Indoor pseudo satellite positioning method based on carrier phase multipath error modeling

Abstract

The invention relates to an indoor pseudo satellite positioning method based on carrier phase multipath error modeling. The method comprises the following steps: acquiring pseudo satellite observation data; a carrier phase observation value is calculated, systematic errors are eliminated, integer ambiguity is fixed, and carrier phase multipath errors are deduced; mapping the actual space layout of the pseudo-satellite into a two-dimensional grid structure, extracting a carrier phase residual error and a carrier-to-noise ratio, and constructing a dual-channel input tensor; constructing and training a spatial topology convolutional neural network model, and generating carrier phase multipath error prediction by taking a dual-channel input tensor as an input feature; a double-thread unscented Kalman filtering positioning framework is designed, correction of a carrier phase observation value and real-time calculation of a two-dimensional position of a user are carried out in sequence through two threads, accurate positioning in an indoor scene is achieved, the multipath effect of an indoor pseudo satellite system is relieved, and indoor positioning accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of indoor pseudo-satellite system positioning technology, and in particular to an indoor pseudo-satellite positioning method based on carrier phase multipath error modeling. Background Technology

[0002] High-precision indoor positioning is a key area in navigation and location services. Pseudosatellite technology, as an important approach to solving this problem, effectively compensates for the insufficient coverage of GNSS signals in enclosed or severely obstructed areas (such as indoors) by deploying ground-based transmitting stations indoors and broadcasting signals compatible with the Global Navigation Satellite System (GNSS). The core advantage of this technology lies in broadcasting signals similar to those of on-orbit satellites, and its positioning principle is consistent with GNSS. It can be used in conjunction with GNSS for positioning or independently to provide indoor location services. Furthermore, utilizing carrier phase observations, pseudosatellites theoretically have the potential to achieve centimeter-level high-precision positioning. Meanwhile, existing commercial GNSS receivers typically only require firmware upgrades to become compatible with pseudosatellite signal reception, which greatly lowers the application threshold, making pseudosatellites an ideal choice for building integrated indoor and outdoor high-precision navigation systems.

[0003] The application of pseudosatellites in high-precision indoor positioning also faces significant challenges, primarily due to the complex indoor signal propagation environment. Unlike the open outdoor environment, indoor spatial structures (walls, ceilings, furniture, etc.) significantly affect signal propagation, leading to severe multipath effects in pseudosatellite positioning systems and consequently impacting the accuracy of user positioning. Compared to outdoor environments, indoor positioning is more complex in terms of signal propagation and spatial layout, and pseudosatellite signals have higher power, resulting in larger, more complex, and more difficult-to-eliminate multipath errors using traditional methods. Therefore, accurately modeling and suppressing the severe multipath errors caused by complex spatial topology has become a core challenge for high-precision indoor pseudosatellite positioning.

[0004] Existing multipath error suppression methods, including traditional data processing and antenna hardware improvements, have alleviated multipath effects to some extent, but they suffer from limitations such as strong hardware dependence, insufficient utilization of pseudosatellite physical layout information, and poor adaptability. In recent years, deep learning, especially convolutional neural networks (CNNs), has been applied in multipath error suppression due to its powerful spatial feature extraction capabilities. However, existing methods are mostly based on the direct input of data matrices and do not directly map the pseudosatellite physical spatial layout into the network structure. Therefore, there is an urgent need for a positioning method that can explicitly model the multipath errors of pseudosatellite systems based on spatial topology information to improve the accuracy of user positioning. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an indoor pseudo-satellite positioning method based on carrier phase multipath error modeling. This method solves the problems of limited accuracy in traditional indoor positioning methods due to the influence of indoor spatial structure on signal propagation, difficulty in eliminating propagation errors in indoor scenes, and insufficient utilization of pseudo-satellite spatial layout information in existing CNN-based indoor positioning methods. By explicitly fusing pseudo-satellite spatial topology relationships and multi-channel features to establish a model for predicting carrier phase multipath errors, this method alleviates the multipath effect of indoor pseudo-satellite systems and improves indoor positioning accuracy.

[0006] To achieve the above technical objectives, the present invention provides the following technical solution: an indoor pseudo-satellite positioning method based on carrier phase multipath error modeling, comprising the following steps: In an indoor experimental setting, a pseudo-satellite and a receiver were deployed. A total station was used to calibrate the coordinates of the pseudo-satellite and the receiver. The receiver then collected observation data from the pseudo-satellite. The carrier phase observations of the receiver and the pseudosatellite are obtained based on pseudosatellite observation data. A reference pseudosatellite is selected for inter-satellite single-difference processing to eliminate systematic errors in the carrier phase observations. The integer ambiguity is fixed based on the known point initialization method. The carrier phase multipath error is derived as the actual carrier phase multipath error used for training the spatial topology convolutional neural network model. The systematic error includes the clock bias and hardware delay of the receiver and the pseudosatellite. The actual spatial layout of pseudo-satellites is mapped to a two-dimensional grid structure. Combining the current user's two-dimensional position and the carrier phase observation value after inter-satellite single-difference processing, the carrier phase residual is extracted from the two-dimensional grid structure and the carrier-to-noise ratio is obtained to construct a dual-channel input tensor. A spatial topological convolutional neural network model containing convolutional layers, pooling layers, and fully connected layers is constructed and trained. The spatial topological convolutional neural network model uses a dual-channel input tensor as input features to generate carrier phase multipath error prediction, and optimizes the model parameters by combining a cross-validation algorithm. A dual-threaded unscented Kalman filter positioning framework is designed. For each observation epoch, the first thread collects pseudo-satellite observation data in real time in an indoor scene, constructs a dual-channel input tensor, and inputs it into a trained spatial topology convolutional neural network model to generate the carrier phase multipath error prediction for that observation epoch. The second thread uses the carrier phase multipath error prediction generated by the first thread to correct the carrier phase observation value after inter-satellite single-difference processing. The corrected carrier phase observation value is then used to perform real-time calculation of the user's two-dimensional position based on unscented Kalman filtering to obtain the user's position estimate and achieve accurate positioning in indoor scenes.

[0007] Optionally, the pseudo-satellites are centrally deployed within a circular area with a radius not less than a preset value and connected to the same pseudo-satellite signal transmitter as a unified clock source; The receivers are sequentially deployed at evenly distributed static sampling points to collect pseudo-satellite observation data from each static sampling point.

[0008] Optionally, the step of obtaining the carrier phase observation values ​​of the receiver and the pseudosatellite based on pseudosatellite observation data includes: Construct carrier phase observation equations to obtain carrier phase observations from the receiver and the pseudosatellite: ; in, For receivers and pseudo-satellites Carrier phase observations between; For receivers and pseudo-satellites The geometric distance between them is calculated based on the coordinates from the pseudo-satellite and receiver from the total station; The speed of light; and Receiver and pseudosatellite respectively Clock difference; and pseudo-satellites Hardware delay with the receiver; The wavelength of the pseudo-satellite signal; , , pseudo-satellites Integer ambiguity, observation noise, and carrier phase multipath error; The step of selecting a reference pseudo-satellite for inter-satellite single-difference processing to eliminate systematic errors in carrier phase observations includes: Current pseudo-satellites Select a pseudo-satellite as the target pseudo-satellite. To reference pseudo-satellites, the inter-satellite single-difference method is used to eliminate systematic errors: ; in, This refers to the carrier phase observation values ​​of the target pseudo-satellite and the reference pseudo-satellite after single-difference processing based on measurement data from the same receiver, i.e., the carrier phase observation values ​​after inter-satellite single-difference processing. The geometric distance between the target pseudosatellite and the reference pseudosatellite is calculated based on the measurement data from the same receiver after single difference, i.e., the geometric distance after inter-satellite single difference processing, which is based on the pseudosatellite coordinates from the total station. This refers to the integer ambiguity after inter-satellite single-difference processing; This refers to the carrier phase multipath error after inter-satellite single-difference processing. This indicates the observation noise after inter-satellite single-difference processing; The method for fixing integer ambiguity based on known point initialization includes: The integer ambiguity is fixed using the known point initialization method, which takes the following form: ; in, The fixed integer ambiguity; This is a rounding function. Indicates the wavelength of pseudo-satellite signals The reciprocal of; The derived carrier phase multipath error includes: Using fixed integer ambiguity Carrier phase observations after inter-satellite single-difference processing Geometric distance values ​​after inter-satellite single-difference processing Combined with pseudo-satellite signal wavelength Derivation of carrier phase multipath error : .

[0009] Optionally, the two-dimensional grid structure is constructed based on the position of the pseudo-satellites in actual space, with each pixel in the grid corresponding to one pseudo-satellite; The dual-channel input tensor includes a carrier phase residual feature channel and a carrier-to-noise ratio feature channel; The step of extracting the carrier phase residual and obtaining the carrier-to-noise ratio includes: extracting the carrier phase residual through unscented Kalman filtering; and obtaining the corresponding carrier-to-noise ratio through pseudo-satellite observation data.

[0010] Optionally, the extraction of carrier phase residuals via unscented Kalman filtering includes: Using the user's two-dimensional position as the state variable and the carrier phase observation value after inter-satellite single-difference processing as the observation value, the predicted value of the observation value is derived based on the unscented Kalman filter and used as the predicted value of the carrier phase observation value after inter-satellite single-difference processing. The difference between the predicted value and the actual carrier phase observation value after inter-satellite single-difference processing is calculated to obtain the carrier phase residual.

[0011] Optionally, the reference pseudo-satellite does not have carrier phase residuals, and the carrier phase residual feature channel of its pixel is masked using masking technology to exclude it from the training process; The carrier phase residual feature channel of the center pixel of the two-dimensional grid structure is excluded using the same masking technique.

[0012] Optionally, the spatial topology convolutional neural network model applies normalization to the input features to alleviate interference caused by the scale difference between carrier phase residual and carrier-to-noise ratio, applies the LeakyReLU activation function to avoid the gradient vanishing problem, is trained with the mean squared error loss function, and optimizes the network parameters based on the results of 10-fold cross-validation.

[0013] The mean squared error loss function calculates the mean squared error loss between the carrier phase multipath error prediction generated by the spatial topology convolutional neural network model and the actual carrier phase multipath error.

[0014] Optionally, the corrected inter-satellite single-difference processed carrier phase observations are presented in the following form: ; in, This represents the integer ambiguity after the initialization method based on known points is fixed. This represents the corrected carrier phase observation; This represents the carrier phase observation value after inter-satellite single-difference processing; The wavelength of the pseudo-satellite signal; Carrier phase multipath error prediction generated for the first thread; The real-time calculation of the user's two-dimensional position using the corrected carrier phase observations based on unscented Kalman filtering includes: using the user's two-dimensional position as the state variable and the corrected carrier phase observations as the observations, deriving the updated value of the state variable based on unscented Kalman filtering, and using it as the user position estimate.

[0015] The present invention also provides an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to execute the indoor pseudo-satellite positioning method based on carrier phase multipath error modeling.

[0016] The present invention also provides a computer-readable storage medium storing computer instructions for causing a processor to execute the described indoor pseudo-satellite positioning method based on carrier phase multipath error modeling.

[0017] By employing the above technical solution, the present invention provides an indoor pseudo-satellite positioning method based on carrier phase multipath error modeling, which has at least the following beneficial effects: (1) Unlike existing methods that convert processed observation data into sequential matrices or two-dimensional projected images, the spatial topology convolutional neural network model constructed in this invention uses the actual spatial layout of pseudo-satellites to construct its input features. The spatial topology of the pseudo-satellite configuration is explicitly embedded into the input layer of the model. Each pixel in its two-dimensional grid structure corresponds to a specific pseudo-satellite, enabling the spatial topology convolutional neural network model to directly capture the spatial correlation between pseudo-satellites during the training process. (2) The present invention uses carrier phase residual and carrier-to-noise ratio as feature channels to construct a structured dual-channel input tensor, which effectively captures the spatial distribution characteristics of carrier phase multipath error; (3) The dual-threaded unscented Kalman filter positioning framework designed in this invention operates in the observation domain, collectively processes the signals of all pseudo-satellites, and outputs the carrier phase observation values ​​corrected by all non-reference pseudo-satellites, thereby achieving high-precision user positioning in indoor scenarios. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of an indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to the present invention; Figure 2 This is a technical roadmap of an embodiment of the present invention; Figure 3 This is a schematic diagram of the multipath effect at the experimental site according to an embodiment of the present invention; Figure 4 This is a spatial information diagram of pseudo-satellites and static sampling points according to an embodiment of the present invention; Figure 5 This is a schematic diagram of mapping pseudo-satellites into a 3×3 two-dimensional grid structure according to an embodiment of the present invention; Figure 6 This is a structural diagram of the spatial topological convolutional neural network model according to an embodiment of the present invention. Detailed Implementation

[0019] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0020] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0021] Please refer to Figures 1-6This illustration shows a specific implementation of this embodiment. This embodiment involves collecting pseudosatellite observation data; calculating carrier phase observations and eliminating systematic errors, fixing integer ambiguity, and deriving carrier phase multipath error; mapping the actual spatial layout of the pseudosatellites into a two-dimensional grid structure, extracting carrier phase residuals and carrier-to-noise ratio, and constructing a dual-channel input tensor; constructing and training a spatial topological convolutional neural network model, using the dual-channel input tensor as input features to generate carrier phase multipath error prediction; and designing a dual-threaded unscented Kalman filter positioning framework, which sequentially corrects carrier phase observations and performs real-time calculation of the user's two-dimensional position in two threads to achieve accurate positioning in indoor scenarios, thereby mitigating the multipath effect of indoor pseudosatellite systems and improving indoor positioning accuracy.

[0022] Please refer to Figure 1 This embodiment proposes an indoor pseudo-satellite positioning method based on carrier phase multipath error modeling, which includes the following steps: Step 1: Experimental System Setup and Data Acquisition In this embodiment, the experimental area has a semi-enclosed structure at the bottom, and the site contains a large number of reflective surfaces such as glass, which causes severe multipath effects during the propagation of pseudosatellite signals. Figure 3 Here is a schematic diagram. Figure 3 In the spatial diagram on the left, solid lines represent the propagation path of direct signals, and dashed lines represent the propagation path of indirect signals. Figure 3 In the reflection diagram on the right, The incident angle of a non-direct signal before it passes the reflector; direct and non-direct signals are superimposed to form a multipath signal.

[0023] This embodiment uses a u-blox C102-F9R receiver. The spatial layout of each pseudosatellite and static sampling point is as follows: Figure 4 As shown, eight pseudo-satellites (G01~G08) are concentrated in a circular area with a radius not exceeding 2m, and u-blox receivers are evenly distributed in A1~E5. Figure 4 (The solid circles in the middle correspond to the 25 known static sampling points in the training set) and T1, T2, T3 ( Figure 4 Pseudo-satellite observation data were collected from three unknown static sampling points (corresponding to the test set) with hollow circular points in the center.

[0024] Step 2: Carrier Multipath Error Extraction (1) Inter-satellite single difference Because pseudorange multipath errors are large and unstable, this invention focuses solely on carrier phase observations for carrier phase multipath error prediction and positioning. Compared to the meter-level accuracy of pseudorange observations, carrier phase measurements offer millimeter-level accuracy, providing a more reliable foundation for achieving sub-meter or centimeter-level positioning accuracy.

[0025] This embodiment uses the carrier phase observation equation as the positioning basis, extracts the carrier phase multipath error of the sampling points observed in step one using the inter-satellite single-difference method, and uses the extracted carrier phase multipath error as supervision for the spatial topological convolutional neural network model. The carrier phase observation equation used in this embodiment is as follows: ; in, For receivers and pseudo-satellites Carrier phase observations between; For receivers and pseudo-satellites The geometric distance between them is calculated based on the coordinates from the pseudo-satellite and receiver from the total station; The speed of light; and Receiver and pseudosatellite respectively Clock difference; and pseudo-satellites Hardware delay with the receiver; The wavelength of the pseudo-satellite signal is defined as the ratio of the speed of light to the frequency of the pseudo-satellite signal transmission, and its value is approximately 0.19 meters. , , pseudo-satellites The integer ambiguity, observation noise, and carrier phase multipath error are all addressed. Unlike traditional satellite positioning systems, the pseudo-satellites in this embodiment are deployed indoors, where carrier phase multipath error is the primary source of error for indoor positioning, while the influence of the atmosphere and ionosphere is almost zero.

[0026] The inter-satellite single-difference method is used to eliminate systematic errors (clock differences and hardware delays between the receiver and the pseudosatellite), retaining only carrier phase multipath errors. A reference pseudosatellite is selected. Based on the carrier phase observation equation, the target pseudo-satellite With reference pseudo-satellite By subtracting the observed values, we get: ; in, This refers to the carrier phase observation values ​​of the target pseudo-satellite and the reference pseudo-satellite after single-difference processing based on measurement data from the same receiver, i.e., the carrier phase observation values ​​after inter-satellite single-difference processing. The geometric distance between the target pseudosatellite and the reference pseudosatellite is calculated based on the measurement data from the same receiver after single difference, i.e., the geometric distance after inter-satellite single difference processing, which is based on the pseudosatellite coordinates from the total station. This refers to the integer ambiguity after inter-satellite single-difference processing; This refers to the carrier phase multipath error after inter-satellite single-difference processing. This indicates the observation noise after inter-satellite single-difference processing.

[0027] Pseudo-satellites (transmitting antennas) share the same clock source, and the receiver clock difference... With pseudo-satellite clock bias The difference is canceled out in the single difference, and since the connection cable between the pseudosatellite signal transmitter and the transmitting antenna is of essentially the same length and specification, the hardware delay caused by the cable ( , The variation is minimal (inter-channel delay is less than 0.015 periods) and does not fluctuate over time, so it can be ignored.

[0028] (2) Fixed integer ambiguity This embodiment uses the Known Point Initialization (KPI) method to obtain the initial ambiguity. After calculating the geometric distance between the receiver and each pseudosatellite using the precise coordinates measured by a total station, the integer ambiguity is fixed using the following formula: ; in, The fixed integer ambiguity; This is a rounding function. Indicates the wavelength of pseudo-satellite signals The reciprocal of.

[0029] The fixed integer ambiguity will be substituted as a known parameter into the carrier phase observation equation to derive the carrier phase multipath error. : ; Therefore, by combining the known coordinates of the pseudosatellite and the receiver, the carrier phase multipath error can be successfully extracted and used as a supervisor for the spatial topological convolutional neural network model.

[0030] Furthermore, the integer ambiguity calculated using the KPI method can be used as a known value for calculating the user's two-dimensional position in the test set during subsequent positioning. If a cycle slip occurs during the observation phase, the ambiguity needs to be recalculated.

[0031] Step 3: Input Tensor Construction (1) Feature extraction In this embodiment, carrier phase residual and carrier-to-noise ratio are selected as input information for the spatial topology convolutional neural network model. The carrier-to-noise ratio can be directly read from pseudo-satellite observation data collected from static sampling points.

[0032] After inter-satellite single-difference processing of the carrier phase observations, the remaining error is only the carrier phase multipath error. Therefore, the carrier phase residual can be regarded as an estimate of the carrier phase multipath error. In this embodiment, the posterior residual of the carrier phase is used as the carrier phase residual. The posterior residual refers to the difference between the actual observation and the predicted value of the observation obtained from the filter. In indoor pseudosatellite positioning systems, the close spatial arrangement between the receiver and the pseudosatellite significantly aggravates the nonlinear characteristics of the observation model. Therefore, this embodiment uses an unscented Kalman filter (UKF) to extract the posterior residual to reduce the negative impact of nonlinear errors in the pseudosatellite system.

[0033] For this embodiment, the state equation and observation equation for the unscented Kalman filter are set as follows: ; in, for The state quantity at any given moment is set by the user at that moment. At time 20, the state variable is set to the given initial two-dimensional position of the user during the initialization of the unscented Kalman filter. Subsequent observation epochs use the updated value of the state variable obtained by the unscented Kalman filter of the previous observation epoch. for The time-based observations are set as carrier phase observations after inter-satellite single-difference processing; and These are the state transition function and the observation function, respectively. and They are respectively Time-of-flight noise and Observational noise during state estimation at time step; In practical applications, to accelerate the convergence speed of unscented Kalman filtering, its initial state variables can be given as fuzzy positions close to the user's initial two-dimensional position (true value).

[0034] Generate and propagate sigma points: ; in, for The Sigma points generated at each moment, and They are respectively State quantity estimates and covariance matrix at time t. For scaling parameters, and Indicates adjustment empirical parameters, Used to control the overall scale of the sigma point's distance from the mean. As an auxiliary scaling parameter, it fine-tunes the distribution shape. This indicates the state dimension, used to determine the number of sigma points and to calculate the scaling parameters. The sigma points are numbered for threshold discrimination based on different numbers of sigma points; in this embodiment... and Set them to 0.1 and 1 respectively.

[0035] Unscented Kalman filtering uses a given state estimate Covariance Matrix generate The state distribution is represented by sigma points; the weight matrix for each sigma point is as follows: ; in, This represents the weight matrix of the sigma points. , , These represent the cases where the number of generated sigma points differs ( , , The corresponding weight matrix; The unscented Kalman filtering process consists of two steps: prediction and update. The prediction step is as follows: ; ; ; in, Based on At any time, through the state transition function After transmission The sigma point at time; Based on Predictions made using weighted statistical methods at all times State quantity at any given moment; Based on The prediction covariance matrix at time 1, Based on The process noise matrix at each time step; The update steps are as follows: ; In the formula for Observations for time prediction; Derive the new information covariance matrix at time k and cross-covariance matrix and the Kalman gain matrix : ; ; ; in, To observe the noise covariance matrix, Indicates the transpose operation; The updated values ​​of the state variables at time k are as follows: ; in, for Updated value of the state variable at time; Carrier phase residual extraction: ; in, for The carrier phase residual at time t.

[0036] (2) Spatial topology mapping like Figure 5 As shown, the actual spatial layout of the eight pseudo-satellites (G01~G08) is mapped to a 3×3 two-dimensional grid structure (corresponding to...). Figure 6 The input layer structure (representing the input shape of the model) uses the center pixel of the grid as the pseudosatellite signal transmitter. Each pixel in the grid corresponds to one pseudosatellite. To accurately capture the spatial correlation of carrier phase multipath errors in the pseudosatellite system, this embodiment combines spatial topology mapping and channel selection to construct a 3×3×2 feature vector as a dual-channel input tensor.

[0037] This invention proposes an innovative explicit spatial feature mapping method for estimating carrier phase multipath errors in pseudosatellites. The input layer of the model is designed with a 3×3 structure, where each pixel corresponds to a pseudosatellite. In this embodiment, pseudosatellite G01 is used as the reference pseudosatellite for inter-satellite single difference. The carrier phase residual value of the pixel containing G01 in the grid is in a missing state. Additionally, the center pixel (pseudosatellite signal transmitter) also contains a missing pseudosatellite. To address this issue, the model uses masking techniques to preserve other feature values ​​such as the carrier-to-noise ratio and observations of G01 and the center pixel. This ensures the integrity of the input tensor while maintaining the normal operation of the spatial topological neural network model, and masks the influence of missing positions on gradient updates during training.

[0038] By combining the carrier phase residual with the carrier-to-noise ratio, a dual-channel input tensor is constructed, including a carrier phase residual feature channel and a carrier-to-noise ratio feature channel, which serve as the input features of the spatial topology convolutional neural network model.

[0039] This invention uses carrier phase residual and carrier-to-noise ratio as feature channels to construct a structured dual-channel input tensor, effectively capturing the spatial distribution characteristics of carrier phase multipath error.

[0040] Step 4: Construction and Training of Spatial Topological Convolutional Neural Model (1) Model building The spatial topological convolutional neural network model structure in this embodiment is as follows: Figure 6 As shown, the model adopts a hierarchical structure of 3 convolutional layers, 1 pooling layer, and a fully connected layer, with the convolutional kernel size designed differently to capture spatial correlations at different scales. Figure 6 In the middle input layer, 1, 2, ..., n represent each input channel; k1, k2 and k n These represent the convolution kernels between the input layer and the convolutional layer, between convolutional layers, and between the convolutional layer and the pooling layer, respectively; MP2 to MP8 in the output layer represent the carrier phase multipath error predictions of the non-reference pseudo-satellites G02 to G08, respectively.

[0041] In the model, shallow convolutions focus on the geometric relationships of pseudo-satellites within a local neighborhood, for example... Figure 6 In the input layer, the shaded regions formed by G01, G02, and G08 are used to extract the spatial correlation of their observed features through convolution operations; deeper convolutions gradually integrate spatial topological correlations over a larger range. This progressive spatial feature propagation mechanism utilizes the spatial relationships between adjacent pseudosatellites and the global spatial topological features of the pseudosatellite system to explicitly spatially model carrier phase multipath errors, enhancing its ability to accurately capture the spatial correlation of multipath errors. Fully connected layers (FC) flatten the nonlinear relationships of the high-dimensional spatial features extracted by the convolutional layers into a single dimension, thereby supporting the parallel output of multiple targets. The model output layer adopts a spatial structure aligned with the input layer, with each pixel corresponding to the carrier phase multipath error predictions (MP2 to MP8) for pseudosatellites G02 to G08. This alignment method between input and output dimensions maintains the spatial consistency of the feature mapping, enabling the nonlinear relationship between observed features and carrier phase multipath errors to be directly correlated through pixel positions.

[0042] Unlike existing methods that convert processed observation data into sequential matrices or two-dimensional projected images, the spatial topology convolutional neural network model constructed in this invention uses the actual spatial layout of pseudosatellites to build its input features. The spatial topology of the pseudosatellite configuration is explicitly embedded into the input layer of the model, and each pixel in its two-dimensional grid structure corresponds to a specific pseudosatellite, enabling the spatial topology convolutional neural network model to directly capture the spatial correlation between pseudosatellites during the training process.

[0043] (2) Training strategy In this embodiment, training set data and test set data can be constructed based on the collected pseudo-satellite observation data, and the training set data can be used for model training.

[0044] Considering the scale difference between carrier-to-noise ratio and carrier phase residuals can interfere with feature weights during model training, this embodiment normalizes the input features on both the training and test sets to balance feature scales. During training, to improve the model's generalization ability and reduce overfitting risk, a 10-fold cross-validation strategy is adopted: the original training set is divided into 10 independent subsets. In each fold, one subset is used as the validation set, and the remaining nine subsets are used as the new training set, for a total of 10 iterations. This ensures the model considers the nonlinear relationship between the feature values ​​and the target value of each sample. The results of all folds are compared to evaluate the overall model performance and reduce the risk of overfitting. Throughout the training process, the model gradually learns the nonlinear spatial relationship of samples in each batch and continuously optimizes the network weights using the validation set results to reduce prediction error. Given that the model performance is similar across all 10-fold cross-validations, the fold with the best performance on the validation set is selected for the testing phase.

[0045] During model training, the LeakyReLU activation function is applied to avoid the vanishing gradient problem, and the mean squared error loss function is used for training. The formulas for the LeakyReLU activation function and the mean squared error loss function are as follows: ; ; In the above formula, This represents the LeakyReLU activation function. It is a very small positive number to provide a small slope when the input is negative to avoid the gradient vanishing problem; This represents the input value of the LeakyReLU activation function, which is the linear output of the neurons in the previous convolutional layer of the model before activation; This represents the mean squared error loss value. Indicates the first The actual carrier phase multipath error of each sample The first one generated by the spatial topological convolutional neural network model represents the first... Carrier phase multipath error prediction for each sample This represents the total number of samples involved in the calculation of mean squared error loss.

[0046] Step 5: Dual-thread UKF Indoor Positioning Correction During the testing phase, the model uses the parameters obtained during the training phase to correct carrier phase observations and locate users on the test set data (and corresponding static sampling points). The positioning effect is then evaluated to verify the model's generalization ability in the same indoor environment.

[0047] After obtaining the trained spatial topology convolutional neural network model, this embodiment designs a dual-threaded unscented Kalman filter positioning framework to achieve real-time multipath error mitigation and high-precision indoor positioning by combining the spatial topology convolutional neural network model with unscented Kalman filtering.

[0048] For each observation epoch: (1) Thread 1 In an indoor setting, pseudosatellite observation data is acquired in real time. Inter-satellite single-difference and KPI methods are used to fix integer ambiguities for user 2D position calculation in thread two. Unscented Kalman filtering is used to extract carrier phase residuals, constructing a dual-channel input tensor which is then fed into a spatial topology convolutional neural network model to generate carrier phase multipath error predictions for that observation epoch.

[0049] (2) Thread 2 The carrier phase multipath error prediction generated by the first thread is used to correct the carrier phase observations after inter-satellite single-difference processing. Then, using the user's two-dimensional position as the state variable and the corrected carrier phase observations as the observations, the updated values ​​of the state variables are derived based on unscented Kalman filtering, and the user's two-dimensional position is calculated in real time to complete the positioning correction and achieve precise single-point positioning calculation based on inter-satellite single-difference.

[0050] This dual-threaded framework ensures that carrier phase observations at each observation epoch can be corrected in real time, enabling real-time positioning correction. The process settings for the dual-threaded unscented Kalman filter are consistent with those for extracting the carrier phase residual. The corrected carrier phase observation value is defined as: ; in This represents the integer ambiguity after the initialization method based on known points is fixed. This represents the corrected carrier phase observation; This represents the carrier phase observation value after inter-satellite single-difference processing; The wavelength of the pseudo-satellite signal; This is the carrier phase multipath error prediction generated by the trained spatial topology convolutional neural network, specifically the carrier phase multipath error prediction generated by the first thread.

[0051] The dual-threaded unscented Kalman filter positioning framework designed in this invention operates in the observation domain, collectively processes the signals of all pseudo-satellites, and outputs the carrier phase observation values ​​corrected by all non-reference pseudo-satellites, thereby achieving high-precision user positioning in indoor scenarios.

[0052] The technical roadmap of this embodiment above can be referred to. Figure 2 .

[0053] This application also provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the indoor pseudo-satellite positioning method based on carrier phase multipath error modeling.

[0054] This application also provides a computer-readable storage medium storing computer instructions that are used to cause a processor to execute the described indoor pseudo-satellite positioning method based on carrier phase multipath error modeling.

[0055] This embodiment also provides the following table 1, which shows the positioning results before and after correction of the carrier phase observations for three test sites (i.e., static sampling points T1, T2, and T3 corresponding to the test set): Table 1. Positioning deviation before and after carrier phase observation correction

[0056] Table 1 shows the positioning deviations of the three test stations before and after correction. After correcting the carrier phase observations using the indoor pseudo-satellite positioning method based on carrier phase multipath error modeling of this invention, the two-dimensional positioning deviations (2D) of stations T1, T2, and T3 decreased from 0.309 m, 0.509 m, and 0.563 m to 0.114 m, 0.165 m, and 0.142 m, respectively, corresponding to accuracy improvements of 62.9%, 67.6%, and 74.8%. In both the X and Y directions, the deviations generally showed a decreasing trend. The Y-direction deviation at station T1 increased slightly from 0.054 m to 0.068 m, reflecting normal fluctuations under conditions of small initial errors. The most significant improvement occurred at station T3 in the Y direction, where the deviation dropped dramatically from 0.540 m to 0.015 m, a reduction of 97.1%. Experimental results demonstrate that the method of this invention can significantly improve the horizontal positioning accuracy of all test stations.

[0057] It should be noted that the basic processing methods for inter-satellite single difference in pseudo-satellite positioning, the known point initialization method for solving integer ambiguity, the unscented Kalman filtering, and the basic principles of 10-fold cross-validation in the model training stage involved in this invention are all common knowledge in the art, so such basic knowledge will not be described in more detail.

[0058] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0059] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0060] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. An indoor pseudo-satellite positioning method based on carrier phase multipath error modeling, characterized in that, include: In an indoor experimental setting, a pseudo-satellite and a receiver were deployed. A total station was used to calibrate the coordinates of the pseudo-satellite and the receiver. The receiver then collected observation data from the pseudo-satellite. The carrier phase observations of the receiver and the pseudosatellite are obtained based on pseudosatellite observation data. A reference pseudosatellite is selected for inter-satellite single-difference processing to eliminate systematic errors in the carrier phase observations. The integer ambiguity is fixed based on the known point initialization method. The carrier phase multipath error is derived as the actual carrier phase multipath error used for training the spatial topology convolutional neural network model. The systematic error includes the clock bias and hardware delay of the receiver and the pseudosatellite. The actual spatial layout of pseudo-satellites is mapped to a two-dimensional grid structure. Combining the current user's two-dimensional position and the carrier phase observation value after inter-satellite single-difference processing, the carrier phase residual is extracted from the two-dimensional grid structure and the carrier-to-noise ratio is obtained to construct a dual-channel input tensor. A spatial topological convolutional neural network model containing convolutional layers, pooling layers, and fully connected layers is constructed and trained. The spatial topological convolutional neural network model uses a dual-channel input tensor as input features to generate carrier phase multipath error prediction, and optimizes the model parameters by combining a cross-validation algorithm. Design a dual-threaded unscented Kalman filter localization framework. For the first thread of each observation epoch, real-time pseudo-satellite observation data is collected in an indoor scene. A dual-channel input tensor is constructed and input into a trained spatial topology convolutional neural network model to generate carrier phase multipath error prediction for that observation epoch. The second thread uses the carrier phase multipath error prediction generated by the first thread to correct the carrier phase observations after inter-satellite single-difference processing. The corrected carrier phase observations are then used to perform real-time calculation of the user's two-dimensional position based on unscented Kalman filtering to obtain the user's position estimate and achieve accurate positioning in indoor scenes.

2. The indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to claim 1, characterized in that: The pseudo-satellites are centrally deployed within a circular area with a radius not less than a preset value and connected to the same pseudo-satellite signal transmitter as a unified clock source. The receivers are sequentially deployed at evenly distributed static sampling points to collect pseudo-satellite observation data from each static sampling point.

3. The indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to claim 1, characterized in that: The acquisition of carrier phase observations of the receiver and the pseudosatellite based on pseudosatellite observation data includes: Construct carrier phase observation equations to obtain carrier phase observations from the receiver and the pseudosatellite: ； in, For receivers and pseudo-satellites Carrier phase observations between; For receivers and pseudo-satellites The geometric distance between them is calculated based on the coordinates from the pseudo-satellite and receiver from the total station; The speed of light; and Receiver and pseudosatellite respectively Clock difference; and pseudo-satellites Hardware delay with the receiver; The wavelength of the pseudo-satellite signal; , , pseudo-satellites Integer ambiguity, observation noise, and carrier phase multipath error; The step of selecting a reference pseudo-satellite for inter-satellite single-difference processing to eliminate systematic errors in carrier phase observations includes: Current pseudo-satellites Select a pseudo-satellite as the target pseudo-satellite. To reference pseudo-satellites, the inter-satellite single-difference method is used to eliminate systematic errors: ； in, This refers to the carrier phase observation values ​​of the target pseudo-satellite and the reference pseudo-satellite after single-difference processing based on measurement data from the same receiver, i.e., the carrier phase observation values ​​after inter-satellite single-difference processing. The geometric distance between the target pseudosatellite and the reference pseudosatellite is calculated based on the measurement data from the same receiver after single difference, i.e., the geometric distance after inter-satellite single difference processing, which is based on the pseudosatellite coordinates from the total station. This refers to the integer blurring after inter-satellite single-difference processing; This refers to the carrier phase multipath error after inter-satellite single-difference processing. This indicates the observation noise after inter-satellite single-difference processing; The method for fixing integer ambiguity based on known point initialization includes: The integer ambiguity is fixed using the known point initialization method, which takes the following form: ； in, The fixed integer ambiguity; This is a rounding function. Indicates the wavelength of pseudo-satellite signals The reciprocal of; The derived carrier phase multipath error includes: Using fixed integer ambiguity Carrier phase observations after inter-satellite single-difference processing Geometric distance values ​​after inter-satellite single-difference processing Combined with pseudo-satellite signal wavelength Derivation of carrier phase multipath error : 。 4. The indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to claim 1, characterized in that: The two-dimensional grid structure is constructed based on the position of the pseudo-satellites in actual space, with each pixel in the grid corresponding to one pseudo-satellite; The dual-channel input tensor includes a carrier phase residual feature channel and a carrier-to-noise ratio feature channel; The step of extracting the carrier phase residual and obtaining the carrier-to-noise ratio includes: extracting the carrier phase residual through unscented Kalman filtering; The corresponding carrier-to-noise ratio is obtained by using pseudosatellite observation data.

5. The indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to claim 4, characterized in that: The extraction of carrier phase residuals through unscented Kalman filtering includes: Using the user's two-dimensional position as the state variable and the carrier phase observation value after inter-satellite single-difference processing as the observation value, the predicted value of the observation value is derived based on the unscented Kalman filter and used as the predicted value of the carrier phase observation value after inter-satellite single-difference processing. The difference between the predicted value and the actual carrier phase observation value after inter-satellite single-difference processing is calculated to obtain the carrier phase residual.

6. The indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to claim 4, characterized in that: The reference pseudo-satellite does not have carrier phase residuals, and the carrier phase residual feature channel of the pixel where it is located is masked using masking technology to exclude it from the training process; The carrier phase residual feature channel of the center pixel of the two-dimensional grid structure is excluded using the same masking technique.

7. The indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to claim 1, characterized in that: The spatial topology convolutional neural network model applies normalization to the input features to alleviate interference caused by the scale difference between carrier phase residual and carrier-to-noise ratio, applies the LeakyReLU activation function to avoid the gradient vanishing problem, is trained with the mean squared error loss function, and optimizes the network parameters based on the results of 10-fold cross-validation. The mean squared error loss function calculates the mean squared error loss between the carrier phase multipath error prediction generated by the spatial topology convolutional neural network model and the actual carrier phase multipath error.

8. The indoor pseudo-satellite positioning method based on carrier phase multipath error modeling according to claim 1, characterized in that: The carrier phase observations after the corrected inter-satellite single-difference processing are presented in the following form: ； in, This represents the integer ambiguity after the initialization method based on known points is fixed. This represents the corrected carrier phase observation; This represents the carrier phase observation value after inter-satellite single-difference processing; The wavelength of the pseudo-satellite signal; Carrier phase multipath error prediction generated for the first thread; The real-time calculation of the user's two-dimensional position using the corrected carrier phase observations based on unscented Kalman filtering includes: using the user's two-dimensional position as the state variable and the corrected carrier phase observations as the observations, deriving the updated value of the state variable based on unscented Kalman filtering, and using it as the user position estimate.

9. An electronic device, characterized in that, The electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the indoor pseudo-satellite positioning method based on carrier phase multipath error modeling as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the indoor pseudo-satellite positioning method based on carrier phase multipath error modeling as described in any one of claims 1-8.

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