An Indoor Positioning Method, System, Medium and Device Based on an Improved WGP Model

Abstract

The present invention relates to an indoor positioning method, system, medium and device based on an improved WGP model, belonging to the field of positioning technology. Based on warped Gaussian process regression and WiFi fingerprint positioning, a two-stage indoor positioning algorithm including offline sampling and fingerprint matching is proposed. In the offline stage, the WGP model is applied to process the output observations by performing a non-linear transformation on the parameters of the Gaussian process. WiFi fingerprint data usually contains non-Gaussian noise, and traditional GPR has limitations in fitting these signal strengths. Therefore, the present application adopts the WGP model. The WGP model not only utilizes the statistical characteristics of the traditional Gaussian process, but also enhances its flexibility through non-linear transformation, thus more effectively dealing with non-Gaussian noise. In terms of accuracy and confidence interval, the WGP model performs better than the standard GPR and the more advanced polynomial Gaussian process regression.

Description

Technical Field

[0001] The present invention relates to the technical field of positioning, and in particular to an indoor positioning method, system, medium and device based on an improved WGP model. Background Technique

[0002] In recent years, with the rapid growth of the penetration rate of mobile devices, the application of location-based services (LBS) in various intelligent buildings has become increasingly widespread. This technology has become an indispensable part of daily life, and the effect of LBS depends to a large extent on the positioning accuracy. The Global Navigation Satellite System (GNSS) can provide sub-meter positioning accuracy for most outdoor LBS scenarios, but the premise is that there must be a good line-of-sight (Los) transmission channel between the satellite and the indoor receiver. However, in an indoor environment, due to signal blockage, GNSS cannot provide sufficient positioning accuracy. Therefore, a reliable indoor positioning and navigation system that can provide precise positioning and navigation in an indoor environment where GNSS signals are blocked is needed. Now, almost all buildings are covered by various WiFis, which may be the infrastructure of some networks or the hotspots of some mobile devices. Due to the characteristics of low cost, low power consumption, easy deployment and high existing deployment rate of Wi-Fi technology, the indoor positioning scheme based on Wi-Fi signal strength value is one of the most promising indoor positioning schemes and also the most widely used scheme.

[0003] The indoor positioning technology based on Wi-Fi is mainly divided into two types: based on propagation model and based on Wi-Fi fingerprint. In the propagation model technology, it mainly relies on the Log-Distance Path Loss (LDPL) model to model the wireless signal environment, and then estimates its position by measuring the received signal strength (RSS) of the target device. However, this method is greatly affected by the environment and it is difficult to accurately construct a dynamically changing indoor environment model, which will seriously affect its positioning accuracy. The positioning technology based on Wi-Fi fingerprint does not rely on range estimation and can better represent the real-time changing indoor signal, and is more suitable for the indoor environment than the propagation model.

[0004] The method based on Wi-Fi fingerprint mainly has two steps: 1) Offline sampling stage: By on-site survey and recording the RSS values received from each access point (AP access point) at the reference point (RP), together with the two-dimensional position coordinates of the reference point, an offline fingerprint database is formed. 2) Online matching stage: Matching the RSS values received at the position to be measured from multiple AP access points with the offline fingerprint database to estimate the position coordinates of the point to be measured.

[0005] There are still some problems to be solved in the indoor positioning technology based on the WiFi fingerprint method. For example, when constructing an offline fingerprint database, a large amount of manpower and material resources need to be invested in the preliminary on-site survey. Moreover, the fingerprint-based positioning method highly depends on the established fingerprint database. Its positioning accuracy largely depends on the density of reference points in the fingerprint database. The more reference points are measured, the denser the generated fingerprint database is, and the higher the positioning accuracy will be. However, at the same time, the cost invested in the early stage will also increase. And if the indoor layout changes or new obstacles appear, it will be very difficult for the original fingerprint database to adapt to the new environment after the change, which causes great trouble for the later maintenance and update. Therefore, a solution that can reduce the workload of the preliminary survey, estimate other reference points based on a small number of reference points to expand the fingerprint database, and can calibrate the fingerprint database in real time according to the environmental changes has become a research hotspot.

[0006] Existing scholars have proposed a Gaussian process regression (GPR) algorithm, which uses the spatial correlation between reference points to calibrate and expand the fingerprint database according to the collected reference point information. There are also scholars who have proposed an LDM_GPR (Log-Distance GPR) algorithm that uses the GPR model to model the RSS error residuals that cannot be simulated by the LDPL model for the characteristics of the indoor environment, improving the performance in dealing with large-scale data sets or complex environments. There are also scholars who have proposed a POLY_GPR (Polynomial Gaussian Process Regression) that uses a polynomial kernel function within the framework. The input features are expanded through polynomial transformation, which can better capture the nonlinear relationship and complex patterns between the input data and improve the prediction performance of the model.

[0007] Considering that in practical applications, the distributions of observed values do not all follow a Gaussian distribution. However, POLY-GPR assumes that the data distribution is Gaussian and fails to fully solve the non-Gaussian problem of the received signal strength (RSS) data in indoor positioning. When dealing with complex signal environments, the positioning results are not accurate and stable enough. Summary of the Invention

[0008] In order to overcome the above-mentioned disadvantages that the positioning results are not accurate and stable enough when the existing technology deals with complex signal environments, the main purpose of the present invention is to provide an indoor positioning method, system, medium and device based on an improved WGP model.

[0009] To achieve the above object, the present invention adopts the following technical solutions. An indoor positioning method based on an improved WGP model includes:

[0010] Obtain the coordinate positions and signal strengths of the reference points, and divide them into known reference points and estimated reference points;

[0011] Based on the POLY_GPR model, warp the parameters in its objective function, map and distort the signal strengths of the known reference points to a high-dimensional space through a non-linear monotonic function, obtain the signal strengths of the mapped known reference points, and then take the partial derivative of the signal strengths of the mapped known reference points using the negative log-likelihood function to obtain the mapped values of the signal strengths of the predicted estimated reference points;

[0012] Map the mapped values of the signal strengths of the predicted estimated reference points back to the true values, obtain the signal strengths of the predicted estimated reference points, and combine the signal strengths of the known reference points and the predicted estimated reference points to obtain an expanded fingerprint database;

[0013] Obtain the signal strength of the unknown point, and perform online positioning on the unknown point based on the expanded fingerprint database through the K-weighted nearest neighbor matching algorithm KNN to obtain the coordinate position of the unknown point.

[0014] Further, mapping and distorting the signal strengths of the known reference points to a high-dimensional space through a non-linear monotonic function includes:

[0015] For each observed data point , transform it through a monotonic function to obtain the data point in the latent space :

[0016]

[0017] represents the observed data point, which is the data point before warping; is the parameter set of the function , represents the wifi signal strength values from each access point in the detected space, represents the noise in the environment.

[0018] The monotonic function is selected as the hyperbolic tangent function, expressed as:

[0019]

[0020] where, controls the amplitude of each tanh function, that is, the height or influence degree of each step, controls the steepness of each tanh function, that is, the slope of the curve or the sharpness of the transition, controls the position or offset of each tanh function on the time axis, is the number of tanh in the function;

[0021] The hyperbolic tangent function is bounded and is corrected by adding a linear term to obtain the following formula:

[0022] .

[0023] The negative log-likelihood function is expressed as follows:

[0024]

[0025] where is the representation of the observed data points in the latent space after transformation, representing the relationship between the observed data and the latent feature space; : is the Jacobian term, representing the derivative of the transformation function, ensuring monotonicity during the transformation process and its impact on likelihood calculation; : is the data point index, used to calculate the partial derivative Jacobian determinant for each data point, : is the number of observed data;

[0026] The Jacobian term is introduced into the negative log-likelihood, where the negative log-likelihood is expressed as follows:

[0027]

[0028] where is the latent target vector, serving as the target for fitting and prediction, is the set of reference points, is the set of hyperparameters, is the covariance matrix constructed in the latent space.

[0029] The formula to be measured for predicting the mapped value of the reference point signal strength is:

[0030]

[0031] where is the predicted value of the signal strength at the point to be measured based on POLY-GPR, represents the warped value of the signal strength at the known location, is the warped value of the signal strength value fitted by the POLY-GPR model at the known location, is the predicted value of the signal strength at the point to be measured based on POLY-GPR;

[0032] For the known location reference point After warping the predicted value using the POLY-GPR model, it is given by the following formula:

[0033]

[0034] The coordinate position of the unknown point includes the following steps:

[0035] Take the position point of the unknown point as the target position, and obtain the position information and signal strength of the reference points around the target position;

[0036] Use the Euclidean distance to obtain the distance between the target position and each reference point;

[0037] Select the K reference points closest to the target position;

[0038] Take the position coordinates of these K neighbors as the estimate of the target position through weighted average to obtain the coordinate position of the unknown point.

[0039] A system for an indoor positioning method based on an improved WGP model includes:

[0040] An acquisition module for obtaining the coordinate position and signal strength of the reference points in the indoor fingerprint database, and dividing them into known reference points and estimated reference points;

[0041] A fingerprint expansion and calibration module warps the parameters in its objective function based on the POLY_GPR model, maps and distorts the signal strength of the known reference points to a high-dimensional space through a non-linear monotonic function to obtain the signal strength of the mapped known reference points, and then takes the partial derivative of the signal strength of the mapped known reference points using the negative log-likelihood function to obtain the mapped value of the predicted signal strength of the estimated reference points; maps the mapped value of the predicted signal strength of the estimated reference points back to the true value to obtain the signal strength of the predicted estimated reference points, and combines the signal strength of the known reference points and the predicted estimated reference points to obtain an expanded fingerprint database;

[0042] A positioning module for obtaining the signal strength of the unknown point, and performing online positioning on the unknown point based on the expanded fingerprint database through the K-weighted nearest neighbor matching algorithm KNN to obtain the coordinate position of the unknown point.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows: It can automatically expand and calibrate the offline fingerprint database to achieve indoor positioning without calibration. To construct a more refined radio map, the WPG model is further proposed. This is a technology that maps the observed values to a high-dimensional space through a complex function so that they have a more reliable regression in the high-dimensional space. It is specifically used to predict the RSS value of WiFi signals and can well capture the uneven RSS distribution in a complex indoor environment. Compared with the traditional offline calibrated RSS database, it can better adapt to the dynamic changes of the environment and continuously update the measurement results. It solves the problem that the positioning results are not accurate and stable enough due to noise in a complex signal environment. By warping the parameter values in the objective function, twisting them into a high-dimensional space and making their distribution in the high-dimensional space conform to the Gaussian distribution, and then using an improved Gaussian regression model in the high-dimensional space to predict the measurement points, and finally mapping the data back to the true value to achieve the purpose of expanding the fingerprint database. Through non-linear transformation, its flexibility is enhanced, thus more effectively dealing with non-Gaussian noise. In terms of accuracy and confidence interval, the WGP model performs better than the standard GPR and the more advanced polynomial Gaussian process regression, making the positioning results more accurate and stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The schematic embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation to the present application.

[0045] Figure 1 It is a schematic diagram of the system framework of the present invention;

[0046] Figure 2 It is a schematic diagram of the layout of the multi-room experimental area and its reference points in Embodiment 1 of the present invention;

[0047] Figure 3 It is a schematic diagram comparing the RSS estimation errors of different methods in Embodiment 1 of the present invention;

[0048] Figure 4 It is a schematic diagram of the error integral curve in Embodiment 1 of the present invention;

[0049] Figure 5 It is a schematic diagram of the positioning error broken line in Embodiment 1 of the present invention;

[0050] Figure 6 It is a schematic diagram of the layout of the single-room experimental area and its reference points in Embodiment 2 of the present invention;

[0051] Figure 7 It is a schematic diagram comparing the RSS estimation errors of different methods in Embodiment 2 of the present invention;

[0052] Figure 8is a schematic diagram of an error integral curve in Example 2 of the present invention;

[0053] Figure 9 It is a schematic diagram of the positioning error line in Example 2 of the present invention. DETAILED DESCRIPTION

[0054] The present invention will be further described below in conjunction with the accompanying drawings and implementation modes.

[0055] The WiFi fingerprint-based approach has two main steps:

[0056] 0) Offline sampling stage: Through on-site survey and recording of the RSS values ​​received from each access point (AP) at the reference point (RP), together with the two-dimensional position coordinates of the reference point, an offline fingerprint database is constructed.

[0057] 2) Online matching stage: The RSS values ​​received from multiple AP points at the location to be measured are matched with the offline fingerprint database to estimate the location coordinates of the location to be measured.

[0058] However, there are still some problems that need to be solved in the indoor positioning technology based on WiFi fingerprint. For example, when building an offline fingerprint database, a lot of manpower and material resources are needed for preliminary on-site surveys. In addition, the fingerprint-based positioning method is highly dependent on the established fingerprint library, and its positioning accuracy depends to a large extent on the density of reference points. The more reference points are measured, the denser the generated fingerprint library is, and the higher the positioning accuracy is, but at the same time, the cost of the initial investment will increase accordingly. Moreover, if the indoor layout changes or new obstacles appear, the original fingerprint library will be difficult to adapt to the new environment, which will bring great difficulties to the subsequent maintenance and update [. Therefore, studying a method that can reduce the workload of preliminary surveys, estimate other reference points based on a small number of reference points to expand the fingerprint library, and calibrate the fingerprint library in real time according to environmental changes has become a current research hotspot.

[0059] In the prior art, a Gaussian process regression (GPR) algorithm was proposed in "Gaussian Processes for Machine Learning", which calibrates and expands the fingerprint database by using the spatial correlation between reference points according to the collected reference point information. A Log-Distance Gaussian Process Regression (LDM-GPR) algorithm was proposed in "Dynamic Online Calibration of Radio Maps for Indoor Positioning in Wireless Local Area Networks", which uses a GPR model to model the RSS error residuals that cannot be simulated by the Log-Distance Path Loss model (LDPL) for the characteristics of the indoor environment, improving the performance in dealing with large-scale data sets or complex environments. A Polynomial Gaussian Process Regression (POLY-GPR) using a polynomial kernel function within the framework was proposed in "WiFi-Based Non-Intrusive Indoor Positioning System with Online Radio Map Construction and Adaptation Function". The input features are expanded through polynomial transformation, which can better capture the nonlinear relationships and complex patterns between the input data, improving the prediction performance of the model. However, POLY-GPR assumes that the data distribution is Gaussian and fails to fully address the non-Gaussianity problem of Received Signal Strength (RSS) data in indoor positioning.

[0060] In contrast, the Warped Gaussian Process (WGP) addresses the limitation of non-Gaussian distributed RSS data by introducing a non-linear transformation. WGP can not only capture the non-linear relationships between input data, but also make the data closer to a Gaussian distribution through non-linear transformation of the observed data, thus showing higher accuracy and reliability in model fitting and prediction. In addition, WGP performs well in dealing with errors and uncertainties, can provide a more reasonable confidence interval, and significantly improves the robustness of the model in complex indoor environments. Therefore, WGP shows obvious innovation and advantages in indoor positioning applications, making it a superior choice compared to traditional GPR and POLY-GPR.

[0061] In the prior art, the GPR-based prediction model will perform special preprocessing on the data before modeling to achieve the transformation of the observed variables. However, its basic assumptions are all: under the given input conditions, the output data of the objective function follows a multivariate Gaussian distribution, and the noise at each observation point is Gaussian noise with the same variance as the data. However, in practical applications, the observed values may all be negative or have greatly varying orders of magnitude. In this case, directly assuming homoscedastic Gaussian noise for modeling is very inaccurate. The RSS values of WiFi cannot be modeled using a simple multivariate Gaussian process model either. Usually, the method adopted by most literature is to perform a logarithmic transformation on the data to make it more in line with the assumptions of the Gaussian process for better modeling. However, if this transformation is only used as a preprocessing step, it obviously does not consider the parameter uncertainty of the transformation itself and its impact on the model structure, nor does it form an integrated probabilistic inference with other parts of the model. This is also inaccurate.

[0062] In the present invention, a GPR model that can self-learn and apply the best transformation is proposed, called WGP. The WGP model is actually a GPR model that can self-learn and apply the best transformation. Compared with the original or improved GPR model, WGP uses the method of non-linear monotonic functions to transform the data from one observation space to another latent space. This method can establish a more complex relationship between the observed values and the latent variables, rather than a simple linear mapping. It can better capture non-linear relationships and data characteristics, provide uncertainty quantification and credibility intervals, making the model more interpretable.

[0063] When introducing the WGP model, a non-linear warping transformation method is adopted to map the data points in the observation space to the data points in the latent space . This process can capture complex non-linear relationships As the latent target vector, it participates in the fitting and prediction of the model. The parameter set defines the specific form of this transformation. The covariance matrix is used to represent the relationship between the data points in the latent space, providing the basic structure for modeling. The reference point set is the basis for constructing the model. This mapping can make the observed data more in line with the Gaussian model, and the negative log-likelihood is:

[0064] (1)

[0065] where is the latent target vector, serving as the target for fitting and prediction. is the reference point set. is the hyperparameter set. is the covariance matrix constructed in the latent space.

[0066] For each observed data point , through the monotonic function , parameterized as transform to obtain the data point in the latent space :

[0067] (2)

[0068] where, : represents the observed data point, which is the data point before warping. is the parameter set of the function , and these parameters define the specific form and characteristics of the transformation. During the warping process, the function must be monotonic to ensure that the transformed data still maintains the order relationship. Monotonicity ensures that the mapping does not produce reverse order phenomena. The mapping should cover the entire real number domain for complete probability modeling. To ensure the correctness of the probability distribution during the warping process, a Jacobian term is introduced into formula (1):

[0069] (3)

[0070] represents the negative log-likelihood function, which is used to calculate the fitting degree of the model and includes the determinant of the covariance matrix and the Jacobian term. is the representation in the latent space after transformation, reflecting the relationship between the observed data and the latent features. is the Jacobian term, representing the derivative of the transformation function, ensuring monotonicity during the transformation process and its impact on likelihood calculation. : data point index, used to calculate the partial derivative Jacobian determinant of each data point. is the number of observed data.

[0071] In the selection of the warping function , finally, the hyperbolic tangent (tanh) function is selected as the warping function:

[0072] (4)

[0073] where, controls the amplitude of each tanh function, that is, the height or influence degree of each step. controls the steepness of each tanh function, that is, the slope of the curve or the sharpness of the transition. controls the position or offset of each tanh function on the time axis. is the number of tanh in the function, which determines the complexity of the function. More tanh functions can construct more complex transformations. In this application, through multiple experiments, is fixed at 5.

[0074] For the warping function constructed by formula (4), since the tanh function itself is bounded and the output is in the range of [-1, 1], while in the latent space the data is Gaussian distributed, which means theoretically it should cover the entire real line, which will lead to when exceeds certain ranges, its inverse function cannot be defined, and thus the corresponding value cannot be found and the inverse mapping fails. Therefore, the present invention uses the following formula to correct this problem:

[0075] (5)

[0076] By adding a linear term, the entire function can be linearly extended, breaking through the boundedness caused by solely relying on the tanh function.

[0077] The prediction formula of WGP is:

[0078] (6)

[0079] Since the warping transformation is performed on the observed data, it is very difficult to calculate the inverse function of the warping function. In this case, the Genetic Algorithm (GA), as a global optimization method, provides an effective numerical solution. The genetic algorithm is known for its independence from the continuity and differentiability of the function and is suitable for solving various complex optimization problems including inverse functions.

[0080] In the model of WGP fused with POLY - GPR, the prediction formula of the signal strength at the point to be measured is updated to:

[0081] (7)

[0082] Where is the predicted value of the signal strength at the measurement point based on POLY - GPR. represents the value of the warped signal strength at the known location. And is the value of the warped signal strength value fitted by the POLY - GPR model at the known location. is the predicted value of the signal strength at the point to be measured based on POLY - GPR.

[0083] In addition, for the known location reference point After warping the predicted values using the POLY-GPR model, they are given by the following formula:

[0084] (8)

[0085] Example:

[0086] To comprehensively evaluate the performance of the WGP algorithm, experiments were conducted in an experimental space consisting of a corridor and two rooms on each side of the corridor. The layout of the experimental area is as Figure 2 shown. Ideal traditional test areas usually use corridors or open spaces as test platforms, which is beneficial for data modeling. This experimental environment includes a corridor and four asymmetric and functionally different rooms on both sides of the corridor, and the overall area presents an irregular shape. Such a complex indoor environment is more suitable for evaluating the performance of the WGP algorithm than an ideal environment.

[0087] During the experiment, by analyzing the presence of WiFi signals, an adaptive screening algorithm was used to determine the four access points (APs) with the largest signal coverage area. This adaptive screening method can make more effective use of existing APs without strict layout requirements for the specific positions of APs, and at the same time improves the generality and applicability of the algorithm. In this experiment, 57 reference points were collected as Figure 2 shown by the circles in, and the position information and RSS values of each reference point were recorded to establish an initial fingerprint database. Subsequently, 20% of the data points were randomly selected from the fingerprint database for the expansion calculation of the fingerprint database. An additional 34 test points were used to evaluate the accuracy of the positioning algorithm.

[0088] For the RSS estimation accuracy, first, experiments on the RSS estimation accuracy were carried out by expanding the fingerprint database using different prediction models. The real-time RSS measurement values of the four access points collected were summarized into a 12*4 RSS matrix. Using these data, ZERO-GPR, POLY-GPR, and WGP were used to predict the RSS values of the remaining 80%, that is, 45 reference points, and error analysis was performed. Figure 3 And Table 1 compares the errors between the average RSS values predicted by three different methods of ZERO-GPR, POLY-GPR, and WGP and the actual RSS values of the reference points.

[0089] Table 1: Estimation Errors of RSS for Different Access Points by Zero-GPR, POLY-GPR, and WGP

[0090]

[0091] The results show that the average RSS estimation error of WGP is the smallest among the four methods. In addition, the standard deviation of the RSS error of WGP is also the lowest, indicating that the RSS values predicted by WGP are more stable than those of other methods.

[0092] For the positioning estimation accuracy, the coordinates are calculated by using the fingerprint databases augmented with different models. Thirty-four new points are randomly selected in the experimental area as test points. For the fingerprint databases augmented with different models, after passing through the KNN positioning algorithm, the calculated coordinates are compared with the true coordinates to verify the positioning estimation accuracy of different models.

[0093] When evaluating the performance of the positioning algorithm, common metrics include positioning error, Cumulative Distribution Function (CDF), etc.

[0094] As Figure 4 shown, the Cumulative Distribution Function (CDF) graph shows the cumulative probability distribution of three different positioning algorithms (ZERO-GPR, POLY-GPR, WGP) in terms of positioning error. It can be seen from the graph that: WGP (black solid line) performs better than the other two algorithms in the vast majority of positioning error ranges. Especially when the positioning error is small, its cumulative probability increases rapidly. This indicates that WGP can achieve a smaller positioning error at most test points. ZERO-GPR (red dashed line) and POLY-GPR (blue dashed line) have a slower increase in cumulative probability when the positioning error is small. Especially, the performance of ZERO-GPR is significantly worse than that of POLY-GPR. As the positioning error increases, POLY-GPR gradually exceeds ZERO-GPR, showing its superiority in the medium error range. When the positioning error is less than 15 meters, the cumulative probability of WGP has exceeded 0.8, indicating that it has better error control at most test points. In contrast, ZERO-GPR and POLY-GPR require a larger error range to achieve the same cumulative probability.

[0095] In summary, WGP performs the best in terms of overall positioning accuracy, especially when the error is small, its advantage is particularly obvious. POLY-GPR ranks second, while ZERO-GPR performs the worst.

[0096] As Figure 5As shown, the positioning error map of each test point shows the specific error conditions of the three algorithms at each test point. There are significant fluctuations in the errors of the three algorithms at different test points. The error change trends of WGP and POLY-GPR are relatively close, indicating that there is a certain consistency between these two methods in terms of error control. The error of ZERO-GPR fluctuates greatly, showing a significant increase in error at multiple test points. The positioning error of WGP at certain test points such as the 3rd, 14th, and 27th test points is significantly smaller than that of the other two algorithms, demonstrating its local advantage in specific situations. These test points may correspond to environments with more complex signals or more interference. Through the non-linear mapping and parameter optimization of its model, WGP can better adapt to these complex environments. Generally speaking, the positioning error of WGP is relatively stable at most test points and is less than 10 meters in most cases. Although POLY-GPR also shows relatively small errors at some test points, its stability is slightly inferior to that of WGP. The error of ZERO-GPR is large and fluctuates violently, indicating its deficiency in dealing with complex signal environments.

[0097] Example 2

[0098] In the experiment on the single-room test site, a 14m * 11m laboratory was selected as the test site. Floor tiles (0.6m * 0.6m) were used as the standard for area division and for surveying reference points. A total of 9 points were selected as reference points.

[0099] In this experiment, by detecting the existing wifi signals in the environment and using the adaptive screening algorithm, the 4 AP points with the largest amount of information were screened out, and 42 reference points were collected. Figure 6 The circles in [], and a fingerprint database was established based on this, and 20% were randomly selected. Figure 6 The 9 triangles in [], and the fingerprint database was expanded by combining the fingerprint database expansion algorithm. 16 additional test points were collected. Figure 6 The asterisks in [], which were used to finally detect the positioning accuracy of the positioning algorithm.

[0100] For the RSS estimation accuracy, the position coordinates and RSS values of 9 reference points were used as data, and ZERO-GPR, POLY-GPR, and WGP were used to predict the RSS values of the remaining 80%, that is, 33 reference points, and comparisons were made. Figure 7 The RSS prediction errors of the three different methods were compared with Table 2.

[0101] Table 2: Estimation Errors of Zero-GPR, POLY-GPR, and WGP for RSS of Different Access Points

[0102]

[0103] It can be concluded that the average RSS estimation error of WGP is the smallest among the four methods. In addition, the standard deviation of the RSS error of WGP is also the smallest among the four methods, indicating that the RSS predicted by WGP is more stable than the existing methods.

[0104] For the positioning estimation accuracy, 16 points were selected as test points in the experimental area in this embodiment. Through the fingerprint database expanded by different models and combined with the KNN positioning algorithm, the final coordinates were calculated. The error between the predicted coordinates and the true coordinates was calculated to verify the positioning accuracy of different methods.

[0105] Figure 8 The cumulative distribution function (CDF) curves of three different models are shown, which are zero-order Gaussian process regression (ZERO-GPR), polynomial Gaussian process regression (POLY-GPR), and polynomial weighted Gaussian process (WGP). The abscissa is the positioning error (unit: meter), and the ordinate is the CDF value. It can be seen from the figure that the WGP model performs best in most error ranges, and its CDF curve is significantly higher than the other two models in the error range of 0 to 2 meters. This indicates that the WGP model has obvious advantages in positioning accuracy. The positioning error of the ZERO-GPR model is the largest, and its CDF curve is lower than the other models in most error ranges. The performance of the POLY-GPR model is between ZERO-GPR and WGP, but in the range of about 1.5 meters of error, the performance of POLY-GPR and WGP is close.

[0106] Figure 9 The change of the positioning error at each test point is shown. The abscissa is the test point index, and the ordinate is the positioning error (unit: meter). It can be seen from the figure that the positioning errors of each model fluctuate greatly at different test points, but the overall trend is consistent with the Figure 8 results of the CDF curve in. The WGP model has a smaller positioning error at most test points, showing better stability and robustness. The ZERO-GPR model has a larger positioning error at multiple test points, especially at the 6th, 10th, and 14th test points, where the error increases significantly. The error curve of the POLY-GPR model is relatively smooth, showing better average performance.

[0107] Through the above analysis, it can be seen that the WGP model is superior to the ZERO-GPR and POLY-GPR models in both positioning accuracy and stability, and it is the best method for positioning effect. This indicates that after expanding the fingerprint database, the WGP model can achieve higher positioning accuracy through the KNN positioning algorithm, providing strong support for the construction of the online RSS fingerprint database.

[0108] The present invention proposes and verifies an improved WiFi fingerprint positioning algorithm based on the WGP model, aiming to solve the limitations of traditional WiFi fingerprint positioning technology in constructing an offline fingerprint database and adapting to environmental changes. Through experimental verification, this method can significantly improve the accuracy and stability of indoor positioning without adding any additional hardware, and shows high feasibility and superiority in practical applications.

[0109] Embodiment 3

[0110] An improved WiFi fingerprint positioning system based on the WGP model is specifically as follows: The ZERO-GPR, POLY-GPR, and WGP models are respectively used to expand the offline fingerprint database for the same sparse reference points and fuse the error calibration model for positioning. Finally, through the comparison of positioning errors, the superiority of the WGP prediction model is proved. Specifically, in the fingerprint database establishment stage, first randomly select 20% of the samples from the reference points determined by on-site survey as known reference points, and obtain their signal strength and two-dimensional position coordinate information as training data. Then, based on the position coordinate and signal strength information of the known points, the three models are respectively used to predict the signal strength values of the remaining 80% of the reference points, fuse them with the information of the previous 20% of the points, and finally form the fingerprint database belonging to each algorithm. In the positioning stage, based on the fingerprint databases predicted by the three models, the K-Nearest Neighbors (KNN) algorithm is used to calculate the final position coordinates and compare them with the actual survey information to calculate the prediction deviation of each point in the three models. The framework diagram of this system is as Figure 1 shown.

[0111] During the process of establishing the fingerprint database, the WGP model proposed in this application is based on the POLY-GPR model proposed by others. By warping the parameter values in the objective function, it is distorted into a high-dimensional space and its distribution in the high-dimensional space conforms to the Gaussian distribution. Then, an improved Gaussian regression model is used in the high-dimensional space to predict the measurement points, and finally the data is mapped back to the true value to achieve the purpose of expanding the fingerprint database. Compared with the existing WiFi fingerprint positioning algorithms that expand the offline fingerprint database by using the Gaussian regression model or the improved Gaussian regression model on the basis that the default observed values conform to the Gaussian distribution, its process is more rigorous and the predicted data obtained is more accurate.

[0112] It should be noted that in the present invention, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or elements inherent to such process, method, article or device.

[0113] The above embodiments are only illustrative examples of the present invention and do not constitute a limitation on the protection scope of the present invention. Any design identical or similar to the present invention falls within the protection scope of the present invention.

Claims

1. An indoor positioning method based on an improved WGP model, characterized in that: include: Obtain the coordinate position and signal strength of the reference points in the indoor fingerprint library, and divide them into known reference points and estimated reference points; Based on the POLY_GPR model, the parameters in its objective function are warped, and the signal strength of the known reference point is distorted to the high-dimensional space through nonlinear monotonic function mapping to obtain the signal strength of the mapped known reference point, and then the signal strength of the mapped known reference point is partially derived using the negative log-likelihood function to obtain the mapping value of the signal strength of the predicted estimated reference point; Mapping the mapping value of the signal strength of the predicted estimated reference point back to the true value to obtain the signal strength of the predicted estimated reference point, and combining the signal strengths of the known reference point and the predicted estimated reference point to obtain an expanded fingerprint library; The signal strength of the unknown point is obtained, and the unknown point is located online based on the expanded fingerprint library through the K-weighted neighbor matching algorithm KNN to obtain the coordinate position of the unknown point.

2. The indoor positioning method based on the improved WGP model as claimed in claim 1, characterized in that: The method of distorting the signal strength of the known reference point to the high-dimensional space through nonlinear monotonic function mapping includes: For each observed data point , through the monotonic function Transform to get the data points in the latent space : represents the observed data point, which is the data point before warping; is a function The parameter set, Indicates the wifi signal strength value from each access point in the detected space. Represents the noise in the environment.

3. The indoor positioning method based on the improved WGP model as claimed in claim 2, characterized in that: The monotonic function Choose the hyperbolic tangent function, expressed as: in, controls the magnitude of each tanh function, i.e. the height or impact of each step, Controls the steepness of each tanh function, that is, the slope of the curve or the sharpness of the transition, Controls the position or offset of each tanh function on the time axis, is the number of tanh in the function; The hyperbolic tangent function is bounded, and is modified by adding a linear term to obtain the following formula: 。 4. The indoor positioning method based on the improved WGP model as claimed in claim 1, characterized in that: The negative log-likelihood function is expressed as follows: in, It is the representation of the observed data points in the latent space after transformation, indicating the relationship between the observed data and the latent feature space; : is the Jacobian term, representing the derivative of the transformation function, ensuring the monotonicity of the transformation process and its impact on the likelihood calculation; t n : Data point index, used to calculate the Jacobian of the partial derivative for each data point, : is the number of observation data; The Jacobian term is introduced into the negative log-likelihood, where the negative log-likelihood is expressed as follows: in, is the potential target vector, which is the target of fitting and prediction, is the set of reference points, is a set of hyperparameters, is the covariance matrix constructed in the latent space.

5. The indoor positioning method based on the improved WGP model as claimed in claim 1, characterized in that: The formula to be tested for the mapping value of the predicted estimated reference point signal strength is: in, is the predicted value of the signal strength of the test point based on POLY-GPR, Indicates the warped value of the signal strength at a known location. It is the warped value of the signal strength value fitted by the POLY-GPR model at a known location. It is the predicted value of the signal strength of the test point based on POLY-GPR; For a known reference point The predicted value using the POLY-GPR model after warping is given by the following formula: 。 6. The indoor positioning method based on the improved WGP model as claimed in claim 1, characterized in that: The coordinate position of the unknown point comprises the following steps: Taking the position of the unknown point as the target position, obtaining the position information and signal strength of the reference points around the target position; Use Euclidean distance to obtain the distance between the target position and each reference point; Select K reference points closest to the target position; The position coordinates of these K neighbors are used as estimates of the target position through weighted averaging to obtain the coordinate position of the unknown point.

7. A system for indoor positioning method based on improved WGP model, characterized in that: include: An acquisition module is used to obtain the coordinate position and signal strength of reference points, which are divided into known reference points and estimated reference points; The fingerprint expansion and calibration module warps the parameters in its objective function based on the POLY_GPR model, distorts the signal strength of the known reference point to the high-dimensional space through nonlinear monotonic function mapping, obtains the signal strength of the mapped known reference point, and then uses the negative log-likelihood function to perform partial derivative processing on the signal strength of the mapped known reference point to obtain the mapping value of the signal strength of the predicted estimated reference point; maps the mapping value of the signal strength of the predicted estimated reference point back to the true value to obtain the signal strength of the predicted estimated reference point, and combines the signal strengths of the known reference point and the predicted estimated reference point to obtain the expanded fingerprint library; The positioning module is used to obtain the signal strength of the unknown point, and to perform online positioning of the unknown point based on the expanded fingerprint library through the K-weighted neighbor matching algorithm KNN to obtain the coordinate position of the unknown point.

8. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

9. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method described in any one of claims 1 to 6 is implemented.

Images