CN116801380B - UWB indoor positioning method based on improved full centroid-Taylor - Google Patents
UWB indoor positioning method based on improved full centroid-Taylor Download PDFInfo
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Abstract
The invention relates to an improved full centroid-Taylor-based UWB indoor positioning method, which comprises the following steps: setting up positioning areas with 4 or more base stations to obtain the distance between the base stations and the mobile tags; dividing all base stations into 3 groups, and calculating the number of all casesAnd displaying; for display ofThe base stations of the group respectively use a full centroid algorithm to obtainA group coordinate; to be used forThe sum of the distances from the group coordinates to the nodes to be positioned is used as an objective function, the value range is constrained and then is imported into a simulated annealing algorithm to find an optimal value; and the optimal value is used as an initial value of a Taylor algorithm, and the final coordinates of the node to be positioned are obtained after the Taylor algorithm is solved. The invention uses a full centroid algorithm aiming at the grouped base stations, searches the optimal value of the built objective function through a simulated annealing algorithm, adapts to the positioning of UWB in a non-line-of-sight environment, and effectively improves the robustness and the positioning precision.
Description
Technical Field
The invention belongs to the technical field of positioning and tracking, and particularly relates to an improved full centroid-Taylor-based UWB indoor positioning method.
Background
In recent years, as mobile robots are applied in a wider range of scenes, such as a greeting robot in a market, a delivery robot in a restaurant, a delivery robot in a logistics warehouse, a navigation robot in a library, etc., they perform self-tasks in the scenes, and apart from effectively controlling them, it is necessary to ensure that they can know exactly where they are, i.e. need to be positioned exactly, all the time. In the indoor positioning field, there are numerous indoor positioning technologies such as radio frequency (radio frequency identification, RFID), wiFi, zigBee and ultra wideband (UltraWide Band, UWB), and these positioning technologies can be applied under different indoor positioning scenarios, where the indoor positioning technology typified by UWB has raised a high research surge in the indoor positioning field in its convenient base station construction manner and high absolute positioning accuracy.
The UWB positioning technology is a wireless carrier communication technology, which utilizes nanosecond non-sine wave narrow wave pulse to transmit data, so that the occupied frequency spectrum range is very wide, and theoretically, the time resolution can be very high due to the high-frequency transmission signal, thereby realizing the centimeter-level precision of indoor positioning. The UWB is mainly technically characterized by high transmission rate, large space capacity, low cost, low power consumption and the like, the transmitter of the UWB is a pulse small-sized excitation antenna, up-conversion required by a traditional transceiver is not required, and therefore a functional amplifier and a mixer are not required, the structural implementation is simpler, but the UWB can greatly reduce the positioning accuracy due to multipath effect in NLOS environment, the defect of the current research on UWB positioning algorithm still exists, the positioning accuracy is higher under the condition that the error obeys ideal Gaussian distribution by the Fang algorithm, chan algorithm and Taylor series expansion method, but the error distribution under NLOS has various forms, and the actual positioning accuracy is reduced; the existing full centroid algorithm is insensitive to distance measurement errors, but is easily interfered by points with larger errors under the condition that the NLOS environment of UWB is more remarkable, and the positioning accuracy is not high.
Disclosure of Invention
In order to solve the technical problems, the invention provides the UWB indoor positioning method based on the improved full centroid-Taylor, overcomes the disadvantage that the positioning accuracy is reduced due to the multipath effect in the NLOS environment of UWB in the traditional full centroid algorithm, increases the step length of full centroid calculation, sets an objective function to find an optimal value through a simulated annealing algorithm, and effectively improves the robustness and the positioning accuracy of UWB in the positioning process.
In order to achieve the technical purpose, the invention is realized by the following technical scheme:
UWB indoor positioning method based on improved full centroid-Taylor comprises the following steps:
S1: setting up a positioning area of more than 4 base stations in an LOS or NLOS environment of UWB, and acquiring the distance between the base stations and the mobile tag by adopting a TDOA ranging method;
s2: dividing all base stations into 3 groups, excluding the situation that 3 base stations are on a straight line, ensuring that 3 base stations of each group can enclose a triangle, and calculating the number of all cases M is more than or equal to 3 and is displayed;
S3: for the display in S2 The base stations with m more than or equal to 3 groups respectively use a full centroid algorithm to obtain/>M is more than or equal to 3 groups of coordinates;
s4: in S3 M is greater than or equal to 3 groups of coordinates, namely the sum of the distances from the coordinates to the node to be positioned (pseudo centroid) is taken as an objective function, the value range of the coordinates of the node to be positioned (pseudo centroid) is constrained, and then the constraint is introduced into a simulated annealing algorithm to find the minimum value of the objective function, namely the self-variable value of the objective function at the minimum value is the optimal value of the coordinates of the node to be positioned (pseudo centroid);
S5: and (3) taking the optimal value of the independent variable obtained from the simulated annealing algorithm in the step (S4) as an initial value of a Taylor algorithm, and obtaining the coordinates of the final node to be positioned after solving the Taylor algorithm.
Preferably, the coordinate resolving process of the final node to be located is as follows:
S5.1: the constructed UWB positioning area has more than 4 base stations, namely BS 1、BS2、BS3、BS4 and the like, and the distance from each base station to a node to be positioned is d 1、d2、d3、d4;
S5.2: after obtaining the distance values from each base station to the node to be positioned in S5.1, grouping all base stations including more than 4 base stations, wherein 3 base stations are in a group, and determining the number of final base station combinations through the conditions that the sum of any two sides of the triangle is larger than the third side and the difference between any two sides is smaller than the third side m≥3；
S5.3: and (3) applying a full centroid algorithm to the base station combination subjected to screening in the step (S5.2), wherein the calculation process is as follows:
wherein (X 1,y1)、(x2,y2) and (X 3,y3) are coordinates of three nodes not in a straight line base station, and (X 1,Y1) is coordinates of a node to be positioned obtained by combining the first base station, and wherein
D 1、d2 and d 3 are ranging values from the base stations 1, 2 and 3 to the node to be positioned respectively; and define
Writing (1) as
Qθ＝b (4)
Solving (4) by least square method
θLS＝(QTQ)-1QTb (5)
Solving to obtain θ LS, which is a solution obtained by combining base stations 1,2 and 3, and similarly calculating solutions 1,2 and 4 and solutions obtained by combining 1, 3 and 4 to obtainA group coordinate; the same applies to the calculation method when the number of base stations is greater than 4.
Preferably, the objective function set in S4 is
Where ζ is the coordinate value of the node to be located (pseudo centroid)While being an argument of the objective function
The distance from the full centroid coordinate value solved in the ith combination in S3 to the pseudo centroid is represented, where (X i,Yi) is the full centroid coordinate value solved in the ith combination.
Preferably, the pseudo centroid coordinate valueThe value range of (2) is initially set asAnd compensating the value range of the pseudo centroid coordinate value, expanding the original range, searching global optimum in a larger value range, and introducing an error threshold eta α to correct the value range of the pseudo centroid coordinate.
Preferably, the range of the pseudo centroid coordinate value is
Preferably, η is an error compensation value of UWB and the value range is (0.1, 0.3).
Preferably, α is a control factor, and the value range is (0, 1).
Preferably, the value introduced into the Taylor series expansion algorithm in S5 is the optimal value obtained from the simulated annealing algorithm in S4And then carrying out iterative computation on the optimal value through a Taylor algorithm to obtain the coordinate values (X, Y) of the final node to be positioned.
The beneficial effects of the invention are as follows:
The invention improves the full centroid algorithm, the traditional full centroid algorithm is to calculate all base stations participating in positioning to obtain the coordinates of the node to be positioned, the improved full centroid algorithm firstly divides all base stations into 3 groups, carries out the full centroid algorithm on the base stations of each group, and then sets an objective function and corrects the value range of independent variables, so that the estimated coordinate value obtained after the simulated annealing algorithm has higher precision and better robustness, and provides a more reliable initial value for the Taylor algorithm. The invention can be suitable for UWB to carry out positioning task under LOS and NLOS environment, and can provide higher positioning precision for positioning carrier.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the improved full centroid-Taylor based UWB indoor two-dimensional positioning method of the present invention;
FIG. 2 is a block diagram of an implementation of the UWB indoor two-dimensional positioning method based on the improved full centroid-Taylor of the present invention;
FIG. 3 is a graph of root mean square error (RootMean Square Error, RMSE) versus three algorithms in an LOS environment;
FIG. 4 is a graphical representation of the RMSE alignment of three algorithms in an NLOS environment;
FIG. 5 is a trace motion diagram of a NLOS-based simulation environment for dynamically calculating a motion trace using the method, chan-Talyor algorithm and WLS-Taylor algorithm, respectively;
fig. 6 is a graph of euclidean distance error comparison of motion trajectories dynamically calculated by using the method, the Chan-Talyor algorithm and the WLS-Taylor algorithm, respectively, in an NLOS-based simulation environment.
Detailed Description
The following description of the technical solutions in the embodiments of the present invention will be clear and complete, and it is obvious that the described embodiments are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
UWB indoor two-dimensional positioning method based on improved full centroid-Taylor comprises the following steps:
S1: setting up a positioning area of more than 4 base stations in an LOS or NLOS environment of UWB, and acquiring the distance between the base stations and the mobile tag by adopting a TDOA ranging method;
s2: dividing all base stations into 3 groups, excluding the situation that 3 base stations are on a straight line, ensuring that 3 base stations of each group can enclose a triangle, and calculating the number of all cases M is more than or equal to 3 and is displayed;
S3: for the display in S2 The base stations with m more than or equal to 3 groups respectively use a full centroid algorithm to obtain/>M is more than or equal to 3 groups of coordinates;
s4: in S3 M is greater than or equal to 3 groups of coordinates, namely the distance from the coordinates to the node to be positioned is taken as an objective function, the value range of the coordinates of the node to be positioned (pseudo centroid) is constrained, and then the constraint range is imported into a simulated annealing algorithm to find the minimum value of the objective function, namely the value of an independent variable of the objective function at the minimum value is the optimal value of the coordinates of the node to be positioned (pseudo centroid);
s5: taking the optimal value obtained from the simulated annealing algorithm in the step S4 as an initial value of a Taylor algorithm, and obtaining the coordinates of the final node to be positioned after solving the Taylor algorithm;
Preferably, the coordinate resolving process of the final node to be located is as follows:
S5.1: the constructed UWB positioning area has more than 4 base stations, namely BS 1、BS2、BS3、BS4 and the like, and the distance from each base station to a node to be positioned is d 1、d2、d3、d4;
S5.2: after obtaining the distance values from each base station to the node to be positioned in S5.1, grouping all base stations including more than 4 base stations, wherein 3 base stations are in a group, and determining the number of final base station combinations through the conditions that the sum of any two sides of the triangle is larger than the third side and the difference between any two sides is smaller than the third side m≥3；
S5.3: and (3) applying a full centroid algorithm to the base station combination subjected to screening in the step (S5.2), wherein the calculation process is as follows:
wherein (X 1,y1)、(x2,y2) and (X 3,y3) are coordinates of three nodes not in a straight line base station, and (X 1,Y1) is coordinates of a node to be positioned obtained by combining the first base station, and wherein
D 1、d2 and d 3 are ranging values from the base stations 1, 2 and 3 to the node to be positioned respectively; and define
Writing (1) as
Qθ＝b (4)
Solving (4) by least square method
θLS＝(QTQ)-1QTb (5)
Solving to obtain θ LS, which is a solution obtained by combining base stations 1,2 and 3, and similarly calculating solutions 1,2 and 4 and solutions obtained by combining 1, 3 and 4 to obtainA group coordinate; the same applies to the calculation method when the number of base stations is greater than 4.
Preferably, the objective function set in S4 is
Where ζ is the coordinate value of the node to be located (pseudo centroid)While being an argument of the objective function
The distance from the full centroid coordinate value solved in the ith combination in S3 to the pseudo centroid is represented, where (X i,Yi) is the full centroid coordinate value solved in the ith combination.
Preferably, the pseudo centroid coordinate valueThe value range of (2) is initially set asAnd compensating the value range of the pseudo centroid coordinate value, expanding the original range, searching global optimum in a larger value range, and introducing an error threshold eta α to correct the value range of the pseudo centroid coordinate.
Preferably, the range of the pseudo centroid coordinate value is
Preferably, η is an error compensation value of UWB and the value range is (0.1, 0.3).
Preferably, α is a control factor, and the value range is (0, 1).
Preferably, the value introduced into the Taylor series expansion algorithm in S5 is the optimal value obtained from the simulated annealing algorithm in S4And then carrying out iterative computation on the optimal value through a Taylor algorithm to obtain the coordinate values (X, Y) of the final node to be positioned.
As shown in FIG. 2, the random points are valued as shown by scattered points in the graph when the simulated annealing algorithm is performed by adopting the method, and the valued range of the centroid coordinate value is obtained according to the range expansion range of all the random points, so that a more reliable initial value is obtained and provided for the Taylor algorithm.
Performing static point positioning analysis, establishing a 6m multiplied by 6m positioning area, wherein coordinates of 4 base stations are BS 1(0,0),BS2(6,0),BS3 (6, 6) and BS 4 (0, 6) respectively, setting coordinates of a node to be positioned as MS (4, 5), and calculating the coordinates of the node to be positioned by using a method, a Chan-Taylor method (using Chan's algorithm to provide initial values for Taylor algorithm) and a WLS-Taylor method (using weighted least square WLS algorithm to provide initial values for Taylor algorithm) respectively based on UWB measurement noise conforming to zero-mean Gaussian distribution to obtain root mean square error (RootMeanSquareError, RMSE) comparison diagrams of three algorithms in the LOS environment as shown in figure 3; the method, the Chan-Taylor method and the WLS-Taylor method are respectively used for calculating the coordinates of the node to be positioned based on UWB measurement noise conforming to positive mean Gaussian distribution, RMSE comparison graphs of three algorithms in the NLOS environment of fig. 4 are obtained, the accuracy of the method in static positioning of the node to be positioned is obviously high after comparison, the error level of smaller noise interference in the LOS environment is smaller than or equal to 10cm, the error level of smaller noise interference in the NLOS environment is smaller than or equal to 30cm, and the error level of smaller noise interference in the NLOS environment is within a normal UWB measurement error range.
The dynamic point positioning analysis is carried out, a 6m multiplied by 6m positioning area is established, coordinates of 4 base stations are BS 1(0,0),BS2(6,0),BS3 (6, 6) and BS 4 (0, 6) respectively, a section of motion track is set, the starting point is A (2,1.007), the end point is B (3.895,4.753), the motion track is dynamically calculated by using the method, the Chan-Talyor algorithm and the WLS-Taylor algorithm based on the simulation environment of NLOS respectively, so as to obtain a track motion diagram as shown in FIG. 5 and a Euclidean distance error comparison diagram as shown in FIG. 6, and similarly, the positioning accuracy of the method is obviously higher than that of other two algorithms, and the average error of the track points of the method is 14.1cm under the NLOS environment through calculation, so that the positioning accuracy of UWB under the NLOS environment is better improved.
In the description of the present specification, the descriptions of the terms "one embodiment," "example," "specific example," and the like, mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended only to assist in the explanation of the invention. The preferred embodiments are not exhaustive or to limit the invention to the precise form disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best understand and utilize the invention. The invention is limited only by the claims and the full scope and equivalents thereof.
Claims (1)
1. The UWB indoor two-dimensional positioning method based on the improved full centroid-Taylor is characterized by comprising the following steps of:
S1: setting up a positioning area of more than 4 base stations in an LOS or NLOS environment of UWB, and acquiring the distance between the base stations and the mobile tag by adopting a TDOA ranging method;
s2: dividing all base stations into 3 groups, excluding the situation that 3 base stations are on a straight line, ensuring that 3 base stations of each group can enclose a triangle, and calculating the number of all cases M is more than or equal to 3 and is displayed;
S3: for the display in S2 The base stations with m more than or equal to 3 groups respectively use a full centroid algorithm to obtain/>M is more than or equal to 3 groups of coordinates;
s4: in S3 M is more than or equal to 3 groups of coordinates, namely the sum of the distances from the coordinates to the node to be positioned to the pseudo centroid is taken as an objective function, and the objective function is introduced into a simulated annealing algorithm after the value range of the coordinates of the node to be positioned is constrained, so as to find the minimum value of the objective function, namely the self-variable value at the minimum value of the objective function is the optimal value of the coordinates of the node to be positioned to the pseudo centroid;
s5: taking the optimal value obtained from the simulated annealing algorithm in the step S4 as an initial value of a Taylor algorithm, and obtaining the coordinates of the final node to be positioned after solving the Taylor algorithm;
the coordinate resolving process of the final node to be located is as follows:
S5.1: the constructed UWB positioning area has more than 4 base stations, namely BS 1、BS2、BS3、BS4 and the like, and the distance from each base station to a node to be positioned is d 1、d2、d3、d4;
S5.2: after obtaining the distance values from each base station to the node to be positioned in S5.1, grouping all base stations including more than 4 base stations, wherein 3 base stations are in a group, and determining the number of final base station combinations through the conditions that the sum of any two sides of the triangle is larger than the third side and the difference between any two sides is smaller than the third side m≥3；
S5.3: and (3) applying a full centroid algorithm to the base station combination subjected to screening in the step (S5.2), wherein the calculation process is as follows:
wherein (X 1,y1)、(x2,y2) and (X 3,y3) are coordinates of three nodes not in a straight line base station, and (X 1,Y1) is coordinates of a node to be positioned obtained by combining the first base station, and wherein
D 1、d2 and d 3 are ranging values from the base stations 1, 2 and 3 to the node to be positioned respectively; and define
Writing (1) as
Qθ＝b (4)
Solving (4) by least square method
θLS＝(QTQ)-1QTb (5)
Solving to obtain θ LS, which is a solution obtained by combining base stations 1,2 and 3, and similarly calculating solutions 1,2 and 4 and solutions obtained by combining 1, 3 and 4 to obtainA group coordinate; the same calculation method is calculated when the number of the base stations is more than 4;
The objective function set in S4 is
In which xi is the coordinate value of the pseudo centroid of the node to be positionedWhile being an argument of the objective function
Representing the distance from the full centroid coordinate value solved in the ith combination mode in S3 to the pseudo centroid, wherein (X i,Yi) is the full centroid coordinate value solved in the ith combination mode;
The pseudo centroid coordinate value The value range of (2) is initially set asCompensating the value range of the pseudo centroid coordinate value, expanding the original range, searching global optimum in a larger value range, and introducing an error threshold eta α to correct the value range of the pseudo centroid coordinate;
the range of the pseudo centroid coordinate value is
The eta is an error compensation value of UWB, and the value range is (0.1, 0.3);
Alpha is a control factor, and the value range is (0, 1);
the value imported into the Taylor series expansion algorithm in the S5 is the optimal value obtained from the simulated annealing algorithm in the S4 And then carrying out iterative computation on the optimal value through a Taylor algorithm to obtain the coordinate values (X, Y) of the final node to be positioned.
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