A joint estimation indoor positioning method, system, medium and device

Abstract

The application discloses a kind of joint estimation indoor positioning method, system, medium and equipment, it is related to indoor positioning technical field, including each anchor node sends signal to neighbor anchor node and collects RSSI data, fitting to collection data, estimate the path loss index of each anchor node;It is carried out k-means clustering analysis, and the most centroid of index is taken as the final path loss index estimation value;Maximum likelihood estimation method and Huber loss are used to build positioning problem, and the positioning problem is converted into the joint optimization problem of mixed semi-definite quadratic cone programming;Through EM algorithm, mixed gaussian noise parameters are dynamically updated, the position of target node and anchor node transmission power are optimized synchronously each time iteration, and the final positioning result is output.The application realizes the positioning of target node in the case where there is malicious anchor node and gaussian mixture noise, improves the accuracy and efficiency of positioning.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of indoor positioning technology, and in particular to a joint estimation indoor positioning method, system, medium and device. BACKGROUND

[0002] An indoor positioning system is a system capable of positioning objects or devices in an environment where a global positioning system (GPS) cannot be used. The GPS consumes a large amount of energy in the positioning process, is relatively expensive to implement, and has poor accuracy, so it is often used for outdoor positioning.

[0003] Existing wireless sensor networks (WSN) are wireless networks formed by a large number of stationary or mobile sensors in a self-organizing and multi-hop manner, capable of detecting, processing and transmitting monitoring information of sensing objects within the network coverage area, and reporting to users, and can be applied to indoor positioning.

[0004] However, due to the simple structure of the wireless sensor network node, the limited storage space and computing power, the poor self-protection ability, and the difficulty in maintenance, it is easy to be attacked maliciously. Although some commonly used RSSI-based positioning algorithms have good performance (such as maximum likelihood estimation method, convex optimization and least squares method), they are all based on signal propagation models, and when the dynamic environment changes and the anchor node is maliciously attacked to cause the transmission power to be tampered with, the error of the traditional positioning algorithm will increase, thereby making it difficult to guarantee the accuracy of positioning. SUMMARY

[0005] The present application provides a joint estimation indoor positioning method, system, medium and device to solve the above problems existing in the prior art, i.e. how to achieve high-precision positioning in a dynamic environment and under malicious attacks in the prior art. The present application provides a joint estimation indoor positioning method, which comprises:

[0006] A plurality of anchor nodes are deployed in an indoor wireless sensor network, and each anchor node is respectively communicated with its neighbor anchor nodes to obtain first RSSI data;

[0007] The first RSSI data is analyzed by least squares fitting using a signal propagation model to estimate the path loss index of each anchor node, and the estimated path loss index is analyzed by k-means clustering, and the centroid with the most index is taken as the final path loss index estimate;

[0008] The anchor nodes respectively communicate with neighbor anchor nodes and target nodes to obtain second RSSI data; based on a signal propagation model, combining the second RSSI data and path loss exponent estimation values of the anchor nodes, a conditional joint probability density function of the transmission power of each anchor node and the position coordinates of each target node is constructed, a logarithmic term in the conditional joint probability density function is linearly approximated, and a Huber loss and an auxiliary variable are introduced to construct a semi-definite programming-second order cone programming (SDP-SOCP) problem;

[0009] The EM algorithm is used to iteratively update the mixed Gaussian noise parameters in the indoor wireless sensor network, and the iteration is stopped when the change of the mixed Gaussian noise parameters is less than a preset threshold, and the final parameter estimation value corresponding to the mixed Gaussian noise parameters is determined;

[0010] Based on the parameter estimation value, the estimated position coordinate vector of the target node and the distance scale parameter are determined by solving the semi-definite programming-second order cone programming (SDP-SOCP) problem, the estimated value of the position coordinates of the corresponding target node is obtained according to the estimated position coordinate vector of the target node, and the estimated value of the transmission power of the anchor node is obtained according to the distance scale parameter.

[0011] Optionally, the signal propagation model is an RSSI model, and specifically includes:

[0012] ;

[0013] Wherein, is the received power at the distance from the transmitter , is the path loss exponent, is the distance between the jth anchor node or target node and the ith anchor node, i is a reference distance, j is the received power of the jth anchor node or target node, is a mixed Gaussian noise. i

[0014] Optionally, the anchor nodes include normal anchor nodes and malicious anchor nodes.

[0015] Optionally, the elbow method is used for k-means clustering analysis of the path loss exponent.

[0016] Optionally, the first-order Taylor expansion method is used for linear approximation of the logarithmic term in the conditional joint probability density function.

[0017] Optionally, the semi-definite programming-second order cone programming (SDP-SOCP) problem is constructed by introducing a Huber loss and an auxiliary variable, specifically including:​​​

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] in, A Represents the set of anchor nodes. Represents the square of the Euclidean distance. r j For power-based distance scaling factor, Represents the selection matrix. Let j be the coordinates of the j-th anchor node. and The second of each of the 2M*2M identity matrices i- Column 1 and Column 2 i transpose of a column express It is a positive semidefinite form. This represents a positive semi-definite matrix of dimension 2M+1, and tr() represents the trace operation of the matrix elements. and Anchor nodes The set of neighbor anchor nodes and neighbor target nodes, R is the communication radius, t i For the first i The coordinates of the target node, This is the path loss index. For the first i The received power of each anchor node or target node, where Q is a 2M×2M symmetric matrix. Let i be the coordinates of the i-th anchor node. q =[ , ,..., ] T Represents the set of target node coordinates. This represents the transpose of the target node coordinate set q. To select matrix E i transpose, For the introduced auxiliary variables, ;

[0023] By introducing auxiliary variables Substituting the Huber constraint, Transform into: and ;in, For Huber threshold, is a constant offset term, is a Huber loss function.

[0024] Optionally, the obtaining an estimated value of the position coordinate of the target node according to the estimated position coordinate vector of the target node and obtaining an estimated value of the transmission power of the anchor node according to the distance scale parameter specifically comprises:

[0025]

[0026]

[0027] wherein, is an estimated position coordinate vector of the target node, is a distance scale parameter, is an estimated coordinate of the ith target node, is an estimated transmission power of the jth anchor node, represents a column vector composed of the 2i-1th to 2i th rows of the orientation vector, is a path loss exponent.

[0028] The application provides a joint estimation indoor positioning system, comprising:

[0029] a deployment module, configured to deploy a plurality of anchor nodes in an indoor wireless sensor network, and to obtain first RSSI data by respectively communicating each anchor node with its neighbor anchor nodes;

[0030] a path loss exponent estimated value determination module, configured to perform least square fitting analysis on the first RSSI data by using a signal propagation model, to estimate the path loss exponent of each anchor node, and to perform k-means clustering analysis on the estimated path loss exponent, and to take the centroid with the most indexes as the final path loss exponent estimated value;

[0031] a construction module, configured to respectively communicate each anchor node with its neighbor anchor nodes and target nodes to obtain second RSSI data, and to construct a conditional joint probability density function of the transmission power of each anchor node and the position coordinate of each target node based on the signal propagation model and in combination with the second RSSI data and the path loss exponent estimated value of each anchor node, to perform linearization approximation processing on the logarithmic term in the conditional joint probability density function, and to introduce a Huber loss and an auxiliary variable to construct a semi-definite programming-second order cone programming SDP-SOCP problem;

[0032] a parameter estimated value determination module, configured to perform iterative updating on a mixed Gaussian noise parameter existing in the indoor wireless sensor network by using an EM algorithm, to stop the iteration when the change of the mixed Gaussian noise parameter is less than a preset threshold, and to determine the final parameter estimated value corresponding to the mixed Gaussian noise parameter.​​

[0033] An estimation module is configured to determine the estimated position coordinate vector of the target node and the distance scale parameter by solving a semi-definite programming-second order cone programming (SDP-SOCP) problem based on the parameter estimation value, obtain the estimation value of the position coordinate of the corresponding target node according to the estimated position coordinate vector of the target node, and obtain the estimation value of the transmission power of the anchor node according to the distance scale parameter.

[0034] The application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the joint estimation indoor positioning method.

[0035] The application provides a computer device, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor realizes the joint estimation indoor positioning method when executing the program.

[0036] Compared with the prior art, the application has the following beneficial effects: the application provides a joint estimation indoor positioning method, which is based on a signal propagation model and obtains the path loss exponent corresponding to each anchor node by least square fitting, analyzes the obtained path loss exponent by clustering, takes the cluster with the largest sample number as the final estimated path loss exponent, and takes the transmission power of the anchor node and the target node coordinates as unknown quantities for estimation, which can effectively reduce the positioning error, and by embedding the EM algorithm into the optimization loop to form a closed loop iteration process of positioning solution, residual analysis and parameter update, the positioning accuracy is ensured and the algorithm complexity is reduced in the presence of malicious anchor nodes and Gaussian mixed noise. BRIEF DESCRIPTION OF DRAWINGS

[0037] The accompanying drawings, which are incorporated into and form part of the specification, illustrate embodiments consistent with the application and, together with the specification, serve to explain the principles of the application.

[0038] Figure 1 A flowchart of a joint estimation indoor positioning method provided by an embodiment of the application is shown in the figure.

[0039] Figure 2 A wireless sensor network positioning schematic diagram provided by an embodiment of the application is shown in the figure.

[0040] Figure 3 A curve of the normalized root mean square error NRMSE(t) changing with the Gaussian noise standard deviation is shown in the figure.

[0041] Figure 4 A curve of the normalized root mean square error NRMSE(t) changing with the number of target nodes is shown in the figure.

[0042] Figure 5 A comparison chart of cumulative error distribution provided for embodiments of the present invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0044] The technical solution of the present invention and how the technical solution of the present invention solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0045] Figure 1 This is a flowchart of a joint estimation indoor positioning method provided by an embodiment of the present invention, such as... Figure 1 As shown in this embodiment, a joint estimation indoor positioning method includes:

[0046] S1: Deploy multiple anchor nodes in an indoor wireless sensor network, and have each anchor node communicate with its neighboring anchor nodes to obtain the first RSSI data.

[0047] For example, N anchor nodes are reasonably deployed in the constructed indoor wireless positioning environment, and their set is as follows: , No. j The coordinates of the anchor nodes are The transmission power is Anchor nodes include both ordinary anchor nodes and malicious anchor nodes.

[0048] S2: The first RSSI data is subjected to least squares fitting analysis using a signal propagation model to estimate the path loss index of each anchor node. The estimated path loss index is then subjected to k-means clustering analysis, and the centroid with the most indexes is taken as the final path loss index estimate.

[0049] For example, the signal propagation model can be used to perform least-squares fitting on the acquired first RSSI data to achieve the following: j The path loss exponent β of each anchor node j The path loss indices of other anchor nodes are estimated in the same way, and finally the path loss indices of each anchor node are obtained, where all unattacked anchor nodes are included. All set to The estimated value is expressed as ,in, For the first j The path loss exponent β of each anchor node j The corresponding estimated values ​​were then subjected to k-means clustering analysis using the elbow method to obtain the final estimated path loss index. .

[0050] For example, the signal propagation model is the RSSI model, which specifically includes:

[0051] ;

[0052] in, For the first j The transmit power of each anchor node, This is the path loss index. For the first i The anchor node or target node and the first anchor node or target node and the first j The distance between anchor nodes For reference distance, For the first i The received power of each anchor node or target node (corresponding to the first RSSI data or the second RSSI data). For mixed Gaussian noise, ,in, For pollution ratio, The variance ratio of outlier noise. Let Variance be the variance of the Gaussian noise. This represents the standard deviation of noise.

[0053] For example, the estimated value is expressed as The elbow method can be used to analyze this data ( j A k-means clustering analysis is performed on the samples to divide them into k clusters. The mean of all samples in the cluster with the largest number of samples (i.e., the centroid with the most indexes) is calculated and used as the final estimate. .

[0054] S3: Each anchor node communicates with its neighboring anchor nodes and the target node to obtain the second RSSI data. Based on the signal propagation model, and combining the second RSSI data and the path loss index estimate of each anchor node, a conditional joint probability density function is constructed for the transmit power of each anchor node and the position coordinates of each target node. The logarithmic term in the conditional joint probability density function is linearized and approximated. By introducing Huber loss and auxiliary variables, a semidefinite programming-second-order cone programming (SDP-SOCP) problem is constructed.

[0055] For example, if the first jIf an anchor node is a malicious anchor node, then P j Not equal to Simultaneously, M target nodes are randomly deployed, and their set is as follows: , No. i The coordinates of the target node (unknown node) are: .

[0056] like Figure 2 As shown, a cooperative positioning method can be used, where anchor nodes can communicate with neighboring anchor nodes and the target node. All anchor nodes communicate with their neighboring anchor nodes and the target node, and collect the received signal strength, i.e., the second RSSI data. The anchor nodes send this data to the aggregation node, which then transmits the data to the fusion center via the Internet, satellite, wireless network, or other means.

[0057] For example, the conditional joint probability density function (PDF) is:

[0058] ;

[0059] In the formula, Representing the observed quantity, Represents an unknown quantity. Indicates the transmission power of each anchor node. Let A represent the set of coordinates of the target (unknown) nodes, and let A be the set of anchor nodes.

[0060] Based on the estimated value of w The target node coordinates and anchor node transmission power can be obtained using the following formula. :

[0061] ;

[0062] in,

[0063] ;

[0064] in, Let be the objective function. To observe the residuals, This is the Huber threshold.

[0065] By analyzing the noise of the signal received from the j-th anchor node at the i-th anchor node or target node. X ij Performing a first-order Taylor expansion yields

[0066] ;

[0067] in, , For the equivalent noise observation variance,

[0068] Can Transform into

[0069] ;

[0070] Introducing an auxiliary variable Q transforms the constraints into standard SDP constraints:

[0071] ;

[0072] ;

[0073] ;

[0074] In the formula, Represents the square of the Euclidean distance. For power-based distance scaling factor, Represents the selection matrix. and The second of each of the 2M*2M identity matrices i- Column 1 and Column 2 i The column transpose, tr() represents the trace operation of matrix elements. and Anchor nodes Let R be the set of neighbor anchor nodes and neighbor target nodes, and R be the communication radius. This represents the transpose of q. To select matrix E i The transpose of Q is a 2M×2M symmetric matrix, an auxiliary matrix related to coordinate estimation, used to characterize the uncertainty or error range of the position estimation. Constraints This ensures that the q and the auxiliary matrix Q satisfy mathematical consistency (i.e., (where is a positive semi-definite matrix), which corresponds to the non-negativity requirement of the position error covariance matrix in the physical world. Since the objective function is still non-convex and SOCP has low complexity, auxiliary variables are introduced to improve algorithm efficiency while maintaining high accuracy. The Huber loss is transformed into SOCP constraints, and the above SDP problem is restated as an SDP-SOCP problem. The specific construction process of the semidefinite programming-second-order cone programming SDP-SOCP problem can include:

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] in, Introducing the auxiliary variable, we use Huber loss to transform the piecewise function into a continuous constraint, i.e. and This can then be further transformed into SOCP constraints.

[0080] S4: The EM algorithm is used to iteratively update the mixed Gaussian noise parameters in the indoor wireless sensor network. The iteration stops when the change in the mixed Gaussian noise parameters is less than a preset threshold, and the final parameter estimate corresponding to the mixed Gaussian noise parameters is determined.

[0081] For example, since the noise is considered to follow a mixture Gaussian distribution, i.e. The EM algorithm can be used to estimate the mixture Gaussian noise parameters, and then iteratively update the mixture Gaussian noise parameters present in indoor wireless sensor networks. Specifically, this is achieved by introducing latent variables representing the noise generation sources. The parameters of the mixed Gaussian noise in the indoor wireless sensor network are iteratively updated, and the complete data likelihood function of the latent variable Z is:

[0082] ;

[0083] in, Main distribution, It is an outlier distribution, based on the current parameter estimates. ,calculate Posterior probability:

[0084] ;

[0085] in, for The posterior probability, For the i-th noise observation sample, The pollution ratio at the t-th iteration. The outlier noise variance ratio at the t-th iteration. Let be the noise standard deviation at the t-th iteration.

[0086] Update parameters To maximize the expected log-likelihood, the expected log-likelihood function is:

[0087] ;

[0088] The derivatives of each parameter are taken and set to zero to maximize the expected log-likelihood, and the parameters of the Gaussian mixture noise are updated. The specific calculation formulas for the updated Gaussian mixture noise parameters are as follows:

[0089] ;

[0090] ;

[0091] ;

[0092] When the parameter change is less than the threshold Stop the iteration when the time is right and obtain the final parameter estimates:

[0093] ;

[0094] in, The pollution ratio is the value of the (final) iteration in the (t+1)th iteration. The outlier noise variance ratio for the (t+1)th iteration (final) is... Let be the noise standard deviation of the (t+1)th iteration (final) .

[0095] S5: Based on the parameter estimates, the estimated position coordinate vector and distance scale parameter of the target node are determined by solving the semidefinite programming-second-order cone programming (SDP-SOCP) problem. The estimated position coordinates of the corresponding target node are obtained based on the estimated position coordinate vector of the target node, and the estimated transmit power of the anchor node is obtained based on the distance scale parameter.

[0096] For example, solving the SDP-SOCP problem may include: using the CVX toolkit to solve the optimization problem and obtain the estimated position coordinate vector of the target node. and distance scale parameters , then calculate and ,in, For the first i The estimated coordinates of each target node For the first j Estimated transmit power of each anchor node, This means taking rows 2i-1 to 2i of the vector to form a column vector. This is the path loss index.

[0097] Through the above steps, the path loss index of the current environment is calculated in real time. The anchor node's transmit power and the target node's coordinates are treated as unknowns. The noise parameters are estimated using the EM algorithm. The problem is iteratively optimized to estimate the anchor node's transmit power and the target node's coordinates.

[0098] Compared to traditional positioning methods, this embodiment not only considers that the path loss exponent is not a fixed value in dynamic environments, but also ensures positioning accuracy and low computational complexity even when the anchor node is maliciously attacked, causing changes in transmission power and mixed Gaussian noise.

[0099] To effectively evaluate the performance of the method described in this embodiment, the following evaluation metrics are introduced:

[0100] The normalized root mean square error (NRMSE) for estimating the target node coordinates is calculated as follows:

[0101] ;

[0102] in, For the first i The estimated coordinates of each target node In the m-th Monte Carlo simulation, the first... i The estimated coordinates of each target node It represents the number of Monte Carlo simulations.

[0103] Figure 3 and Figure 4 They are respectively The curves showing the changes in Gaussian noise standard deviation and the number of target nodes were compared with those of the Least Median Squaring (LMS), Least Squares (LLS), Cramerlow's Lower Bound (CRLB), and the Cooperative Secure Localization (CLGM) algorithm based on a Gaussian Mixture Robust Model proposed in this invention. Among them, CLGM showed better performance.

[0104] Figure 5 The graph shows a comparison of the cumulative error distributions of LMS, LLS, and the algorithm of this embodiment. It can be seen from the graph that the error of this embodiment is significantly smaller than that of the traditional algorithm.

[0105] The above describes a joint estimation indoor positioning method provided by one or more embodiments of this specification. Based on the same idea, this specification also provides a corresponding joint estimation indoor positioning system, including:

[0106] The deployment module is used to deploy multiple anchor nodes in an indoor wireless sensor network, and to enable each anchor node to communicate with its neighboring anchor nodes to obtain the first RSSI data.

[0107] The path loss index estimation module is used to perform least squares fitting analysis on the first RSSI data using a signal propagation model to estimate the path loss index of each anchor node, and to perform k-means clustering analysis on the estimated path loss index, taking the centroid with the most indexes as the final path loss index estimate.

[0108] The module is used to enable each anchor node to communicate with its neighboring anchor nodes and the target node to obtain the second RSSI data. Based on the signal propagation model, combined with the second RSSI data and the path loss index estimate of each anchor node, the conditional joint probability density function of the transmit power of each anchor node and the position coordinates of each target node is constructed. The logarithmic term in the conditional joint probability density function is linearized and approximated. By introducing Huber loss and auxiliary variables, a semidefinite programming-second-order cone programming (SDP-SOCP) problem is constructed.

[0109] The parameter estimation module is used to iteratively update the mixed Gaussian noise parameters in the indoor wireless sensor network using the EM algorithm. The iteration stops when the change in the mixed Gaussian noise parameters is less than a preset threshold, and the final parameter estimate corresponding to the mixed Gaussian noise parameters is determined.

[0110] The estimation module is used to determine the estimated position coordinate vector and distance scale parameter of the target node by solving the semidefinite programming-second-order cone programming (SDP-SOCP) problem based on the parameter estimation value. It obtains the estimated position coordinate value of the corresponding target node based on the estimated position coordinate vector of the target node, and obtains the estimated value of the transmit power of the anchor node based on the distance scale parameter.

[0111] Specific limitations regarding the joint estimation indoor positioning system can be found in the limitations of the joint estimation indoor positioning method described above, and will not be repeated here. Each module in the aforementioned joint estimation indoor positioning system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0112] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the joint estimation indoor positioning method provided above.

[0113] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described joint estimation indoor positioning method.

[0114] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0115] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this invention.

Claims

1. A joint estimation method for indoor positioning, characterized in that, include: In an indoor wireless sensor network, multiple anchor nodes are deployed, and each anchor node communicates with its neighboring anchor nodes to obtain the first RSSI data. The first RSSI data was subjected to least squares fitting analysis using a signal propagation model to estimate the path loss index of each anchor node. The estimated path loss index was then subjected to k-means clustering analysis, and the centroid with the most indexes was taken as the final path loss index estimate. Each anchor node communicates with its neighboring anchor nodes and the target node to obtain second RSSI data. Based on the signal propagation model, and combining the second RSSI data and the path loss index estimate of each anchor node, a conditional joint probability density function of the transmit power of each anchor node and the position coordinates of each target node is constructed. The logarithmic term in the conditional joint probability density function is linearized and approximated. By introducing Huber loss and auxiliary variables, a semidefinite programming-second-order cone programming (SDP-SOCP) problem is constructed. The EM algorithm is used to iteratively update the mixed Gaussian noise parameters in the indoor wireless sensor network. The iteration stops when the change in the mixed Gaussian noise parameters is less than a preset threshold, and the final parameter estimate corresponding to the mixed Gaussian noise parameters is determined. Based on the parameter estimates, the estimated position coordinate vector and distance scale parameter of the target node are determined by solving the semidefinite programming-second-order cone programming (SDP-SOCP) problem. The estimated position coordinates of the corresponding target node are obtained based on the estimated position coordinate vector of the target node, and the estimated transmit power of the anchor node is obtained based on the distance scale parameter. The process of obtaining the estimated position coordinates of the target node based on the estimated position coordinate vector of the target node, and obtaining the estimated transmission power of the anchor node based on the distance scale parameter, specifically includes: ； ； in, Let be the estimated position coordinate vector of the target node. For distance scale parameters, Let be the estimated coordinates of the i-th target node. Let j be the estimated transmit power of the j-th anchor node. This means taking rows 2i-1 to 2i of the vector to form a column vector. This is the path loss index.

2. The joint estimation indoor positioning method as described in claim 1, characterized in that, The signal propagation model is the RSSI model, specifically including: ； in, For distance from the transmitter The received power at that location, This is the path loss index. For the first i The anchor node or target node and the first anchor node or target node and the first j The distance between anchor nodes For reference distance, For the first i The received power of each anchor node or target node. It is mixed Gaussian noise.

3. The joint estimation indoor positioning method as described in claim 1, characterized in that, The anchor nodes include ordinary anchor nodes and malicious anchor nodes.

4. The joint estimation indoor positioning method as described in claim 1, characterized in that, The path loss index was analyzed using k-means clustering with the elbow method.

5. The joint estimation indoor positioning method as described in claim 1, characterized in that, The logarithmic term in the conditional joint probability density function is linearized using a first-order Taylor expansion method.

6. The joint estimation indoor positioning method as described in claim 1, characterized in that, The method of constructing a semidefinite programming-second-order cone programming (SDP-SOCP) problem by introducing Huber loss and auxiliary variables specifically includes: in, A Represents the set of anchor nodes. Represents the square of the Euclidean distance. r j For power-based distance scaling factor, Represents the selection matrix. Let j be the coordinates of the j-th anchor node. and The second of each of the 2M*2M identity matrices i- Column 1 and Column 2 i transpose of a column express It is a positive semidefinite form. This represents a positive semi-definite matrix of dimension 2M+1, and tr() represents the trace operation of the matrix elements. and Anchor nodes The set of neighbor anchor nodes and neighbor target nodes, R is the communication radius, t i For the first i The coordinates of the target node, This is the path loss index. For the first i The received power of each anchor node or target node, where Q is a 2M×2M symmetric matrix. Let i be the coordinates of the i-th anchor node. q =[ , ,..., ] T Represents the set of target node coordinates. This represents the transpose of the target node coordinate set q. To select matrix E i transpose, For the introduced auxiliary variables, ; By introducing auxiliary variables Substituting the Huber constraint, Transform into: and ;in, For Huber threshold, For constant offset terms, Here is the Huber loss function.

7. A joint estimation indoor positioning system, characterized in that, Implementing the joint estimation indoor positioning method according to any one of claims 1-6, comprising: The deployment module is used to deploy multiple anchor nodes in an indoor wireless sensor network, and to enable each anchor node to communicate with its neighboring anchor nodes to obtain the first RSSI data. The path loss index estimation module is used to perform least squares fitting analysis on the first RSSI data using a signal propagation model to estimate the path loss index of each anchor node, and to perform k-means clustering analysis on the estimated path loss index, taking the centroid with the most indexes as the final path loss index estimate. The module is used to enable each anchor node to communicate with its neighboring anchor nodes and the target node to obtain the second RSSI data. Based on the signal propagation model, combined with the second RSSI data and the path loss index estimate of each anchor node, the conditional joint probability density function of the transmit power of each anchor node and the position coordinates of each target node is constructed. The logarithmic term in the conditional joint probability density function is linearized and approximated. By introducing Huber loss and auxiliary variables, a semidefinite programming-second-order cone programming (SDP-SOCP) problem is constructed. The parameter estimation module is used to iteratively update the mixed Gaussian noise parameters in the indoor wireless sensor network using the EM algorithm. The iteration stops when the change in the mixed Gaussian noise parameters is less than a preset threshold, and the final parameter estimate corresponding to the mixed Gaussian noise parameters is determined. The estimation module is used to determine the estimated position coordinate vector and distance scale parameter of the target node by solving a semidefinite programming-second-order cone programming (SDP-SOCP) problem based on the parameter estimation values. It then obtains the estimated position coordinates of the corresponding target node based on the estimated position coordinate vector and the estimated transmit power of the anchor node based on the distance scale parameter. Specifically, obtaining the estimated position coordinates of the corresponding target node based on the estimated position coordinate vector and the estimated transmit power of the anchor node based on the distance scale parameter includes: ； ； in, Let be the estimated position coordinate vector of the target node. For distance scale parameters, Let be the estimated coordinates of the i-th target node. Let j be the estimated transmit power of the j-th anchor node. This means taking rows 2i-1 to 2i of the vector to form a column vector. This is the path loss index.

8. A computer-readable storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, implements the joint estimation indoor positioning method according to any one of claims 1-6.

9. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the joint estimation indoor positioning method according to any one of claims 1-6.

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