Indoor positioning method and system based on improved WGP model, medium and equipment

Abstract

The invention discloses an indoor positioning method and system based on an improved WGP model, a medium and equipment, relates to the technical field of positioning, and provides a two-stage indoor positioning algorithm comprising offline sampling and fingerprint matching based on warped Gaussian process regression and WiFi fingerprint positioning. In the off-line stage, a WGP model is applied to process an output observation value by performing nonlinear transformation of parameters on a Gaussian process. WiFi fingerprint data generally comprises non-Gaussian noise, and the traditional GPR has limitation when fitting the signal intensities, so that the application adopts a WGP model. The WGP model not only utilizes the statistical characteristics of the traditional Gaussian process, but also enhances the flexibility of the WGP model through nonlinear transformation, so that non-Gaussian noise is processed more effectively. In the aspects of accuracy and confidence interval, the WGP model is superior to the standard GPR and more advanced polynomial Gaussian process regression.

Description

Technical Field

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

[0002] In recent years, with the rapid growth of mobile device penetration, location-based services (LBS) have become more and more widely used in various intelligent buildings. This technology has become an indispensable part of daily life, and the effectiveness of LBS depends largely on the accuracy of positioning. 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 indoor environments, GNSS cannot provide sufficient positioning accuracy due to signal obstruction. Therefore, a reliable indoor positioning and navigation system is needed that can provide accurate positioning and navigation in indoor environments where GNSS signals are shielded. Now, almost all buildings are covered by various WiFi, which may be the infrastructure of some networks or the hotspots of some mobile devices. Since WiFi technology has the characteristics of low cost, low power consumption, easy deployment and high existing deployment rate, the indoor positioning solution based on WiFi signal strength value is one of the most promising indoor positioning solutions and the most widely used solution.

[0003] WiFi-based indoor positioning technology is mainly divided into two types: based on propagation model and based on WiFi fingerprint. In the propagation model technology, it mainly relies on the logarithmic distance path loss model (Log-Distance Path Loss, LDPL) to model the wireless signal environment, and then infers its location 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 build a dynamically changing indoor environment model, which will seriously affect its positioning accuracy. The positioning technology based on WiFi fingerprint technology does not rely on range estimation, can better represent the real-time changing indoor signals, and is more suitable for indoor environments than the propagation model.

[0004] The WiFi fingerprint-based method has two main steps: 1) Offline sampling phase: Through field survey and recording of 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 phase: The RSS values ​​received from multiple AP access points at the location to be tested are matched with the offline fingerprint database to estimate the location coordinates of the location to be tested.

[0005] There are still some problems to be solved in the indoor positioning technology based on WiFi fingerprint method. For example, when building an offline fingerprint database, a lot of manpower and material resources are needed for preliminary on-site survey. Moreover, the fingerprint-based positioning method is heavily dependent on the established fingerprint library. Its positioning accuracy depends largely on the density of reference points in the fingerprint library. The more reference points are measured, the denser the generated fingerprint library is, and the higher the positioning accuracy is. However, at the same time, the cost of initial investment will also increase. Moreover, if the indoor layout changes or new obstacles appear, the original fingerprint library will be difficult to adapt to the new environment after the change, which will cause great trouble for later maintenance and updating. Therefore, a solution that can reduce the workload of preliminary survey, 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 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 library based on the collected reference point information. Other scholars have proposed an LDM_GPR (Log-Distance GPR) algorithm that uses the GPR model to model the RSS error residual that the LDPL model cannot simulate based on the characteristics of the indoor environment, thereby improving the performance in processing large-scale data sets or complex environments. Other scholars have proposed a POLY_GPR (Polynomial Gaussian Process Regression) algorithm that uses a polynomial kernel function within the framework. The input features are expanded through polynomial transformations, which can better capture the nonlinear relationships and complex patterns between the input data and improve the prediction performance of the model.

[0007] Considering that in practical applications, the distribution of observations does not always obey the Gaussian distribution, and however, POLY-GPR assumes that the data distribution is Gaussian, and fails to completely solve the non-Gaussian problem of 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 shortcomings of the above-mentioned prior art that the positioning results are not accurate and stable enough when processing 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 solution, an indoor positioning method based on an improved WGP model, comprising:

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

[0011] 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 by the negative log-likelihood function to obtain the mapping value of the signal strength of the predicted estimated reference point;

[0012] 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;

[0013] 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.

[0014] Furthermore, the signal strength of the known reference point is distorted to the high-dimensional space through nonlinear monotonic function mapping, including:

[0015] For each observation data point w i , the data point z in the latent space transformed by the monotonic function g i :

[0016] z i =g(w i ; Ψ) = g(f(x i )+ε i )

[0017] w i represents the observed data point, which is the data point before warping; ψ is the parameter set of function g, f(x i ) represents the wifi signal strength value from each access point in the detected space, ε i Represents the noise in the environment.

[0018] The monotone function g is selected as the hyperbolic tangent function, which is expressed as:

[0019]

[0020] Among them, a j controls the magnitude of each tanh function, i.e. the height or impact of each step, b j Controls the steepness of each tanh function, that is, the slope of the curve or the sharpness of the transition, c j Controls the position or offset of each tanh function on the time axis, where I is the number of tanh in the function;

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

[0022]

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

[0024]

[0025] Among them, g(w i ) is the representation of the observed data point 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 of each data point, N: is the number of observations;

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

[0027]

[0028] Among them, z N is the potential target vector, which is the target of fitting and prediction, X is the reference point set, θ is the hyperparameter set, and C N is the covariance matrix constructed in the latent space.

[0029] The formula to be tested for the mapping value of the predicted estimated reference point signal strength is:

[0030]

[0031] in, is the predicted value of the signal strength of the test point based on POLY-GPR, z represents the warped value of the signal strength at the known position, and u z is the warped value of the signal strength value fitted by the POLY-GPR model at a known position, y *,poly It is the predicted value of the signal strength of the test point based on POLY-GPR.

[0032] For a known reference point u z,i The predicted value using the POLY-GPR model after warping is given by the following formula:

[0033]

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

[0035] 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;

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

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

[0038] 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.

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

[0040] The acquisition module is used to obtain the coordinate position and signal strength of the reference points in the indoor fingerprint library, which are divided into known reference points and estimated reference points;

[0041] The fingerprint expansion and calibration module warps the parameters in the 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;

[0042] 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.

[0043] Compared with the prior art, the beneficial effects of the present invention are: it can automatically expand and calibrate the offline fingerprint database to achieve calibration-free indoor positioning. In order to build a more sophisticated radio map, the WPG model is further proposed. This is a technology that maps observation values ​​to high-dimensional space through complex functions to make it have a more reliable regression in high-dimensional space. It is specifically used to predict the RSS value of WiFi signals and can well capture the uneven RSS distribution in complex indoor environments. 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. The problem of inaccurate and unstable positioning results due to noise in complex signal environments is solved. By warping the parameter values ​​in the objective function, it is distorted to high-dimensional space and its distribution in high-dimensional space conforms to the Gaussian distribution. Then, the improved Gaussian regression model is used in the high-dimensional space to predict the test points, and finally the data is mapped back to the true value to achieve the purpose of expanding the fingerprint library. Its flexibility is enhanced by nonlinear transformation, so that non-Gaussian noise can be more effectively processed. 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 further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute improper limitations on the present application.

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

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

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

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

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

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

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

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

[0053] Fig. 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] 1) 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 is proposed in "Gaussian process for machine learning", which uses the spatial correlation between reference points to calibrate and expand the fingerprint library based on the collected reference point information. A log-distance Gaussian process regression (LDM-GPR) algorithm is proposed in "Dynamic online calibration radio map for indoor positioning in wireless local area network", which uses the GPR model to model the RSS error residual that cannot be simulated by the log-distance path loss model (LDPL) according to the characteristics of the indoor environment, thereby improving the performance in processing large-scale data sets or complex environments. A polynomial Gaussian process (POLY-GPR) using a polynomial kernel function in the framework is proposed in "Non-intrusive indoor positioning system based on WiFi with online radio map construction and adaptation function". 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. However, POLY-GPR assumes that the data distribution is Gaussian and fails to completely solve the non-Gaussian problem of received signal strength (RSS) data in indoor positioning.

[0060] In contrast, the Warped Gaussian Process (WGP) fundamentally solves this limitation by introducing nonlinear transformations to process non-Gaussian RSS data. WGP can not only capture the nonlinear relationship between input data, but also make the data closer to Gaussian distribution by performing nonlinear transformations on the observed data, thus showing higher accuracy and reliability in model fitting and prediction. In addition, WGP performs well in handling errors and uncertainties, can provide more reasonable confidence intervals, 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 than traditional GPR and POLY-GPR.

[0061] In the prior art, the prediction model based on GPR will perform special preprocessing on the data before modeling to achieve the conversion of observed variables, but its basic assumptions are: under the given input conditions of the objective function, the output data obeys the multivariate Gaussian distribution, and the noise of each observation point is Gaussian noise with the same variance as the data. However, in practical applications, the observed values ​​may all be negative numbers or values ​​with large changes in magnitude. In this case, it is very imprecise to directly assume the homoscedastic Gaussian noise for modeling, and the RSS value of WiFi cannot be modeled with a simple multivariate Gaussian process model. Usually, the method adopted by most literature is to logarithmically transform the data to make it more consistent with the assumption of Gaussian process in order to better model. However, if this transformation is only used as a preprocessing step, it obviously does not take into account the parameter uncertainty of the transformation itself and the impact on the model structure, nor does it form an integrated probability inference with other parts of the model. This is also imprecise.

[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 a nonlinear monotonic function method to transform data from one observation space to another latent space. This method can establish a more complex relationship between observations and latent variables instead of a simple linear mapping. It can better capture nonlinear relationships and data features, provide uncertainty quantification and credibility intervals, and make the model more interpretable.

[0063] When the WGP model is introduced, a nonlinear warping transformation method is used to transform the data points w in the observation space. i Mapped to the data point z in the latent space i This process can capture complex nonlinear relationships. i As a potential target vector, it participates in the model fitting and prediction. The model parameter set Ψ defines the specific form of this transformation. The covariance matrix C N It is used to represent the relationship between data points in the latent space and provides the basic structure for modeling. The reference point set X is the basis for building the model. This mapping can make the observed data more consistent with the Gaussian model, and the negative log likelihood is:

[0064]

[0065] Among them, z N is the potential target vector, which is the target of fitting and prediction. X is the set of reference points. θ is the set of hyperparameters. C N is the covariance matrix constructed in the latent space.

[0066] For each observation data point w i, parameterized by the monotonic function g as the data point z in the latent space transformed by ψ i :

[0067] z i =g(w i ; Ψ) = g(f(x i )+ε i ) (2)

[0068] Among them, w i : represents the observed data point, which is the data point before warping. ψ is the parameter set of the function g, which defines the specific form and characteristics of the transformation. During the warping process, the function g must be monotonic to ensure that the transformed data still maintains the order relationship. Monotonicity ensures that the mapping will not produce inversion. The mapping should cover the entire real number domain to facilitate complete probability modeling. In order to ensure the correctness of the probability distribution during the warping process, the Jacobian term is introduced into formula (1):

[0069]

[0070] Represents the negative log-likelihood function, which is used to calculate the degree of fit of the model and includes the determinant of the covariance matrix and the Jacobian term. g(w i ) is the representation in the latent space after transformation, which reflects 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 and its impact on the likelihood calculation. N : The data point index used to calculate the Jacobian of the partial derivative for each data point. N: is the number of observations.

[0071] In the selection of the warping function g, the hyperbolic tangent (tanh) function was finally chosen as the warping function:

[0072]

[0073] Among them, a j Controls the magnitude of each tanh function, i.e. the height or impact of each step. j Controls the steepness of each tanh function, that is, the slope of the curve or the sharpness of the transition. j Controls the position or offset of each tanh function on the time axis. I is the number of tanh functions in the function, which determines the complexity of the function. More tanh functions can construct more complex transformations. In this application, after multiple experiments, the value of I is fixed to 5.

[0074] The distortion function constructed by formula (4) is bounded, and the output is in the range of [-1,1]. In the latent space z, the data is Gaussian distributed, which means that z should theoretically cover the entire real number line. This will result in that when z exceeds a certain range, its inverse function cannot be defined, and the corresponding y value cannot be found, and the reverse mapping fails. Therefore, the present invention uses the following formula to correct this problem:

[0075]

[0076] By adding the linear term y, the entire function can still expand linearly when y takes an extreme value or changes greatly, breaking through the boundedness caused by relying solely on the tanh function.

[0077] The prediction formula of WGP is:

[0078]

[0079] Since the observed data is warped, it is difficult to calculate the inverse function of the warping function. In this case, the genetic algorithm (GA) provides an effective numerical solution as a global optimization method. 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 the inverse function.

[0080] In the WGP model after integrating POLY-GPR, the signal strength prediction formula of the test point is updated as follows:

[0081]

[0082] in is the predicted value of the signal strength at the measurement point based on POLY-GPR. z represents the warped value of the signal strength at the known position. z It is the warped value of the signal strength value fitted by the POLY-GPR model at a known location. *,poly It is the predicted value of the signal strength of the test point based on POLY-GPR.

[0083] In addition, for a known reference point u z,i The predicted value using the POLY-GPR model after warping is given by the following formula:

[0084]

[0085] Example:

[0086] In order to fully 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. Figure 2 As shown in the figure, the ideal traditional test area usually uses corridors or open spaces as test platforms, which is conducive to modeling data. The experimental environment includes a corridor and four asymmetrical rooms with different functions on both sides of the corridor. The overall area presents an irregular shape. This complex indoor environment is more suitable for evaluating the performance of the WGP algorithm than the ideal environment.

[0087] During the experiment, the presence of WiFi signals was analyzed and an adaptive screening algorithm was used to determine the four access points (APs) with the largest signal coverage area. This adaptive screening method can more effectively utilize existing APs without requiring strict layout requirements for the specific location of the APs, while improving the versatility and applicability of the algorithm. This experiment collected 57 reference points such as Figure 2 As shown in the circle in the figure, the location information and RSS value of each reference point are recorded to establish the initial fingerprint library. Subsequently, 20% of the data points are randomly selected from the fingerprint library for fingerprint library expansion calculation. The additional 34 test points are used to evaluate the accuracy of the positioning algorithm.

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

[0089] Table 1: Estimation errors of Zero-GPR, POLY-GPR, and WGP for RSS of different access points

[0090] method AP1 / dBm AP2 / dBm AP3 / dBm AP4 / dBm ZERO-GPR 79.36 60.59 73.17 60.61 POLY-GPR 41.99 20.42 7.61 24.52 WGP 9.38 15.67 7.20 21.86

[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 RSS error of WGP is also the lowest, indicating that the RSS value predicted by WGP is more stable than that of other methods.

[0092] For the positioning estimation accuracy, the coordinates are solved by using the fingerprint library expanded by different models. 34 new points are randomly found in the experimental area as test points. For the fingerprint library expanded by different models, the coordinates calculated by the KNN positioning algorithm are compared with the real coordinates to verify the positioning estimation accuracy of different models.

[0093] When evaluating the performance of a positioning algorithm, commonly used indicators include positioning error, cumulative distribution function (CDF), etc.

[0094] like Figure 4 As shown in the figure, the cumulative distribution function (CDF) diagram shows the cumulative probability distribution of three different positioning algorithms (ZERO-GPR, POLY-GPR, and WGP) in terms of positioning error. It can be seen from the figure that WGP (black solid line) performs better than the other two algorithms in most positioning error ranges, especially when the positioning error is small, its cumulative probability grows faster. This shows that WGP can achieve a smaller positioning error at most test points. The cumulative probability of ZERO-GPR (red dotted line) and POLY-GPR (blue dotted line) grows slowly when the positioning error is small, especially the performance of ZERO-GPR is obviously worse than POLY-GPR. As the positioning error increases, POLY-GPR gradually exceeds ZERO-GPR, showing its superiority in the medium error range. The cumulative probability of WGP has exceeded 0.8 in the range of positioning error less than 15 meters, indicating that its error control is better 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 best in overall positioning accuracy, especially when the error is small, its advantage is particularly obvious. POLY-GPR is second, and ZERO-GPR performs the worst.

[0096] like Figure 5 As shown in the figure, the positioning error diagram of each test point shows the specific error of the three algorithms at each test point. The errors of the three algorithms at different test points all fluctuate greatly. The error change trends of WGP and POLY-GPR are relatively close, indicating that the two methods have a certain consistency in error control. The error fluctuation of ZERO-GPR is large, and it shows a significant increase in error at multiple test points. The positioning error of WGP at some test points, such as the 3rd, 14th and 27th test points, is significantly smaller than that of the other two algorithms, showing its local advantages under specific circumstances. These test points may correspond to environments with more complex signals or more interference. WGP can better adapt to these complex environments through the nonlinear mapping and parameter optimization of its model. Overall, the positioning error of WGP is relatively stable at most test points, and in most cases it is less than 10 meters. Although POLY-GPR also shows a small error at some test points, its stability is slightly inferior to WGP. The error of ZERO-GPR is large and fluctuates violently, showing its shortcomings in dealing with complex signal environments.

[0097] Example 2

[0098] In the single-room test site experiment, a 14m*11m laboratory was selected as the experimental site. The area was divided according to the floor tiles (0.6m*0.6m) and the reference points were surveyed. A total of 9 points were selected as reference points.

[0099] In this experiment, by detecting the WiFi signals in the environment, the four AP points with the largest amount of information were selected through the adaptive screening algorithm, and 42 reference points were collected. Figure 6 The circles in the figure are used to build a fingerprint library, and 20% are randomly selected. Figure 6 The 9 triangles in the fingerprint library are combined with the fingerprint library expansion algorithm to expand the fingerprint library. 16 additional test points are collected. Figure 6 The asterisk in the figure is used to finally detect the positioning accuracy of the positioning algorithm.

[0100] For 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 a comparison was made. Figure 7 Table 2 compares the RSS prediction errors of three different methods.

[0101] Table 2: Estimation errors of Zero-GPR, POLY-GPR, and WGP for RSS of different access points

[0102] method AP1 / dBm AP2 / dBm AP3 / dBm AP4 / dBm ZERO-GPR 3.55 2.32 2.79 2.64 POLY-GPR 3.68 1.53 1.53 2.13 WGP 2.54 1.47 1.49 1.93

[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 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, this embodiment selects 16 points in the experimental area as test points. The final coordinates are solved by using the fingerprint library expanded by different models and combined with the KNN positioning algorithm. The error between the predicted coordinates and the actual coordinates is calculated to verify the positioning accuracy of different methods.

[0105] Figure 8The cumulative distribution function (CDF) curves of three different models are shown. These three models are zero-order Gaussian process regression (ZERO-GPR), polynomial Gaussian process regression (POLY-GPR), and polynomial weighted Gaussian process (WGP). The horizontal axis is the positioning error (unit: meter), and the vertical axis is the CDF value. As can be seen from the figure, 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 shows that the WGP model has a clear advantage in positioning accuracy. The ZERO-GPR model has the largest positioning error, 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 error range of about 1.5 meters, the performance of POLY-GPR and WGP is close.

[0106] Fig. 9 The figure shows the changes in positioning error at each test point. The horizontal axis is the test point index and the vertical axis is the positioning error (unit: meter). It can be seen from the figure that the positioning error of each model at different test points fluctuates greatly, but the overall trend is the same as Figure 8 The CDF curve results in are consistent. The WGP model has a small positioning error at most test points, showing good stability and robustness. The ZERO-GPR model has a large 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 good average performance.

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

[0108] This paper 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 building 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 has shown high feasibility and superiority in practical applications.

[0109] Example 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 used to expand the offline fingerprint library of the same sparse reference points and fuse the error calibration model for positioning, and finally the positioning error is compared to prove the superiority of the WGP prediction model. Specifically, in the fingerprint library establishment stage, 20% of the samples are randomly selected from the reference points determined by the on-site survey as known reference points, and their signal strength and two-dimensional position coordinate information are obtained as training data. Then, the three models are used to predict the signal strength values ​​of the remaining 80% of the reference points based on the position coordinates and signal strength information of the known points, and the signal strength values ​​are fused with the information of the first 20% of the points to finally form the fingerprint library belonging to each algorithm. In the positioning stage, the fingerprint library predicted by the three models uses the K-Nearest Neighbors (KNN) algorithm to solve 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 the system is shown in the figure below. Figure 1 shown.

[0111] In the process of establishing the fingerprint library, the WGP model proposed in this application is based on the POLY-GPR model proposed by et al., by warping the parameter values ​​in the objective function to make it distorted to a high-dimensional space and its distribution in the high-dimensional space conforms to the Gaussian distribution, and then using the improved Gaussian regression model in the high-dimensional space to predict the test points, and finally mapping the data back to the true value to achieve the purpose of expanding the fingerprint library. Compared with the existing WiFi fingerprint positioning algorithm to expand the offline fingerprint library method, which uses the Gaussian regression model or the improved Gaussian regression model to expand the fingerprint library based on the default observation value conforming to the Gaussian distribution, its process is more rigorous and the resulting prediction data is more accurate.

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

[0113] The above embodiments are merely examples of the present invention and do not limit the protection scope of the present invention. All designs that are the same or similar to the present invention fall 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 by 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 observation data point w i , the data point z in the latent space transformed by the monotonic function g i : z i =g(w i ;Ψ)=g(f(x i )+ε i ) w i represents the observed data point, which is the data point before warping; ψ is the parameter set of function g, f(x i ) represents the wifi signal strength value from each access point in the detected space, ε i 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 monotone function g is selected as the hyperbolic tangent function, which is expressed as: Among them, a j controls the magnitude of each tanh function, i.e. the height or impact of each step, b j Controls the steepness of each tanh function, that is, the slope of the curve or the sharpness of the transition, c j Controls the position or offset of each tanh function on the time axis, where I is the number of tanh in the function; The hyperbolic tangent function is bounded and is modified by adding a linear term y 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: Among them, g(w i ) is the representation of the observed data point 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 of each data point, N: is the number of observations; The Jacobian term is introduced into the negative log-likelihood, where the negative log-likelihood is expressed as follows: Among them, z N is the potential target vector, which is the target of fitting and prediction, X is the reference point set, θ is the hyperparameter set, and C N 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, z represents the warped value of the signal strength at the known position, and u z is the warped value of the signal strength value fitted by the POLY-GPR model at a known position, y *,poly It is the predicted value of the signal strength of the test point based on POLY-GPR. For a known reference point u z,i 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 the 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.

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