CN-122017889-A - Offshore single-station single-epoch model perception regularization VTEC estimation method

CN122017889ACN 122017889 ACN122017889 ACN 122017889ACN-122017889-A

Abstract

The invention discloses a marine single-station single-epoch model perception regularization VTEC estimation method, and belongs to the field of ionosphere inversion. The method comprises the steps of firstly extracting total delay of an oblique ionosphere by using non-differential non-combination PPP, correcting satellite DCB by combining an external DCB product, then constructing an ionosphere VTEC inversion observation equation, calculating equation matrix condition numbers to quantify pathological conditions, further constructing a model perception regularization method consisting of a selective structured matrix, a self-adaptive regularization factor and a numerical value stabilization term, dynamically adjusting regularization strength according to the condition numbers, and finally superposing the regularization term to a least square expression to solve a stable VTEC model coefficient and solve a current epoch VTEC value. The method effectively suppresses the problem of unstable VTEC inversion value caused by small errors under pathological conditions, and remarkably improves the reliability and precision of ionosphere modeling of the marine observation limited area.

Inventors

QI KE
ZHANG HONGYI
HU TONG
WANG BO
QIU ZHIJIN
ZOU JING
LI ZHIQIAN

Assignees

山东省科学院海洋仪器仪表研究所

Dates

Publication Date: 20260512
Application Date: 20260415

Claims (9)

1. The marine single-station single-epoch model perception regularized VTEC estimation method is characterized by comprising the following steps of: Step 1, extracting and correcting total delay of an oblique ionosphere by using GNSS observation data, navigation ephemeris and PPP-B2B or HAS correction information; Step 2, mapping the corrected total delay of the oblique ionosphere into VTEC based on a projection function, and constructing a VTEC mathematical model; Step 3, an observation equation is established according to the VTEC mathematical model, a least square design matrix is extracted, a normal equation matrix is established, and the condition number of the normal equation matrix is calculated so as to evaluate the disease state of the matrix; Step 4, constructing a model perception regularization method consisting of a selective structured matrix, a regularization factor and a numerical stability term, and adaptively adjusting regularization strength according to the condition number of the normal equation matrix; and 5, superposing the selective structured matrix, the regularization factor and the numerical stability term to a least square expression, solving to obtain a VTEC model coefficient, and further solving the VTEC value of the current epoch.
2. The method for estimating the VTEC by using the marine single-station single-epoch model perception regularization as claimed in claim 1, wherein the step 1 specifically comprises the following sub-steps: Step 1.1, calculating satellite position coordinates according to navigation ephemeris data, and calculating satellite altitude and azimuth by combining a receiver position; Step 1.2, adopting a non-differential non-combination precise single point positioning technology to process pseudo-range and carrier phase observation values of a current epoch, extracting total delay of an oblique ionosphere containing satellite differential code deviation and receiver differential code deviation, wherein the expression is as follows: ; In the formula, For the total delay of the ionosphere in the bias direction with satellite DCB and receiver DCB, For the total electron content in the oblique direction, , Is a coefficient of ionospheric delay difference between two frequencies, And The frequencies of satellite observations L 1 and L 2 , respectively, r is the receiver identification, c is the speed of light, In order for the receiver DCB to be present, Is satellite DCB; step 1.3, receiving and decoding Beidou PPP-B2B or Galileo HAS data stream in real time to obtain satellite DCB correction; step 1.4, eliminating satellite DCB in the total delay of the oblique ionosphere by using the satellite DCB correction to obtain the corrected total delay of the oblique ionosphere: ; In the formula, The corrected total delay of the oblique ionosphere is obtained.
3. The method for estimating the VTEC by using the marine single-station single-epoch model perception regularization as recited in claim 2, wherein the step 2 specifically includes the following sub-steps: step 2.1, calculating the zenith distance z at the receiver by using a satellite altitude through a standard geometric conversion formula; Step 2.2, calculating a projection function value based on the improved ionosphere single-layer projection function model: ; ; In the formula, Representing the value of the projection function, For the zenith distance at ionosphere IPP , As the average radius of the earth, For the ionosphere single-layer height, Correcting factors for single-layer projection functions; step 2.3, calculating the geographic coordinates of the ionosphere puncture points according to the satellite azimuth angle, the altitude angle and the receiver position by utilizing a spherical triangle formula and coordinate conversion, and sequentially converting the geographic coordinates into a geomagnetic coordinate system and a solar-solid geomagnetic coordinate system to obtain the solar-solid geomagnetic latitude of the puncture points He Ri Gu geomagnetic longitude ; And 2.4, substituting the daily fixed geomagnetic coordinates into the selected VTEC mathematical model to construct the VTEC mathematical model suitable for the single station.
4. The method for estimating the VTEC by using the marine single-station single-epoch model perception regularization as claimed in claim 3, wherein the VTEC mathematical model is one of a first-order plane linear model, an asymmetric quadratic polynomial model, a full quadratic polynomial model or a spherical harmonic model, and the mode of substituting coordinates is as follows: First order planar linear model: ; Asymmetric quadratic polynomial model: ; full quadratic polynomial model: ; Spherical harmonic model: ; In the formula, Representing the position at IPP The value of the sum of the values, And Meaning the day-fixed geomagnetic latitude and day-fixed geomagnetic longitude of the ionosphere puncture point respectively, And The maximum order and the number of times of the spherical harmonic function are respectively; is a regularized Legend function; And Is the spherical harmonic coefficient.
5. The method for estimating the VTEC by using the marine single-station single-epoch model as defined in claim 4, wherein the step 3 specifically comprises the following sub-steps: step 3.1, substituting the projection function value, the VTEC mathematical model and the receiver DCB term into a corrected total delay formula of the oblique ionosphere to construct an ionosphere VTEC inversion model, wherein the formula is as follows: ; In the formula, To correct for the total delay of the bias ionosphere, Representing an improved ionospheric single layer projection function, Representing a mathematical model of the VTEC and, For the receiver DCB; Further converting it into the observation equation: ; In the formula, Is a physical constant coefficient of the value of ; Step 3.2, writing the observation equation into a matrix form Wherein For vectors of bias ionosphere total delay observations under a single epoch for all visible satellites, The matrix is designed for least squares and, The method comprises the steps that a to-be-estimated parameter vector comprises VTEC model coefficients and a receiver DCB of each GNSS system; Step3.3, constructing a normal equation matrix by utilizing the least square principle ; Step 3.4, singular value decomposition is carried out on the normal equation matrix, and the maximum singular value is calculated And minimum singular values Further obtain the condition number The pathogenicity of the matrix is quantitatively designed according to the method; 。
6. the method for estimating the VTEC by using the marine single-station single-epoch model as defined in claim 5, wherein the step 4 specifically comprises the following substeps: step 4.1, constructing a selectively structured matrix The matrix is a diagonal matrix, and diagonal elements of the diagonal matrix do not impose constraint on constant terms, but impose unit constraint on higher-order parameters, specifically defined as: ; In the formula, Is that Is a diagonal matrix of the (a), Representing diagonalization operators for inputting vectors Mapping into a diagonal matrix, wherein diagonal elements of the diagonal matrix are components of the input vector, and non-diagonal elements are 0; for the total number of valid observations under that epoch, The piecewise function of the element on the main diagonal is defined as: ; In the formula, Step 4.2, constructing a numerical stable term for the parameter serial number to be estimated : ; In the formula, For the numerical stability term, For the total number of all unknowns to be solved in the observation equation, Is a very small constant value, and is a very small constant, To a trace operator; step 4.3, determining regularization factors by adopting a policy-dividing mode according to the type of the selected VTEC mathematical model Establishing With condition number Increasing the regularization strength when the condition number increases, and decreasing otherwise; Step 4.4, selectively structuring the matrix Regularization factor And numerical stability term And combining to form an adaptive regularization term for correcting the original least squares problem.
7. The method for marine single-station single-epoch model-aware regularization VTEC estimation of claim 6, wherein the regularization factor The calculation formula is as follows: ; In the formula, Represents the median of the number of bits taken in, Is a matrix Is used to determine the set of singular values of (c), For the total number of all unknowns to be solved in the observation equation, As the maximum of the singular values of the values, For the second largest singular value, The LP, SH, AQ, FQ models are a first-order plane linear model, a spherical harmonic model, an asymmetric quadratic polynomial model and a full quadratic polynomial model respectively.
8. The method for estimating the VTEC by using the marine single-station single-epoch model as defined in claim 6, wherein the step 5 specifically comprises the following substeps: Step 5.1, selectively structuring the matrix Regularization factor And numerical stability term The final solution expression of the offshore single-station single-epoch model perception regularized VTEC estimation method is constructed by being added into an original least square equation: ; In the formula, Is that A rank identity matrix; Step 5.2, solving the expression to obtain the parameter vector to be estimated The VTEC model coefficients and the receiver DCB of each GNSS system are included; step 5.3, obtaining the geographical coordinates of the receiver position according to the precise single-point positioning technology, and converting the geographical coordinates to the latitude under the day-to-solid geomagnetic coordinate system And longitude ; And 5.4, substituting the solved VTEC model coefficient and the day-fixed geomagnetic coordinates at the receiver into the selected VTEC mathematical model, and calculating to obtain the VTEC value at the receiver of the current epoch.
9. The method of claim 2, wherein the non-differential non-combined precise single point positioning technique uses GNSS pseudorange and carrier phase observations to solve for receiver position, clock bias, tropospheric delay, and total delay of the diagonal ionosphere including hardware delay from epoch to epoch by kalman filter or least squares filter.

Description

Offshore single-station single-epoch model perception regularization VTEC estimation method Technical Field The invention relates to the field of ionosphere VTEC inversion, in particular to a marine single-station single-epoch model perception regularization VTEC estimation method. Background The vertical total electronic content (Vertical Total Electron Content, VTEC) of the ionosphere at sea is one of the core parameters characterizing the ionosphere state, whose changes directly affect the propagation characteristics of Global Navigation Satellite System (GNSS) signals. The VTEC information with high precision and high time resolution has important research significance and application value in the fields of offshore electric wave communication, space-based radar imaging, communication, navigation, time service and the like in deep sea ocean navigation. Currently, the ocean area lacks a fixed observation infrastructure for a long time, and the number of offshore GNSS stations is rare and distributed discretely. This current situation results in a significant lack of constraint capability of the existing global ionosphere model in the ocean area, and significant uncertainty exists in the ionosphere structural features. The refined depiction of the ionosphere state in the ocean area has become a key bottleneck restricting the performance of related applications. Under the background of limited offshore observation conditions, single-station ionosphere inversion becomes an important technical approach for describing the ionosphere change of the ocean area. The core logic of ionosphere VTEC inversion is to estimate the VTEC model coefficients, and then reconstruct the VTEC sequence of the target region using the coefficients. Conventionally, the estimation of VTEC model coefficients mostly employs the least squares method. However, in a single-station observation scenario, the spatial distribution of ionosphere puncture points presents significant geometric degradation characteristics in a short time, resulting in a least squares design matrix approaching singular, which exhibits severe morbidity. The pathological condition makes the estimation result of the model coefficient extremely sensitive to observation noise and tiny disturbance, and numerical oscillation and non-physical abnormality are extremely easy to cause. Due to the instability of the model coefficients, it is difficult to obtain stable and reliable single-station VTEC values by the traditional least square method. Therefore, a method capable of effectively inhibiting the morbidity of a design matrix and improving the robustness of VTEC estimation under single-station and single-epoch conditions is needed to meet the requirement of high-precision inversion of an ionization layer in a complex offshore environment. Disclosure of Invention In order to solve the technical problems, the invention provides a marine single-station single-epoch model perception regularized VTEC estimation method, so as to effectively inhibit the morbidity of a least squares design matrix and enhance the robustness and rationality of VTEC model coefficient estimation under single-station single-epoch observation conditions, thereby realizing the purpose of ionosphere VTEC inversion with high precision and high reliability under a marine complex environment. In order to achieve the above purpose, the technical scheme of the invention is as follows: An offshore single-station single-epoch model perception regularization VTEC estimation method comprises the following steps: Step 1, extracting and correcting total delay of an oblique ionosphere by using GNSS observation data, navigation ephemeris and PPP-B2B or HAS correction information; Step 2, mapping the corrected total delay of the oblique ionosphere into VTEC based on a projection function, and constructing a VTEC mathematical model; Step 3, an observation equation is established according to the VTEC mathematical model, a least square design matrix is extracted, a normal equation matrix is established, and the condition number of the normal equation matrix is calculated so as to evaluate the disease state of the matrix; Step 4, constructing a model perception regularization method consisting of a selective structured matrix, a regularization factor and a numerical stability term, and adaptively adjusting regularization strength according to the condition number of the normal equation matrix; and 5, superposing the selective structured matrix, the regularization factor and the numerical stability term to a least square expression, solving to obtain a VTEC model coefficient, and further solving the VTEC value of the current epoch. In the above scheme, the step 1 specifically includes the following sub-steps: Step 1.1, calculating satellite position coordinates according to navigation ephemeris data, and calculating satellite altitude and azimuth by combining a receiver position; Step 1.2, adopting a non-differential n