CN112822633B - Positioning method, system, terminal equipment and readable storage medium based on error compensation - Google Patents
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- H—ELECTRICITY
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- H04W4/02—Services making use of location information
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- 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
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Abstract
The invention discloses a positioning method, a system, a terminal device and a readable storage medium based on error compensation, wherein the method comprises the following steps: s1: acquiring coordinate information of an anchor point and angle information of the anchor point and a positioning node; s2: calculating state matrixes A and B by adopting a least square method based on the coordinate information and the angle information of the anchor point acquired in the step S1; s3: constructing an auxiliary formula by using the state matrixes A and B in the step S2 to calculate a two-dimensional accurate solution of the positioning node with error compensation; s4: and based on the three-dimensional space structure, obtaining another dimensional accurate solution of the positioning node by using the two-dimensional accurate solution obtained in the step S3, and further obtaining a three-dimensional accurate solution of the positioning node. According to the method, the variance compensation processing is carried out through the acquired angle and distance information, the target positioning of an indoor three-dimensional space is realized, and the target positioning precision is effectively improved.
Description
Technical Field
The invention belongs to the technical field of indoor positioning, and particularly relates to a positioning method, a positioning system, terminal equipment and a readable storage medium based on error compensation.
Background
Indoor positioning and tracking is a technology for detecting the positions of personnel, facility equipment and articles in an indoor space in real time through various sensors, and is most widely applied at present. The problem of indoor positioning involves estimating the position of an object from a plurality of noisy sensor measurements. The positioning performance can be unambiguously characterized by some metric, such as calculating the lower Cramer-Rao bound (equal to the Fisher Information Matrix (FIM)), which is typically used to generate an uncertainty ellipse that characterizes the spatial variance distribution of the valid estimates (i.e., the estimates that reach the lower bound). The Cramer-Rao lower bound is a function of the sensor-target geometry and many authors minimize the measure of the lower variance bound by identifying this geometry.
In recent years, with the development of mobile networks and intelligent terminals, the demand for services based on indoor locations is increasing. Although navigation systems such as GPS and beidou can better solve the problem of outdoor positioning, the satellite signal strength and quality are drastically reduced in indoor and other sheltered environments. The signal quality and strength of the ground cellular mobile network in the room are far superior to those of the satellite, but the positioning accuracy of the mobile cellular network is poor so far due to the limitation of the signal broadband, and the requirement of indoor positioning cannot be met. Different positioning technologies can be adopted according to different indoor positioning requirements. The classification can be carried out according to different data acquisition and data processing modes. In terms of data acquisition modes, different algorithms need to acquire information with a certain emphasis, such as distance, angle, time or information of surrounding nodes, and the purpose of the algorithms is to acquire data related to positioning and make the data become the basis of positioning calculation.
Common positioning algorithms include trilateration, TOA, TDOA, chan algorithm, Talor series method, etc. The principle of the trilateration method is that the positions of three nodes are known, the distances from unknown points to the three points are known, three circles are made by taking the three distances as the radius, and the obtained intersection points are the distances of the unknown points. TOA (time of arrival positioning algorithm) refers to the time of sending and returning signals from a sending point to a receiving point, and since the signal speed is determined, the distance can be calculated according to the time, and then positioning can be performed by using a least square method and the like. TDOA (time difference of arrival location algorithm) refers to an improvement in the way that the actual location is originally calculated by absolute time, and the distance difference is obtained by detecting the time difference between the arrival of the signal at two nodes. Two TDOAs are available from three different nodes, one TDOA can determine a hyperbola where a known node is in focus, and the location of the target node is at the intersection of the two hyperbolas. The Chan algorithm can map the distance difference to the coordinates of the target node, and under the LOS (Line of Sight) environment, the estimation value of the coordinates can reach the Cramer-Rao lower bound through twice weighted linear LS estimation. However, in the case of a non-Line of Sight (NLOS) between indoor floors, etc., due to the presence of obstacles such as walls, multipath effects occur, which distort signal propagation, resulting in a large positioning error of coordinates calculated by methods such as trilateration, TOA, TDOA, chan algorithm, etc.
Therefore, the present invention is directed to solving the problem of indoor positioning, and how to improve positioning accuracy and reduce positioning error.
Disclosure of Invention
The invention aims to provide a positioning method, a positioning system, a positioning terminal and a readable storage medium based on error compensation, which carry out variance compensation processing through acquired angle and distance information and realize target positioning of an indoor three-dimensional space.
In one aspect, the present invention provides a positioning method based on error compensation, including the following steps:
s1: acquiring coordinate information of an anchor point and angle information of the anchor point and a positioning node;
the angle information is a measured value of an azimuth angle between an anchor point and a mapping point of a positioning node in a two-dimensional plane;
s2: calculating state matrixes A and B by adopting a least square method based on the coordinate information and the angle information of the anchor point acquired in the step S1;
s3: constructing an auxiliary formula by using the state matrixes A and B in the step S2 to calculate a two-dimensional accurate solution of the positioning node with error compensation;
s4: and based on the three-dimensional space structure, obtaining another dimensional accurate solution of the positioning node by using the two-dimensional accurate solution obtained in the step S3, and further obtaining a three-dimensional accurate solution of the positioning node.
Alternatively, the auxiliary formula in step S3 is as follows:
in the formula (I), the compound is shown in the specification,
is a two-dimensional x, y coordinate solution of the positioning node with error compensation, n is the total number of anchor points, gammamaxFor the maximum root γ of the constructed third-order polynomial function det (P (γ)) -0, T is the transposed sign of the matrix, si2＝(xsi ysi) ' two-dimensional x, y coordinates representing the ith anchor point; the above-mentionedThe third-order polynomial function det (P (γ)) -0 satisfies the function P (γ):
it should be understood that the error inherent in the actual positioning is considered, the variance compensation is further introduced to obtain the positioning formula with the error compensation, and through verification, the positioning result of the method is more accurate compared with the positioning result without the compensation. In some implementations, the solution of the positioning node obtained by using the above-mentioned auxiliary formula is directly used as an accurate solution of the positioning node, which is also capable of satisfying the requirement of the present invention to improve the indoor positioning accuracy. In still other implementations, in order to further improve the positioning accuracy, a weighting tool variable method is further introduced to modify the former, specifically as follows:
the process of calculating the two-dimensional accurate solution of the positioning node with error compensation by using the auxiliary formula in step S3 is as follows:
firstly, the solution of the two-dimensional x, y coordinates of the positioning node calculated by the auxiliary formula is calculated
As an estimated value;
then, processing the estimated value by adopting a weighting tool variable method, and taking the obtained solution as an accurate value of a two-dimensional x, y coordinate, wherein the formula is as follows:
wherein the content of the first and second substances,
the accurate value G of the two-dimensional x, y coordinate of the positioning node obtained by adopting a weighting tool variable methodbc，WbcRespectively, a tool variable matrix and a weighting matrix, expressed as follows:
wherein s is1、snRespectively representing x and y coordinate values of a 1 st anchor point and an nth anchor point;
respectively 1 st anchor point, nth anchor point and mapping point of positioning node in two-dimensional plane, using estimated value
And calculating to satisfy the following conditions:
wherein the content of the first and second substances,
are respectively estimated values
And (4) x and y coordinate values.
Alternatively, the formula for obtaining another dimensional exact solution of the positioning node in step S4 using the two dimensional exact solution obtained in step S3 is as follows:
wherein z istTo locate the z-axis coordinate value of the node,
is the z-axis coordinate value of the ith anchor point, thetaiIs T-Si line and X-O-YThe included angle of the plane; t (1), T (2) is the x, y coordinate value in the accurate solution obtained by the positioning node in step S3,
two-dimensional x, y coordinate values, τ, representing the ith anchor pointi(i 1.., n) is an error term, n is the total number of anchor points, and T is the transposed symbol of the matrix.
Alternatively, the state matrices a and B calculated in step S2 by the least squares method are as follows:
wherein psi1、ψnRespectively the azimuth angle of the 1 st anchor point, the nth anchor point and the mapping point of the positioning node in the two-dimensional plane,
representing the two-dimensional x, y coordinates of the ith anchor point.
Optionally, the coordinates of any two anchor points involved in the calculation are not exactly the same.
In a second aspect, the present invention provides a positioning system based on the above method, including:
the information acquisition module: the anchor point positioning method comprises the steps of obtaining coordinate information of an anchor point and angle information of the anchor point and a positioning node;
an initial solution positioning module: the state matrixes A and B are calculated by adopting a least square method based on the obtained coordinate information and angle information of the anchor point;
the accurate positioning solving module: the two-dimensional accurate solution of the positioning node with the error compensation is calculated by using the state matrixes A and B to construct an auxiliary formula;
a three-dimensional positioning module: and obtaining another dimensional accurate solution of the positioning node by using the obtained two dimensional accurate solution based on the three dimensional space structure, thereby obtaining the three dimensional accurate solution of the positioning node.
In a third aspect, the present invention provides a terminal, including a processor and a memory, where the memory stores a computer program, and the processor calls the computer program to execute: a method for positioning based on error compensation.
In a fourth aspect, the present invention provides a readable storage medium storing a computer program, the computer program being called by a processor to execute: a method for positioning based on error compensation.
Advantageous effects
The positioning method based on error compensation provided by the invention has an obvious effect in indoor positioning, and takes the problem that the positioning accuracy is not high finally due to the multipath effect caused by the existence of obstacles such as walls and the like in the existing indoor positioning technology into consideration, and the error compensation is introduced into the positioning algorithm, namely, the variance compensation processing is carried out through the obtained angle and distance information, so that the target positioning of an indoor three-dimensional space is realized. The method can be applied to positioning of sensors between different floors in real life, has wide application prospect, and solves the problem of difficult actual indoor positioning.
In a further preferred scheme of the invention, the method combines a least square method and a tool variable method for positioning, the positioning precision is further improved, and the finally obtained positioning result is a progressive unbiased value, and compared with a stand field method and a tool variable method, the positioning result is improved to a great extent under the condition of variance change or sensor quantity change.
Drawings
Fig. 1 is a flow chart of indoor positioning with error compensation in an example of the present invention.
FIG. 2 is a schematic diagram of the angular relationship between a target node and a known node in a two-dimensional plane.
Fig. 3 is a schematic diagram of the relative position of an object between three-dimensional floors.
Fig. 4 is a schematic view of angles between nodes in a three-dimensional sensor network.
Detailed Description
The positioning method based on error compensation provided by the invention has obvious effect in indoor positioning and high positioning precision. The present invention will be further described with reference to the following embodiments, which take indoor positioning as an example, and regard the anchor point as a position coordinate, and establish a connection at an unknown node, and the measured value of the azimuth angle between the two mapped points in the two-dimensional plane is known.
Example 1
When the target node is positioned, an unknown node t ═ x (x) exists in the three-dimensional spacet yt zt) ', with n anchor nodes
In a fixed and known position, the two-dimensional X-O-Y plane has n azimuth angles psii(i 1.. n), anchor nodes s, respectivelyiMeasurement of azimuth angle between the mapped point of unknown node t on the X-O-Y plane (i.e. the point of view of the X-O-Y plane
And T0＝(xt yt) Angle of' T0＝(xt yt) ' is the mapping point of the unknown node t on X-O-Y), the angle is provided with an error term ei(i ═ 1.., n), i.e.:
ψi＝φi+ei
wherein phi isiIs the actual angle value, the following relationship exists:
wherein phi isi∈(-π,π)。
At this time, two assumed prior conditions are satisfied:
condition 1: e.g. of the typeiAre gaussian independent identically distributed variables whose expectation is 0 and variance is σ2And is at a true azimuth angle phiiAre independent of each other.
Condition 2: each one of which is
And
in between, at least one is not constant, i.e. each anchor point in the coordinate system cannot be repeated.
Based on the above, as shown in fig. 1, the indoor positioning method based on error compensation provided in this embodiment includes the following steps:
s1: and acquiring coordinate information of the anchor point and angle information of the anchor point and the positioning node.
Wherein n anchor nodes are acquired
And angle information psi of each anchor point and positioning nodei(i＝1,...,n)。
S2: the state matrices a and B are calculated by the least square method based on the coordinate information and angle information of the anchor point acquired in step S1.
According to the structural relationship of the sensor, a pseudo linear equation describing the relationship between the node t and other anchor nodes is as follows:
from the above equation, a statfield (least squares) estimate is obtained
Comprises the following steps:
wherein:
and is
Position estimate of node t due to the presence of error term
Is biased and can be improved by a weighted tool variable method to improve accuracy, the weighted tool variable estimate of node t
Comprises the following steps:
wherein the tool variable matrix and the weighting matrix are respectively:
thus far, the resulting weighted tool variable estimates
The initial solution of the target node t is obtained by using a least square method. In order to improve the positioning accuracy, the present invention introduces error compensation, i.e., performs step S3.
S3: and constructing an auxiliary formula by using the state matrixes A and B of the step S2 to calculate a two-dimensional accurate solution of the positioning node with error compensation.
The theory is derived as follows:
firstly:
wherein:
then define theorem 1:
introduction 1: e (cose)isinei)＝0，
Where E (-) represents the mathematical expectation.
2, leading: when the condition det (P (γ)) ═ 0 exists, γmax＝E(sin2ei) Is the most probabilistically real number when n approaches infinity.
using the theory of principle, can obtain
Can be used forDiscovery, -P (E (sin)2ei) Is semi-positive, its null space is
In the form of such a one-dimensional vector, β is a real number, let the vector be
Is R3*1Any vector in space, so there are:
first item on the right side of the above formula
Second term-vTP(E(sin2ei) V is greater than 0. Thus when it is used as
When the maximum value of γ is such that det (P (γ)) -0.
Therefore, solving the maximum root of the third-order polynomial function det (P (γ)) ═ 0 can yield γmax。
Thus, a position estimate with error compensation for node T is obtained
When n approaches infinity, and when E (cos 2E)i) When the signal is not equal to 0, the signal is transmitted,
two rows before the position converging on node T, i.e. T0。
Up to this point, calculated using the above formula
Is a solution of the two-dimensional x, y coordinates of the location node with error compensation.
In this embodiment, in order to further improve the positioning accuracy, a tool variable matrix and a weighting matrix are respectively constructed
And is provided with
The weighted tool variable estimate with bias compensation is
Due to the use of error compensation, the obtained positioning result is found through simulation
The result is much more accurate than the result of the pure least square method.
S4: and based on the three-dimensional space structure, obtaining another dimensional accurate solution of the positioning node by using the two-dimensional accurate solution obtained in the step S3, and further obtaining a three-dimensional accurate solution of the positioning node.
The coordinates of the unknown node in the x-axis and y-axis, i.e., T, are obtained by step S3bc-wiv(1) And Tbc-wiv(2) Let us order
In three-dimensional space, there is the following formula model:
wherein, taui(i 1.., n) is an error term, which is also gaussian-independent and identically distributed. ThetaiIs the included angle between the T-Si line and the X-O-Y plane.
Obtaining a formula of a third-dimensional coordinate of the unknown node by solving the formula:
in the formula, T is a matrix transposition symbol.
Example 2:
the difference between this embodiment and embodiment 1 is that in this embodiment, the estimated value with error compensation is obtained in step S3
As an accurate solution, and applied to the calculation of step S4.
Application example:
as shown in fig. 3, assuming there are n children on a three-dimensional floor, each child has a watch with a sensor, angle information between the sensors can be obtained, assuming one of the children is lost, his location is unknown, and the locations of the remaining children are known. As shown in fig. 4, in the three-dimensional space, there is an unknown node t ═ (x)t yt zt) ', with n anchor nodes
In a fixed and known position, in the two-dimensional plane X-O-Y, i.e. as shown in figure 2, there are n azimuth angles psii(i ═ 1.. times, n), which are anchor nodes s, respectivelyiAzimuthal measurements between mapped points on the X-O-Y plane with unknown nodes t (i.e.
And T0＝(xt yt) Angle of'), angle with error term ei(i＝1,...,n)。
Then, the positioning result is obtained by the manner of the above steps S1-S4.
In some implementations, the present invention further provides a positioning system based on the indoor positioning method, including:
the information acquisition module: the anchor point positioning method comprises the steps of obtaining coordinate information of an anchor point and angle information of the anchor point and a positioning node;
an initial solution positioning module: the state matrixes A and B are calculated by adopting a least square method based on the obtained coordinate information and angle information of the anchor point;
the accurate positioning solving module: the two-dimensional accurate solution of the positioning node with the error compensation is calculated by using the state matrixes A and B to construct an auxiliary formula;
a three-dimensional positioning module: and obtaining another dimensional accurate solution of the positioning node by using the obtained two dimensional accurate solution based on the three dimensional space structure, thereby obtaining the three dimensional accurate solution of the positioning node.
For the specific implementation process of each unit module, refer to the corresponding process of the foregoing method. It should be understood that, the specific implementation process of the above unit module refers to the method content, and the present invention is not described herein in detail, and the division of the above functional module unit is only a division of a logic function, and there may be another division manner in the actual implementation, for example, multiple units or components may be combined or may be integrated into another system, or some features may be omitted, or may not be executed. Meanwhile, the integrated unit can be realized in a hardware form, and can also be realized in a software functional unit form.
In some implementations, the present invention also provides a terminal comprising a processor and a memory, the memory storing a computer program, the processor invoking the computer program to perform: a method for positioning based on error compensation.
The detailed implementation process of each step refers to the content of the foregoing method.
In some implementations, the invention also provides a readable storage medium storing a computer program for invocation by a processor to perform: a method for positioning based on error compensation.
The detailed implementation process of each step refers to the content of the foregoing method.
It should be understood that in the embodiments of the present invention, the Processor may be a Central Processing Unit (CPU), and the Processor may also be other general purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other Programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, and the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The memory may include both read-only memory and random access memory, and provides instructions and data to the processor. The portion of memory may also include non-volatile random access memory. For example, the memory may also store device type information.
The readable storage medium is a computer readable storage medium, which may be an internal storage unit of the controller according to any of the foregoing embodiments, for example, a hard disk or a memory of the controller. The readable storage medium may also be an external storage device of the controller, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like provided on the controller. Further, the readable storage medium may also include both an internal storage unit of the controller and an external storage device. The readable storage medium is used for storing the computer program and other programs and data required by the controller. The readable storage medium may also be used to temporarily store data that has been output or is to be output.
Based on such understanding, the technical solution of the present invention essentially or partially contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned readable storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the invention is not to be limited to the examples described herein, but rather to other embodiments that may be devised by those skilled in the art based on the teachings herein, and that various modifications, alterations, and substitutions are possible without departing from the spirit and scope of the present invention.
Claims (8)
1. A positioning method based on error compensation is characterized in that: the method comprises the following steps:
s1: acquiring coordinate information of an anchor point and angle information of the anchor point and a positioning node;
the angle information is a measured value of an azimuth angle of a mapping point of an anchor point and a positioning node in a two-dimensional plane;
s2: calculating state matrixes A and B by adopting a least square method based on the coordinate information and the angle information of the anchor point acquired in the step S1;
s3: constructing an auxiliary formula by using the state matrixes A and B in the step S2 to calculate a two-dimensional accurate solution of the positioning node with error compensation;
s4: obtaining another dimensional accurate solution of the positioning node by using the two dimensional accurate solution obtained in the step S3 based on the three dimensional space structure, and further obtaining a three dimensional accurate solution of the positioning node;
the auxiliary formula in step S3 is as follows:
in the formula (I), the compound is shown in the specification,
is a two-dimensional x, y coordinate solution of the positioning node with error compensation, n is the total number of anchor points, gammamaxFor the maximum root γ of the constructed third-order polynomial function det (P (γ)) -0, T is the transposed sign of the matrix,
two-dimensional x, y coordinates representing the ith anchor point; the third-order polynomial function det (P (gamma)) -0 is the function P (gamma) satisfying:
2. the method of claim 1, wherein: the process of calculating the two-dimensional accurate solution of the positioning node with error compensation by using the auxiliary formula in step S3 is as follows:
firstly, the solution of the two-dimensional x, y coordinates of the positioning node calculated by the auxiliary formula is calculated
As an estimated value;
then, processing the estimated value by adopting a weighting tool variable method, and taking the obtained solution as an accurate value of a two-dimensional x, y coordinate, wherein the formula is as follows:
wherein the content of the first and second substances,
the accurate value G of the two-dimensional x, y coordinate of the positioning node obtained by adopting a weighting tool variable methodbc，WbcRespectively, a tool variable matrix and a weighting matrix, tableShown below:
wherein s is1、snRespectively representing x and y coordinate values of a 1 st anchor point and an nth anchor point;
respectively 1 st anchor point, nth anchor point and mapping point of positioning node in two-dimensional plane, using estimated value
And calculating to satisfy the following conditions:
wherein the content of the first and second substances,
are respectively estimated values
And (4) x and y coordinate values.
3. The method of claim 1, wherein: the formula for obtaining another dimensional exact solution of the positioning node using the two dimensional exact solution obtained in step S3 in step S4 is as follows:
wherein z istTo locate the z-axis coordinate value of the node,
is the z-axis coordinate value of the ith anchor point, thetaiIs the included angle between the T-Si line and the X-O-Y plane; t (1), T (2) is the x, y coordinate value in the accurate solution obtained by the positioning node in step S3,
two-dimensional x, y coordinate values, τ, representing the ith anchor pointi(i 1.., n) is an error term, n is the total number of anchor points, and T is the transposed symbol of the matrix.
4. The method of claim 1, wherein: the state matrices a and B calculated by the least square method in step S2 are as follows:
wherein psi1、ψnRespectively the azimuth angle of the 1 st anchor point, the nth anchor point and the mapping point of the positioning node in the two-dimensional plane,
representing the two-dimensional x, y coordinates of the ith anchor point.
5. The method of claim 4, wherein: the coordinates of any two anchor points involved in the calculation are not exactly the same.
6. A positioning system based on the method of any one of claims 1-5, characterized by: the method comprises the following steps:
the information acquisition module: the anchor point positioning method comprises the steps of obtaining coordinate information of an anchor point and angle information of the anchor point and a positioning node;
an initial solution positioning module: the state matrixes A and B are calculated by adopting a least square method based on the obtained coordinate information and angle information of the anchor point;
the accurate positioning solving module: the two-dimensional accurate solution of the positioning node with the error compensation is calculated by using the state matrixes A and B to construct an auxiliary formula;
a three-dimensional positioning module: and obtaining another dimensional accurate solution of the positioning node by using the obtained two dimensional accurate solution based on the three dimensional space structure, thereby obtaining the three dimensional accurate solution of the positioning node.
7. A terminal device characterized by: comprising a processor and a memory, the memory storing a computer program that the processor calls to perform: the process steps of any one of claims 1 to 5.
8. A readable storage medium, characterized by: a computer program is stored, which is invoked by a processor to perform: the process steps of any one of claims 1 to 5.
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