Ionospheric electron density inversion method based on marine VTEC constraint

Abstract

The application discloses a method for inverting ionospheric electron density based on marine VTEC constraint, and belongs to the technical field of ionospheric remote sensing and GNSS ionospheric monitoring. The method comprises the following steps: acquiring the longitude, latitude, annual accumulated day and universal time of a specified position on the sea to generate an initial electron density profile; acquiring the VTEC observation value and its observation error parameter corresponding to the time at the specified position on the sea; constructing a prior covariance matrix of the relative correction amount of the electron density; establishing an integral relationship between the electron density profile and the VTEC; constructing a posterior updating target function and adding a vertical continuity constraint and a smoothness constraint to solve the optimal relative correction amount; and correcting the initial electron density profile by using the optimal relative correction amount. The application can effectively constrain the inversion of the electron density profile by using the VTEC observation under the condition of lacking independent vertical detection data, can inhibit non-physical changes, and can improve the stability and accuracy of the inversion of the ionospheric electron density profile on the sea and in remote areas.

Description

Technical Field

[0001] This invention belongs to the field of ionospheric remote sensing and GNSS ionospheric monitoring technology, and specifically relates to a method for inverting ionospheric electron density based on marine VTEC constraints. Background Technology

[0002] The ionospheric electron density profile is a crucial parameter describing the vertical structure of the ionosphere. It can be used for space weather monitoring, radio propagation modeling, Global Navigation Satellite System (GNSS) error correction, and ionospheric state estimation in oceanic and remote areas. Empirical ionospheric models can generate electron density profiles under given time, location, and space weather conditions, but their results primarily reflect long-term statistical characteristics and may deviate from actual conditions under local, short-term, or perturbed conditions. GNSS observations provide Vertical Total Electron Content (VTEC) information, reflecting the total number of electrons integrated along the height direction, but they cannot directly provide the distribution of electron density at different altitudes. Therefore, if only VTEC is used to freely correct high-dimensional electron density profiles, non-physical results such as excessively wide peaks, excessive expansion of the top-side region, or local oscillations can easily occur.

[0003] Existing methods typically use empirical models to directly provide the profile, or parameterize the empirical profile using total electron content. However, in single-station GNSS or offshore platform observation scenarios, independent vertical data such as ionospheric altimeters and occultation profiles are often difficult to obtain, and VTEC can only provide integral constraints. Therefore, an electron density inversion method is needed that can utilize VTEC observation information while maintaining the rationality of the profile's vertical structure. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides an ionospheric electron density inversion method based on marine VTEC constraints. This method aims to effectively constrain and correct empirical ionospheric electron density profiles in marine or remote environments lacking independent vertical detection data. It also aims to suppress non-physical profile changes and improve the stability, accuracy, and physical rationality of electron density profile inversion results.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: A method for inverting ionospheric electron density based on marine VTEC constraints includes the following steps: Step 1: Obtain the longitude, latitude, annual day and UT of the specified location at sea, and generate the initial electron density profile on the corresponding height grid based on the ionospheric empirical model; Step 2: Obtain the observed value of the vertical total electron content at the specified location at sea at the corresponding time, and determine the observation error parameter of the observed value of the vertical total electron content; Step 3: Based on the initial electron density profile and height grid, construct the prior covariance matrix of the electron density relative correction amount; Step 4: Construct a height integral weight vector based on the height grid, and use the height integral weight vector to establish an integral relationship between the electron density profile and the total vertical electron content; Step 5: Based on the observed total vertical electron content, observation error parameters, height integral weight vector, and prior covariance matrix, construct the posterior update objective function for the relative correction of electron density; Step 6: Add the continuity and smoothness constraints of the electron density profile in the height direction to the posterior update objective function, and solve for the optimal relative correction amount; Step 7: Correct the initial electron density profile according to the optimal relative correction amount to obtain the corrected electron density profile.

[0006] In the above scheme, in step 1, the initial electron density profile is generated by an empirical ionospheric model, wherein the empirical ionospheric model is one of the international reference ionospheric model, the NeQuick model, or the Chapman model; the expression for the initial electron density profile is as follows: ; in, This is the initial electron density profile vector. For the first Each height level, The total number of floors is the height. For height The initial electron density at that location.

[0007] In the above scheme, in step 2, the observed total vertical electron content is derived from one of the following: global ionospheric grid products, regional ionospheric grid products, or GNSS inversion results from a single marine station. The observed total vertical electron content at the specified location is recorded as... The error parameter for the vertical total electron content includes the standard deviation or variance, which characterizes the uncertainty of the vertical total electron content. The variance of the vertical total electron content observation error is expressed as: in, The variance of the vertical total electron content observation error. This represents the standard deviation corresponding to the observed total electron content in this vertical direction.

[0008] In the above scheme, the relative correction amount of the electron density profile in step 3 is expressed as: ; in, For height The relative correction to the electron density at that location. For height The corrected electron density, For height The initial electron density is given; it can be written in vector form: .

[0009] In the above scheme, step 3 involves constructing a priori covariance matrix based on the correlation between different altitude layers: ; in, Represented as the prior covariance matrix The Middle Line 1 Column elements, Relative correction amount The prior covariance matrix, , For height, , The prior standard deviation of the corresponding height layer. The vertical correlation length is used to control the rate at which the correlation between different height layers decays with height intervals.

[0010] In the above scheme, the prior standard deviation corresponding to each height level Represented as: ; in, Based on the prior standard deviation, and These are the additional prior standard deviations of the peak value and the top center height of layer F2, respectively. and These are the peak height of layer F2 and the height of the top center, respectively. and These are the width parameters for the peak height and top center height of layer F2, respectively.

[0011] In the above scheme, in step 4, the height integral weight vector is used to divide the electron density profile on the discrete height layer into the vertical total electron content. Based on the physical relationship of electron density integration along the height direction, the vertical total electron content is expressed as: ; Further written in matrix form: ; in, This is a highly integrated weight vector under highly discretized conditions. For the first The integral weights corresponding to each height layer This is a discrete height layer electron density profile. This indicates the total number of height levels.

[0012] In the above scheme, in step 5, based on the height integral weight vector Observed values ​​of total vertical electron content at specified locations and its standard deviation and prior covariance matrix The initial electron density profile is updated posteriorly; an objective function containing observation residuals and prior constraints is constructed: ; in, Represents the Hadamard product. and A column vector of all 1s with the same dimension.

[0013] In the above scheme, in step 6, the continuity constraint is a first-order difference constraint, used to limit abrupt changes in the relative correction amount between adjacent height layers; the smoothness constraint is a second-order difference constraint, used to limit anomalies in the curvature of the relative correction amount; the vertical structure constraint is added to the objective function as a regularization term, and its form is: ; in, It is a first-order difference matrix. It is a second-order difference matrix. The weights are first-order smoothing constraints. The weights are second-order smoothing constraints; The first-order difference is expressed as: ; The second-order difference is expressed as: ; Solving the above objective function yields the optimal relative correction amount. .

[0014] In the above scheme, step 7 involves correcting the initial electron density profile based on the optimal relative correction amount to obtain the final electron density profile: ; Simultaneously, key profile parameters were further calculated based on the corrected electron density profile: ; ; in, The peak electron density of the F2 layer. Given the peak height of the F2 layer, calculate the integral electron content corresponding to the corrected profile: .

[0015] Through the above technical solution, the ionospheric electron density inversion method based on marine VTEC constraint provided by the present invention has the following beneficial effects: 1. This invention enables the correction of empirical electron density profiles using VTEC observations in the absence of independent vertical ionospheric probe data; 2. This invention controls the intensity of the influence of VTEC observation on profile correction by setting VTEC observation error parameters, thereby reducing the risk of observation errors being directly transmitted to the electron density profile; 3. This invention constructs a highly correlated prior covariance structure to maintain a continuous correlation between the relative correction amounts of different height layers, thereby improving the physical rationality of the profile update results; 4. This invention suppresses drastic fluctuations in the relative correction amount through first-order and second-order difference constraints, thereby improving the smoothness of the electron density profile; 5. This invention can set different degrees of freedom for the area near the peak of the F2 layer and the top side region, thereby enhancing the adjustability of key height sections while maintaining profile stability; 6. The present invention can also describe the peak electron density and peak height of the F2 layer in an explicit parameterization manner, making the profile correction process easier to interpret and control; 7. This invention is applicable to single-station GNSS ionospheric inversion scenarios such as marine platforms, remote areas, and those lacking ionospheric altimeters or occultation profile data.

[0016] In summary, the ionospheric electron density inversion method based on marine vertical total electron content constraints provided by this invention can combine marine VTEC observation information, empirical model initial profiles, and prior structures of electron density profiles without relying on independent ionospheric vertical observation data, thus achieving constraint correction of the ionospheric electron density profile. This method can suppress non-physical profile changes while utilizing VTEC observation information, improving the stability and applicability of ionospheric electron density profile inversion results in marine and remote areas. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0018] Figure 1 This is a schematic diagram of the ionospheric electron density inversion method based on marine VTEC constraints disclosed in an embodiment of the present invention; Figure 2This is a comparison chart of the electron density profile inversion results under marine VTEC constraints in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0020] This invention provides a method for ionospheric electron density inversion based on marine VTEC constraints, such as... Figure 1 As shown, it includes the following steps: Step 1: Obtain the initial electron density profile based on the latitude, longitude, day of the year, and UTC of the specified location. The initial electron density profile is generated by an empirical ionospheric model, which may include one of the IRI model, the NeQuick model, or the Chapman model.

[0021] In this embodiment, based on the longitude, latitude, annual day of birth, and UTC of a specified location at sea, the initial electron density profile corresponding to that location is obtained using the IRI model. Its expression can be given as: ; in, For the first Discrete layer height, The total number of floors is the height. For height The initial electron density at that location.

[0022] Step 2: Based on the global ionospheric grid product, regional ionospheric grid product, or marine single-station GNSS inversion results corresponding to the specified location, obtain VTEC observation values ​​and determine their error parameters.

[0023] VTEC is derived from one of the following: global ionospheric grid products, regional ionospheric grid products, or marine single-station GNSS inversion results. The VTEC observation value corresponding to a specified location is denoted as... VTEC error parameters include standard deviation or variance, which characterize the uncertainty of VTEC and are generally provided by ionospheric products or single-station GNSS calculations. The variance of VTEC observation error can be expressed as: ; in, VTEC observation error variance This represents the standard deviation corresponding to the VTEC observation.

[0024] Step 3: Based on the initial electron density profile and height grid, construct the prior covariance matrix of the relative correction to the electron density. The relative correction to the electron density profile is expressed as: ; in, For height The relative correction to the electron density at that location. For height The corrected electron density, For height The initial electron density. Express it in vector form: ; Construct a prior covariance matrix based on the correlation between different altitude layers: ; in, Represented as the prior covariance matrix The Middle Line 1 Column elements, Relative correction amount The prior covariance matrix, , For height, , The prior standard deviation of the corresponding height layer. The vertical correlation length is used to control the rate at which the correlation between different height layers decays with height intervals.

[0025] Prior standard deviation for each height level It can be represented as: ; in, Based on the prior standard deviation, and These are the additional prior standard deviations of the peak value and the top center height of layer F2, respectively. and These are the peak height of layer F2 and the height of the top center, respectively. and These are the width parameters for the peak height and top center height of layer F2, respectively.

[0026] The above parameters can be determined from initial profiles, historical profile statistics, or empirical values.

[0027] Step 4: The height integral weight vector is used to divide the electron density profile on the discrete height layer into VTECs. Based on the physical relationship of electron density integration along the height direction, VTECs can be expressed as: ; Further written in matrix form: ; in, This is a highly integrated weight vector under highly discretized conditions. For the first The integral weights corresponding to each height layer This is a discrete height layer electron density profile.

[0028] Step 5, based on the height integration weight vector , and its standard deviation and prior covariance matrix The initial electron density profile is then updated posteriorly. An objective function is constructed that includes observation residuals and prior constraints: ; in, Represents the Hadamard product. and A column vector of all 1s with the same dimension.

[0029] Step 6: Vertical structural constraints include first-order and second-order difference constraints. First-order difference constraints limit abrupt changes in the relative correction amount between adjacent height layers, while second-order difference constraints limit curvature anomalies in the relative correction amount. Vertical structural constraints can be added as regularization terms to the objective function, and their form is: ; in, It is a first-order difference matrix. It is a second-order difference matrix. The weights are first-order smoothing constraints. These are the weights for second-order smoothing constraints.

[0030] The first-order difference can be expressed as: ; The second-order difference can be expressed as: ; The objective function is solved using regularized least squares or iterative optimization methods to obtain the optimal relative correction. .

[0031] Step 7: Correct the initial electron density profile according to the optimal relative correction amount to obtain the final electron density profile: ; Furthermore, key profile parameters can be calculated based on the corrected electron density profile: ; in, The peak electron density of the F2 layer. Given the peak height of the F2 layer, calculate the integral electron content corresponding to the corrected profile: ; In this embodiment, a designated marine location at 13.7281 UT, latitude 24.7698°, and longitude -100.2421° on day 1 of 2026 was selected for inversion. After GIM interpolation, the VTEC was 17.9383 TECU, the initial IRI profile integral VTEC was 15.6067 TECU, the VTEC observation standard deviation was set to 2.350 TECU, and the vertical correlation length was set to 150.0 km. The basic relative prior standard deviation was set to 0.06, the additional prior standard deviation near the F2 layer peak was set to 0.20, and the additional prior standard deviation of the top ionosphere was set to 0.02. The first-order and second-order difference constraint weights were set to 0.200 and 5.000, respectively. The height-width parameter near the F2 layer peak was set to 95 km, and the height-width parameter of the top ionosphere was set to 320 km.

[0032] like Figure 2 As shown, in this embodiment, after correction using the method of the present invention, the cross-sectional area integral VTEC is increased to 16.7777 TECU, and the difference with GIM VTEC is reduced from 2.3316 TECU to 1.1606 TECU; simultaneously, NmF2 is reduced from 5.5528e+05 cells / cm² in IRI. -3 Revised to 6.2880e+05 per cm -3 The COSMIC occultation result is close to 6.3103e+05 per cm. -3 This demonstrates that the method can effectively constrain and correct the initial electron density profile using VTEC observations.

[0033] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for inverting ionospheric electron density based on marine VTEC constraints, characterized in that, Includes the following steps: Step 1: Obtain the longitude, latitude, annual day and UT of the specified location at sea, and generate the initial electron density profile on the corresponding height grid based on the ionospheric empirical model; Step 2: Obtain the observed value of the vertical total electron content at the specified location at sea at the corresponding time, and determine the observation error parameter of the observed value of the vertical total electron content; Step 3: Based on the initial electron density profile and height grid, construct the prior covariance matrix of the electron density relative correction amount; Step 4: Construct a height integral weight vector based on the height grid, and use the height integral weight vector to establish an integral relationship between the electron density profile and the total vertical electron content; Step 5: Based on the observed total vertical electron content, observation error parameters, height integral weight vector, and prior covariance matrix, construct the posterior update objective function for the relative correction of electron density; Step 6: Add the continuity and smoothness constraints of the electron density profile in the height direction to the posterior update objective function, and solve for the optimal relative correction amount; Step 7: Correct the initial electron density profile according to the optimal relative correction amount to obtain the corrected electron density profile; In step 5, based on the height integration weight vector Observed values ​​of total vertical electron content at specified locations and its standard deviation and prior covariance matrix The initial electron density profile is updated posteriorly; an objective function containing observation residuals and prior constraints is constructed: ； in, Represents the Hadamard product. To and A column vector of all 1s with the same dimension; This is the initial electron density profile vector; This is a relative correction amount; The variance of the vertical total electron content observation error; ； in, This represents the standard deviation of the observed total electron content in this vertical direction. In step 6, the continuity constraint is a first-order difference constraint, used to limit abrupt changes in the relative correction amount between adjacent height layers; the smoothness constraint is a second-order difference constraint, used to limit anomalies in the curvature of the relative correction amount; the vertical structure constraint is added to the objective function as a regularization term, and its form is: ； in, It is a first-order difference matrix. It is a second-order difference matrix. The weights are first-order smoothing constraints. The weights are second-order smoothing constraints; The first-order difference is expressed as: ； The second-order difference is expressed as: ； Solving the above objective function yields the optimal relative correction amount. .

2. The ionospheric electron density inversion method based on marine VTEC constraint according to claim 1, characterized in that, In step 1, the initial electron density profile is generated by an empirical ionospheric model, which is one of the international reference ionospheric model, the NeQuick model, or the Chapman model; the initial electron density profile is expressed as: ； in, This is the initial electron density profile vector. For the first Each height level, The total number of floors is the height. For height The initial electron density at that location.

3. The ionospheric electron density inversion method based on marine VTEC constraint according to claim 1, characterized in that, In step 2, the vertical total electron content observation value is derived from one of the following: global ionospheric grid product, regional ionospheric grid product, or GNSS inversion result of a single marine station. The vertical total electron content observation value corresponding to the specified location is recorded as... The error parameter for the vertical total electron content includes the standard deviation or variance, which characterizes the uncertainty of the vertical total electron content. The variance of the vertical total electron content observation error is expressed as: ； in, The variance of the vertical total electron content observation error. This represents the standard deviation corresponding to the observed total electron content in this vertical direction.

4. The ionospheric electron density inversion method based on marine VTEC constraint according to claim 1, characterized in that, In step 3, the relative correction to the electron density profile is expressed as: ； in, For height The relative correction to the electron density at that location. For height The corrected electron density, For height The initial electron density is given; it can be written in vector form: 。 5. The ionospheric electron density inversion method based on marine VTEC constraint according to claim 4, characterized in that, In step 3, a priori covariance matrix is ​​constructed based on the correlation between different altitude layers: ； in, Represented as the prior covariance matrix The Middle Line 1 Column elements, Relative correction amount The prior covariance matrix, , For height, , The prior standard deviation of the corresponding height layer. The vertical correlation length is used to control the rate at which the correlation between different height layers decays with height intervals.

6. The ionospheric electron density inversion method based on marine VTEC constraint according to claim 5, characterized in that, Prior standard deviation for each height level Represented as: ； in, Based on the prior standard deviation, and These are the additional prior standard deviations of the peak value and the top center height of layer F2, respectively. and These are the peak height of layer F2 and the height of the top center, respectively. and These are the width parameters for the peak height and top center height of layer F2, respectively.

7. The ionospheric electron density inversion method based on marine VTEC constraint according to claim 1, characterized in that, In step 4, the height integral weight vector is used to divide the electron density profile on the discrete height layer into the vertical total electron content. Based on the physical relationship of electron density integration along the height direction, the vertical total electron content is expressed as: ； Further written in matrix form: ； in, This is a highly integrated weight vector under highly discretized conditions. For the first The integral weights corresponding to each height layer This is a discrete height layer electron density profile. Indicates the total number of floors by height. For the first Each layer of height.

8. The ionospheric electron density inversion method based on marine VTEC constraint according to claim 1, characterized in that, In step 7, the initial electron density profile is corrected according to the optimal relative correction amount to obtain the final electron density profile: ； Simultaneously, key profile parameters were further calculated based on the corrected electron density profile: ； ； in, The peak electron density of the F2 layer. Given the peak height of the F2 layer, calculate the integral electron content corresponding to the corrected profile: ； in, This is a highly integrated weight vector under highly discretized conditions.

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