A method for predicting the propagation delay of long-wave ground waves based on universal kriging.
By constructing a long-wave ground wave propagation delay prediction model using the universal kriging method, the problem of low theoretical prediction accuracy of long-wave ground wave propagation delay is solved, achieving high-precision delay prediction, reducing costs and improving prediction accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-05-30
- Publication Date
- 2026-03-13
AI Technical Summary
Existing technologies have relatively low theoretical prediction accuracy for long-wave ground wave propagation delay, making it difficult to achieve high-precision time delay prediction over a wide area.
A propagation delay prediction model was established using the universal kriging method. By building a longwave ground wave propagation delay monitoring system, propagation delay and latitude and longitude data were acquired and processed. The universal kriging method was used to construct a propagation delay prediction model that varies with latitude and longitude. Data was acquired using a Loran-C receiver, a GPS receiver, and a time counter. Data flags were judged and outliers were corrected to establish a model of the relationship between propagation delay and latitude and longitude.
It achieves high-precision prediction of long-wave ground wave propagation delay, saving manpower, material resources and time costs, improving prediction accuracy and reducing the error of measured data.
Smart Images
Figure CN116840867B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of land-based longwave navigation / timing technology, specifically relating to a method for predicting the propagation delay of longwave ground waves based on the pan-kriging method. Background Technology
[0002] Land-based longwave navigation / timing systems, such as the Loland C system, eLoland system, and Changhe-2 system, have outstanding advantages such as wide coverage, all-weather operation, strong anti-interference capability, high reliability, and good stability. They are an important part of the modern PNT system.
[0003] The longwave ground wave propagation delay refers to the time required from the moment the longwave signal current waveform on the transmitting antenna of the longwave transmitter reaches its third positive zero-crossing point to the moment the same third positive zero-crossing point is generated on the receiving antenna. This is the time required for the longwave signal to propagate along its path. The longwave ground wave propagation delay at the receiving point is not only related to the frequency of the longwave transmitter and the path distance between the transmitter and receiver, but also affected by factors such as the spatiotemporal variation of atmospheric refractive index, the non-uniform distribution of earth conductivity, and topographic relief along the path. Therefore, the actual longwave signal undergoes a series of complex physical processes during propagation, including reflection, refraction, and diffraction, altering its direction, phase, and velocity, resulting in a phase delay that differs from that in a vacuum.
[0004] Due to spatiotemporal variations in terrain, weather, and day-night cycles along the propagation path, electrical parameters such as earth conductivity and atmospheric refractive index exhibit spatiotemporal changes. Accurate calculation of propagation distance, earth conductivity, and atmospheric refractive index is crucial for obtaining precise values for propagation delay through theoretical prediction. Therefore, the prediction accuracy of ground wave signal propagation delay obtained through theoretical methods is relatively low. Compared to theoretical prediction methods, propagation delay measured by instruments has higher accuracy, and accurate delay data is essential for studying long-wave ground wave propagation delay. Based on the above analysis, the propagation delay of user points at other locations within the region is predicted using precisely measured data. Summary of the Invention
[0005] The purpose of this invention is to provide a method for predicting the propagation delay of long-wave ground waves based on the pan-kriging method, which achieves high-precision prediction of the propagation delay of long-wave ground waves within a region and solves the problem of low prediction accuracy of ground wave signal propagation delay obtained by theoretical prediction in the prior art.
[0006] The technical solution adopted in this invention is a long-wave ground wave propagation delay prediction method based on the pan-kriging method, which is implemented according to the following steps:
[0007] Step 1: Build a longwave ground wave propagation delay monitoring system to obtain longwave ground wave propagation delay and latitude and longitude data for different points in the same area;
[0008] Step 2: Process the propagation delay data of different points obtained in Step 1 to obtain the final latitude and longitude data and propagation delay data of different points;
[0009] Step 3: Classify the latitude and longitude data and propagation delay data of different points obtained in Step 2. Use the latitude and longitude data and corresponding propagation delay data of a portion of the measured points as training data, and use the latitude and longitude data and corresponding propagation delay data of the remaining measured points as validation data.
[0010] Step 4: Establish a propagation delay prediction model that varies with latitude and longitude using the universal kriging method;
[0011] Step 5: Use the training data from Step 3 to train the model established in Step 4, and use the propagation delay prediction model to predict the propagation delay of long-wave ground waves.
[0012] The invention is further characterized in that,
[0013] The specific structure of the longwave ground wave propagation delay monitoring system in step 1 is as follows: It includes a Loran-C receiver, which is communicatively connected to a Loran-C antenna. The Loran-C receiver provides basic information about each longwave navigation / timing station and tracks the Group Repetition Information (GRI) signal transmitted by the navigation / timing stations. A GPS receiver is communicatively connected to a GPS antenna, providing location information and a 1PPS time reference signal. Both the Loran-C receiver and the GPS receiver are connected to a time counter via a serial interface. The time counter compares the GRI signal output by the Loran-C receiver with the 1PPS signal output by the GPS receiver to output longwave ground wave propagation delay data. The Loran-C receiver, GPS receiver, and time counter are all connected to an industrial PC via a serial interface to transmit and save the longwave ground wave propagation delay data and latitude / longitude information to the industrial PC.
[0014] Step 2 is as follows:
[0015] Step 2.1: For the propagation delay data obtained in Step 1, check the data flag bit to determine whether the current data is normal and usable. If the flag bit shows that the data is normal and usable, then extract the current data; otherwise, discard the current data.
[0016] Step 2.2: Correct the outliers in the available data from Step 2.1 to obtain the final propagation delay data.
[0017] In step 2.2, a moving average is used to correct outliers.
[0018] The specific algorithm steps for establishing the model using the pan-kriging method in step 4 are as follows:
[0019] (1) In the spatial region Ω, the non-stationary regionalized variable at any point x is Z(x), which can be represented by Z(x) = m(x) + R(x), where x is the measured value of the measurement point, m(x) is the trend function, R(x) is the residual, m(x) is a deterministic spatial component, and R(x) is a regionalized variable with an expected value of 0. Where p l (x) is a function of x; k is a function of p. l The number of (x); a l It is p l The corresponding coefficient of (x), assuming there are n known sample points x in the spatial region Ω. i Then the attribute value Z(x0) at an unknown point x0 can be obtained from the known sample points x. i The attribute value Z(x) i The estimation is done using a weighted average with parameters, i.e.: In the formula, Z*(x0) refers to the estimated value of Z(x0) at the unknown point x0;
[0020] (2) The universal kriging method satisfies the unbiasedness condition, that is:
[0021] To satisfy the unbiasedness condition, it is necessary to satisfy the following: Where Z*(x0) is the universal kriging estimate of the propagation delay at x0, E[Z*(x0)] is the mathematical expectation of the universal kriging estimate of the propagation delay at x0, and a l It is p l The corresponding coefficient of (x), λ i This refers to the weighting coefficient for reference point i;
[0022] (3) The universal kriging method satisfies the optimal condition, which can be obtained by estimating the variance σ0. 2 This means, that is: C(x i ,x j ) refers to the variable Z(x) i ) and Z(x j The covariance of λ i It is to estimate the variance σ0 2 The minimum weighting coefficient, where n is the number of measured points;
[0023] (4) Achieving λ by introducing the Lagrange multiplier method i To solve this, first, create a new objective function J:
[0024]
[0025] Where μ l To minimize the objective function J, we use the Lagrange multipliers, and then apply the objective function J to each of the n weighted coefficients λ. i Find the partial derivatives, set them to 0, and finally... By combining these equations, we can obtain the pan-Kriging equations:
[0026]
[0027] The Lagrange multiplier μ obtained by solving l and weighting coefficient λ i ;
[0028] (5) The weighting coefficient λ i Substitute The generalized Kriging estimate of the propagation delay Z*(x0) can be obtained.
[0029] Step 5 is as follows: Process the training data in Step 3, and use the pan-kriging method in Step 4 to establish a propagation delay prediction model that varies with latitude and longitude. Use latitude and longitude as the input of the model and the spatial component of the propagation delay as the output of the model. Use measured data for training to obtain a predicted value that is closer to the actual value of the ground wave propagation delay in the target area.
[0030] The beneficial effects of this invention are that the long-wave ground wave propagation delay prediction method based on universal kriging constructs a model of the relationship between latitude and longitude and propagation delay. The propagation delay of the signal exhibits a trend change with the location along the path, and universal kriging interpolation can accurately predict this trend. Universal kriging considers not only the spatial relationship between the user point and known sample points but also the spatial correlation between location points, making it a linear non-stationary interpolation method that takes into account the trend changes in spatial regions. The spatial trend change of propagation delay with spatial location can be fitted using universal kriging. Compared to methods based entirely on actual measurements, this method saves significant manpower, material resources, and time costs. Attached Figure Description
[0031] Figure 1 This is a flowchart illustrating the present invention;
[0032] Figure 2 This is a schematic diagram of the long-wave ground wave propagation delay monitoring system in this invention;
[0033] Figure 3 This is a schematic diagram of the selected location points in an embodiment of the present invention;
[0034] Figure 4 This is a comparison chart of the propagation delay prediction effects in embodiments of the present invention.
[0035] In the diagram, 1. Loran-C antenna, 2. GPS antenna, 3. Loran-C receiver, 4. Time counter, 5. GPS receiver, 6. Industrial PC. Detailed Implementation
[0036] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0037] This invention presents a method for predicting the propagation delay of long-wave ground waves based on the universal kriging method. The flowchart is as follows: Figure 1 As shown, please follow these steps:
[0038] Step 1: Build a longwave ground wave propagation delay monitoring system to obtain longwave ground wave propagation delay and latitude and longitude data for different points in the same area;
[0039] The specific structure of the longwave ground wave propagation delay monitoring system in step 1 is as follows: It includes a Loran-C receiver 3, which is communicatively connected to a Loran-C antenna 1. The Loran-C receiver 3 provides basic information about each longwave navigation / timing station and tracks the Group Repetition Information (GRI) signal transmitted by the navigation / timing station. A GPS receiver 5 is communicatively connected to a GPS antenna 2, providing location information and a 1PPS time reference signal. Both the Loran-C receiver 3 and the GPS receiver 5 are connected to a time counter 4 via a serial interface. The time counter 4 compares the GRI signal output by the Loran-C receiver 3 with the 1PPS signal output by the GPS receiver 3 to output longwave ground wave propagation delay data. The Loran-C receiver 3, GPS receiver 5, and time counter 4 are all connected to an industrial PC 6 via a serial interface to transmit and save the longwave ground wave propagation delay data and latitude / longitude information to the industrial PC 6.
[0040] Step 2: Process the propagation delay data of different points obtained in Step 1 to obtain the final latitude and longitude data and propagation delay data of different points;
[0041] Step 2 is as follows:
[0042] Step 2.1: For the propagation delay data obtained in Step 1, check the data flag bit to determine whether the current data is normal and usable. If the flag bit shows that the data is normal and usable, then extract the current data; otherwise, discard the current data.
[0043] Step 2.2: Correct the outliers in the available data from Step 2.1 to obtain the final propagation delay data.
[0044] In step 2.2, a moving average is used to correct outliers.
[0045] Step 3: Classify the latitude and longitude data and propagation delay data of different points obtained in Step 2. Use the latitude and longitude data and corresponding propagation delay data of a portion of the measured points as training data, and use the latitude and longitude data and corresponding propagation delay data of the remaining measured points as validation data.
[0046] Step 4: Establish a propagation delay prediction model that varies with latitude and longitude using the universal kriging method;
[0047] The specific algorithm steps for establishing the model using the pan-kriging method described in step 4 are as follows:
[0048] (1) In the spatial region Ω, the non-stationary regionalized variable at any point x is Z(x), which can be represented by Z(x) = m(x) + R(x), where x is the measured value of the measurement point, m(x) is the trend function, R(x) is the residual, m(x) is a deterministic spatial component, and R(x) is a regionalized variable with an expected value of 0. Where p l (x) is a function of x; k is a function of p. l The number of (x); a l It is p l The corresponding coefficient of (x), assuming there are n known sample points x in the spatial region Ω. i Then the attribute value Z(x0) at an unknown point x0 can be obtained from the known sample points x. i The attribute value Z(x) i The estimation is done using a weighted average with parameters, i.e.: In the formula, Z*(x0) refers to the estimated value of Z(x0) at the unknown point x0;
[0049] (2) The universal kriging method satisfies the unbiasedness condition, that is:
[0050] To satisfy the unbiasedness condition, it is necessary to satisfy the following: Where Z*(x0) is the universal kriging estimate of the propagation delay at x0, E[Z*(x0)] is the mathematical expectation of the universal kriging estimate of the propagation delay at x0, and a l It is p l The corresponding coefficient of (x), λ i This refers to the weighting coefficient for reference point i;
[0051] (3) The universal kriging method satisfies the optimal condition, which can be obtained by estimating the variance σ0. 2 This means, that is: C(x i ,x j ) refers to the variable Z(x) i ) and Z(x jThe covariance of λ i It is to estimate the variance σ0 2 The minimum weighting coefficient, where n is the number of measured points;
[0052] (4) Achieving λ by introducing the Lagrange multiplier method i To solve this, first, create a new objective function J:
[0053]
[0054] Where μ l To minimize the objective function J, we use the Lagrange multipliers, and then apply the objective function J to each of the n weighted coefficients λ. i Find the partial derivatives, set them to 0, and finally... By combining these equations, we can obtain the pan-Kriging equations:
[0055]
[0056] The Lagrange multiplier μ obtained by solving l and weighting coefficient λ i ;
[0057] (5) The weighting coefficient λ i Substitute The generalized Kriging estimate of the propagation delay Z*(x0) can be obtained.
[0058] Step 5: Use the training data from Step 3 to train the model established in Step 4, and use the propagation delay prediction model to predict the propagation delay of long-wave ground waves.
[0059] The training data in step 3 is processed, and the propagation delay prediction model that varies with latitude and longitude is established using the pan-kriging method in step 4. Latitude and longitude are used as the input of the model, and the spatial component of the propagation delay is used as the output of the model. The model is trained using measured data to obtain a predicted value that is closer to the actual value of the ground wave propagation delay in the target area.
[0060] Example 1
[0061] This invention discloses a method for predicting the propagation delay of long-wave ground waves based on universal kriging, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:
[0062] Step 1: Establish a long-wave ground wave propagation delay monitoring system, such as... Figure 2 As shown, longwave ground wave propagation delay data and latitude and longitude information are obtained;
[0063] The long-term monitoring system structure for long-wave ground wave propagation delay in step 1 is as follows: It includes a Loran-C receiver 3, which is communicatively connected to a Loran-C antenna 1. The Loran-C receiver 3 provides basic information about each long-wave navigation / timing station and tracks the Group Repetition Information (GRI) signal transmitted by the navigation / timing station. A GPS receiver 5 is communicatively connected to a GPS antenna 2, providing location information and a 1PPS time reference signal. Both the Loran-C receiver 3 and the GPS receiver 5 are connected to a time counter 4 via a serial interface. The time counter 4 compares the GRI signal output by the Loran-C receiver 3 with the 1PPS signal output by the GPS receiver 3 to output long-wave ground wave propagation delay data. The Loran-C receiver 3, GPS receiver 5, and time counter 4 are all connected to an industrial PC 6 via a serial interface to transmit and save the long-wave ground wave propagation delay data and latitude / longitude information to the industrial PC 6.
[0064] Step 2: In this invention, the 6000M station in Pucheng, Shaanxi Province, is selected as the long-wave transmitter. Measurements are taken from the 6000M station in Pucheng, Shaanxi Province to... Figure 3 The propagation time delay is calculated for multiple points within the region enclosed by the midline. The propagation distance ranges from 90 to 120 km, the deflection angle from the launch pad is between 206.1° and 219.3°, and the spatial region spans approximately 370 km. 2 Within the experimental area, the propagation paths of long-wave signals are similar, and the differences in terrain and topography between adjacent points are small, with good geographic spatial correlation.
[0065] Step 2 is as follows:
[0066] Step 2.1: Measure the latitude, longitude and propagation delay data of 100 points within the area, using 5 consecutive minutes of data for each measurement point as the standard.
[0067] Step 2.2: For the propagation delay data obtained in Step 1, check the data flag to determine if the current data is usable. If the flag indicates that the data is usable, extract the current data; otherwise, discard the current data.
[0068] Step 2.3: Use a moving average to correct outliers in the data from Step 2.2.
[0069] Step 3: Establish a propagation delay prediction model that varies with latitude and longitude using the universal kriging method;
[0070] Step 3.1: A total of 100 sets of measurement data were obtained in the experimental area. 70 sets of data were selected from the experimental measurement data to form the training samples of the model, and 30 sets of data were used to verify the effect of the model.
[0071] Step 4: Based on the training samples in Step 3.1, use the propagation delay prediction model to make predictions and obtain the predicted values of propagation delay within the region.
[0072] Step 4 is as follows:
[0073] Step 4.1: When using a propagation delay prediction model to predict propagation delay, the input and output must correspond, that is, a set of input data corresponds to a set / one output. Therefore, the data needs to be processed. The specific data processing is as follows:
[0074] Step 4.1.1: When the distribution of a certain feature in the model differs greatly, it will have a significant impact on the actual output of the model. Therefore, it is necessary to process the input data of the model to make different features have the same scale, so as to facilitate the comparison and weighting of different features in the model, thereby improving the accuracy of the model correction.
[0075] The standard deviation method is used to process the features. The formulas for standardizing the longitude and latitude of the model input and the propagation delay of the model output are as follows:
[0076]
[0077] In the formula, q refers to the original sample data; q * This refers to the standardized data of the original sample data q; σ refers to the average value of the sample data; N This refers to the standard deviation of the sample data. Equation (4) is used to standardize the longitude, latitude, and propagation delay respectively. The standardized data conforms to a standard normal distribution. In this invention, the propagation delay prediction and verification are as follows:
[0078] (1) Prediction of propagation delay: Using the universal kriging method in step 4.1.1 as input, the latitude and longitude data in step 4.1.1 are used to obtain the predicted value of propagation delay.
[0079] (2) Propagation Delay Verification: A direct performance comparison can be made by comparing the predicted propagation delay with the measured propagation delay in the test set. Quantitative performance comparison can be measured in the following ways: first, the number of samples whose absolute prediction error falls within a certain error range, and its percentage in the test set; second, the RMSE (Root Mean Square Error) and MAE (Mean Absolute Error) values. The absolute prediction error is defined as:
[0080] Absolute prediction error = |predicted value - measured value| (5)
[0081] The formulas for calculating RMSE and MAE are as follows:
[0082]
[0083]
[0084] In the formula, x i and x i ′ represents the measured value and the predicted value, respectively, and l represents the number of samples in the test set.
[0085] Step 4.2: Use the universal kriging method to process the training samples and establish a propagation delay prediction model for the region as latitude and longitude change.
[0086] Step 4.3: Input the latitude and longitude data of the validation sample into the model to obtain propagation delay prediction values that better match the latitude and longitude points in the region.
[0087] Combination Figure 4 To verify the accuracy and effectiveness of the method of this invention, a verification experiment was conducted, and a field test was designed in the Xi'an area. First, a small amount of measured data was acquired within the area using the monitoring system in step 1. This data was then used to train the propagation delay prediction model established in step 3. Seventy measured points were selected as training samples, and 30 points were selected as verification samples. The RMSE and MAE of the propagation delay calculated theoretically were 347.38 ns and 289.59 ns, respectively. After training with the propagation delay prediction model, the RMSE and MAE of the propagation delay were 91.13 ns and 76.52 ns, respectively, showing a significant improvement and verifying the effectiveness of this invention.
[0088] Example 2
[0089] This invention presents a method for predicting the propagation delay of long-wave ground waves based on the universal kriging method. The flowchart is as follows: Figure 1 As shown, please follow these steps:
[0090] Step 1: Build a longwave ground wave propagation delay monitoring system to obtain longwave ground wave propagation delay and latitude and longitude data for different points in the same area;
[0091] The specific structure of the longwave ground wave propagation delay monitoring system in step 1 is as follows: It includes a Loran-C receiver 3, which is communicatively connected to a Loran-C antenna 1. The Loran-C receiver 3 provides basic information about each longwave navigation / timing station and tracks the Group Repetition Information (GRI) signal transmitted by the navigation / timing station. A GPS receiver 5 is communicatively connected to a GPS antenna 2, providing location information and a 1PPS time reference signal. Both the Loran-C receiver 3 and the GPS receiver 5 are connected to a time counter 4 via a serial interface. The time counter 4 compares the GRI signal output by the Loran-C receiver 3 with the 1PPS signal output by the GPS receiver 3 to output longwave ground wave propagation delay data. The Loran-C receiver 3, GPS receiver 5, and time counter 4 are all connected to an industrial PC 6 via a serial interface to transmit and save the longwave ground wave propagation delay data and latitude / longitude information to the industrial PC 6.
[0092] Step 2: Process the propagation delay data of different points obtained in Step 1 to obtain the final latitude and longitude data and propagation delay data of different points;
[0093] Step 2 is as follows:
[0094] Step 2.1: For the propagation delay data obtained in Step 1, check the data flag bit to determine whether the current data is normal and usable. If the flag bit shows that the data is normal and usable, then extract the current data; otherwise, discard the current data.
[0095] Step 2.2: Correct the outliers in the available data from Step 2.1 to obtain the final propagation delay data.
[0096] In step 2.2, a moving average is used to correct outliers.
[0097] Step 3: Classify the latitude and longitude data and propagation delay data of different points obtained in Step 2. Use the latitude and longitude data and corresponding propagation delay data of a portion of the measured points as training data, and use the latitude and longitude data and corresponding propagation delay data of the remaining measured points as validation data.
[0098] Step 4: Establish a propagation delay prediction model that varies with latitude and longitude using the universal kriging method;
[0099] Step 5: Use the training data from Step 3 to train the model established in Step 4, and use the propagation delay prediction model to predict the propagation delay of long-wave ground waves.
[0100] The training data in step 3 is processed, and the propagation delay prediction model that varies with latitude and longitude is established using the pan-kriging method in step 4. Latitude and longitude are used as the input of the model, and the spatial component of the propagation delay is used as the output of the model. The model is trained using measured data to obtain a predicted value that is closer to the actual value of the ground wave propagation delay in the target area.
[0101] Example 3
[0102] This invention presents a method for predicting the propagation delay of long-wave ground waves based on the universal kriging method. The flowchart is as follows: Figure 1 As shown, please follow these steps:
[0103] Step 1: Build a longwave ground wave propagation delay monitoring system to obtain longwave ground wave propagation delay and latitude and longitude data for different points in the same area;
[0104] The specific structure of the longwave ground wave propagation delay monitoring system in step 1 is as follows: It includes a Loran-C receiver 3, which is communicatively connected to a Loran-C antenna 1. The Loran-C receiver 3 provides basic information about each longwave navigation / timing station and tracks the Group Repetition Information (GRI) signal transmitted by the navigation / timing station. A GPS receiver 5 is communicatively connected to a GPS antenna 2, providing location information and a 1PPS time reference signal. Both the Loran-C receiver 3 and the GPS receiver 5 are connected to a time counter 4 via a serial interface. The time counter 4 compares the GRI signal output by the Loran-C receiver 3 with the 1PPS signal output by the GPS receiver 3 to output longwave ground wave propagation delay data. The Loran-C receiver 3, GPS receiver 5, and time counter 4 are all connected to an industrial PC 6 via a serial interface to transmit and save the longwave ground wave propagation delay data and latitude / longitude information to the industrial PC 6.
[0105] Step 2: Process the propagation delay data of different points obtained in Step 1 to obtain the final latitude and longitude data and propagation delay data of different points;
[0106] Step 3: Classify the latitude and longitude data and propagation delay data of different points obtained in Step 2. Use the latitude and longitude data and corresponding propagation delay data of a portion of the measured points as training data, and use the latitude and longitude data and corresponding propagation delay data of the remaining measured points as validation data.
[0107] Step 4: Establish a propagation delay prediction model that varies with latitude and longitude using the universal kriging method;
[0108] The specific algorithm steps for establishing the model using the pan-kriging method described in step 4 are as follows:
[0109] (1) In the spatial region Ω, the non-stationary regionalized variable at any point x is Z(x), which can be represented by Z(x) = m(x) + R(x), where x is the measured value of the measurement point, m(x) is the trend function, R(x) is the residual, m(x) is a deterministic spatial component, and R(x) is a regionalized variable with an expected value of 0. Where p l (x) is a function of x; k is a function of p. l The number of (x); a l It is p l The corresponding coefficient of (x), assuming there are n known sample points x in the spatial region Ω. i Then the attribute value Z(x0) at an unknown point x0 can be obtained from the known sample points x. i The attribute value Z(x) i The estimation is done using a weighted average with parameters, i.e.: In the formula, Z*(x0) refers to the estimated value of Z(x0) at the unknown point x0;
[0110] (2) The universal kriging method satisfies the unbiasedness condition, that is:
[0111] To satisfy the unbiasedness condition, it is necessary to satisfy the following: Where Z*(x0) is the universal kriging estimate of the propagation delay at x0, E[Z*(x0)] is the mathematical expectation of the universal kriging estimate of the propagation delay at x0, and a l It is p l The corresponding coefficient of (x), λ i This refers to the weighting coefficient for reference point i;
[0112] (3) The universal kriging method satisfies the optimal condition, which can be obtained by estimating the variance σ0. 2 This means, that is: C(x i ,x j ) refers to the variable Z(x) i ) and Z(x j The covariance of λ i It is to estimate the variance σ0 2 The minimum weighting coefficient, where n is the number of measured points;
[0113] (4) Achieving λ by introducing the Lagrange multiplier method i To solve this, first, create a new objective function J:
[0114]
[0115] Where μ lTo minimize the objective function J, we use the Lagrange multipliers, and then apply the objective function J to each of the n weighted coefficients λ. i Find the partial derivatives, set them to 0, and finally... By combining these equations, we can obtain the pan-Kriging equations:
[0116]
[0117] The Lagrange multiplier μ obtained by solving l and weighting coefficient λ i ;
[0118] (5) The weighting coefficient λ i Substitute The generalized Kriging estimate of the propagation delay Z*(x0) can be obtained.
[0119] Step 5: Use the training data from Step 3 to train the model established in Step 4, and use the propagation delay prediction model to predict the propagation delay of long-wave ground waves.
[0120] The training data in step 3 is processed, and the propagation delay prediction model that varies with latitude and longitude is established using the pan-kriging method in step 4. Latitude and longitude are used as the input of the model, and the spatial component of the propagation delay is used as the output of the model. The model is trained using measured data to obtain a predicted value that is closer to the actual value of the ground wave propagation delay in the target area.
Claims
1. A method for predicting the propagation delay of long-wave ground waves based on universal kriging, characterized in that, The specific steps are as follows: Step 1: Build a longwave ground wave propagation delay monitoring system to obtain longwave ground wave propagation delay and latitude and longitude data for different points in the same area; Step 2: Process the propagation delay data of different points obtained in Step 1 to obtain the final latitude and longitude data and propagation delay data of different points; Step 3: Divide the latitude and longitude data and propagation delay data of different points into training data and validation data; Step 4: Establish a propagation delay prediction model that varies with latitude and longitude using the universal kriging method; Step 5: Use the training data from Step 3 to train the model established in Step 4, and use the propagation delay prediction model to predict the propagation delay of long-wave ground waves.
2. The method for predicting long-wave ground wave propagation delay based on universal kriging as described in claim 1, characterized in that, The specific structure of the longwave ground wave propagation delay monitoring system in step 1 is as follows: it includes a Loran-C receiver (3), which is connected to a Loran-C antenna (1). The Loran-C receiver (3) is used to provide basic information of each longwave navigation / timing station and to track the group repeat information GRI signal transmitted by the navigation / timing station. The GPS receiver (5) is connected to the GPS antenna (2) for communication. The GPS receiver (5) is used to provide location information and time reference signal 1PPS signal. The Loran-C receiver (3) and the GPS receiver (5) are both connected to the time counter (4) through a serial interface. The time counter (4) is used to compare the GRI signal output by the Loran-C receiver (3) and the 1PPS signal output by the GPS receiver (3) to output long wave ground wave propagation delay data. The Loran-C receiver (3), the GPS receiver (5), and the time counter (4) are all connected to the industrial PC (6) through a serial interface to transmit and save the long wave ground wave propagation delay data and latitude and longitude information to the industrial PC (6).
3. The method for predicting long-wave ground wave propagation delay based on universal kriging as described in claim 2, characterized in that, Step 2 is described in detail below: Step 2.1: For the propagation delay data obtained in Step 1, check the data flag bit to determine whether the current data is normal and usable. If the flag bit shows that the data is normal and usable, then extract the current data. Conversely, discard the current data; Step 2.2: Correct the outliers in the available data from Step 2.1 to obtain the final propagation delay data.
4. The method for predicting long-wave ground wave propagation delay based on universal kriging as described in claim 3, characterized in that, In step 2.2, a moving average is used to correct outliers.
5. The method for predicting long-wave ground wave propagation delay based on universal kriging as described in claim 4, characterized in that, The specific algorithm steps for establishing the model using the pan-kriging method described in step 4 are as follows: (1) In spatial regions In, any point The non-stationary regional variable at the location is , Depend on It means that among them These are the measured values at the measurement points. It is a trend function; It is a residual. It is a deterministic spatial component. It is a regionalized variable with an expected value of 0, and ,in for The function; It is a function The number of; yes The corresponding coefficients, assuming spatial region The CCP Known sample points Then a certain unknown point Attribute values at From known sample points attribute values Estimating using a parameterized weighted average, i.e.: In the formula, It refers to unknown points Place The estimated value, Reference point Weighting coefficients; (2) The universal kriging method satisfies the unbiasedness condition, that is: To satisfy the unbiasedness condition, it is necessary to satisfy the following: ,in for The pan-Kriging estimate of propagation delay, for The mathematical expectation of the universal Kriging estimate of the propagation delay. yes The corresponding coefficient, Reference point Weighting coefficients; (3) The universal kriging method satisfies the optimal condition by estimating the variance. This means, that is: , Refers to variables and The covariance, where n is the number of measured points; (4) Achieving the effect of introducing the Lagrange multiplier method To solve this, firstly, a new objective function is created. : in Let Lagrange multipliers be the factors that make the objective function... To minimize the value of the objective function, For each of the n weighting coefficients Find the partial derivatives, set them to 0, and finally... The simultaneous system of pan-Kriging equations is as follows: The Lagrange multiplier obtained by solving and weighting coefficients ; (5) Weighting coefficients Substitute The pan-Kriging estimate of the propagation delay is obtained. .
6. The method for predicting long-wave ground wave propagation delay based on universal kriging as described in claim 5, characterized in that, Step 5 is as follows: The training data in step 3 is processed, and the propagation delay prediction model that varies with latitude and longitude is established using the pan-kriging method in step 4. Latitude and longitude are used as the input of the model, and the spatial component of the propagation delay is used as the output of the model. The model is trained using measured data to obtain a predicted value that is closer to the actual value of the ground wave propagation delay in the target area.