Indoor positioning method and apparatus based on a fingerprint database, and medium

Abstract

The application discloses an indoor positioning method and device based on a fingerprint database and a medium, and the method comprises the following steps: selecting high-density reference points in a positioning environment; selecting low-density reference points from the high-density reference point set, constructing an observation matrix by using the low-density reference point set, and constructing a transformation matrix by using the high-density reference point set; measuring the signal strength of an access point at the low-density reference points; solving and optimizing the access point, and performing inverse transformation to obtain the estimated value of the signal strength on the high-density reference points, and combining the corresponding coordinates to obtain a fingerprint database based on the high-density reference points; obtaining the signal strength of the access point at the to-be-positioned position, calculating the distance of the signal strength vector in the fingerprint database, and calculating the coordinates of the to-be-positioned terminal according to the corresponding coordinates. The application can obtain the signal strength of each access point at the high-density reference points by conversion through the signal strength of a small amount of reference points, reduce the workload of constructing the fingerprint database, reduce the cost, and is simple to calculate.

Description

Technical Field

[0001] This invention relates to the field of indoor positioning technology, and in particular to an indoor positioning method, device and medium based on a fingerprint database. Background Technology

[0002] In indoor environments, due to the presence of numerous non-line-of-sight propagation paths, accurate distance measurement is difficult, and traditional positioning methods often fail to achieve good results, resulting in significant positioning errors. RF fingerprint positioning is one of the most competitive technologies for indoor positioning, but constructing RF fingerprints is a labor-intensive process, and these fingerprints need to be updated as the environment changes.

[0003] In the patent "Indoor Fingerprint Positioning System Method Based on Compressed Sensing DTMB and FM Signals (Chinese Patent Application No. CN201911137849.2)," the solution uses broadcast television video bands and FM band signals for positioning. These signals are not commonly used mobile communication signals. If used for positioning, dedicated transceiver equipment needs to be deployed, and the terminal to be located is also required to be able to transmit and receive the corresponding frequency band information, which obviously increases hardware costs.

[0004] In the patent "Indoor Wireless Terminal Positioning Method Based on Bayesian Compressed Sensing (Chinese Patent Application No. CN201210077542.X)," the solution is based on the assumption that the terminal to be located will only appear on a single pre-defined grid point. Therefore, a sparse sampling model can be constructed to recover the location. However, if the terminal to be located does not appear exactly on the pre-defined grid point, but deviates to a certain extent, the sparse model may not hold true, introducing errors. In addition, this solution introduces a compressed sensing model in the online stage and uses sparse signal recovery to restore the location of the terminal to be located, which has the problems of large computational load and long time consumption, and may not be suitable for scenarios that are sensitive to positioning time. Summary of the Invention

[0005] This invention provides an indoor positioning method, device, and medium based on a fingerprint database. The method constructs a fingerprint database by converting the signal strength of each access point at a high density of reference points through the measurement and conversion of signal strength at a small number of reference points, and calculates the target location by comparing the closest coordinates in the fingerprint database.

[0006] To achieve the above objectives, embodiments of the present invention provide an indoor positioning method based on a fingerprint database, comprising: In the positioning environment, a first reference point is selected as the high-density reference point set, denoted as HFP, where the number of the first reference points satisfies N=2. n n is a positive even number; The first reference points are vectorized according to their positions and numbered using n-bit binary codes. The set of numbers of the first reference points forms an algebraic group structure with respect to the addition of n-dimensional binary vectors, denoted as the group. ; A second reference point is selected from the high-density reference point set as a low-density reference point set, denoted as LFP, wherein the number of the second reference points is M, and the second reference points satisfy the condition of constituting the support set of the Bent function on the group G; Constructing an observation matrix using the low-density reference point set The transformation matrix A is constructed using the high-density reference point set. G ; The signal strength of the access point in the positioning environment is measured at the second reference point and recorded as an M-dimensional vector; To solve the optimization problem for the access point, the M-dimensional vector of the access point is expanded into an N-dimensional vector; By performing an inverse transformation on each of the N-dimensional vectors, an estimated value of the signal strength of the access point at the first reference point is obtained; By combining the estimated signal strength of the access point at the first reference point and the coordinates of the corresponding first reference point, a fingerprint database based on a high-density set of reference points is obtained. Obtain the signal strength of the access point of the terminal to be located in the positioning environment, and record it as the first signal strength vector; Calculate the distance between the first signal strength vector and the second signal strength vector of each row in the fingerprint database based on the high-density reference point set; Take the k smallest distances among the distances, and calculate the coordinates of the terminal to be located based on the corresponding coordinates in the fingerprint database based on the high-density reference point set, so as to obtain the position of the terminal to be located.

[0007] Furthermore, an observation matrix is ​​constructed using the aforementioned low-density reference point set. The transformation matrix A is constructed using the high-density reference point set. G Specifically, this includes: constructing the group characteristics corresponding to each element in group G. Furthermore, given an M-element subset D within a group G, for any characteristic of the group, an M*N matrix can be constructed. : ,in The elements are either 1 or -1 multiplied by a constant; Based on the above definition, an observation matrix is ​​constructed using the aforementioned low-density reference point set. : ; Construct transformation matrix A using the high-density reference point set. G ,in It is a symmetric matrix containing only -1 and 1 multiplied by a constant element, i.e. = And matrix Construct an N-order unitary matrix that satisfies E, where E represents the identity matrix.

[0008] Furthermore, the optimization problem for the access point, which involves expanding the M-dimensional vector of the access point into an N-dimensional vector, specifically includes: The optimization problem to be solved can be: ; Or it could be a noise error optimization problem: ,in The allowable noise threshold; Or it could be any equivalent or other convex optimization problem derived from the above optimization problem; By solving the optimization problem, an N-dimensional vector can be obtained. .

[0009] Furthermore, the formula for calculating the inverse transform is: ,in That is, the estimated signal strength of each access point at the first reference point.

[0010] Furthermore, the step of taking the k smallest distances from the distances and calculating the coordinates of the terminal to be located based on their corresponding coordinates in the fingerprint database based on the high-density reference point set to obtain the location of the terminal to be located is specifically as follows: Take the k smallest distances from the given distances, and denote them as: ; The coordinates of the corresponding second signal intensity vector are found in the fingerprint database based on the high-density reference point set, and denoted as: , ; Calculate the coordinates of the terminal to be located. , obtain coordinates ( , ).

[0011] Accordingly, embodiments of the present invention also provide an indoor positioning device based on a fingerprint database, comprising: The first reference point selection module is used to select a first reference point in the positioning environment, which is used as a high-density reference point set, denoted as HFP, where the number of first reference points satisfies N=2. nWhere n is a positive even number; the first reference points are vectorized and arranged according to their positions and numbered using n-bit binary codes. The set of numbers of the first reference points forms an algebraic group structure with respect to the addition of n-dimensional binary vectors, denoted as group. ; The second reference point selection module is used to select a second reference point from the high-density reference point set as a low-density reference point set, denoted as LFP, where the number of second reference points is M and they satisfy the condition of forming the support set of the Bent function on the group G. The observation matrix construction module is used to construct an observation matrix using the low-density reference point set. ; The transformation matrix construction module is used to construct transformation matrix A using the high-density reference point set. G ; The signal strength measurement module is used to measure the signal strength of the access point in the positioning environment at the second reference point and record it as an M-dimensional vector; The optimization module is used to solve the optimization problem for the access point and expand the M-dimensional vector of the access point into an N-dimensional vector. A high-density signal strength calculation module is used to perform an inverse transformation on each of the N-dimensional vectors to obtain an estimated value of the signal strength of the access point at the first reference point; The fingerprint database acquisition module is used to combine the estimated value of the signal strength of each access point on the first reference point and the coordinates of the corresponding first reference point to obtain a fingerprint database based on a high-density reference point set.

[0012] The module for obtaining the signal strength of the terminal to be located is used to obtain the signal strength of the access point of the terminal to be located in the positioning environment and record it as the first signal strength vector. The distance calculation module is used to calculate the distance between the first signal strength vector and the second signal strength vector of each row in the fingerprint database based on the high-density reference point set; The module for calculating the coordinates of the terminal to be located is used to take the k smallest distances among the distances and calculate the coordinates of the terminal to be located based on the coordinates of the corresponding second signal strength vector in the fingerprint database based on the high-density reference point set, so as to obtain the position of the terminal to be located.

[0013] Furthermore, the module for constructing the observation matrix specifically includes: The group characteristic corresponding to each element in the constructive group G is: Furthermore, given an M-element subset D within a group G, for any characteristic of the group, an M*N matrix can be constructed. : ,in The elements are either 1 or -1 multiplied by a constant; Based on the above definition, an observation matrix is ​​constructed using the aforementioned low-density reference point set. : ; Furthermore, the solution optimization module specifically includes: The optimization problem to be solved can be: ; Or it could be a noise error optimization problem: ,in The allowable noise threshold; Or it could be any equivalent or other convex optimization problem derived from the above optimization problem; By solving the optimization problem, an N-dimensional vector can be obtained. .

[0014] Furthermore, the module for calculating the coordinates of the terminal to be located specifically includes: Take the k smallest distances from the given distances, and denote them as: ; The coordinates of the corresponding second signal intensity vector are found in the fingerprint database based on the high-density reference point set, and denoted as: , ; Calculate the coordinates of the terminal to be located. , obtain coordinates ( , ).

[0015] Accordingly, embodiments of the present invention also provide a computer-readable storage medium, the computer-readable storage medium including a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to execute any of the above-described indoor positioning methods based on a fingerprint database.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention uses the signal strength RSS of WiFi signals to reduce hardware costs. By combining compressed sensing, it utilizes the sparsity characteristics of the signal strength RSS of WiFi signals under specific transformations to propose a method to obtain the signal strength of each access point at a high density of reference points by measuring the signal strength at a small number of reference points and transforming it, thus reducing the workload of constructing RF fingerprints. In addition, the transformation matrix and observation matrix introduced herein are all composed of 1 or -1 multiplied by a constant, making the calculation simple and easy to implement. Attached Figure Description

[0017] Figure 1This is a flowchart illustrating steps S1 to S6 of an indoor positioning method based on a fingerprint database provided in Embodiment 1 of the present invention. Figure 2 This is a flowchart illustrating steps S7 to S11 of an indoor positioning method based on a fingerprint database provided in Embodiment 1 of the present invention. Figure 3 This is a schematic diagram of the positioning environment and the first reference point in Embodiment 2 of the present invention; Figure 4 This is a schematic diagram of an indoor positioning device based on a fingerprint database provided in Embodiment 4 of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] See Figure 1 and Figure 2 This is a flowchart illustrating an indoor positioning method based on a fingerprint database provided in Embodiment 1 of the present invention.

[0020] Embodiment 1 of the present invention provides an indoor positioning method based on a fingerprint database, comprising steps S1 to S11: S1, Select a first reference point in the positioning environment as a high-density reference point set, denoted as HFP, where the number of the first reference points satisfies N=2. n n is a positive even number; S2, arrange the first reference points according to their positions using vectorization and number them with n-bit binary codes. Then, construct an algebraic group from the set of numbers of the first reference points using n-dimensional binary vector addition, denoted as the group. ; S3, select a second reference point from the high-density reference point set as a low-density reference point set, denoted as LFP, wherein the number of the second reference points is M, and the second reference points satisfy the condition of forming a support set for the Bent function on the group G; S4, Construct an observation matrix using the low-density reference point set. The transformation matrix A is constructed using the high-density reference point set. G ; S5, Measure the signal strength of the access point in the positioning environment at the second reference point and record it as an M-dimensional vector; S6, Solve the optimization problem for the access point, and expand the M-dimensional vector of the access point into an N-dimensional vector; S7. Perform an inverse transformation on each of the N-dimensional vectors to obtain an estimated value of the signal strength of the access point at the first reference point. S8. Combine the estimated value of the signal strength of the access point at the first reference point and the coordinates of the corresponding first reference point to obtain a fingerprint database based on a high-density set of reference points. S9, obtain the signal strength of the access point of the terminal to be located in the positioning environment, and record it as the first signal strength vector; S10, calculate the distance between the first signal strength vector and the second signal strength vector of each row in the fingerprint database based on the high-density reference point set; S11, take the k smallest distances among the distances, and calculate the coordinates of the terminal to be located based on the corresponding coordinates in the fingerprint database based on the high-density reference point set, so as to obtain the location of the terminal to be located.

[0021] In steps S1-S2, specifically, N=2 is uniformly selected in the positioning environment. n There are several high-density reference points at known locations, where n is an even number (n≥2), denoted as the 0th reference point to the 2nd reference point. n -1 reference points, these high-density reference points constitute the fingerprint database we want to build or update, denoted as HFP. These high-density reference points are vectorized according to their position, such as from top to bottom, from left to right, etc., and numbered using n-bit binary codes. The set of high-density reference point numbers can be viewed as an additive group in an n-dimensional linear space over a binary field, where the addition operation is a binary addition of n-dimensional vectors. We denote this group as... For ease of description, these numbers may be represented by their corresponding decimal numbers, such as 0, 1, up to 2, as appropriate. n -1.

[0022] In step S3, it should be noted that the Bent function is defined as follows: a Boolean function. It is called a Bent function if and only if for any Their Walsh transforms all satisfy or - ,here Let represent an n-dimensional linear space over a bivariate finite field.

[0023] The definition of a Boolean function is: from a bivariate finite field to n-dimensional vector space A mapping to a 1-dimensional vector space is called an n-ary Boolean function, and the set of all n-ary Boolean functions is denoted as . .

[0024] The Walsh transform is defined as follows: Let... Called mapping: for The Walsh transform is called for The Walsh transform value at u, where This represents the inner product of two vectors.

[0025] Step S4 specifically includes: The group characteristic corresponding to each element in the constructive group G is: Among them, the so-called characteristics refer to the characteristics of the group The homomorphism from the complex multiplication group with an absolute value of 1 to the group Each element in ) can be used to construct a feature according to the definition; Given an M-element subset D within a group G, for any characteristic of the group, we can construct an M*N matrix. : ,in The elements are either 1 or -1 multiplied by a constant; Based on the above definition, an observation matrix is ​​constructed using the aforementioned low-density reference point set. : ; Construct transformation matrix A using the high-density reference point set. G ,in It is a symmetric matrix containing only -1 and 1 multiplied by a constant element, i.e. = And matrix Construct an N-order unitary matrix that satisfies E, where E represents the identity matrix.

[0026] In step S6, the optimization problem to be solved can be: ; Or it could be a noise error optimization problem: ,in The allowable noise threshold; Or it could be any equivalent or other convex optimization problem derived from the above optimization problem; By solving the optimization problem, an N-dimensional vector can be obtained. .

[0027] It is worth noting that solving these optimization problems can also be transformed into solving other convex optimization problems, such as: or wait.

[0028] Furthermore, in step S7, the calculation formula for the inverse transform is: ,in That is, the estimated signal strength of each access point at the first reference point.

[0029] Furthermore, step S11 specifically includes: Take the k smallest distances from the given distances, and denote them as: ; The coordinates of the corresponding second signal intensity vector are found in the fingerprint database based on the high-density reference point set, and denoted as: ; Calculate the coordinates of the terminal to be located. , obtain coordinates ( , ).

[0030] It should be noted that the above-mentioned distance calculation algorithm and fingerprint positioning method can also be calculated using other positioning algorithms, which will not be elaborated here.

[0031] It should be noted that, as can be seen from the positioning process, the coordinates of the terminal to be located are calculated by comparing the RSS vector measured online with the fingerprints in the fingerprint database and using the coordinates of the corresponding fingerprints that are close to each other, i.e., similar fingerprints.

[0032] It is known that the density of fingerprint points has a significant impact on localization results; denser fingerprints are more conducive to improving localization accuracy. For example, the localization accuracy will be significantly different between fingerprints spaced 10 meters apart and those spaced 3 meters apart. However, building a fingerprint database requires a huge amount of testing work, so it is necessary to study methods to generate high-density RSS fingerprints from fewer measurement points.

[0033] See Figure 3 This is a schematic diagram of the positioning environment and the first reference point in Embodiment 2 of the present invention.

[0034] In the second embodiment of the invention, a fingerprint database is constructed in an office area of ​​approximately 30 meters × 20 meters. Six access points are set up in this positioning environment, and 16 (i.e., 2) fingerprints are taken from within the office area. 4 One first reference point is used as a high-density reference point; The high-density reference points are numbered sequentially using 4-bit binary codes, as shown in the table below, and denoted as follows: As a group Elements within;

[0035] Low-density reference points are selected from the high-density reference points, and these low-density reference points satisfy the condition that they constitute the support set of the Bent function on the group G, i.e. ; The support set is the set of function values. The set of non-zero independent variables yields the following low-density reference points: {(1,0,1,1),(1,1,1,0),(1,0,1,0),(0,1,0,1),(1,1,0,1),(0,1,1,1)}; Using the aforementioned low-density reference point set to construct the observation matrix, we obtain:

[0036] Using the wireless signal strength RSS as a signal characteristic, the signal strength of the access point is measured at six low-density reference points to obtain the low-density signal strength vector: ,...,

[0037] For the optimization problem of access points with low-density reference points, the 6-dimensional signal strength vector of the access point is extended into a 16-dimensional vector. : ; Optionally, in Example 3, the RSS at low-density reference points is expanded to the RSS at all high-density reference points by addressing the noise error optimization problem: ,i=1,2,...6, where The allowable noise threshold.

[0038] Each of the above Perform an inverse transformation to obtain an estimated value of the signal strength of the access point at the first reference point;

[0039] Put all By combining the results, we get:

[0040]

[0041] Based on the coordinates of its corresponding high-density reference points, a high-density fingerprint database for this positioning environment is obtained:

[0042] The RF fingerprint system acquires the signal strength of the access point (AP) in the test environment of the terminal to be located during the online phase, and forms an RSS vector:

[0043] Bundle The first in i The RSS signal strength vector corresponding to each fingerprint is denoted as:

[0044] calculate and Vector distance between: ; Take the k smallest distances from the given distances, and denote them as: ; exist The corresponding coordinates are retrieved from the fingerprint database and denoted as: , ; Calculate the coordinates of the terminal to be located. , obtain coordinates ( , ).

[0045] In Embodiment 4, if more reference points are selected, and the fingerprint database is constructed in the office area of ​​Embodiment 2, then 256 (i.e., 2) are chosen. 8 A high-density reference point, The high-density reference points are numbered sequentially using 8-bit binary codes, and denoted as follows: As a group Elements within; Among them, the wireless signal strength RSS is used as the signal feature. The signal strength RSS vector of the access point at the low-density reference point can be denoted as: A single RF fingerprint can be recorded as If s=0,1,...,255, then the RF fingerprint database to be constructed is denoted as }; Similar to Embodiment 2 of the present invention, low-density reference points are selected from the high-density reference points, and the low-density reference points satisfy the condition that they constitute the support set of the Bent function on the group G. The support set is the set of reference points that makes the function values... Given a set of non-zero independent variables, we construct an 8-variable Bent function, i.e.:

[0046] The low-density reference point is obtained based on the above function. Subsequent steps are the same as those in Embodiment 2 of the invention, and will not be repeated here.

[0047] In summary, the fingerprint database-based positioning method provided in this invention reduces hardware costs by using the signal strength RSS of WiFi signals. By combining compressed sensing and utilizing the sparsity characteristics of the signal strength RSS of WiFi signals under specific transformations, a method is proposed to obtain the signal strength of each access point at a high-density reference point by measuring the signal strength at a small number of reference points and transforming it, thereby reducing the workload of constructing RF fingerprints. In addition, the transformation matrix and observation matrix introduced herein are all composed of 1 or -1 multiplied by a constant, making the calculation simple and easy to implement.

[0048] Accordingly, this invention provides an indoor positioning device based on a fingerprint database, which can implement all the processes of the indoor positioning method based on a fingerprint database provided in any of the above embodiments. The functions and technical effects of each module and unit in the device are the same as those of the indoor positioning method based on a fingerprint database provided in the above embodiments, and will not be repeated here.

[0049] See Figure 4 This is a schematic diagram of an indoor positioning device based on a fingerprint database provided in Embodiment 4 of the present invention.

[0050] The device includes: The first reference point selection module 1 is used to select a first reference point in the positioning environment, which is used as a high-density reference point set, denoted as HFP, where the number of first reference points satisfies N=2. n n is a positive even number; the first reference points are vectorized and arranged according to their positions and numbered using n-bit binary codes. The set of numbers for the first reference points is denoted as group. ; The second reference point selection module 2 is used to select a second reference point from the high-density reference point set as a low-density reference point set, denoted as LFP, where the number of second reference points is M and they satisfy the condition of forming the support set of the Bent function on the group G. Module 3 for constructing the observation matrix is ​​used to construct the observation matrix using the low-density reference point set. ; Module 4 for constructing the transformation matrix is ​​used to construct the transformation matrix A using the high-density reference point set. G ; The signal strength measurement module 5 is used to measure the signal strength of the access point in the positioning environment at the second reference point and record it as an M-dimensional vector. The optimization module 6 is used to solve the optimization problem for the access point and expand the M-dimensional vector of the access point into an N-dimensional vector. The high-density signal strength calculation module 7 is used to perform an inverse transformation on each of the N-dimensional vectors to obtain an estimated value of the signal strength of the access point at the first reference point. The fingerprint database acquisition module 8 is used to combine the estimated value of the signal strength of each access point on the first reference point and the coordinates of the corresponding first reference point to obtain a fingerprint database based on a high-density reference point set.

[0051] The signal strength acquisition module 9 of the terminal to be located is used to acquire the signal strength of the access point of the terminal to be located in the positioning environment and record it as the first signal strength vector. The distance calculation module 10 is used to calculate the distance between the first signal strength vector and the second signal strength vector of each row in the fingerprint database based on the high-density reference point set; The module 11 for calculating the coordinates of the terminal to be located is used to take the k smallest distances among the distances and calculate the coordinates of the terminal to be located based on the coordinates of the corresponding second signal strength vector in the fingerprint database based on the high-density reference point set, so as to obtain the location of the terminal to be located.

[0052] Furthermore, in the construction of the observation matrix module 3, specifically: The group characteristic corresponding to each element in the constructive group G is: Furthermore, given an M-element subset D within a group G, for any characteristic of the group, an M*N matrix can be constructed. : ,in The elements are either 1 or -1 multiplied by a constant; Based on the above definition, an observation matrix is ​​constructed using the aforementioned low-density reference point set. : ; Furthermore, the solution optimization module 5 specifically comprises: The optimization problem to be solved can be: ; Or it could be a noise error optimization problem: ,in The allowable noise threshold; Or it could be any equivalent or other convex optimization problem derived from the above optimization problem; By solving the optimization problem, an N-dimensional vector can be obtained. .

[0053] Furthermore, in the module 10 for calculating the coordinates of the terminal to be located, specifically: Take the k smallest distances from the given distances, and denote them as: ; The coordinates of the corresponding second signal intensity vector are found in the fingerprint database based on the high-density reference point set, and denoted as: , ; Calculate the coordinates of the terminal to be located. , obtain coordinates ( , ).

[0054] This invention also provides a computer-readable storage medium, which includes a stored computer program, wherein the computer program, when running, controls the device where the computer-readable storage medium is located to execute the indoor positioning method based on a fingerprint database as described in any of the above embodiments.

[0055] Through the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary hardware platforms, and of course, it can also be implemented entirely by hardware. Based on this understanding, all or part of the technical solution of the present invention that contributes to the background technology can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0056] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An indoor positioning method based on a fingerprint database, characterized in that, include: In the positioning environment, a first reference point is selected as the high-density reference point set, denoted as HFP, where the number of the first reference points satisfies N=2. n n is a positive even number; The first reference points are vectorized according to their positions and numbered using n-bit binary codes. The set of numbers of the first reference points forms an algebraic group structure with respect to the addition of n-dimensional binary vectors, denoted as the group. ; A second reference point is selected from the high-density reference point set as a low-density reference point set, denoted as LFP, wherein the number of the second reference points is M, and the second reference points satisfy the condition of constituting the support set of the Bent function on the group G; Constructing an observation matrix using the low-density reference point set The transformation matrix A is constructed using the high-density reference point set. G Specifically, this includes: The group characteristic corresponding to each element in the constructed group G is: Furthermore, given an M-element subset D within a group G, for any characteristic of the group, an M*N matrix can be constructed. : ,in The elements are either 1 or -1 multiplied by a constant; Based on the above definition, an observation matrix is ​​constructed using the aforementioned low-density reference point set. : ； Construct transformation matrix A using the high-density reference point set. G ,in It is a symmetric matrix containing only -1 and 1 multiplied by a constant element, i.e. = And matrix Construct an N-order unitary matrix that satisfies E, where E represents the identity matrix; The signal strength of the access point in the positioning environment is measured at the second reference point and recorded as an M-dimensional vector; The optimization problem for the access point is solved by expanding the M-dimensional vector of the access point into an N-dimensional vector; specifically including: The optimization problem to be solved is: ; Or it could be a noise error optimization problem: ,in The allowable noise threshold; By solving the optimization problem, an N-dimensional vector can be obtained. ; By performing an inverse transformation on each of the N-dimensional vectors, an estimated value of the signal strength of the access point at the first reference point is obtained; By combining the estimated signal strength of the access point at the first reference point and the coordinates of the corresponding first reference point, a fingerprint database based on a high-density set of reference points is obtained. The signal strength of the access point at the terminal to be located in the positioning environment is obtained and recorded as the first signal strength vector; Calculate the distance between the first signal strength vector and the second signal strength vector of each row in the fingerprint database based on the high-density reference point set; Take the k smallest distances among the distances, and calculate the coordinates of the terminal to be located based on their corresponding coordinates in the fingerprint database based on the high-density reference point set, so as to obtain the position of the terminal to be located.

2. The indoor positioning method based on a fingerprint database as described in claim 1, characterized in that, The formula for calculating the inverse transform is: ,in That is, the estimated signal strength of each access point at the first reference point.

3. The indoor positioning method based on a fingerprint database as described in claim 1, characterized in that, The process involves selecting the k smallest distances from the given distances and calculating the coordinates of the terminal to be located based on their corresponding coordinates in the fingerprint database based on a high-density reference point set, thereby obtaining the location of the terminal to be located. Specifically: Take the k smallest distances from the given distances, and denote them as: ; The coordinates of the corresponding second signal intensity vector are found in the fingerprint database based on the high-density reference point set, and denoted as: , ; Calculate the coordinates of the terminal to be located. , obtain coordinates ( , ).

4. An indoor positioning device based on a fingerprint database, characterized in that, The device includes: The first reference point selection module is used to select a first reference point in the positioning environment, which is used as a high-density reference point set, denoted as HFP, where the number of first reference points satisfies N=2. n Where n is a positive even number; the first reference points are vectorized and arranged according to their positions and numbered using n-bit binary codes. The set of numbers of the first reference points forms an algebraic group structure with respect to the addition of n-dimensional binary vectors, denoted as group. ; The second reference point selection module is used to select a second reference point from the high-density reference point set as a low-density reference point set, denoted as LFP, where the number of second reference points is M and they satisfy the condition of forming the support set of the Bent function on the group G. The observation matrix construction module is used to construct an observation matrix using the low-density reference point set. Specifically, this includes: The group characteristic corresponding to each element in the constructed group G is: Furthermore, given an M-element subset D within a group G, for any characteristic of the group, an M*N matrix can be constructed. : ,in The elements are either 1 or -1 multiplied by a constant; Based on the above definition, an observation matrix is ​​constructed using the aforementioned low-density reference point set. : ； The transformation matrix construction module is used to construct transformation matrix A using the high-density reference point set. G ; The signal strength measurement module is used to measure the signal strength of the access point in the positioning environment at the second reference point and record it as an M-dimensional vector; The optimization module is used to solve the optimization problem for the access point, expanding the M-dimensional vector of the access point into an N-dimensional vector; specifically: The optimization problem to be solved is: ; Or it could be a noise error optimization problem: ,in The allowable noise threshold; By solving the optimization problem, an N-dimensional vector can be obtained. ; A high-density signal strength calculation module is used to perform an inverse transformation on each of the N-dimensional vectors to obtain an estimated value of the signal strength of the access point at the first reference point; The fingerprint database acquisition module is used to combine the estimated value of the signal strength of each access point on the first reference point and the coordinates of the corresponding first reference point to obtain a fingerprint database based on a high-density set of reference points. The module for obtaining the signal strength of the terminal to be located is used to obtain the signal strength of the access point of the terminal to be located in the positioning environment and record it as the first signal strength vector. The distance calculation module is used to calculate the distance between the first signal strength vector and the second signal strength vector of each row in the fingerprint database based on the high-density reference point set; The module for calculating the coordinates of the terminal to be located is used to take the k smallest distances among the distances and calculate the coordinates of the terminal to be located based on the coordinates of the corresponding second signal strength vector in the fingerprint database based on the high-density reference point set, so as to obtain the position of the terminal to be located.

5. The indoor positioning device based on a fingerprint database as described in claim 4, characterized in that, The module for calculating the coordinates of the terminal to be located specifically includes: Take the k smallest distances from the given distances, and denote them as: ; The coordinates of the corresponding second signal intensity vector are found in the fingerprint database based on the high-density reference point set, and denoted as: , ; Calculate the coordinates of the terminal to be located. , obtain coordinates ( , ).

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device containing the computer-readable storage medium to perform an indoor positioning method based on a fingerprint database as described in any one of claims 1 to 3.

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