Double-frequency ionosphere delay estimation method and device

Abstract

The invention discloses a double-frequency ionosphere delay estimation method and device, filtering estimation is performed on the double-frequency ionosphere delay amount and the change rate thereof based on a state modeling recursive estimation method such as a Kalman filter, the high-frequency noise of double-frequency ionosphere elimination combined positioning is effectively reduced, the dynamic trend of ionosphere delay is reserved after filtering, and the positioning accuracy is improved. And the positioning result is smoother and more stable, and meanwhile, the real-time change of the ionosphere is adapted.

Description

Technical Field

[0001] The present application relates to, but is not limited to, satellite navigation technology, and in particular to a dual-frequency ionospheric delay estimation method and device. Background Art

[0002] In the pseudorange single-point positioning of the Global Navigation Satellite System (GNSS), in order to improve positioning accuracy and reliability under active ionospheric conditions, a dual-frequency ionospheric elimination combination method is usually used to correct the ionospheric delay error. This method eliminates the influence of the first-order ionospheric delay by combining pseudorange observations at two different frequencies. However, this combination also amplifies the noise in the original pseudorange observations, resulting in high-frequency jitter in the positioning results and reduced stability. Therefore, although this method can improve the positioning deviation problem, it introduces a new accuracy fluctuation problem. Summary of the Invention

[0003] The present application provides a dual-frequency ionospheric delay estimation method and device, which can ensure the ionospheric error elimination capability while improving the combined noise characteristics and enhancing the overall performance of the positioning system.

[0004] An embodiment of the present invention provides a dual-frequency ionospheric delay estimation method, including:

[0005] Based on a process model that can model the dynamic characteristics of ionospheric delay, the ionospheric delay change rate is modeled, and a state model including the ionospheric delay and its change rate is constructed. The constructed state model is discretized to obtain a state update model.

[0006] According to the constructed state update model, an observation model is established using the dual-frequency ionospheric elimination combined observation value constructed by the dual-frequency pseudorange observation;

[0007] According to the state update model and the observation model, a recursive estimation method based on state modeling is used to recursively estimate the ionospheric delay and its changing rate.

[0008] In one exemplary embodiment, the present invention further comprises:

[0009] The ionospheric delay obtained by the recursive estimation is used to correct the pseudorange observation value and output a positioning result.

[0010] In an exemplary embodiment, constructing a state model including ionospheric delay and its rate of change, and discretizing the constructed state model to obtain a state update model includes:

[0011] Obtain dual-frequency pseudorange observation data, which includes pseudorange observation values of two different frequency signals;

[0012] According to the functional relationship between ionospheric delay and frequency, the dual-frequency ionospheric-free combined observation value is calculated;

[0013] Setting the state vector to be a two-dimensional state vector including the ionospheric delay and its rate of change, modeling the ionospheric delay rate of change using a first-order Markov process, and establishing the state model of the continuous-time state;

[0014] Discretizing the state model to obtain a state transfer matrix required by the state update model;

[0015] Based on the linear time-invariant system process noise propagation model, a covariance matrix of the process noise required by the state update model in discrete epochs is constructed.

[0016] In one exemplary embodiment, the two-dimensional state vector is Where, I is the ionospheric delay, is the ionospheric delay variation rate;

[0017] The modeling using a first-order Markov process includes:

[0018] in, is the state model, α is the anti-correlation time constant, and w is the system process noise.

[0019] In an exemplary embodiment, the discretizing the state model includes:

[0020] Wherein, the subscripts k and k+1 represent the physical quantities corresponding to the kth epoch and the k+1th epoch respectively, Φ is the state transfer matrix, W k,k+1 is the system process noise from epoch k to epoch k+1.

[0021] In an exemplary embodiment, the observation model is: Z k+1 =HX k+1 +V=[1 0]X k+1 +V k+1 , where Z kv1 is the measurement value of epoch k, H is the observation matrix, V k+1 is the observation noise, and the variance of the observation noise is R k+1 .

[0022] In an exemplary embodiment, the recursive estimation method based on state modeling includes: a Kalman filtering algorithm.

[0023] In an exemplary embodiment, the recursive estimation of the ionospheric delay and its rate of change using a state modeling-based recursive estimation method based on the state update model and the observation model includes the following process of recursively executing between epochs to achieve continuous estimation and real-time update of the ionospheric delay:

[0024] At each epoch, based on the state posterior estimate and error covariance of the previous epoch, the state transition model is used to perform time update to predict the state prior and error covariance of the current epoch;

[0025] Combined with the observation value of the current epoch, the measurement update is performed according to the observation model, the Kalman gain is calculated, the state and covariance are corrected, and the posterior estimate of the state of the current epoch is obtained;

[0026] The ionospheric delay estimate in the state posterior estimation is output for subsequent pseudorange correction.

[0027] An embodiment of the present application further provides a computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions are used to execute any of the above-described dual-frequency ionospheric delay estimation methods.

[0028] An embodiment of the present application further provides a computer device, including a memory and a processor, wherein the memory stores the following instructions executable by the processor: used to execute the steps of any of the above-mentioned dual-frequency ionospheric delay estimation methods.

[0029] The embodiment of the present application further provides a dual-frequency ionospheric delay estimation device, comprising: a construction module, an establishment module, and an estimation module; wherein,

[0030] A construction module is used to model the ionospheric delay change rate based on a process model that can model the dynamic characteristics of the ionospheric delay, construct a state model including the ionospheric delay and its change rate, and discretize the constructed state model to obtain a state update model;

[0031] Establishing a module for updating the model according to the constructed state and establishing an observation model using dual-frequency ionospheric elimination combined observation values constructed by dual-frequency pseudorange observations;

[0032] The estimation module is used to recursively estimate the ionospheric delay and its changing rate according to the state update model and the observation model using a recursive estimation method based on state modeling.

[0033] In an exemplary embodiment, the method further includes: a processing module configured to correct the pseudorange using the ionospheric delay obtained by the recursive estimation and output a positioning result.

[0034] In an exemplary embodiment, the dual-frequency ionospheric delay estimation device is provided in a GNSS receiver, or in an external computing platform capable of inputting GNSS observation data.

[0035] The dual-frequency ionospheric delay estimation method provided in the embodiment of the present application uses a recursive estimation method based on state modeling, such as a Kalman filter, to filter and estimate the dual-frequency ionospheric delay and its rate of change, effectively reducing the high-frequency noise of the dual-frequency ionospheric-eliminating combined positioning. After filtering, the dynamic trend of the ionospheric delay is retained, making the positioning results smoother and more stable while also adapting to real-time changes in the ionosphere.

[0036] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The purposes and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings are used to provide a further understanding of the technical solution of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the technical solution of the present application and do not constitute a limitation on the technical solution of the present application.

[0038] Figure 1 Schematic diagram of the flow of the dual-frequency ionospheric delay estimation method in an embodiment of the present application;

[0039] Figure 2 Schematic diagram of the processing process of ionospheric delay correction based on combined pseudorange and state estimation in an embodiment of the present application;

[0040] Figure 3 Schematic diagram of the composition structure of the dual-frequency ionospheric delay estimation device in an embodiment of the present application. DETAILED DESCRIPTION

[0041] To make the purpose, technical solutions and advantages of this application more clear, the embodiments of this application will be described in detail below with reference to the accompanying drawings. It should be noted that, unless there is a conflict, the embodiments and features in the embodiments of this application can be combined with each other in any way.

[0042] To facilitate understanding of the present application, the present application will be described more fully below with reference to the accompanying drawings. The accompanying drawings provide embodiments of the present application. However, the present application may be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to make the disclosure of the present application more thorough and comprehensive.

[0043] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application pertains. The terms used herein in the specification of this application are for the purpose of describing specific embodiments only and are not intended to limit this application.

[0044] It is understood that the terms "first" and "second" used in this application are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. In the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0045] It can be understood that the “connection” in the following embodiments should be understood as “electrical connection”, “communication connection”, etc. if there is transmission of electrical signals or data between the connected circuits, modules, units, etc.

[0046] As used herein, the singular forms "a," "an," and "the" may also include the plural forms, unless the context clearly indicates otherwise. It should also be understood that the terms "include," "comprising," "having," and the like specify the presence of stated features, integers, steps, operations, components, parts, or combinations thereof, but do not preclude the presence or addition of one or more other features, integers, steps, operations, components, parts, or combinations thereof. Furthermore, the term "and / or" as used in this specification includes any and all combinations of the relevant listed items.

[0047] Pseudorange measurement is a widely used fundamental method in Global Navigation Satellite System (GNSS) positioning technology. This method receives and demodulates the spread-spectrum noise-coded signal transmitted by the satellite, measures the signal propagation time, and thus obtains the pseudorange observation between the receiver antenna and the satellite. To accurately determine the receiver's position, it is necessary to compensate and correct for various errors contained in the pseudorange, including satellite clock error, orbit error, receiver clock error, and delay errors caused by the ionosphere and troposphere in the signal propagation path. Once these errors are corrected, the receiver's position can be determined through the geometric intersection of multiple satellites.

[0048] Among the many error sources, ionospheric delay error is one of the key factors affecting pseudorange measurement accuracy. For pseudorange single-point positioning receivers, an important method to address the ionospheric delay correction problem is to use a dual-frequency ionospheric-free combination model. The dual-frequency ionospheric-free combination model estimates the function characteristics of ionospheric delay and carrier frequency, thereby combining two signal observations at different frequencies to obtain a new dual-frequency observation that does not include ionospheric delay. The advantage of this dual-frequency observation is that it does not include ionospheric delay, which can effectively eliminate ionospheric errors during periods of ionospheric activity and enhance the reliability of positioning results. However, the combined observation also amplifies the noise of the pseudorange measurement, resulting in significant high-frequency jitter in the positioning results and reduced stability.

[0049] In summary, although the dual-frequency ionospheric elimination combination effectively alleviates the positioning deviation problem caused by ionospheric error, it also causes the problems of measurement noise amplification and unstable results.

[0050] In order to improve the combined noise characteristics while ensuring the ionospheric error elimination capability, so as to enhance the overall performance of the positioning system, the embodiment of the present application provides a dual-frequency ionospheric delay estimation method, such as Figure 1 As shown, this may include:

[0051] Step 100: Based on a process model capable of modeling the dynamic characteristics of ionospheric delay, the ionospheric delay change rate is modeled, a state model including the ionospheric delay and its change rate is constructed, and the constructed state model is discretized to obtain a state update model.

[0052] In one exemplary embodiment, step 100 may include:

[0053] Obtain dual-frequency pseudorange observation data observed by the GNSS receiver. The dual-frequency pseudorange observation data includes pseudorange observation values of two different frequency signals;

[0054] According to the functional relationship between ionospheric delay and frequency, the dual-frequency ionospheric-free combined observation value is calculated;

[0055] Set the state vector to a two-dimensional state vector containing the ionospheric delay and its rate of change Ionospheric delay variation rate The first-order Markov process is used for modeling, and a state model of continuous time state is established to describe the state evolution relationship;

[0056] Discretize the state model of the continuous time state to obtain the state transfer matrix required by the state update model;

[0057] Based on the linear time-invariant system process noise propagation model, the covariance matrix of the process noise in discrete epochs required by the state update model is constructed.

[0058] Taking the BeiDou system (BDS) as an example, the two different frequency signals may include the B1 signal and the B3 signal, which are navigation signals modulated on the B1 frequency point and the B3 frequency point, respectively. In one embodiment, the pseudorange observation values (ρ) of the B1 signal and the B3 signal can be obtained from the GNSS receiver. B1 and ρ B3 ). The pseudo-range observation model of the B1 signal and B3 signal tracked by the receiver is shown in formula (1):

[0059]

[0060] In formula (1), ρ B1 and ρ B3 are the pseudo-range observation values of B1 signal and B3 signal respectively, c is the speed of light, r is the distance between the receiver and the antenna, δt u,B1 and δt u,B3 are the equivalent clock errors of B1 and B3 signals (comprehensive clock error composed of receiver clock error and receiver hardware delay), δt s is the satellite clock error, T tropo is the tropospheric delay component, I B1 and I B3 are the ionospheric delay components of the B1 and B3 signals, ε ρ,B1 and ε ρ,B3 are the observation noise of B1 signal and B3 signal respectively.

[0061] In an exemplary embodiment, the dual-frequency deionospheric combined observation value can be calculated according to formula (2):

[0062]

[0063] In formula (2), I B1,IF is the ionospheric delay of the B1 signal calculated using the dual-frequency ionospheric elimination model, f B1 and f B3 are the frequencies of B1 and B3 signals respectively. The calculated I B1,IF The observations are input into the subsequent filter, that is, the calculated dual-frequency ionospheric-eliminating combined observations are used as ionospheric observations for subsequent filtering estimation.

[0064] The actual ionospheric delay of a satellite I B1 Ionospheric delay calculated with the ionospheric elimination model B1,IF There is a relationship as shown in formula (3):

[0065] I B1 =I B1,IF -dt 13 -ε p13 (3)

[0066] In formula (3), dt 13 is the inter-frequency delay between B1 and B3 signals, ε p13 is the amplified random noise.

[0067] In this embodiment of the present application, a GNSS receiver acquires pseudorange observations at different frequencies (e.g., B1 and B3) and constructs a dual-frequency, ionospheric-free combined observation volume using the relationship between ionospheric delay and carrier frequency. This dual-frequency, ionospheric-free combined observation volume in this embodiment of the present application effectively eliminates the first-order ionospheric delay error and significantly improves the accuracy of GNSS pseudorange positioning in periods and regions with significant ionospheric disturbances.

[0068] In an exemplary embodiment, the ionospheric delay variation rate can be calculated according to formula (4): The first-order Markov process is used for modeling:

[0069]

[0070] In formula (4), is the state model, α is the anti-correlation time constant, w is the system process noise, and the variance of the system process noise is q (i.e., the power spectral density of the system process noise). In practical applications, this parameter can be determined based on the activity of the ionosphere, which can be determined by the difference between the ionosphere delay obtained by statistical formula (2) and the ionosphere empirical model. is the set state vector, where I is the ionospheric delay, is the ionospheric delay variation rate.

[0071] In an exemplary embodiment, the process model that can model the dynamic characteristics of ionospheric delay may include, but is not limited to, first-order Markov process, other dynamic process modeling methods such as high-order Markov, state autoregression, random walk, etc.

[0072] According to linear system theory, the equivalent discretization form of formula (4) can be expressed as shown in formula (5):

[0073]

[0074] In formula (5), the subscripts k and k+1 represent the physical quantities corresponding to the kth epoch and the k+1th epoch respectively, Φ is the state transfer matrix, and W k,k+1 is the system process noise from epoch k to epoch k+1.

[0075] In an exemplary embodiment, discretizing a state model of a continuous-time state to obtain a state transfer matrix required by a state update model may include:

[0076] The state model is discretized using the zero-order hold method, where T is the time interval from epoch k to epoch k+1. Taking the first-order Taylor expansion term, the state transfer matrix can be obtained as shown in formula (6):

[0077]

[0078] In formula (6), α is the anti-correlation time constant.

[0079] In an exemplary embodiment, the state model may be discretized by using a zero-order hold method or a first-order Taylor expansion.

[0080] In one exemplary embodiment, the system process noise is expressed as follows using the general solution of the linear time-invariant system:

[0081]

[0082] Therefore, as shown in formula (8), based on the linear time-invariant system process noise propagation model, the covariance matrix Q of the process noise in discrete epochs required for the state update model is constructed: k,k+1 :

[0083]

[0084] In formula (8), q is the power spectral density of the system process noise, T is the time interval between discrete epochs, that is, the time from epoch k to epoch k+1, α is the attenuation coefficient of the first-order Markov process, Φ(τ_ is the form of the state transfer matrix over time, Φ T )τ_ is the transpose of the state transfer matrix. The covariance matrix Q shown in formula (8) k,k+1 It accurately expresses the uncertainty growth of the state variable caused by the system process noise q and the state dynamic characteristics (controlled by α) within a sampling period T, and is used in the time update step of the Kalman filter to reflect the credibility of the predicted state.

[0085] In the embodiment of the present application, two-dimensional state variables of ionospheric delay and its rate of change are introduced in state modeling, and the ionospheric delay is regarded as a dynamic process evolving over time. This enables the estimation model to not only output the current value of the ionosphere, but also capture its changing trend, thereby enhancing the adaptability to scenarios with rapid ionospheric changes.

[0086] In this embodiment, a first-order Markov process is used to model the ionospheric rate of change, constructing a continuous-time state model and performing discretization. This state model effectively simulates the time correlation and dynamic characteristics of the actual ionosphere, ensuring that the filter's ability to predict actual ionospheric changes is enhanced.

[0087] Step 101: Based on the constructed state update model, an observation model is established using dual-frequency ionospheric-free combined observation values constructed from dual-frequency pseudorange observations.

[0088] In an exemplary embodiment, the observation model is the observation equation of the state model, which represents the linear relationship between the observation quantity and the ionospheric delay state variable. The dual-frequency deionospheric combination observation value calculated by formula (2) is the observation value, that is, Z k+1 =I B1,IF,k+1 , observation model Z k+1 As shown in formula (9):

[0089] Z k+1 =HX k+1 +V=[1 0]X l+1 +V k+1 (9)

[0090] In formula (7), Z k+1 is the measurement value of epoch k, H is the observation matrix, V k+1 is the observation noise, and the variance of the observation noise is R k+1 .

[0091] In an exemplary embodiment, further, the variance parameter of the observation noise can be adaptively set according to the ionospheric activity level, and the ionospheric activity level can be determined by the deviation of the statistical combination observation value and the standard ionospheric model, which is used to adjust the weight parameter of the filtering process.

[0092] Step 102: According to the state update model and the observation model, a recursive estimation method based on state modeling is used to recursively estimate the ionospheric delay and its rate of change.

[0093] In one exemplary embodiment, a recursive estimation method based on state-space modeling refers to a method capable of recursively estimating the ionospheric delay and its rate of change in a state model, achieving technical objectives such as smoothing, noise immunity, and dynamic estimation, such as a Kalman filter algorithm. The Kalman filter is used as an example below for convenience, but is not intended to limit the scope of protection of this application.

[0094] In an exemplary embodiment, the state update model and the linear observation model are input into a Kalman filter to recursively estimate the ionospheric delay and its rate of change.

[0095] In an exemplary embodiment, the following process is recursively performed between epochs to achieve continuous estimation and real-time update of ionospheric delay. Step 102 may include:

[0096] At each epoch, based on the state posterior estimate and error covariance of the previous epoch, the state transition model is used for time update to predict the state prior and error covariance of the current epoch;

[0097] Combined with the observation value of the current epoch, the measurement update is performed according to the observation model, the Kalman gain is calculated, the state and covariance are corrected, and the posterior estimate of the state of the current epoch is obtained;

[0098] The ionospheric delay estimate in the state posterior estimation is output for subsequent pseudorange correction.

[0099] In an exemplary embodiment, performing a time update at each epoch and predicting a state priori value and an error covariance at the next moment based on a state transition model may include:

[0100] The posterior estimate of the state based on the previous epoch X k and the error covariance matrix P k , use formula (10) and formula (11) to calculate the state prior estimate and the covariance matrix of the state prior estimate

[0101]

[0102] In one embodiment, the process may further include initializing the state vector and the error covariance matrix before step 102. In one embodiment, the initial state estimate is It can be 0 or an empirical value. In one embodiment, the initial covariance matrix P0 can be set to a diagonal matrix to reflect the initial uncertainty.

[0103] In an exemplary embodiment, introducing actual observations based on the observation model, performing measurement updates, and obtaining a posterior state estimate may include:

[0104] After obtaining the dual-frequency ionospheric combined observation value Z k+1 Then, use formula (12)-formula (14) to perform measurement update:

[0105] The Kalman gain matrix is calculated using formula (12):

[0106]

[0107] Use formula (13) to update the state posterior estimate:

[0108]

[0109] Formula (14) is used to update the covariance matrix of the state posterior estimate:

[0110]

[0111] In the Kalman recursive formulas shown in formulas (10) to (14), is the prior estimate of the state for the predicted k+1 epoch, P k is the error covariance matrix of the posterior estimate of the state at epoch k, K is the error covariance matrix of the prior estimate of the state for the prediction k+1 epoch. k+1 is the gain matrix for the k+1 epoch, is the posterior estimate of the state at epoch k+1, is the error covariance matrix of the posterior estimate of the state at epoch k+1. k+1 It is the observation value used by the filter at the k+1th epoch, which comes from the dual-frequency pseudo-range observation of the actual GNSS receiver. In the embodiment of the present application, in the Kalman filter observation model, Z k+1 is the ionospheric delay observation value calculated by the receiver at the k+1th epoch using the dual-frequency ionospheric elimination combination formula, Z k+1 The measurement updates that participate in filtering as observation input.

[0112] In an embodiment of the present application, in terms of filtering processing, a Kalman filter is used to recursively estimate the combined observation values. Compared with the method of directly using the dual-frequency combination values for correction, the filtering process provided in the embodiment of the present application effectively suppresses the random noise introduced by the combination coefficient amplification, thereby significantly smoothing the positioning results and reducing short-term jitter.

[0113] The dual-frequency ionospheric delay estimation method provided in the embodiment of the present application uses a recursive estimation method based on state modeling, such as a Kalman filter, to filter and estimate the dual-frequency ionospheric delay and its rate of change, effectively reducing the high-frequency noise of the dual-frequency ionospheric-eliminating combined positioning. After filtering, the dynamic trend of the ionospheric delay is retained, making the positioning results smoother and more stable while also adapting to real-time changes in the ionosphere.

[0114] In the embodiment of the present application, based on a process model that can model the dynamic characteristics of ionospheric delay, the ionospheric delay change rate is modeled and discretized to obtain a state update model of the ionospheric delay and its change rate. Then, the dual-frequency ionospheric combination delay and its change rate are filtered according to the Kalman optimal estimation theory, which effectively reduces the high-frequency noise of the dual-frequency ionospheric combination positioning. After filtering, the dynamic trend of the ionospheric delay is retained, making the positioning results smoother and more stable while also being able to adapt to real-time changes in the ionosphere.

[0115] In an exemplary embodiment, the dual-frequency ionospheric delay estimation method provided in the embodiment of the present application may further include:

[0116] The ionospheric delay estimate output by the filter is used in the ionospheric correction step in the positioning process to correct the pseudorange observation data.

[0117] Step 103: Use the ionospheric delay obtained by recursive estimation to correct the pseudorange observation value and output a smoother and more stable positioning result.

[0118] This step specifically includes the following sub-steps:

[0119] At each epoch k+1, according to the updated state posterior estimate Get the ionospheric delay estimate from the Kalman filter output The ionospheric delay estimate output by the Kalman filter As the ionospheric correction value for the current epoch;

[0120] Ionospheric delay estimation using Kalman filter output The original pseudorange observation value ρ is calculated using the following formula B1,k+1 Perform ionospheric correction to obtain the corrected pseudorange observation value ρ corr,k+1 :

[0121] The pseudo-range observation values corrected by multiple satellites are input into the positioning solution module to calculate the receiver position;

[0122] Outputs an estimate of the current position and can form a continuous positioning track over multiple epochs.

[0123] In one exemplary embodiment, at each epoch k+1, the ionospheric delay estimate output by the Kalman filter is is the state posterior estimate output by the Kalman filter The first component, the ionospheric delay estimate output by the Kalman filter It comes from the update of the state prediction value of the previous epoch and integrates the current combined observation value Z k+1 .

[0124] The dual-frequency ionospheric delay estimation method provided in the embodiment of the present application reduces the high-frequency noise introduced by the dual-frequency ionospheric elimination combination in GNSS pseudorange positioning, while retaining the dynamic change characteristics of the ionospheric delay. Through the embodiment of the present application, while ensuring the ability to eliminate ionospheric errors, the combined noise characteristics are improved, thereby enhancing the overall performance of the positioning system.

[0125] Based on the dual-frequency ionospheric delay estimation method provided in the embodiment of the present application, Figure 2 The schematic diagram of the processing process of ionospheric delay correction based on combined pseudorange and state estimation is shown, Figure 2As shown, it generally includes: first, constructing a state model representing the ionospheric delay and its rate of change, and performing state prediction (such as the state prediction of the ionospheric delay and its rate of change in step 201) and state covariance prediction (such as the state covariance prediction in step 202) at each epoch, calculating the Kalman gain matrix (such as the calculation of the gain matrix K in step 203) in combination with the measurement noise (such as determining the variance R of the measurement noise according to the carrier-to-noise ratio in step 208), and then performing Kalman filter update (such as the Kalman measurement correction in step 204), outputting the posterior state estimate and error covariance (such as the filtered ionospheric delay machine and its rate of change and state covariance information in step 205). On this basis, the ionospheric delay estimates of all visible satellites are aggregated (e.g., the ionospheric delays of all visible satellites are collected to construct an ionospheric activity measurement in step 206). This is then compared and analyzed with the original dual-frequency combined observations (e.g., the original dual-frequency ionospheric delays in step 207) to construct an ionospheric activity measurement. This measurement is used to drive the process noise adaptive adjustment module (e.g., the adaptive adjustment of the process noise variance q based on the ionospheric activity in step 209). This adjustment adjusts the system process noise variance q based on the degree of ionospheric fluctuations and is fed back to the covariance prediction module (e.g., the state covariance prediction in step 202). Furthermore, the receiver observation quality (e.g., carrier-to-noise ratio) is used to dynamically set the observation noise variance R and participate in the gain calculation process. Figure 2 The process shown constitutes a dynamic closed-loop filtering structure, which has good robustness and adaptability while ensuring the accuracy of ionospheric delay estimation.

[0126] The present application also provides a computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions are used to execute any of the dual-frequency ionospheric delay estimation methods described above.

[0127] The present application further provides a computer device, comprising a memory and a processor, wherein the memory stores the following instructions executable by the processor: used to execute the steps of any of the above-mentioned dual-frequency ionospheric delay estimation methods.

[0128] The dual-frequency ionospheric delay estimation method provided in the embodiment of the present application can be implemented inside a GNSS receiver or in an external computing platform with GNSS observation data input capability, such as post-processing software, a differential positioning server, or a cloud-based navigation service system.

[0129] Figure 3 FIG. 1 is a schematic diagram of the composition structure of the dual-frequency ionospheric delay estimation device in an embodiment of the present application. Figure 3 As shown, it can include: a construction module, a building module, and an estimation module; wherein,

[0130] A construction module is used to model the ionospheric delay change rate based on a process model that can model the dynamic characteristics of the ionospheric delay, construct a state model including the ionospheric delay and its change rate, and discretize the constructed state model to obtain a state update model;

[0131] Establishing a module for updating the model according to the constructed state and establishing an observation model using dual-frequency ionospheric elimination combined observation values constructed by dual-frequency pseudorange observations;

[0132] The estimation module is used to recursively estimate the ionospheric delay and its changing rate according to the state update model and the observation model using a recursive estimation method based on state modeling.

[0133] The dual-frequency ionospheric delay estimation device provided in the embodiment of the present application performs filtered estimation of the dual-frequency ionospheric delay and its rate of change based on a recursive estimation method of state modeling, such as a Kalman filter, effectively reducing the high-frequency noise of the dual-frequency ionospheric-eliminating combined positioning, and retaining the dynamic trend of the ionospheric delay after filtering, making the positioning results smoother and more stable while also adapting to real-time changes in the ionosphere.

[0134] In one embodiment, the building blocks may be used to:

[0135] Obtain dual-frequency pseudorange observation data, including pseudorange observation values of two different frequency signals; calculate the dual-frequency ionospheric combination observation value based on the functional relationship between ionospheric delay and frequency; set the state vector to a two-dimensional state vector containing ionospheric delay and its change rate Ionospheric delay variation rate A first-order Markov process is used for modeling to establish a state model of continuous-time states that describes the state evolution relationship; the state model of continuous-time states is discretized to obtain the state transfer matrix required by the state update model; based on the linear time-invariant system process noise propagation model, the covariance matrix of the process noise in discrete epochs required by the state update model is constructed.

[0136] In one embodiment, the estimation module may be used to:

[0137] The following process is recursively executed between epochs to achieve continuous estimation and real-time update of ionospheric delay: at each epoch, based on the state posterior estimate and error covariance of the previous epoch, the state transition model is used to perform time update, and the state prior and error covariance of the current epoch are predicted; combined with the observation value of the current epoch, measurement update is performed according to the observation model, the Kalman gain is calculated, the state and covariance are corrected, and the state posterior estimate of the current epoch is obtained; and the ionospheric delay estimate in the state posterior estimate is output for subsequent pseudorange correction.

[0138] In an exemplary embodiment, the dual-frequency ionospheric delay estimation device provided in an embodiment of the present application may further include: a processing module for correcting the pseudorange using the ionospheric delay obtained by recursive estimation to output a smoother and more stable positioning result.

[0139] The dual-frequency ionospheric delay estimation device provided in the embodiment of the present application reduces the high-frequency noise introduced by the dual-frequency ionospheric elimination combination in GNSS pseudorange positioning, while retaining the dynamic change characteristics of the ionospheric delay. Through the embodiment of the present application, while ensuring the ability to eliminate ionospheric errors, the combined noise characteristics are improved, thereby enhancing the overall performance of the positioning system.

[0140] In one embodiment, the processing module may be configured to:

[0141] At each epoch k+1, according to the updated state posterior estimate Get the ionospheric delay estimate from the Kalman filter output The ionospheric delay estimate output by the Kalman filter As the ionospheric correction value of the current epoch; the ionospheric delay estimate output by Kalman filtering The original pseudorange observation value ρ is calculated using the following formula B1,k+1 Perform ionospheric correction to obtain the corrected pseudorange observation value ρ corr,l+1 : The pseudo-range observation values after correction of multiple satellites are input into the positioning solution module to calculate the position of the receiver; the current position estimate is output and a continuous positioning trajectory can be formed in multiple epochs.

[0142] In an exemplary embodiment, the dual-frequency ionospheric delay estimation device provided in an embodiment of the present application is set in a GNSS receiver, or is implemented in an external computing platform with GNSS observation data input capability, such as post-processing software, a differential positioning server, or a cloud navigation service system.

[0143] Although the embodiments disclosed in this application are as described above, the contents described are merely embodiments adopted to facilitate understanding of this application and are not intended to limit this application. Any person skilled in the art to which this application belongs may make any modifications and changes in the form and details of the implementation without departing from the spirit and scope disclosed in this application. However, the scope of patent protection of this application shall still be based on the scope defined by the attached claims.

Claims

1. A dual-frequency ionospheric delay estimation method, characterized in that: include: Based on a process model that can model the dynamic characteristics of ionospheric delay, the ionospheric delay change rate is modeled, and a state model including the ionospheric delay and its change rate is constructed. The constructed state model is discretized to obtain a state update model. According to the constructed state update model, an observation model is established using the dual-frequency ionospheric elimination combined observation value constructed by the dual-frequency pseudorange observation; According to the state update model and the observation model, a recursive estimation method based on state modeling is used to recursively estimate the ionospheric delay and its changing rate.

2. The dual-frequency ionospheric delay estimation method according to claim 1, further comprising: The ionospheric delay obtained by the recursive estimation is used to correct the pseudorange observation value and output a positioning result.

3. The dual-frequency ionospheric delay estimation method according to claim 1 or 2, wherein: The state model including the ionospheric delay and its change rate is constructed, and the constructed state model is discretized to obtain a state update model, including: Obtain dual-frequency pseudorange observation data, which includes pseudorange observation values of two different frequency signals; According to the functional relationship between ionospheric delay and frequency, the dual-frequency ionospheric-free combined observation value is calculated; Setting the state vector to be a two-dimensional state vector including the ionospheric delay and its rate of change, modeling the ionospheric delay rate of change using a first-order Markov process, and establishing the state model of the continuous-time state; Discretizing the state model to obtain a state transfer matrix required by the state update model; Based on the linear time-invariant system process noise propagation model, a covariance matrix of the process noise required by the state update model in discrete epochs is constructed.

4. The dual-frequency ionospheric delay estimation method according to claim 3, wherein: The two-dimensional state vector is Where, I is the ionospheric delay, is the ionospheric delay variation rate; The modeling using a first-order Markov process includes: in, is the state model, α is the anti-correlation time constant, and w is the system process noise.

5. The dual-frequency ionospheric delay estimation method according to claim 3, wherein: The discretization processing of the state model includes: Wherein, the subscripts k and k+1 represent the physical quantities corresponding to the kth epoch and the k+1th epoch respectively, Φ is the state transfer matrix, W k,k+1 is the system process noise from epoch k to epoch k+1.

6. The dual-frequency ionospheric delay estimation method according to claim 1 or 2, wherein: The observation model is: Z k+1 =HX k+1 +V=[1 0]X k+1 +V k+1 , where Z k+1 is the measurement value of epoch k, H is the observation matrix, V k+1 is the observation noise, and the variance of the observation noise is R k+1 .

7. The dual-frequency ionospheric delay estimation method according to claim 1 or 2, wherein: The recursive estimation method based on state modeling includes: a Kalman filtering algorithm.

8. The dual-frequency ionospheric delay estimation method according to claim 7, wherein: The recursive estimation method based on state modeling is used to recursively estimate the ionospheric delay and its rate of change according to the state update model and the observation model, including the following process of recursively executing between epochs to achieve continuous estimation and real-time update of the ionospheric delay: At each epoch, based on the state posterior estimate and error covariance of the previous epoch, the state transition model is used to perform time update to predict the state prior and error covariance of the current epoch; Combined with the observation value of the current epoch, the measurement update is performed according to the observation model, the Kalman gain is calculated, the state and covariance are corrected, and the posterior estimate of the state of the current epoch is obtained; The ionospheric delay estimate in the state posterior estimation is output for subsequent pseudorange correction.

9. A computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions are used to execute the dual-frequency ionospheric delay estimation method according to any one of claims 1 to 8.

10. A computer device comprising a memory and a processor, wherein: The memory stores the following instructions executable by the processor: used to execute the steps of the dual-frequency ionospheric delay estimation method according to any one of claims 1 to 8.

11. A dual-frequency ionospheric delay estimation device, characterized in that: include: Building module, establishing module, estimating module; among them, A construction module is used to model the ionospheric delay change rate based on a process model that can model the dynamic characteristics of the ionospheric delay, construct a state model including the ionospheric delay and its change rate, and discretize the constructed state model to obtain a state update model; Establishing a module for updating the model according to the constructed state and establishing an observation model using dual-frequency ionospheric elimination combined observation values constructed by dual-frequency pseudorange observations; The estimation module is used to recursively estimate the ionospheric delay and its changing rate according to the state update model and the observation model using a recursive estimation method based on state modeling.

12. The dual-frequency ionospheric delay estimation device according to claim 11, further comprising: The processing module is used to correct the pseudorange using the ionospheric delay obtained by the recursive estimation and output a positioning result.

13. The dual-frequency ionospheric delay estimation device according to claim 11 or 12, wherein: The dual-frequency ionospheric delay estimation device is arranged in a GNSS receiver, or in an external computing platform with a GNSS observation data input capability.

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