A standard single point positioning method based on big data cross-modal residual model compensation

Abstract

The application provides a standard single point positioning method based on a big data cross-modal residual model compensation, adopts a non-directional graph to establish the connection between the time and the residual, the space and the residual, the satellite elevation angle and the residual, and the satellite azimuth angle and the residual conditions, then utilizes random walk to establish the global relationship, and finally performs cross-modal representation learning on the tuples generated by the random walk to establish a historical relationship model. In prediction, the final prediction result is obtained according to the input space condition, the satellite elevation angle condition and the satellite azimuth angle condition combined with the output strategy. The residual is finally compensated into the standard single point positioning algorithm. The application has higher precision, does not need to depend on external networks at all times, and can ensure that the update of the model can be used for localization calculation with the best precision within 60 days.

Description

Technical Field

[0001] This invention belongs to the field of navigation and positioning, and in particular relates to a standard single-point positioning method based on big data cross-modal residual model compensation. Background Technology

[0002] As one of the primary observations of satellite signals, pseudorange plays a crucial role. Although the accuracy of pseudorange positioning is not as high as that of increasingly sophisticated precise point positioning and real-time differential positioning methods, its simple algorithms, convenient station setup, and low dependence on external network information make it irreplaceable in many positioning scenarios. However, there is currently a lack of detailed research on the patterns of pseudorange errors. A thorough understanding and prediction of its residuals will contribute to a better understanding of satellite signal systems.

[0003] From standard point positioning (SNP) to precise point positioning (SNP), and then to differential positioning, GNSS positioning accuracy has been continuously improving. However, this improvement has brought drawbacks such as longer convergence times and increased dependence on external network information. As the simplest, most real-time, and most widely used positioning algorithm, standard point positioning still has its unique advantages. Currently, the most common standard positioning algorithms are derived iteratively using least squares or Kalman filtering methods. However, in the iteration process, since the pseudorange residual is not a known quantity, it is often ignored or added to the coordinate and clock error unknowns for simultaneous solution. This is a significant factor contributing to the relatively low accuracy of standard point positioning.

[0004] Existing technologies also estimate observation noise, which can be broadly categorized into three types: First, treating it as a stochastic model based on elevation angle; Bernese software treats it as a cosine function model, GAMIT software as a sine function model, and Barnes software as an exponential function model. Second, using stochastic models for signal-to-noise ratio. Third, locating the observation and then using least squares to continuously correct its observation residuals. However, these are not models purely for pseudorange residuals and have relatively low accuracy. Summary of the Invention

[0005] To gain a clearer understanding of the pseudorange residual variation patterns and improve the accuracy of standard point positioning (SPO), this invention proposes a SPO method based on big data cross-modal residual model compensation. This invention uses an undirected graph to establish relationships between time and residual, space and residual, satellite elevation angle and residual, and satellite azimuth angle and residual conditions. Then, random walks are used to establish global relationships. Finally, the tuples generated by the random walks are used for cross-modal representation learning to establish a historical relationship model. In prediction, the final prediction result is obtained by combining the input spatial conditions, satellite elevation angle conditions, and satellite azimuth angle conditions with the output strategy. This residual is then compensated into the standard SPO algorithm. Compared to traditional standard SPO methods, this method achieves higher accuracy and does not require constant reliance on external networks. Updating the model every 2 to 3 months ensures that the model maintains its optimal performance for localized computation within 50 days.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A standard single-point localization method based on big data cross-modal residual model compensation includes the following steps:

[0008] Step 1: Obtain the pseudorange residual;

[0009] Step 2: Construct an undirected graph;

[0010] Step 3: Construct random walk tuples;

[0011] Step 4: Establish a cross-modal representation model;

[0012] Step 5: Obtain the prediction strategy;

[0013] Step 6: Design a standard single-point positioning method.

[0014] Further, step 1 includes:

[0015] The pseudorange residuals were calculated using precise ephemeris and observation files:

[0016]

[0017] In the formula These are pseudorange observations of station r and satellite j at frequency i. Its true distance, c is the speed of light, dt r dt (j) These are receiver clock bias and satellite clock bias, cI (j) (t) is the ionospheric delay, cT (j) (t) represents the tropospheric delay, ε′ ρ For residuals;

[0018] The obtained pseudorange residuals are combined with the corresponding satellite number, elevation angle, azimuth angle, observation station coordinates and observation station time to form a data set. Each element in the data set is regarded as a node.

[0019] Furthermore, in step 2, the undirected graph indicates whether nodes are related and the degree of correlation, and the weights between nodes are set to their frequency of occurrence.

[0020] Further, step 3 includes:

[0021]

[0022] In the formula, v (t) It is the current node, p() is the probability, p(v (t+1) |v (t) ) indicates from v (t) Node selects next node v (t +1) The probability is given by β(), where β() represents the set of neighboring nodes and d() represents the number of neighboring nodes. A random walk sequence W = RandomWalk(G,v0,T) = (v0,v1, ...,v2) is generated. T-1 ), where RandomWalk() represents the random walk algorithm, G represents the undirected graph relation, v0 represents the starting node, and T represents the sequence length.

[0023] Further, step 4 includes:

[0024] Based on the characteristics of the data set, four undirected graphs were constructed, and random walk sequences were established for each graph. This represents the relationships in an undirected graph, where X and Y represent a class of nodes, ∪ represents an association, and δ represents a relationship. XY The probability that node i generates node j, representing the correlation between nodes, is:

[0025]

[0026] In the formula u j v i u k Let X be the embedding vector of node j, node i, and node k, where k represents all nodes adjacent to node i, and X represents the set of nodes adjacent to i; the actual calculated probability is:

[0027]

[0028] In the formula ε ij is the edge weight of node i and node j, and X represents the set of nodes adjacent to i;

[0029] Define G XY The loss function is:

[0030]

[0031] In the formula, KuL represents the KL divergence, expressed as: Where n represents the possible values ​​of random variables p and q, X represents the set of nodes adjacent to i, and Y represents the set of nodes adjacent to j. Therefore, the final loss function F for training four undirected graphs simultaneously is as follows:

[0032]

[0033] In the formula These represent the loss functions for observation station coordinates and residuals, satellite elevation angle and residuals, satellite azimuth angle and residuals, and satellite number and residuals, respectively.

[0034] To reduce computational overhead, a negative sampling method is adopted, and the final learned loss function S is:

[0035]

[0036] Where σ() represents the sigmoid function, M represents the number of negative samples used, and u j v i u k It is the embedding vector of node j, node i and node k, where k represents all nodes adjacent to node i.

[0037] Further, step 5 includes:

[0038] After obtaining the residual prediction model, prediction is performed. Due to the characteristics of pseudorange residuals, nodes that are closer in time are more reliable. The input conditions include the satellite's elevation and azimuth angles and the observation station coordinates. Using the input conditions, the 10 closest residual values ​​in the model's mapping space are calculated. The final prediction result is obtained by weighting these 10 residual values ​​based on their most recent historical occurrence time. The weighting method is as follows:

[0039]

[0040]

[0041] In the formula, α is the weight, α i It is the weight of the i-th predicted value, t now ,t s ,t start These represent the current time, the time the predicted value was in the historical model, and the model start time, respectively.

[0042] Further, step 6 includes:

[0043] L=GX+ε′ ρ(10)

[0044] G = [g1, g2, ..., g] i (11)

[0045]

[0046] X = (G T G) -1 G T L (13)

[0047] In equation (11), g i As shown in equation (12), is the intermediate parameter, where They represent r respectively i Partial derivatives with respect to x, y, and z;

[0048] Pseudorange positioning is shown in equations (10)-(13), where L represents the difference between the pseudorange and geometric distance between the receiver and the GNSS satellite, which is the pseudorange residual.

[0049] Beneficial effects:

[0050] 1. This invention constructs a unified spatial description of diverse heterogeneous information: This invention can predict pseudorange observation residuals under different time and space conditions, satellite elevation angles, and satellite azimuth angles. These conditions have different descriptive dimensions and include numerical elements, textual elements, and coordinate elements, making it more applicable.

[0051] 2. This invention uses graph neural networks and natural language processing to handle multi-factor prediction problems: This invention involves not only time factors, but also spatial factors, as well as other factors such as satellite number, elevation angle, and azimuth angle. These factors are difficult to describe uniformly using time series analysis or spatial analysis models. By using graph neural networks and natural language processing, the above information is placed in the same dimension, simplifying the problem processing difficulty.

[0052] 3. This invention treats pseudorange residuals as known quantities for standard single-point positioning: This invention addresses the problem of previous standard single-point positioning methods that roughly estimated or ignored residuals, and performs inverse residual compensation, which further improves the accuracy of standard single-point positioning. Attached Figure Description

[0053] Figure 1 This is a flowchart of a standard single-point localization method based on big data cross-modal residual model compensation according to the present invention;

[0054] Figure 2 For G XY The diagram represents the relationships between nodes. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0056] like Figure 1 As shown, the standard single-point localization method based on big data cross-modal residual model compensation according to the present invention includes the following steps:

[0057] Step 1: Obtain pseudorange residuals:

[0058] The pseudorange residuals were calculated using precise ephemeris and observation files:

[0059]

[0060] In the formula These are pseudorange observations of station r and satellite j at frequency i. Its true distance, c is the speed of light, dt r dt (j) These are receiver clock bias and satellite clock bias, cI (j) (t) is the ionospheric delay, cT (j) (t) represents the tropospheric delay, ε′ ρ This is the desired residual.

[0061] The true distance is calculated using precise satellite ephemeris and known coordinates of the observatory. Ionospheric delay is determined using the Saastamoinen model, tropospheric delay is eliminated using dual-frequency measurement, satellite clock bias is obtained from precise ephemeris, and since observatory clock bias is difficult to obtain directly, it is replaced by clock bias from historical results used for PPP positioning settlement.

[0062] The acquired pseudorange residuals, along with the corresponding satellite number, elevation angle, azimuth angle, observation station coordinates, and time, form a data set. Each element in the data set is considered a node.

[0063] Step 2: Construct an undirected graph:

[0064] An undirected graph can indicate whether nodes are related and the degree of their relationship. The weights between nodes are set to the frequency of their occurrence.

[0065] Step 3: Construct random walk tuples:

[0066]

[0067] In the formula, v (t) It is the current node, p() is the probability, p(v (t+1) |v(t) ) indicates from v (t) Node selects next node v (t +1) The probability is given by β(), where β() represents the set of neighboring nodes and d() represents the number of neighboring nodes. A random walk sequence W = RandomWalk(G,v0,T) = (v0,v1, ...,v2) is generated. T-1 ), where RandomWalk() represents the random walk algorithm, G represents the undirected graph relation, v0 represents the starting node, and T represents the sequence length.

[0068] Step 4: Establish a cross-modal representation model:

[0069] Based on the characteristics of the data set, such as Figure 2 As shown, four sets of undirected graphs are constructed, and random walk sequences are established for each. Based on the characteristics of the data set, four sets of undirected graphs are constructed, and random walk sequences are established for each. Example 1 illustrates the relationships in an undirected graph, where X and Y represent a class of nodes, ∪ represents an association, and δ represents a relationship. XY The degree of association between nodes is represented by the probability that node i generates node j:

[0070]

[0071] In the formula u j v i u k Let X be the embedding vector of node j, node i, and node k, where k represents all nodes adjacent to node i, and X represents the set of nodes adjacent to i; the actual calculated probability is:

[0072]

[0073] In the formula ε ij Let G be the edge weights of nodes i and j, and X represent the set of nodes adjacent to i. Therefore, what needs to be learned is to make the theoretical probability approximate the true probability. XY The loss function is:

[0074]

[0075] In the formula, KuL represents the KL divergence, expressed as: Where n represents the possible values ​​of random variables p and q, X represents the set of nodes adjacent to i, and Y represents the set of nodes adjacent to j.

[0076]

[0077] In the formula These represent the loss functions for the observation station coordinates and residuals, the satellite elevation angle and residuals, the satellite azimuth angle and residuals, and the satellite number and residuals, respectively.

[0078] Because this computation is too large, a negative sampling method will be used to reduce the computational load. Therefore, the final learned loss function is:

[0079]

[0080] Where σ() represents the sigmoid function, M represents the number of negative samples used, and u j v i u k It is the embedding vector of node j, node i and node k, where k represents all nodes adjacent to node i.

[0081] Step 5: Obtain the prediction strategy:

[0082] Once the residual prediction model is obtained, prediction can be performed. Due to the characteristics of pseudorange residuals, points that are closer in time are more reliable. The input conditions include the satellite's elevation and azimuth angles, and the observation station coordinates. Based on these, the 10 most likely values ​​are predicted. The final prediction result is obtained by weighting the predicted values ​​according to the most recent occurrence time in history. The weighting method is as follows:

[0083]

[0084]

[0085] In the formula, α is the weight, α i The weight of the i-th predicted value, t now ,t s ,t start These are the current time, the time the predicted value was in the historical model, and the model start time, respectively.

[0086] Step 6: Design the positioning method:

[0087] L=GX+ε′ ρ (10)

[0088] G = [g1, g2, ..., g] i (11)

[0089]

[0090] X = (G T G) -1 G T L (13)

[0091] In equation (11), g iAs shown in equation (12), where They represent r respectively i Partial derivatives with respect to x, y, and z;

[0092] Pseudorange positioning is shown in equations (10)-(13), where L represents the difference between the pseudorange and geometric distance between the receiver and the GNSS satellite, called the pseudorange residual. In this method, the pseudorange residual is compensated, therefore

[0093] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A standard single-point localization method based on big data cross-modal residual model compensation, characterized in that, Includes the following steps: Step 1: Obtain the pseudorange residuals; the pseudorange residuals are calculated using precise ephemeris and observation files: (1) In the formula It is an observation station With satellite Pseudorange observation at frequency i For its true distance, It's the speed of light. , These are receiver clock bias and satellite clock bias, It is ionospheric delay. It is a tropospheric delay. For residuals; The obtained pseudorange residuals are combined with the corresponding satellite number, elevation angle, azimuth angle, observation station coordinates and observation station time to form a data set. Each element in the data set is regarded as a node. Step 2: Construct an undirected graph; the undirected graph indicates whether nodes are related and the degree of relatedness, and the weights between nodes are set to their frequency of occurrence; Step 3: Construct random walk tuples; include: (2) In the formula, It is the current node. It's probability. Indicates from Node selects next node The probability, () represents the set of neighboring nodes, d() represents the number of neighboring nodes, and a random walk sequence is generated. ,in ) represents the random walk algorithm, and G represents the undirected graph relation. T represents the starting node, and T represents the sequence length. Step 4: Establish a cross-modal representation model, including: To suit the characteristics of the dataset, four undirected graphs were constructed, and random walk sequences were created for each graph. Nodes were then trained. Generate nodes The probability is thus obtained from the actual calculated probability; the relationship of the undirected graph is defined. The loss function is calculated, and the final loss function F is trained on four sets of undirected graphs; the final learned loss function S is calculated. Step 5: Obtain the prediction strategy, including: after obtaining the residual prediction model, perform prediction work. Due to the characteristics of pseudorange residuals, nodes that are closer in time are more reliable. The input conditions include the elevation and azimuth angles of the satellite number and the coordinates of the observation station. Calculate the 10 closest residual values ​​in the model mapping space using the input conditions. Perform weighted calculation based on the most recent occurrence time of the 10 residual values ​​to obtain the final prediction result. Step 6: Design a standard single-point positioning method, including: The difference between the pseudorange and the geometric distance between the receiver and the GNSS satellite is called the pseudorange residual.

2. The standard single-point localization method based on big data cross-modal residual model compensation according to claim 1, characterized in that, Step 4 includes: by This represents the relationships in an undirected graph, where X and Y represent a class of nodes, and ∪ represents an association. Representing the degree of association between nodes, training nodes Generate nodes The probability is: (3) In the formula , , It is a node ,node The embedding vector of node k, where k represents all nodes adjacent to node i, and X represents the set of nodes adjacent to i; the actual calculated probability is: (4) In the formula is the edge weight of node i and node j, and X represents the set of nodes adjacent to i; definition The loss function is: (5) In the formula, KuL represents the KL divergence, expressed as: , where n represents the possible values ​​of random variables p and q, X represents the set of nodes adjacent to i, and Y represents the set of nodes adjacent to j; The final loss function F for training four sets of undirected graphs is as follows: (6) In the formula These represent the loss functions for observation station coordinates and residuals, satellite elevation angle and residuals, satellite azimuth angle and residuals, and satellite number and residuals, respectively. To reduce computational overhead, a negative sampling method is adopted, and the final learned loss function S is: (7) in, () represents the sigmoid function, and M represents the number of negative samples used. , , It is a node ,node The embedding vector of node i and node k, where k represents all nodes adjacent to node i.

3. The standard single-point localization method based on big data cross-modal residual model compensation according to claim 2, characterized in that, In step 5, the weighting method is as follows: (8) (9) In the formula As weight, It is the weight of the i-th predicted value. These represent the current time, the time the predicted value was in the historical model, and the model start time, respectively.

4. The standard single-point localization method based on big data cross-modal residual model compensation according to claim 3, characterized in that, Step 6 includes: (10) (11) (12) (13) In formula (11) As shown in equation (12), is the intermediate parameter, where They represent Partial derivatives with respect to x, y, and z; Pseudorange positioning is shown in equations (10)-(13), where, .

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