An ionospheric delay estimation method considering non-absolute zero constraint in high latitude region

Abstract

The application provides an ionospheric delay estimation method considering non-absolute zero constraint in high latitude areas. The application introduces ionospheric piercing point data of multiple historical moments and multiple geographical positions; a linear ionospheric delay calculation model is constructed; the multiple historical moments and the multiple geographical positions are compared with a latitude threshold in sequence to obtain multiple high-latitude geographical positions of multiple historical moments and multiple low-latitude geographical positions of multiple historical moments; a low-latitude observation equation and a high-latitude observation equation are constructed; the low-latitude observation equation and the high-latitude observation equation are combined to obtain an optimized parameter vector of an ionospheric model considering non-absolute zero constraint in high latitude areas; each ionospheric piercing point data of each geographical position in real time is taken to calculate and output the optimized ionospheric delay of the real-time geographical position. The application has the advantages of obviously relieving the high-latitude anomaly of the Beidou Klobuchar model and significantly improving the correction performance of the Beidou Klobuchar model in the southern hemisphere.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of satellite navigation and positioning, and particularly relates to an ionospheric delay estimation method considering non-absolute zero constraints in high latitude areas. BACKGROUND

[0002] The ionospheric delay is an important error source affecting satellite navigation and positioning, and the error caused by the ionospheric delay can reach several meters to tens of meters, which needs to be corrected by effective correction methods. Users of dual-frequency or multi-frequency receivers generally eliminate the ionospheric influence by means of observation value combination.

[0003] For single-frequency receiver users, different ionospheric correction models and algorithms are needed. The Klobuchar model is the most widely used broadcast ionospheric model. The Beidou Klobuchar model broadcast by the Beidou system is improved for China and surrounding areas based on the Klobuchar model. The Beidou Klobuchar model takes the height of the single-layer model as 375 km, and describes the diurnal variation of the vertical ionospheric delay in the geographic coordinate system using semi-cosine waves with constant bias. The eight parameters broadcast by the Beidou Klobuchar model are calculated according to the measured data of the global navigation satellite system dual-frequency monitoring station located in the Chinese region, and a set of parameters is updated every two hours. The model has the advantages of simple algorithm structure, fewer parameters, and fast calculation speed. Long-term analysis of actual data shows that the average correction accuracy of the Beidou Klobuchar model is better than 65%. However, the current research on the model shows that the Beidou Klobuchar model has defects such as decreased correction accuracy in the southern hemisphere and abnormal ionospheric correction values at high latitudes. SUMMARY

[0004] In order to solve the above technical problems, the application provides an ionospheric delay estimation method considering non-absolute zero constraints in high latitude areas.

[0005] The technical scheme of the method of the application is an ionospheric delay estimation method considering non-absolute zero constraints in high latitude areas, and the specific steps are as follows:

[0006] Step 1: introducing ionospheric piercing point data of multiple geographic positions at multiple historical times;

[0007] Step 2: constructing a linearized ionospheric delay calculation model;

[0008] Step 3: comparing the multiple geographic positions at the multiple historical times with the latitude threshold in sequence to obtain multiple high-latitude geographic positions at the multiple historical times and multiple low-latitude geographic positions at the multiple historical times;

[0009] Step 4: Using ionospheric puncture point data from multiple low-latitude geographical locations at multiple historical moments as input data, construct the low-latitude observation equation by combining it with a linearized ionospheric delay calculation model; using ionospheric puncture point data from multiple high-latitude geographical locations at multiple historical moments as input data, construct the high-latitude observation equation by combining it with a linearized ionospheric delay calculation model and an amplitude constraint model; combining the low-latitude and high-latitude observation equations simultaneously, and solving them through least squares iteration, obtain the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions;

[0010] Step 5: Obtain real-time ionospheric puncture point data for each geographic location, and calculate the optimized ionospheric delay for the real-time geographic location by combining the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions. Output the optimized ionospheric delay for the real-time geographic location.

[0011] Preferably, the ionospheric puncture point data at different geographical locations at multiple historical moments mentioned in step 1 are defined as follows:

[0012] Signal(u t，j v t，j )

[0013] t∈[1,T], j∈[1,N]

[0014] Among them, Signal(u t，j v t，j ) represents the ionospheric puncture point data at the j-th geographical location at the t-th historical moment, u t，j v represents the longitude of the j-th geographical location at the t-th historical moment. t，j Let T represent the latitude of the j-th geographical location at the t-th historical moment, T represent the number of historical moments, and N represent the number of geographical locations.

[0015] As a preferred embodiment, the linearized ionospheric delay calculation model described in step 2 is specifically defined as follows:

[0016]

[0017]

[0018] Among them, I k α represents the ionospheric delay calculated in the k-th iteration. i，k-1 Let α represent the i-th order parameter of the fitted amplitude term in the (k-1)th iteration, where: 0，k-1 Let α represent the 0th-order parameter of the fitted amplitude term in the (k-1)th iteration. 1，k-1 Let α represent the first-order parameter of the fitted amplitude term in the (k-1)th iteration. 2，k-1 Let α represent the second-order parameter of the fitted amplitude term in the (k-1)th iteration. 3，k-1β represents the third-order parameter of the fitted amplitude term in the (k-1)th iteration. i，k-1 Let β represent the i-th order parameter of the fitted periodic term in the (k-1)th iteration, where: 0，k-1 Let β represent the 0th-order parameter of the fitted periodic term in the (k-1)th iteration. 1，k-1 Let β represent the first-order parameter of the fitted periodic term in the (k-1)th iteration. 2，k-1 Let β represent the second-order parameter of the fitted periodic term in the (k-1)th iteration. 3，k-1 This represents the third-order parameter of the fitted periodic term in the (k-1)th iteration. I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 For the i-th order parameter α of the fitted amplitude term i The partial derivative coefficients, I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 For the i-th order parameter β of the fitted periodic term i The partial derivative coefficients, Let time represent the i-th latitude corresponding to the j-th geographical location at the t-th historical moment. t T represents the local time corresponding to the t-th historical moment, and T0 represents the time corresponding to the maximum ionospheric delay.

[0019] definition The amplitude term fitted to the linearized ionospheric delay calculation model during the (k-1)th iteration:

[0020] when Time to take

[0021] definition The periodic term fitted to the linearized ionospheric delay calculation model during the (k-1)th iteration:

[0022] when Time to take

[0023] when Time to take

[0024] Step 3 involves sequentially comparing multiple geographical locations at multiple historical moments with latitude thresholds, as detailed below:

[0025] If the latitude of each geographical location at each historical moment is greater than a latitude threshold, it is defined as a high-latitude geographical location at each historical moment, as follows:

[0026]

[0027] t∈[1,T],j h h∈[1, N], h∈[1, N1]

[0028] in, This represents the longitude corresponding to the h-th high-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. h The longitude of a geographical location The latitude corresponding to the h-th high-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. h The latitude of each geographical location, T represents the number of historical moments, N represents the number of geographical locations, and N1 represents the number of high-latitude geographical locations;

[0029] If the latitude of each geographic location at each historical moment is less than or equal to a latitude threshold, it is defined as a low-latitude geographic location at each historical moment, as follows:

[0030]

[0031] t∈[1,T],j l ∈[1, N], l∈[1, N2]

[0032] N = N1 + N2

[0033] in, This represents the longitude corresponding to the l-th low-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. l The longitude of a geographical location The latitude corresponding to the l-th low-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. l The latitude of each geographical location, T represents the number of historical moments, N represents the number of geographical locations, and N2 represents the number of low-latitude geographical locations;

[0034] As a preferred embodiment, the low-latitude observation equation described in step 4 is as follows:

[0035]

[0036] X 0 =[α 0，0 α 1，0 α 2，0 α 3，0 ,β 0，0 ,β 1，0 ,β 2，0 ,β 3，0 ]

[0037]

[0038]

[0039] t∈[1,T],j l∈[1, N], l∈[1, N2]

[0040] Where T represents the number of historical moments, N represents the number of geographical locations, and N² represents the number of low-latitude geographical locations. This represents the ionospheric puncture point data at the l-th low-latitude geographical location at the t-th historical moment. This represents the longitude corresponding to the l-th low-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. l The longitude of a geographical location The latitude corresponding to the l-th low-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. l The latitude of a geographical location, X 0 The parameter vector representing the original model's broadcast: where α 0，0 This represents the zeroth-order parameter value of the fitted amplitude term during the broadcast, i.e., the initial zeroth-order parameter value of the fitted amplitude term during the zeroth iteration in step 2; α 1，0 This represents the first-order parameter value of the fitted amplitude term during the broadcast, i.e., the initial value of the first-order parameter of the fitted amplitude term during the 0th iteration in step 2; α 2，0 This represents the second-order parameter value of the fitted amplitude term during broadcasting, i.e., the initial value of the second-order parameter of the fitted amplitude term during the 0th iteration in step 2; α 3，0 This represents the third-order parameter value of the fitted amplitude term during broadcasting, i.e., the initial value of the third-order parameter of the fitted amplitude term in step 2 during the 0th iteration, β. 0，0 This represents the zeroth-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial zeroth-order parameter value of the fitted periodicity term during the zeroth iteration in step 2; β 1，0 This represents the first-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the first-order parameter of the fitted periodicity term during the 0th iteration in step 2; β 2，0 This represents the second-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the second-order parameter of the fitted periodicity term during the 0th iteration in step 2; β 3，0 This represents the third-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the third-order parameter of the fitted periodicity term during the 0th iteration in step 2. Let dα0 represent the correction values ​​for the 0th-order parameter of the fitted amplitude term; dα1 represent the correction value for the 1st-order parameter of the fitted amplitude term; dα2 represent the correction value for the 2nd-order parameter of the fitted amplitude term; dα3 represent the correction value for the 3rd-order parameter of the fitted amplitude term; dβ0 represent the correction value for the 0th-order parameter of the fitted period term; dβ1 represent the correction value for the 1st-order parameter of the fitted period term; dβ2 represent the correction value for the 2nd-order parameter of the fitted period term; dβ3 represent the correction value for the 3rd-order parameter of the fitted period term; and B represent the correction values ​​for the 0th-order parameter of the fitted period term. l This represents the coefficient matrix of the low-latitude observation equation, where: I represents the ionospheric delay calculated in the (k-1)th iteration.k-1 The partial derivatives with respect to the 0th-order parameter of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted periodic term.

[0041] The high-latitude observation equation described in step 4 is as follows:

[0042]

[0043]

[0044]

[0045] t∈[1,T],j h h∈[1, N], h∈[1, N1]

[0046] Where T represents the number of historical moments, N represents the number of geographical locations, and N1 represents the number of high-latitude geographical locations. This represents the ionospheric puncture point data at the h-th high-latitude geographical location at the t-th historical moment. This represents the longitude corresponding to the h-th high-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. h The longitude of a geographical location The latitude corresponding to the h-th high-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. h The latitude of a geographical location, B h Let the coefficient matrix of the high-latitude observation equation be denoted as: I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted periodic term, This represents the coefficient matrix of the observation equation corresponding to the amplitude constraints added in the high-latitude region.

[0047] Step 4 involves simultaneously solving the low-latitude observation equations and the high-latitude observation equations, as detailed below:

[0048]

[0049] Step 4 describes the use of least squares iteration to obtain the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions, as detailed below:

[0050] Signal(u) represents the ionospheric puncture point data at the j-th geographical location at the t-th historical moment. t，j v t，j ) as input data, As output data, the parameter vector of the optimized ionospheric model considering non-absolute zero constraints in high-latitude regions is obtained by least squares iteration.

[0051] The parameter vector of the optimized ionospheric model considering non-absolute zero constraints in high-latitude regions, as described in step 4, is specifically defined as follows:

[0052]

[0053] Among them, X* This represents the optimized parameter vector. This represents the 0th-order parameter of the optimized fitted amplitude term. This represents the first-order parameter of the optimized fitted amplitude term. This represents the second-order parameter of the optimized fitted amplitude term. This represents the third-order parameter of the optimized fitted amplitude term. This represents the 0th-order parameter of the optimized fitting periodicity term. This represents the first-order parameter of the optimized fitting periodicity term. This represents the second-order parameter of the optimized fitting periodicity term. This represents the third-order parameter of the optimized fitting periodicity term;

[0054] Preferably, the real-time ionospheric puncture point data for each geographical location in step 5 is defined as follows:

[0055]

[0056] rt∈[1,T R ], rj∈[1, N R ]

[0057] in, This represents the ionospheric puncture point data at the rj-th geographical location at the rt-th real-time moment. This represents the longitude of the rj-th geographical location at the rt-th real-time moment. T represents the latitude of the rj-th geographical location at the rt-th real-time moment. R N represents the number of real-time moments. R Indicates the number of geographical locations;

[0058] The optimized ionospheric delay based on real-time geographic location in step 5 is defined as follows:

[0059]

[0060]

[0061]

[0062] like

[0063] like

[0064] like

[0065] Among them, I *The optimized ionospheric delay is obtained by using the optimized ionospheric model calculation formula that takes into account the non-absolute zero constraints in high-latitude regions, as described in step 5. DC is the nighttime ionospheric delay constant, and T0 is the initial phase value. This represents the local time corresponding to the rt-th real-time moment. This represents the latitude of the rj-th geographical location at the rt-th real-time moment. This represents the 0th-order parameter of the optimized fitted amplitude term. This represents the first-order parameter of the optimized fitted amplitude term. This represents the second-order parameter of the optimized fitted amplitude term. This represents the third-order parameter of the optimized fitted amplitude term. This represents the 0th-order parameter of the optimized fitting periodicity term. This represents the first-order parameter of the optimized fitting periodicity term. This represents the second-order parameter of the optimized fitting periodicity term. This represents the third-order parameter of the optimized fitting periodicity term; The amplitude term is fitted to the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions. The periodic term is fitted to the optimized ionospheric model that takes into account the non-absolute zero constraint in high-latitude regions.

[0066] The present invention also provides a computer-readable medium storing a computer program executed by an electronic device, which, when run on the electronic device, causes the electronic device to perform the steps of the method for estimating ionospheric delay taking into account the non-absolute zero constraint in high-latitude regions.

[0067] This invention addresses the shortcomings of the current BeiDou Klobuchar model, focusing on the impact of its symmetry processing strategy on the correction accuracy in the Southern Hemisphere and the model's anomalies at high latitudes. Therefore, it creatively proposes an ionospheric model that considers non-absolute zero constraints in high-latitude regions. This ionospheric model, which considers non-absolute zero constraints in high-latitude regions, does not change the number of parameters in the original model, removes the symmetry processing strategy, and adds Southern Hemisphere background ionospheric constraints. Simultaneously, during parameter fitting, zero constraints are added to the amplitude term in high-latitude regions and solved together with the established observation equations. This ionospheric model that considers non-absolute zero constraints in high-latitude regions significantly optimizes the overall correction performance of the BeiDou Klobuchar model, significantly improves Southern Hemisphere accuracy, and significantly alleviates high-latitude anomalies. Attached Figure Description

[0068] Fig. 1 : Flowchart of the method according to an embodiment of the present invention;

[0069] Fig. 2 Timing diagram of the corrected performance in an embodiment of the present invention.

[0070] Specific examples verification

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0073] The following is combined with Figs. 1-2 The technical solution of this invention is a method for estimating ionospheric delay considering the non-absolute zero constraint in high-latitude regions, as detailed below:

[0074] Step 1: Import ionospheric puncture point data from multiple geographical locations at multiple historical moments;

[0075] The ionospheric puncture point data at different geographical locations at multiple historical moments mentioned in step 1 are defined as follows:

[0076] Signal(u t，j v t，j )

[0077] t∈[1,T], j∈[1,N]

[0078] Among them, Signal(u t，j v t，j ) represents the ionospheric puncture point data at the j-th geographical location at the t-th historical moment, u t，j v represents the longitude of the j-th geographical location at the t-th historical moment. t，j Let T represent the latitude of the j-th geographical location at the t-th historical moment, T represent the number of historical moments, and N represent the number of geographical locations.

[0079] Step 2: Construct a linearized ionospheric delay calculation model;

[0080] The linearized ionospheric delay calculation model described in step 2 is specifically defined as follows:

[0081]

[0082]

[0083] Among them, I k α represents the ionospheric delay calculated in the k-th iteration. i，k-1 Let α represent the i-th order parameter of the fitted amplitude term in the (k-1)th iteration, where: 0，k-1 Let α represent the 0th-order parameter of the fitted amplitude term in the (k-1)th iteration. 1，k-1 Let α represent the first-order parameter of the fitted amplitude term in the (k-1)th iteration. 2，k-1 Let α represent the second-order parameter of the fitted amplitude term in the (k-1)th iteration. 3，k-1 β represents the third-order parameter of the fitted amplitude term in the (k-1)th iteration. i，k-1 Let β represent the i-th order parameter of the fitted periodic term in the (k-1)th iteration, where: 0，k-1 Let β represent the 0th-order parameter of the fitted periodic term in the (k-1)th iteration. 1，k-1 Let β represent the first-order parameter of the fitted periodic term in the (k-1)th iteration. 2，k-1 Let β represent the second-order parameter of the fitted periodic term in the (k-1)th iteration. 3，k-1 This represents the third-order parameter of the fitted periodic term in the (k-1)th iteration. I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 For the i-th order parameter α of the fitted amplitude term i The partial derivative coefficients, I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 For the i-th order parameter β of the fitted periodic term i The partial derivative coefficients, Let time represent the i-th latitude corresponding to the j-th geographical location at the t-th historical moment. t T represents the local time corresponding to the t-th historical moment, and T0 represents the time corresponding to the maximum ionospheric delay.

[0084] definition The amplitude term fitted to the linearized ionospheric delay calculation model during the (k-1)th iteration:

[0085] when Time to take

[0086] definition The periodic term fitted to the linearized ionospheric delay calculation model during the (k-1)th iteration:

[0087] when Time to take

[0088] when Time to take

[0089] Step 3: Compare multiple geographical locations at multiple historical moments with latitude thresholds in turn to obtain multiple high-latitude geographical locations at multiple historical moments and multiple low-latitude geographical locations at multiple historical moments.

[0090] Step 3 involves sequentially comparing multiple geographical locations at multiple historical moments with latitude thresholds, as detailed below:

[0091] If the latitude of each geographical location at each historical moment is greater than a latitude threshold, it is defined as a high-latitude geographical location at each historical moment, as follows:

[0092]

[0093] t∈[1,T],j h h∈[1, N], h∈[1, N1]

[0094] in, This represents the longitude corresponding to the h-th high-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. h The longitude of a geographical location The latitude corresponding to the h-th high-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. h The latitude of each geographical location, T represents the number of historical moments, N represents the number of geographical locations, and N1 represents the number of high-latitude geographical locations;

[0095] If the latitude of each geographic location at each historical moment is less than or equal to a latitude threshold, it is defined as a low-latitude geographic location at each historical moment, as follows:

[0096]

[0097] t∈[1,T],j l ∈[1, N], l∈[1, N2]

[0098] N = N1 + N2

[0099] in, This represents the longitude corresponding to the l-th low-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. l The longitude of a geographical location The latitude corresponding to the l-th low-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. l The latitude of each geographical location, T represents the number of historical moments, N represents the number of geographical locations, and N2 represents the number of low-latitude geographical locations;

[0100] Step 4: Using ionospheric puncture point data from multiple low-latitude geographical locations at multiple historical moments as input data, construct the low-latitude observation equation by combining it with a linearized ionospheric delay calculation model; using ionospheric puncture point data from multiple high-latitude geographical locations at multiple historical moments as input data, construct the high-latitude observation equation by combining it with a linearized ionospheric delay calculation model and an amplitude constraint model; combining the low-latitude and high-latitude observation equations simultaneously, and solving them through least squares iteration, obtain the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions;

[0101] The low-latitude observation equation described in step 4 is as follows:

[0102]

[0103] X 0 =[α 0，0 α 1，0 α 2，0 α 3，0 ,β 0，0 ,β 1，0 ,β 2，0 ,β 3，0 ]

[0104]

[0105]

[0106] t∈[1,T],j l ∈[1, N], l∈[1, N2]

[0107] Where T represents the number of historical moments, N represents the number of geographical locations, and N² represents the number of low-latitude geographical locations. This represents the ionospheric puncture point data at the l-th low-latitude geographical location at the t-th historical moment. This represents the longitude corresponding to the l-th low-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. l The longitude of a geographical location The latitude corresponding to the l-th low-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. l The latitude of a geographical location, X 0 The parameter vector representing the original model's broadcast: where α 0，0 This represents the zeroth-order parameter value of the fitted amplitude term during the broadcast, i.e., the initial zeroth-order parameter value of the fitted amplitude term during the zeroth iteration in step 2; α 1，0 This represents the first-order parameter value of the fitted amplitude term during the broadcast, i.e., the initial value of the first-order parameter of the fitted amplitude term during the 0th iteration in step 2; α 2，0This represents the second-order parameter value of the fitted amplitude term during broadcasting, i.e., the initial value of the second-order parameter of the fitted amplitude term during the 0th iteration in step 2; α 3，0 This represents the third-order parameter value of the fitted amplitude term during broadcasting, i.e., the initial value of the third-order parameter of the fitted amplitude term in step 2 during the 0th iteration, β. 0，0 This represents the zeroth-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial zeroth-order parameter value of the fitted periodicity term during the zeroth iteration in step 2; β 1，0 This represents the first-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the first-order parameter of the fitted periodicity term during the 0th iteration in step 2; β 2，0 This represents the second-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the second-order parameter of the fitted periodicity term during the 0th iteration in step 2; β 3，0 This represents the third-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the third-order parameter of the fitted periodicity term during the 0th iteration in step 2. Let dα0 represent the correction values ​​for the 0th-order parameter of the fitted amplitude term; dα1 represent the correction value for the 1st-order parameter of the fitted amplitude term; dα2 represent the correction value for the 2nd-order parameter of the fitted amplitude term; dα3 represent the correction value for the 3rd-order parameter of the fitted amplitude term; dβ0 represent the correction value for the 0th-order parameter of the fitted period term; dβ1 represent the correction value for the 1st-order parameter of the fitted period term; dβ2 represent the correction value for the 2nd-order parameter of the fitted period term; dβ3 represent the correction value for the 3rd-order parameter of the fitted period term; and B represent the correction values ​​for the 0th-order parameter of the fitted period term. l This represents the coefficient matrix of the low-latitude observation equation, where: I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted periodic term.

[0108] The high-latitude observation equation described in step 4 is as follows:

[0109]

[0110]

[0111]

[0112] t∈[1,T],j h h∈[1, N], h∈[1, N1]

[0113] Where T represents the number of historical moments, N represents the number of geographical locations, and N1 represents the number of high-latitude geographical locations. This represents the ionospheric puncture point data at the h-th high-latitude geographical location at the t-th historical moment. This represents the longitude corresponding to the h-th high-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. h The longitude of a geographical location The latitude corresponding to the h-th high-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. h The latitude of a geographical location, B h Let the coefficient matrix of the high-latitude observation equation be denoted as: I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted periodic term, This represents the coefficient matrix of the observation equation corresponding to the amplitude constraints added in the high-latitude region.

[0114] Step 4 involves simultaneously solving the low-latitude observation equations and the high-latitude observation equations, as detailed below:

[0115]

[0116] Step 4 describes the use of least squares iteration to obtain the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions, as detailed below:

[0117] Signal(u) represents the ionospheric puncture point data at the j-th geographical location at the t-th historical moment. t，j v t，j ) as input data, As output data, the parameter vector of the optimized ionospheric model considering non-absolute zero constraints in high-latitude regions is obtained by least squares iteration.

[0118] The parameter vector of the optimized ionospheric model considering non-absolute zero constraints in high-latitude regions, as described in step 4, is specifically defined as follows:

[0119]

[0120] Among them, X * This represents the optimized parameter vector. This represents the 0th-order parameter of the optimized fitted amplitude term. This represents the first-order parameter of the optimized fitted amplitude term. This represents the second-order parameter of the optimized fitted amplitude term. This represents the third-order parameter of the optimized fitted amplitude term. This represents the 0th-order parameter of the optimized fitting periodicity term. This represents the first-order parameter of the optimized fitting periodicity term. This represents the second-order parameter of the optimized fitting periodicity term. This represents the third-order parameter of the optimized fitting periodicity term;

[0121] Step 5: Obtain real-time ionospheric puncture point data for each geographic location, and calculate the optimized ionospheric delay for the real-time geographic location by combining the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions. Output the optimized ionospheric delay for the real-time geographic location.

[0122] The real-time ionospheric puncture point data for each geographical location mentioned in step 5 is defined as follows:

[0123]

[0124] rt∈[1,T R ], rj∈[1, N R ]

[0125] in, This represents the ionospheric puncture point data at the rj-th geographical location at the rt-th real-time moment. This represents the longitude of the rj-th geographical location at the rt-th real-time moment. T represents the latitude of the rj-th geographical location at the rt-th real-time moment. R N represents the number of real-time moments. R Indicates the number of geographical locations;

[0126] The optimized ionospheric delay based on real-time geographic location in step 5 is defined as follows:

[0127]

[0128]

[0129]

[0130] like

[0131] like

[0132] like

[0133] Among them, I * The optimized ionospheric delay, DC = 5 × 10, is obtained by using the optimized ionospheric model calculation formula that takes into account the non-absolute zero constraints in high-latitude regions, as described in step 5. -9 The ionospheric time delay constant is T0 = 50400, which is the initial phase value. This represents the local time corresponding to the rt-th real-time moment. This represents the latitude of the rj-th geographical location at the rt-th real-time moment. This represents the 0th-order parameter of the optimized fitted amplitude term. This represents the first-order parameter of the optimized fitted amplitude term. This represents the second-order parameter of the optimized fitted amplitude term. This represents the third-order parameter of the optimized fitted amplitude term. This represents the 0th-order parameter of the optimized fitting periodicity term. This represents the first-order parameter of the optimized fitting periodicity term. This represents the second-order parameter of the optimized fitting periodicity term. This represents the third-order parameter of the optimized fitting periodicity term; The amplitude term is fitted to the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions. The periodic term is fitted to the optimized ionospheric model that takes into account the non-absolute zero constraint in high-latitude regions.

[0134] Considering that the ionospheric model taking into account the non-absolute zero constraints in high-latitude regions uses the global ionospheric grid data provided by the International Navigation Satellite System (INS) as the fitting data source, a different data source was used than that of the BeiDou Klobuchar model. The Northern Hemisphere portion of the INS global ionospheric grid data, the same as that used in the model taking into account the non-absolute zero constraints in high-latitude regions, was used to refit the BeiDou Klobuchar model, resulting in a symmetrically processed BeiDou Klobuchar model, which was then compared with the model taking into account the non-absolute zero constraints in high-latitude regions. The symmetrically processed BeiDou Klobuchar model also applied the same additional zero constraint to the high-latitude amplitude term as the model taking into account the non-absolute zero constraints in high-latitude regions during parameter fitting. Using the INS global ionospheric grid data as a reference, the correction performance of the three models in the high-latitude regions of the Northern Hemisphere was evaluated over a full year. The average accuracy is shown in Table 1.

[0135] Table 1. Average correction accuracy of the three models in high-latitude regions throughout the year.

[0136]

[0137] Table 1 shows that the symmetrically processed BeiDou Klobuchar model and the ionospheric model considering non-absolute zero constraints in high-latitude regions have comparable accuracy in high-latitude regions of the Northern Hemisphere, and both outperform the BeiDou Klobuchar model. Compared with the BeiDou Klobuchar model, the symmetrically processed BeiDou Klobuchar model reduces the root mean square error by 51.3% and improves the correction rate by 12%, indicating that our proposed improved algorithm with zero constraints on the high-latitude additional amplitude term can effectively improve the ionospheric correction accuracy of the BeiDou Klobuchar model in high-latitude regions.

[0138] Similarly, using global ionospheric grid data provided by the International Navigation Satellite System Service, the correction performance of the three models in different hemispheres throughout the year was evaluated, and the time series plots of their root mean square error values ​​are shown below. Fig. 2 As shown. From Fig. 2The results show a significant difference in accuracy between the BeiDou Klobuchar model and the symmetrically processed BeiDou Klobuchar model in the Northern and Southern Hemispheres, with the Southern Hemisphere showing significantly lower accuracy. However, the ionospheric model considering non-absolute zero constraints in high-latitude regions shows a significant improvement in accuracy in the Southern Hemisphere. The mean root mean square errors (RMS) of the BeiDou Klobuchar model, the symmetrically processed BeiDou Klobuchar model, and the ionospheric model considering non-absolute zero constraints in high-latitude regions in the Southern Hemisphere are 6.5, 5.8, and 4.6 (total electron content), respectively. The ionospheric model considering non-absolute zero constraints in high-latitude regions improves accuracy by 20.7% and 29.2% in the Southern Hemisphere compared to the symmetrically processed BeiDou Klobuchar model and the BeiDou Klobuchar model, respectively.

[0139] Fig. 2 BDSK represents the BeiDou Klobuchar model. sym The BeiDou Klobuchar model, BDSK, represents symmetric processing. non-sym This represents an ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions.

[0140] A specific embodiment of the present invention also provides a computer-readable medium.

[0141] The computer-readable medium is a server workstation;

[0142] The server workstation stores the computer program executed by the electronic device. When the computer program runs on the electronic device, it causes the electronic device to execute the steps of the ionospheric delay estimation method considering the non-absolute zero constraint in high-latitude regions according to the embodiments of the present invention.

[0143] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0144] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions, characterized in that, Includes the following steps: Step 1: Import ionospheric puncture point data from multiple geographical locations at multiple historical moments; Step 2: Combine ionospheric puncture point data from multiple geographical locations at multiple historical moments to construct a linearized ionospheric delay calculation model; Step 3: Compare multiple geographical locations at multiple historical moments with latitude thresholds in turn to obtain multiple high-latitude geographical locations at multiple historical moments and multiple low-latitude geographical locations at multiple historical moments. Step 4: Using ionospheric puncture point data from multiple low-latitude geographical locations at multiple historical moments as input data, construct the low-latitude observation equation by combining it with a linearized ionospheric delay calculation model; using ionospheric puncture point data from multiple high-latitude geographical locations at multiple historical moments as input data, construct the high-latitude observation equation by combining it with a linearized ionospheric delay calculation model and an amplitude constraint model; combining the low-latitude and high-latitude observation equations simultaneously, and solving them through least squares iteration, obtain the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions; Step 5: Obtain real-time ionospheric puncture point data for each geographic location, and calculate the optimized ionospheric delay for the real-time geographic location by combining the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions. Output the optimized ionospheric delay for the real-time geographic location.

2. The method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions according to claim 1, characterized in that: The ionospheric puncture point data at different geographical locations at multiple historical moments mentioned in step 1 are defined as follows: Signal(u t，j ,v t，j ) t∈[1,T], j∈[1,N] Among them, Signal(u t,j ,v t,j ) represents the ionospheric puncture point data at the j-th geographical location at the t-th historical moment, u t,j v represents the longitude of the j-th geographical location at the t-th historical moment. t,j Let T represent the latitude of the j-th geographical location at the t-th historical moment, T represent the number of historical moments, and N represent the number of geographical locations.

3. The method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions according to claim 2, characterized in that: The linearized ionospheric delay calculation model described in step 2 is specifically defined as follows: Among them, I k α represents the ionospheric delay calculated in the k-th iteration. i,k-1 Let α represent the i-th order parameter of the fitted amplitude term in the (k-1)th iteration, where: 0,-1 Let α represent the 0th-order parameter of the fitted amplitude term in the (k-1)th iteration. 1,-1 Let α represent the first-order parameter of the fitted amplitude term in the (k-1)th iteration. 2,-1 Let α represent the second-order parameter of the fitted amplitude term in the (k-1)th iteration. 3,-1 β represents the third-order parameter of the fitted amplitude term in the (k-1)th iteration. i,k-1 Let β represent the i-th order parameter of the fitted periodic term in the (k-1)th iteration, where: 0,k-1 Let β represent the 0th-order parameter of the fitted periodic term in the (k-1)th iteration. 1,k-1 Let β represent the first-order parameter of the fitted periodic term in the (k-1)th iteration. 2,k-1 Let β represent the second-order parameter of the fitted periodic term in the (k-1)th iteration. 3,-1 This represents the third-order parameter of the fitted periodic term in the (k-1)th iteration. I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 For the i-th order parameter α of the fitted amplitude term i The partial derivative coefficients, I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 For the i-th order parameter β of the fitted periodic term i The partial derivative coefficients, Let time represent the i-th latitude corresponding to the j-th geographical location at the t-th historical moment. t T represents the local time corresponding to the t-th historical moment, and T0 represents the time corresponding to the maximum ionospheric delay. definition The amplitude term fitted to the linearized ionospheric delay calculation model during the (k-1)th iteration: when Time to take definition The periodic term fitted to the linearized ionospheric delay calculation model during the (k-1)th iteration: when Time to take when Time to take 4. The method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions according to claim 3, characterized in that: Step 3 involves comparing multiple geographical locations at multiple historical moments sequentially with latitude thresholds, as detailed below: If the latitude of each geographical location at each historical moment is greater than a latitude threshold, it is defined as a high-latitude geographical location at each historical moment, as follows: t∈[1,T],j h ∈[1,N],h∈[1,N1] in, This represents the longitude corresponding to the h-th high-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. h The longitude of a geographical location The latitude corresponding to the h-th high-latitude geographical location at the t-th historical moment is, i.e., the j-th latitude at the t-th historical moment. h The latitude of each geographical location, T represents the number of historical moments, N represents the number of geographical locations, and N1 represents the number of high-latitude geographical locations; If the latitude of each geographic location at each historical moment is less than or equal to a latitude threshold, it is defined as a low-latitude geographic location at each historical moment, as follows: t∈[1,T], j l ∈[1,N],l∈[1,N2] N = N1 + N2 in, This represents the longitude corresponding to the l-th low-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. l The longitude of a geographical location The latitude corresponding to the l-th low-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. l The latitude of each geographical location, T represents the number of historical moments, N represents the number of geographical locations, and N2 represents the number of low-latitude geographical locations.

5. The method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions according to claim 4, characterized in that: The low-latitude observation equation described in step 4 is as follows: X 0 ＝[α 0,0 ,α 1,0 ,α 2,0 ,α 3,0 ,β 0,0 ,β 1,0 ,β 2,0 ,β 3,0 ] t∈[1,T], j l ∈[1,N],l∈[1,N2] Where T represents the number of historical moments, N represents the number of geographical locations, and N² represents the number of low-latitude geographical locations. This represents the ionospheric puncture point data at the l-th low-latitude geographical location at the t-th historical moment. This represents the longitude corresponding to the l-th low-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. l The longitude of a geographical location The latitude corresponding to the l-th low-latitude geographical location at the t-th historical moment is the j-th latitude at the t-th historical moment. l The latitude of a geographical location, X 0 The parameter vector representing the original model's broadcast: where α 0,0 This represents the zeroth-order parameter value of the fitted amplitude term during the broadcast, i.e., the initial zeroth-order parameter value of the fitted amplitude term during the zeroth iteration in step 2; α 1,0 This represents the first-order parameter value of the fitted amplitude term during the broadcast, i.e., the initial value of the first-order parameter of the fitted amplitude term during the 0th iteration in step 2; α 2,0 This represents the second-order parameter value of the fitted amplitude term during broadcasting, i.e., the initial value of the second-order parameter of the fitted amplitude term during the 0th iteration in step 2; α 3, This represents the third-order parameter value of the fitted amplitude term during broadcasting, i.e., the initial value of the third-order parameter of the fitted amplitude term in step 2 during the 0th iteration, β. 0,0 This represents the zeroth-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial zeroth-order parameter value of the fitted periodicity term during the zeroth iteration in step 2; β 1,0 This represents the first-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the first-order parameter of the fitted periodicity term during the 0th iteration in step 2; β 2,0 This represents the second-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the second-order parameter of the fitted periodicity term during the 0th iteration in step 2; β 3,0 This represents the third-order parameter value of the fitted periodicity term during broadcasting, i.e., the initial value of the third-order parameter of the fitted periodicity term during the 0th iteration in step 2. Let dα0 represent the correction values ​​for the 0th-order parameter of the fitted amplitude term; dα1 represent the correction value for the 1st-order parameter of the fitted amplitude term; dα2 represent the correction value for the 2nd-order parameter of the fitted amplitude term; dα3 represent the correction value for the 3rd-order parameter of the fitted amplitude term; dβ0 represent the correction value for the 0th-order parameter of the fitted period term; dβ1 represent the correction value for the 1st-order parameter of the fitted period term; dβ2 represent the correction value for the 2nd-order parameter of the fitted period term; dβ3 represent the correction value for the 3rd-order parameter of the fitted period term; and B represent the correction values ​​for the 0th-order parameter of the fitted period term. l This represents the coefficient matrix of the low-latitude observation equation, where: I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted periodic term; The high-latitude observation equation described in step 4 is as follows: t∈[1,T],j h ∈[1,N],h∈[1,N1] Where T represents the number of historical moments, N represents the number of geographical locations, and N1 represents the number of high-latitude geographical locations. This represents the ionospheric puncture point data at the h-th high-latitude geographical location at the t-th historical moment. This represents the longitude corresponding to the h-th high-latitude geographical location at the t-th historical moment, i.e., the j-th latitude location at the t-th historical moment. h The longitude of a geographical location The latitude corresponding to the h-th high-latitude geographical location at the t-th historical moment is, i.e., the j-th latitude at the t-th historical moment. h The latitude of each geographical location, Bh represents the coefficient matrix of the high-latitude observation equation, where: I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted amplitude term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the 0th-order parameter of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the first-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives of the second-order parameters of the fitted periodic term; I represents the ionospheric delay calculated in the (k-1)th iteration. k-1 The partial derivatives with respect to the third-order parameters of the fitted periodic term, This represents the coefficient matrix of the observation equation corresponding to the amplitude constraints added in the high-latitude portion.

6. The method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions according to claim 5, characterized in that: Step 4 involves simultaneously solving the low-latitude observation equations and the high-latitude observation equations, as detailed below: Step 4 describes the use of least squares iteration to obtain the parameter vector of the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions, as detailed below: Signal(u) represents the ionospheric puncture point data at the j-th geographical location at the t-th historical moment. t,j ,v t,j ) as input data, As output data, the parameter vector of the optimized ionospheric model considering non-absolute zero constraints in high-latitude regions is obtained by least squares iteration. The parameter vector of the optimized ionospheric model considering non-absolute zero constraints in high-latitude regions, as described in step 4, is specifically defined as follows: Among them, X * This represents the optimized parameter vector. This represents the 0th-order parameter of the optimized fitted amplitude term. This represents the first-order parameter of the optimized fitted amplitude term. This represents the second-order parameter of the optimized fitted amplitude term. This represents the third-order parameter of the optimized fitted amplitude term. This represents the 0th-order parameter of the optimized fitting periodicity term. This represents the first-order parameter of the optimized fitting periodicity term. This represents the second-order parameter of the optimized fitting periodicity term. This represents the third-order parameter of the optimized fitting periodic term.

7. The method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions according to claim 6, characterized in that: The real-time ionospheric puncture point data for each geographical location mentioned in step 5 is defined as follows: rt∈[1,T R ],rj∈[1,N R ] in, This represents the ionospheric puncture point data at the rj-th geographical location at the rt-th real-time moment. This represents the longitude of the rj-th geographical location at the rt-th real-time moment. T represents the latitude of the rj-th geographical location at the rt-th real-time moment. R N represents the number of real-time moments. R This indicates the number of geographical locations.

8. The method for estimating ionospheric delay considering non-absolute zero constraints in high-latitude regions according to claim 7, characterized in that: The optimized ionospheric delay based on real-time geographic location in step 5 is defined as follows: like like like Among them, I * The optimized ionospheric delay, obtained by using the optimized ionospheric model calculation formula considering the non-absolute zero constraints in high-latitude regions as described in step 5, is the nighttime ionospheric delay constant, with 0 representing the initial phase value. This represents the local time corresponding to the rt-th real-time moment. This represents the latitude of the rj-th geographical location at the rt-th real-time moment. This represents the 0th-order parameter of the optimized fitted amplitude term. This represents the first-order parameter of the optimized fitted amplitude term. This represents the second-order parameter of the optimized fitted amplitude term. This represents the third-order parameter of the optimized fitted amplitude term. This represents the 0th-order parameter of the optimized fitting periodicity term. This represents the first-order parameter of the optimized fitting periodicity term. This represents the second-order parameter of the optimized fitting periodicity term. This represents the third-order parameter of the optimized fitting periodicity term; The amplitude term is fitted to the optimized ionospheric model that takes into account the non-absolute zero constraints in high-latitude regions. The periodic term is fitted to the optimized ionospheric model that takes into account the non-absolute zero constraint in high-latitude regions.

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