation result into an improved Taylor algorithm to obtain the positioning coordinate value of the label
a. The anchor node A obtained by the formula (7) aboveiAnd anchor node A1The distance difference between the mobile tag T and the mobile tag T is expressed by the following equation (10)
Figure FDA0003646424390000031
The first order Taylor expansion is performed to obtain the following formula (11):
Figure FDA0003646424390000032
Figure FDA0003646424390000033
b. as defined below:
Figure FDA0003646424390000034
Figure FDA0003646424390000035
c. expression (11) is expressed in a matrix form of expression (12) below:
ΔPT＝(HTC-1H)-1HTC-1ΔρT； (12)
d. repeating the above steps for recursion, and when the value of (12) is less than the preset threshold, adding Δ P to the initial positioning result of the anchor node algorithmTAnd the coordinate value corrected for the Taylor is the positioning coordinate of the label.
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