Carrier phase cycle slip detection and repair method, device and computer readable medium

Abstract

This application discloses a carrier phase cycle slip detection and repair method, apparatus, and computer-readable medium. The method obtains a first observation set by acquiring multiple carrier phase observations from an observation satellite, generates corresponding least-squares observation vectors and observation matrices, and generates an observation weight matrix through observation weighting. Then, based on the least-squares observation vectors, observation matrices, and observation weight matrix, it searches the first observation set for observations that satisfy the residual condition (characterizing that the carrier phase observations have not experienced cycle slips) using a least-squares residual verification method, obtaining a second observation set. Based on the second observation set, it determines the target observations in the first observation set that have experienced cycle slips and performs cycle slip repair processing. Therefore, this application proposes a cycle slip detection and repair scheme based on least-squares residual verification, relying solely on carrier observations and not limiting the number of frequency points. It has high applicability to PPP or RTK algorithms using single-frequency or multi-frequency observations.

Description

Technical Field

[0001] This application belongs to the field of satellite navigation technology, and in particular relates to a carrier phase cycle slip detection and repair method, device and computer-readable medium. Background Technology

[0002] With the popularization and development of satellite navigation technology, the demand for high-precision positioning services based on the Global Navigation Satellite System (GNSS) has become increasingly important. GNSS high-precision positioning services, whether precise point positioning (PPP) or real-time dynamic relative positioning (RTK), cannot function without carrier phase observations, and the continuity of these observations is also highly critical. Typically, interruptions in carrier phase tracking, or carrier integer or half-cycle slips occurring during continuous tracking without timely processing, will significantly impact the performance of PPP or RTK.

[0003] To effectively detect cycle slips, the following solutions are currently offered:

[0004] One type is the geometrically independent combination method. This method uses the subtraction of dual-frequency carrier observations from the same satellite to eliminate geometric effects and analyzes whether the combined observations remain stable across epochs to detect cycle slips. However, this method cannot distinguish which frequency observation caused the cycle slip after it occurs, and it may also miss detections when the same cycle slip occurs at two frequencies simultaneously.

[0005] Another type is the code phase-assisted method, such as the MW combination method. This type of method is limited by the tracking accuracy of the code phase, and the detection accuracy cannot be guaranteed, especially for small cycle slips, which are particularly prone to missed detection. At the same time, both of the above methods heavily rely on multi-frequency observations, which is very unfriendly to the cost control of the receiver.

[0006] The third type of method is the Doppler observation-assisted method, which utilizes the differential relationship between Doppler and carrier phase. It uses the instantaneous Doppler measurement multiplied by time to approximate the epoch change in carrier phase. This is effective when the receiver clock is stable and the carrier dynamics are relatively stable. However, if the carrier acceleration is large or the clock frequency changes drastically, the dynamic error may exceed one wavelength, leading to detection and correction errors. In addition, there are currently attempts to detect large cycle slips based on the differential relationship between Doppler and carrier phase, while simultaneously using a geometrically independent combination method to detect small cycle slips. However, this method also has limitations such as requiring multi-frequency tracking and the potential for missed detections when cycle slips occur simultaneously at multiple frequencies. Summary of the Invention

[0007] In view of this, this application provides a carrier phase cycle slip detection and repair method, apparatus and computer-readable medium to solve the problem of cycle slip detection and repair of carrier phase observations, and overcome at least some of the defects of existing cycle slip detection and repair methods.

[0008] The specific plan is as follows:

[0009] A method for carrier phase cycle slip detection and repair includes:

[0010] Perform a preset cycle slip detection preparation process to obtain at least multiple carrier phase observation values ​​of the observed satellite through the cycle slip detection preparation process, and obtain a first observation set;

[0011] Generate the least squares observation vector and observation matrix corresponding to each observation value in the first observation set, and generate the observation weight matrix through observation weighting;

[0012] Based on the least squares observation vector, the observation matrix, and the observation weight matrix, the least squares residual verification method is used to search for each observation value that satisfies the preset residual condition from the first observation set, thereby obtaining a second observation set composed of the searched observation values; the preset residual condition is a condition that can be used to characterize that the carrier phase observation value has not experienced a cycle slip.

[0013] The target observation value that has cycle slip in the first observation set is determined based on the second observation set, and the target observation value is subjected to cycle slip repair processing.

[0014] Optionally, the step of performing a preset cycle slip detection preparation process includes:

[0015] Collect multiple carrier phase observations from adjacent epochs of the observation satellite and prepare to broadcast ephemeris.

[0016] Optionally, the step of generating the least-squares observation vector and observation matrix corresponding to each observation value in the first observation set, and generating the observation weight matrix through observation weighting processing, includes:

[0017] If the number of observation satellites corresponding to the first observation set is not less than a preset number:

[0018] The carrier phase increment is determined based on the carrier phase observations of adjacent epochs in the first observation set, and the satellite position increment and satellite clock error increment in the carrier phase increment are compensated using broadcast ephemeris, so as to generate the least squares observation vector through compensation processing.

[0019] The observation matrix is ​​determined based on the receiver position and satellite position;

[0020] The observation weight matrix is ​​obtained by weighting each observation in the first observation set using prior information.

[0021] The preset quantity is the minimum number of satellites required to ensure the effectiveness of least squares residual verification.

[0022] Optionally, the step of searching for observations that satisfy preset residual conditions from the first observation set using the least squares observation vector, the observation matrix, and the observation weight matrix, through least squares residual verification, to obtain a second observation set composed of the searched observations, includes:

[0023] Step 1: Determine the accuracy factor corresponding to the current constellation configuration of the observed satellites; if the accuracy factor is higher than a preset first threshold, the process ends; otherwise, proceed to Step 2.

[0024] Step 2: Perform weighted least squares estimation on the vector to be estimated, and generate a residual vector based on the estimation results; the vector to be estimated consists of the receiver's position increment and clock error increment;

[0025] Step 3: Determine whether the residuals corresponding to each observation in the residual vector in the current residual observation set all satisfy the preset residual conditions; if not, proceed to step 4; if yes, proceed to step 5; wherein, the initial value of the residual observation set is the first observation set;

[0026] Step 4: Determine the current number of observed satellites. If the current number of observed satellites is higher than the preset number, delete a corresponding number of observations from the remaining observation set based on the preset deletion strategy, thereby updating the remaining observation set. After deletion, return to Step 1 until the residuals corresponding to each observation in the resulting remaining observation set all meet the preset residual conditions, then proceed to Step 5. Wherein, the number of remaining observed satellites after deletion is not less than the preset number.

[0027] Step 5: If the current precision factor is lower than the preset second threshold, use the current remaining observation set as the second observation set; if the current precision factor is not lower than the second threshold, add the deleted observations one by one to the current remaining observation set, and after each addition of an observation that updates the remaining observation set, return to step 3. If the updated remaining observation set satisfies the conditions in step 3, retain the added observations in the remaining observation set until the traversal of each deleted observation is completed, and use the current remaining observation set as the second observation set.

[0028] The second threshold is lower than the first threshold.

[0029] Optionally, deleting a corresponding number of observations from the remaining observation set based on a preset deletion strategy includes:

[0030] Determine the sum of squares of the residuals corresponding to each observation in the current remaining observation set;

[0031] Based on the sum of squares, delete a corresponding number of high residual observations in descending order of the corresponding residuals, ensuring that the number of remaining observation satellites after deletion is not less than the preset number.

[0032] Optionally, the preset quantity is 5.

[0033] Optionally, the step of determining the target observation value that has a cycle slip in the first observation set based on the second observation set, and performing cycle slip repair processing on the target observation value, includes:

[0034] Each observation value in the first observation set that was deleted compared to the second observation set is identified as the target observation value that caused the cycle slip;

[0035] Determine whether the current precision factor is lower than the second threshold;

[0036] If the value is lower, cycle slip correction is performed on each target observation value based on the optimal estimate of the vector to be estimated; the optimal estimate of the vector to be estimated is the last least squares estimation result of the vector to be estimated.

[0037] If the value is not lower than the target value, then no cycle slip repair operation will be performed.

[0038] Optionally, the step of performing cycle slip repair on the target observation based on the optimal estimate of the vector to be estimated includes:

[0039] Based on the optimal estimate of the vector to be estimated, determine the residuals of each target observation;

[0040] Based on the residuals of each target observation and the corresponding carrier wavelength, cycle slip repair is performed on each target observation.

[0041] Optionally, the above method also includes:

[0042] Determine if the number of successfully repaired observations is zero;

[0043] If it is not zero, return to step one and repeat the carrier phase cycle slip detection and repair process based on least squares estimation until the number of successfully repaired observations in the current round is zero.

[0044] If the value is zero, then the process ends.

[0045] A carrier phase cycle slip detection and repair device, comprising:

[0046] A preparation processing unit is used to perform a preset cycle slip detection preparation process to obtain at least multiple carrier phase observation values ​​of the observed satellite through the cycle slip detection preparation process, thereby obtaining a first observation set.

[0047] The generation unit is used to generate the least squares observation vector and observation matrix corresponding to each carrier phase observation value, and to generate the observation weight matrix through observation weighting processing.

[0048] The search unit is used to search for each observation value that satisfies a preset residual condition from the first observation set according to the least squares observation vector, the observation matrix, and the observation weight matrix, through the least squares residual verification method, to obtain a second observation set composed of the searched observation values; the preset residual condition is a condition used to characterize that the carrier phase observation value has not experienced a cycle slip.

[0049] The detection and repair unit is used to determine the target observation value that has cycle slip in the first observation set based on the second observation set, and to perform cycle slip repair processing on the target observation value.

[0050] A computer-readable medium having a computer program stored thereon, the computer program comprising program code for performing the methods described in any of the preceding descriptions.

[0051] A computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods described in any of the preceding descriptions.

[0052] In summary, the carrier phase cycle slip detection and repair method, apparatus, and computer-readable medium provided in this application obtain at least multiple carrier phase observation values ​​of the observed satellite by performing a preset cycle slip detection preparation process to obtain a first observation set. A least-squares observation vector and observation matrix corresponding to each observation value in the first observation set are generated, and an observation weight matrix is ​​generated through observation weighting. Based on the least-squares observation vector, observation matrix, and observation weight matrix, each observation value satisfying a preset residual condition is searched from the first observation set using a least-squares residual verification method to obtain a second observation set composed of the searched observation values. The preset residual condition is a condition that can be used to characterize that the carrier phase observation value has not experienced a cycle slip. Then, the target observation value in the first observation set that has experienced a cycle slip is determined based on the second observation set, and cycle slip repair processing is performed on the target observation value.

[0053] As can be seen, this application proposes a carrier phase cycle slip detection and repair scheme based on least squares residual verification, which relies solely on carrier observations and does not limit the number of frequency points. By directly detecting the carrier phase, it avoids the anxiety of "primary star selection" and breaks the limitation that the primary star selection must be guaranteed to be problem-free. It is applicable to both PPP and RTK, and since it does not limit the number of frequency points, it has high applicability to PPP or RTK algorithms using single-frequency or multi-frequency observations. Attached Figure Description

[0054] The above and other features, advantages, and aspects of the embodiments of this application will become more apparent from the accompanying drawings and the following detailed description. Throughout the drawings, the same or similar reference numerals denote the same or similar elements. It should be understood that the drawings are schematic, and the originals and elements are not necessarily drawn to scale.

[0055] Figure 1 This is a flowchart illustrating the carrier phase cycle slip detection and repair method provided in this application;

[0056] Figure 2 This application provides a complete and detailed process for carrier phase cycle slip detection and repair.

[0057] Figure 3 This is a structural diagram of the carrier phase cycle slip detection and repair device provided in this application. Detailed Implementation

[0058] Embodiments of this application will now be described in more detail with reference to the accompanying drawings. While some embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this application. It should be understood that the drawings and embodiments of this application are for illustrative purposes only and are not intended to limit the scope of protection of this application.

[0059] The term "comprising" and its variations as used herein are open-ended inclusions, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0060] It should be noted that the concepts of "first" and "second" mentioned in this application are only used to distinguish different devices, modules or units, and are not used to limit the order of functions performed by these devices, modules or units or their interdependencies.

[0061] It should be noted that the terms "a" and "a plurality of" used in this application are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0062] This application discloses a carrier phase cycle slip detection and repair method, apparatus, computer-readable medium, and computer program product, which is used to overcome at least some of the defects of existing cycle slip detection and repair methods by implementing a carrier phase cycle slip detection and repair scheme that relies solely on carrier observations and does not limit the number of frequency points.

[0063] See Figure 1 The flowchart shown illustrates the carrier phase cycle slip detection and repair method. The carrier phase cycle slip detection and repair method provided in this application includes the following processing steps:

[0064] Step 101: Perform a preset cycle slip detection preparation process to obtain at least multiple carrier phase observation values ​​of the observed satellite through the cycle slip detection preparation process, and obtain the first observation set.

[0065] In the cycle slip detection preparation process, multiple carrier phase observations of adjacent epochs of the observed satellite (the navigation satellite being observed) can be collected, and broadcast ephemeris can be prepared.

[0066] Specifically, it can collect all available carrier phase observations (k is a positive integer) from the observation satellite from epoch k to k+1 for subsequent carrier phase cycle slip detection and repair processing.

[0067] Assume the frequency L of satellite s i The carrier observation value is Then the observation models for epochs k and k+1 are respectively:

[0068]

[0069]

[0070] In equations (1)-(2), and Let r represent the satellite position coordinates at epochs k and k+1, respectively. k and r k+1 Let δT represent the receiver position coordinates at epochs k and k+1, respectively. k and δT k+1 Let these represent the receiver clock errors at epochs k and k+1, respectively. and Let these represent the satellite clock errors at epochs k and k+1, respectively. and L represents epochs k and k+1 respectively. i Ionospheric delay included in the observations, and These represent the tropospheric delays included in the observations at epochs k and k+1, respectively. and L represents epochs k and k+1 respectively. i Integer ambiguity of carrier phase observations and These represent the carrier phase observation noise at epochs k and k+1, respectively.

[0071] This application embodiment uses the least squares residual verification method to detect and repair carrier phase cycle slips based on collected carrier phase observations. Therefore, the number of observation satellites corresponding to the first observation set should not be less than a preset number. This preset number represents the minimum number of satellites required to ensure the effectiveness of the least squares residual verification. In other words, if the number of satellites corresponding to the carrier phase observations collected in this step is less than the minimum number of satellites required to ensure the effectiveness of the least squares residual verification, least squares residual detection cannot be performed, and therefore cycle slip detection and repair cannot be performed. This allows the subsequent cycle slip detection and repair process to terminate directly. Conversely, if the number of satellites is not less than the minimum number, the subsequent cycle slip detection and repair process can continue.

[0072] Step 102: Generate the least squares observation vector and observation matrix corresponding to each observation value in the first observation set, and generate the observation weight matrix through observation weighting.

[0073] If the number of observed satellites corresponding to the first observation set is not less than the above-mentioned preset number, the carrier phase increment can be further determined based on the carrier phase observation values ​​of adjacent epochs in the first observation set, and the satellite position increment and satellite clock error increment in the carrier phase increment can be compensated using broadcast ephemeris, so as to generate the least squares observation vector through compensation processing.

[0074] Specifically, by performing a difference operation between equation (2) and equation (1), the carrier phase increment for epochs k to k+1 can be obtained. For positioning algorithms running in real time on the receiver, their data update period is usually less than 1 second. Therefore, the ionosphere and troposphere in equations (1) and (2) usually change very little. Therefore, the carrier phase increment observation model for epochs k to k+1 can be expressed as:

[0075]

[0076] In equation (3), For the satellite position increment from epoch k to k+1, Δr k,k+1 Let ΔδT be the receiver position increment from epoch k to k+1. k,k+1 For the receiver clock bias increment from epoch k to k+1, For the satellite clock bias increment from epoch k to k+1, L for epochs k to k+1 i The integer ambiguity change of the carrier phase observation, i.e., the carrier cycle slip value, is determined if carrier phase tracking is continuous and no cycle slip occurs. This is the observation noise of the carrier phase increment (its noise variance is twice that of the carrier observation noise).

[0077] By transforming equation (3), we can obtain:

[0078]

[0079] In equation (4), The vector to be estimated includes the receiver's position increment and clock error increment, specifically representing a four-dimensional vector composed of the receiver's three-dimensional position increment and clock error increment, H. j Used to construct the observation matrix If carrier tracking is continuous and no cycle slip occurs, i.e. So This is the observation noise (whose noise variance is twice that of the carrier observation noise).

[0080] According to the least squares estimation theory, it is only necessary to observe the carrier phase of four satellites. The position increment and clock error increment of the receiver can be solved by equation (4) to obtain the vector to be estimated, x. Its estimation accuracy is determined by two factors:

[0081] 11) Observation noise

[0082] Typically, the observation accuracy of carrier phase can reach about 1% of a cycle (i.e., 2 mm), and the accuracy of satellite position changes and clock changes provided by broadcast ephemeris can generally reach the centimeter level or above. However, due to the very large distance between the receiver and the satellite, the accuracy of the above formula... It is not sensitive to orbital errors, therefore the least squares observation y = [y1 y2 … y] in equation (4) is... N ] T The measurement noise can be controlled at the cm level;

[0083] 12) Precision factor

[0084] Right now,

[0085] By setting a reasonable DOP threshold, the estimation accuracy of x can be guaranteed to the cm level.

[0086] The method in this application is essentially based on the epochal difference of the single-station carrier phase as the data basis for cycle slip detection and repair. It does not rely on the assistance of other observations, nor does it rely on multi-frequency observations. In other words, it is applicable to both single-frequency and multi-frequency applications.

[0087] For single-frequency applications, H in equation (5) j The parameters are all different, and there are only four parameters to be estimated (i.e., the four-dimensional vector corresponding to the vector x to be estimated, which consists of the receiver's three-dimensional position increment and clock error increment). Therefore, only four satellites are needed to ensure that the DOP matrix is ​​positive definite and to complete the least squares estimation. For multi-frequency applications, the H values ​​observed at several frequency points of the same satellite in the above formula are different. j Since they are the same, adding multiple frequency observations does not increase the observation redundancy of least squares estimation. Therefore, the total number of satellites required is the same as that for single-frequency applications. However, the introduction of multiple frequency observations will help reduce the accuracy factor and thus improve the estimation accuracy. At the same time, the consistency between multiple frequency observations of the same satellite can also serve as one of the prior information sources for the observation weighting strategy.

[0088] The purpose of this application is to detect and repair cycle slip, that is, to address the issue in equation (4). An estimation cannot be made. Since the number of unknowns is always greater than the number of observations, it is impossible to make an estimate. However, based on the applicant's research and analysis, two very important pieces of information can be utilized:

[0089] twenty one) It has the characteristic of being an integer multiple of the wavelength, and is very likely to be 0;

[0090] 22) A set of observations that satisfies the least squares residual check method can be used to search for all observations. At the same time, the optimal estimates of receiver position and clock error increment can be obtained, which will require at least five satellites to ensure the effectiveness of least squares residual verification.

[0091] Accordingly, the preset quantity can be 5.

[0092] Based on this, assuming N usable carrier phase observations are obtained in step 101, the least squares observation vector y = [y1 y2 … y] can be formed by calculating the carrier phase increments from k to k+1 epochs and compensating for the satellite position increments and satellite clock error increments using broadcast ephemeris. N ] T Here, broadcast ephemeris is used to compensate for the satellite position increments and satellite clock error increments. Specifically, the satellite position increments and clock error increments can be obtained using navigation messages (ephemeris) and are known quantities (the receiver position increments and clock error increments are unknown and are parameters to be estimated).

[0093] Simultaneously, the receiver location and satellite location can be used to calculate the observation matrix.

[0094] Prior information can be used to weight each observation corresponding to the first observation set to obtain an observation weight matrix. This includes, but is not limited to, prior information such as the corresponding carrier-to-noise ratio, the locking strength of the phase-locked loop, and the consistency of multi-frequency observations, to weight all observations and form an observation weight matrix W.

[0095] The following is an optional example of observation weighting:

[0096] First, initialize all observation weights to the same value. If a certain observation experiences a significant decrease or fluctuation in its carrier-to-noise ratio or phase-locked loop locking strength, indicating a higher probability of cycle slip, its weight can be appropriately reduced. Specifically, if multiple frequency observations are available, here we assume y... m and y n Let y be the least squares observation value obtained from two frequency points of a certain satellite. m With y n Significant wavelength or half-wavelength differences indicate that one or both of these frequency points have experienced carrier cycle slips, which can significantly reduce their observation weights.

[0097] Step 103: Based on the least squares observation vector, observation matrix, and observation weight matrix, search for each observation value that satisfies the preset residual condition from the first observation set using the least squares residual verification method, and obtain the second observation set composed of the searched observation values.

[0098] Whether it is a single-frequency application or a multi-frequency application, the core idea of ​​this application is to obtain a set of reliable observations that meet the preset residual conditions from the first observation set, namely the second observation set, to remove the geometric influence of receiver-satellite, and subsequently detect and repair the observations that have cycle slips based on the second observation set.

[0099] Among them, the preset residual condition is a condition that can be used to characterize that the carrier phase observation value has not experienced a cycle slip.

[0100] The reliability of observations in the second observation set is specifically guaranteed by the least-squares DOP matrix and the small requirement of minimum residuals. This step, which involves searching for observations in the first observation set that satisfy the preset residual conditions to obtain the second observation set, can be further implemented as follows:

[0101] Step 1: Determine the accuracy factor corresponding to the current constellation configuration of the observed satellites. If the accuracy factor is higher than a preset first threshold, the subsequent processing flow ends. If it is not higher than the first threshold, proceed to Step 2.

[0102] Specifically, it can analyze the current constellation configuration of the observation satellites and calculate its corresponding accuracy factor DOP = (H T H) -1 .

[0103] Simultaneously set the highest detection threshold DOP for the precision factor. max In this embodiment, it is referred to as the first threshold.

[0104] If the calculated precision factor is higher than the first threshold, i.e., DOP > DOP max If the least squares estimation accuracy is too poor to guarantee cycle slip detection accuracy, the detection fails, and the subsequent processing can be terminated. Conversely, if the calculated accuracy factor is not higher than this first threshold, i.e., DOP ≤ DOP... max If so, proceed to step two to continue the subsequent processing flow.

[0105] Step 2: Perform weighted least squares estimation on the vector to be estimated, and generate a residual vector based on the estimation results; the vector to be estimated consists of the receiver's position increment and clock error increment.

[0106] When DOP≤DOP max Then, a weighted least squares estimation is performed on the vector to be estimated, specifically based on the following weighted least squares formula:

[0107] x=[(H T WH) -1 WH T ]y.

[0108] Based on the estimation results, the residual vector v = y - Hx is generated according to equation (4).

[0109] Step 3: Determine whether the residuals corresponding to each observation in the current residual observation set all satisfy the preset residual conditions; if not, proceed to step 4; if yes, proceed to step 5.

[0110] The initial value of the remaining observation set is the first observation set. That is, initially, the value of the remaining observation set is the first observation set.

[0111] The aforementioned preset residual conditions are used as a standard for detecting the residuals of observed values. For example, |v can be specifically set. j |<λ j The detection standard for -θ can be exemplarily set as: |v j |<λ j -θ, where λ jThe carrier wavelength or half-wavelength represents the carrier phase observation value, and varies depending on the phase detection method used to form the carrier-locked loop for each observation. If the carrier phase observation value has no half-cycle ambiguity, then λ j λ represents the wavelength; if there is half-cycle ambiguity, then λ j This represents half the wavelength, and θ is the cycle slip detection margin, typically taken as θ = λ. j / 2.

[0112] In step three, the residuals corresponding to each observation in the current residual observation set are checked one by one in the residual vector to see if they meet the set residual conditions, such as whether they satisfy |v j |<λ j If all residuals of each observation satisfy the condition -θ, proceed to step five; otherwise, if they do not satisfy the condition (i.e., there are residuals among all residuals of each observation that do not satisfy the above residual condition), proceed to step four.

[0113] Based on the established residual conditions, a set of observations can be searched from all observations using the least squares residual verification method, such that it satisfies...

[0114] Step 4: Determine the current number of observed satellites. If the current number of observed satellites is higher than the preset number mentioned above, delete the corresponding number of observations from the current remaining observation set based on the preset deletion strategy, so as to update the remaining observation set. After the deletion is completed, return to Step 1 until the residuals corresponding to each observation in the obtained remaining observation set all meet the preset residual conditions, and then proceed to Step 5. Wherein, the number of remaining observed satellites after the deletion is not less than the preset number mentioned above.

[0115] If there are residuals among all the residuals of each observation that do not meet the above residual conditions, the number of the corresponding observation satellites can be further counted. If the number of satellites is not higher than the preset number (e.g., 5), the subsequent processing flow ends. If it is higher than the preset number, the subsequent processing continues.

[0116] Optionally, if the current number of observed satellites exceeds the preset number mentioned above, a corresponding number of observations can be deleted from the current remaining observation set based on the following preset deletion strategy:

[0117] 31) Determine the sum of squares of the residuals corresponding to each observation in the current remaining observation set;

[0118] 32) Based on the sum of squares of each residual, delete the corresponding number of high residual observations in descending order of the corresponding residuals, and ensure that the number of remaining observation satellites after deletion is not less than the preset number mentioned above.

[0119] Specifically, the sum of squares of the residuals corresponding to all observations in the current remaining observation set can be calculated as D = v T v. Sort all observations in descending order of their corresponding residuals, and delete several observations with the largest residuals depending on the size of D, while ensuring that the number of remaining observation satellites after deletion is not less than the preset number, such as not less than five.

[0120] The larger D is, the higher the probability of having more cycle slip observations (of course, there may be very few cycle slip observations, but the number of cycle slips is relatively large). In order to speed up the search efficiency, the larger D is, the more observations are deleted. At the same time, it should be ensured that the number of remaining observation satellites after deletion is no less than five. That is, too many observations should not be deleted at once, otherwise the algorithm's iterative convergence result will be incorrect.

[0121] After deletion, the remaining observation set is updated once, and the process returns to step one to loop until a set of observations that can satisfy the residual conditions (detection criteria) of step three is found, at which point the process moves to step five. It is easy to understand that the set of observations that can satisfy the residual conditions of step three is the latest remaining observation set.

[0122] Step 5: If the current precision factor is lower than the preset second threshold, use the current remaining observation set as the second observation set; if the current precision factor is not lower than the preset second threshold, add the deleted observations one by one to the current remaining observation set, and after each addition of an observation that updates the remaining observation set, return to step 3. If the updated remaining observation set satisfies the conditions in step 3, retain the added observations in the remaining observation set until the traversal of each deleted observation is completed, and use the current remaining observation set as the second observation set.

[0123] In addition to the highest detection threshold DOP of the precision factor max That is, the first threshold, and also sets an intermediate detection threshold DOP for the precision factor. c In this embodiment, it is referred to as the second threshold, wherein the second threshold is lower than the first threshold. The DOP passes the first threshold. max Second Door DOP c The DOP value is divided into three intervals: (0, DOP) c ], (DOP c DOP max ], (DOP max , infinity).

[0124] The optimal situation is when the satellite's actual accuracy factor falls within the first interval (0, DOPc), satisfying both cycle slip detection and repair requirements. The next best is when it falls within the second interval (DOPc, DOPmax), where the accuracy is sufficient for both cycle slip repair and detection. The third interval (DOPc, DOPmax) is the least desirable. max (Infinity) is the worst case, in which the probability of error in cycle slip detection will be very high, and thus neither the accuracy requirements of cycle slip detection nor the accuracy requirements of cycle slip repair can be met.

[0125] In this step, if the current precision factor is lower than the second threshold DOP c If all observations in the current residual observation set are considered reliable, the current residual observation set is directly used as the second observation set, provided that the current precision factor is not lower than the second threshold DOP. c Then, each of the previously deleted observations is added to the current set of remaining observations one by one (only one observation is added per round), and the detection process described in step three is repeated. If the detection passes (i.e., the residuals of each observation after addition meet the set residual conditions), the added observation is retained in the set of remaining observations. The purpose of this process is to try to recover the wrongly deleted observations if the current constellation configuration is poor, so as to improve the constellation configuration. Accordingly, this process is used to try to improve DOP until the traversal of each deleted observation is completed, and the current set of remaining observations is used as the second set of observations.

[0126] Step 104: Determine the target observation value that has cycle slip in the first observation set based on the second observation set, and perform cycle slip repair processing on the target observation value.

[0127] After searching for all observations that meet the preset residual conditions and obtaining the second observation set, the observations in the first observation set that have been deleted compared to the second observation set can be identified as target observations that have experienced cycle slips (or are highly likely to experience cycle slips) and need to be processed for cycle slip repair.

[0128] Optionally, when performing cycle slip repair on the detected target observations, first determine whether the current precision factor is lower than the second threshold DOP. c If it is not lower than the required level, then the DOP requirement is not met. <DOP c In this case, no cycle slip repair operation is performed on the target observations; that is, through DOP... cSetting a threshold further restricts the repair action, preventing the erroneous assumption of a cycle slip and subsequent repair. Such an incorrect repair value entering the processing stage would be difficult for subsequent PPP / RTK algorithms to handle. Alternatively, in this case, all deleted observations (i.e., all target observations) can be marked as observations that have experienced a cycle slip (or are highly likely to experience one), and then submitted to the PPP or RTK algorithm for re-initialization.

[0129] Conversely, if the current precision factor is lower than the second threshold, i.e., DOP <DOP c Then, cycle slip repair is performed on the target observations based on the optimal estimate of the vector to be estimated x, where the optimal estimate of the vector to be estimated x is the result of the last least squares estimation of the vector to be estimated x. Specifically, the residuals of each target observation (i.e., all deleted observations) can be determined based on the optimal estimate of the vector to be estimated x, and the carrier cycle slip value of the target observation can be estimated based on the residuals of each target observation and the corresponding carrier wavelength. Optionally, the formula can be used. Estimate the carrier cycle slip value of the target observation, where ROUND(v j / λ j ) indicates that for v j / λ j After rounding, the target observation is corrected for cycle slip based on the estimated carrier cycle slip value.

[0130] Furthermore, optionally, if the residuals corresponding to the target observations after repair... To meet the small quantity requirement, i.e., w j If the absolute value is less than the set threshold, the observation is marked as successfully repaired, and... Feedback compensation is added to the carrier observations; otherwise, it is marked as unrepaired.

[0131] In other implementations, it can be determined whether the number of successfully repaired observations is 0. If the number of successfully repaired observations is not 0, the process returns to step one and repeatedly executes the carrier phase cycle slip detection and repair process based on least squares estimation to ensure the correctness and reliability of the detection and repair results, until no observations are repaired, at which point the processing flow ends. For a detailed overview of the carrier phase cycle slip detection and repair process, please refer to [link to relevant documentation]. Figure 2 As shown.

[0132] In summary, the carrier phase cycle slip detection and repair method provided in this application obtains at least multiple carrier phase observation values ​​of the observed satellite by performing a preset cycle slip detection preparation process to obtain a first observation set. It then generates a least-squares observation vector and observation matrix corresponding to each observation value in the first observation set, and generates an observation weight matrix through observation weighting. Based on the least-squares observation vector, observation matrix, and observation weight matrix, it searches for each observation value in the first observation set that satisfies a preset residual condition using a least-squares residual verification method, thus obtaining a second observation set composed of the searched observation values. The preset residual condition is a condition that can be used to characterize that the carrier phase observation value has not experienced a cycle slip. Finally, it determines the target observation value in the first observation set that has experienced a cycle slip based on the second observation set, and performs cycle slip repair processing on the target observation value.

[0133] As can be seen, this application proposes a carrier cycle slip detection and repair scheme based on least squares residual verification, which relies solely on carrier phase observations and does not limit the number of frequency points. By directly detecting the carrier phase, it avoids "primary star selection" anxiety and breaks the limitation that the double-difference primary star selection must be problem-free. It is applicable to both PPP and RTK, and because it does not limit the number of frequency points, it has high applicability to PPP or RTK algorithms using single-frequency or multi-frequency observations.

[0134] Corresponding to the above-described carrier phase cycle slip detection and repair method, this application also provides a carrier phase cycle slip detection and repair device, the structure of which is as follows: Figure 3 As shown, it includes:

[0135] The preparation processing unit 10 is used to perform a preset cycle slip detection preparation process to obtain at least multiple carrier phase observation values ​​of the observed satellite through the cycle slip detection preparation process, so as to obtain a first observation set.

[0136] The generation unit 20 is used to generate the least squares observation vector and observation matrix corresponding to each carrier phase observation value, and to generate the observation weight matrix through observation weighting processing.

[0137] The search unit 30 is used to search for each observation value that satisfies a preset residual condition from the first observation set according to the least squares observation vector, the observation matrix, and the observation weight matrix, through the least squares residual verification method, to obtain a second observation set composed of the searched observation values; the preset residual condition is a condition used to characterize that the carrier phase observation value has not experienced a cycle slip.

[0138] The detection and repair unit 40 is used to determine the target observation value that has cycle slip in the first observation set according to the second observation set, and to perform cycle slip repair processing on the target observation value.

[0139] In one embodiment, the preparation processing unit 10 is specifically used for:

[0140] Collect multiple carrier phase observations from adjacent epochs of the observation satellite and prepare to broadcast ephemeris.

[0141] In one embodiment, the generating unit 20 is specifically used for:

[0142] If the number of observation satellites corresponding to the first observation set is not less than a preset number:

[0143] The carrier phase increment is determined based on the carrier phase observations of adjacent epochs in the first observation set, and the satellite position increment and satellite clock error increment in the carrier phase increment are compensated using broadcast ephemeris, so as to generate the least squares observation vector through compensation processing.

[0144] The observation matrix is ​​determined based on the receiver position and satellite position;

[0145] The observation weight matrix is ​​obtained by weighting each observation in the first observation set using prior information.

[0146] The preset quantity is the minimum number of satellites required to ensure the effectiveness of least squares residual verification.

[0147] In one embodiment, the search unit 30 is specifically used for:

[0148] Step 1: Determine the accuracy factor corresponding to the current constellation configuration of the observed satellites; if the accuracy factor is higher than a preset first threshold, the process ends; otherwise, proceed to Step 2.

[0149] Step 2: Perform weighted least squares estimation on the vector to be estimated, and generate a residual vector based on the estimation results; the vector to be estimated consists of the receiver's position increment and clock error increment;

[0150] Step 3: Determine whether the residuals corresponding to each observation in the residual vector in the current residual observation set all satisfy the preset residual conditions; if not, proceed to step 4; if yes, proceed to step 5; wherein, the initial value of the residual observation set is the first observation set.

[0151] Step 4: Determine the current number of observed satellites. If the current number of observed satellites is higher than the preset number, delete a corresponding number of observations from the remaining observation set based on the preset deletion strategy, thereby updating the remaining observation set. After deletion, return to Step 1 until the residuals corresponding to each observation in the resulting remaining observation set all meet the preset residual conditions, then proceed to Step 5. Wherein, the number of remaining observed satellites after deletion is not less than the preset number.

[0152] Step 5: If the current precision factor is lower than the preset second threshold, use the current remaining observation set as the second observation set; if the current precision factor is not lower than the preset second threshold, add the deleted observations one by one to the current remaining observation set, and after each addition of an observation that updates the remaining observation set, return to step 3. If the updated remaining observation set satisfies the conditions in step 3, retain the added observations in the remaining observation set until the traversal of each deleted observation is completed, and use the current remaining observation set as the second observation set.

[0153] The second threshold is lower than the first threshold.

[0154] In one embodiment, when the search unit 30 deletes a corresponding number of observations from the remaining observation set based on a preset deletion strategy, it is specifically used for:

[0155] Determine the sum of squares of the residuals corresponding to each observation in the current remaining observation set;

[0156] Based on the sum of squares, delete a corresponding number of high residual observations in descending order of the corresponding residuals, ensuring that the number of remaining observation satellites after deletion is not less than the preset number.

[0157] In one embodiment, the preset quantity is 5.

[0158] In one embodiment, the detection and repair unit 40 is specifically used for:

[0159] Each observation value in the first observation set that was deleted compared to the second observation set is identified as the target observation value that caused the cycle slip;

[0160] Determine whether the current precision factor is lower than the second threshold;

[0161] If the value is lower, cycle slip correction is performed on each target observation value based on the optimal estimate of the vector to be estimated; the optimal estimate of the vector to be estimated is the last least squares estimation result of the vector to be estimated.

[0162] If the value is not lower than the target value, then no cycle slip repair operation will be performed.

[0163] In one embodiment, when the detection and repair unit 40 performs cycle slip repair on the target observation based on the optimal estimate of the vector to be estimated, it is specifically used for:

[0164] Based on the optimal estimate of the vector to be estimated, determine the residuals of each target observation;

[0165] Based on the residuals of each target observation and the corresponding carrier wavelength, cycle slip repair is performed on each target observation.

[0166] In one embodiment, the above-described apparatus further includes a post-processing unit for:

[0167] Determine if the number of successfully repaired observations is zero;

[0168] If it is not zero, return to step one and repeat the carrier phase cycle slip detection and repair process based on least squares estimation until the number of successfully repaired observations in the current round is zero.

[0169] If the value is zero, then the process ends.

[0170] The carrier phase cycle slip detection and repair apparatus provided in this application is described simply because it corresponds to the carrier phase cycle slip detection and repair method provided in the above method embodiments. For any similarities, please refer to the description of the above method embodiments, which will not be elaborated here.

[0171] This application also provides a computer-readable medium having a computer program stored thereon, the computer program comprising program code for performing the carrier phase cycle slip detection and repair method as provided in the above method embodiments.

[0172] In the context of this application, a computer-readable medium (machine-readable medium) can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0173] It should be noted that the computer-readable medium described above in this application can be a computer-readable signal medium, a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0174] The aforementioned computer-readable medium may be contained within an electronic device or may exist independently without being assembled into an electronic device.

[0175] This application also provides a computer program product, which includes a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the carrier phase cycle slip detection and repair method provided in the above method embodiments.

[0176] Specifically, according to embodiments of this application, the processes described in the above-described reference flowcharts can be implemented as computer software programs. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from a storage device, or installed from a ROM. When the computer program is executed by a processing device, it performs the functions defined in the methods of the embodiments of this application.

[0177] In summary, the carrier phase cycle slip detection and repair method, apparatus, computer-readable medium, and computer program product provided in this application have at least the following technical advantages:

[0178] a) It effectively utilizes all available carrier observations and does not rely on the assistance of other observations. It has high applicability to PPP or RTK algorithms that use single-frequency or multi-frequency observations. Its detection effect covers the traditional geometrically independent combination detection method. It is equivalent to using redundant carrier observations. With the assistance of navigation messages (ephemeris), it removes the geometric influence between the receiver and the satellite. At the same time, it overcomes the shortcomings of the geometrically independent combination detection method. It does not require tracking multiple frequency points of all satellites at the same time. For example, five carrier observations from any frequency point of 5 satellites can be used to detect whether a cycle slip has occurred.

[0179] b) This application directly detects the carrier phase. The input of the method is essentially the epoch difference of the single-station carrier phase. This approach avoids the anxiety of "primary star selection" and breaks the limitation that the primary star selection of the double difference must be guaranteed to be problem-free. It is applicable to both PPP and RTK.

[0180] c) It is applicable to both dynamic and static station application scenarios. For static station application scenarios, Δr in equation (4) k,k+1 =0, which reduces the number of parameters to be estimated to 1, allowing for further improvement in detection efficiency and reliability.

[0181] It should be noted that although the subject matter has been described using language specific to structural features and / or methodological logic, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are merely illustrative examples of implementing the claims.

[0182] While several specific implementation details are included in the foregoing discussion, these should not be construed as limiting the scope of this application. Certain features described in the context of individual embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments.

[0183] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described application concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions claimed in this application.

Claims

1. A method for carrier phase cycle slip detection and repair, characterized in that, The method comprises the following steps: performing a preset cycle slip detection preparation process to obtain a first observation set by at least obtaining a plurality of carrier phase observations of an observation satellite through the cycle slip detection preparation process; generating a least square observation vector and an observation matrix corresponding to each observation value in the first observation set, and generating an observation weight matrix through observation weighting processing; searching for each observation value satisfying a preset residual condition from the first observation set through a least square residual checking method according to the least square observation vector, the observation matrix and the observation weight matrix, to obtain a second observation set composed of the searched observation values; the preset residual condition is a condition that can be used to represent that the carrier phase observation value has not occurred cycle slip; determining a target observation value of the first observation set that has occurred cycle slip according to the second observation set, and performing cycle slip repair processing on the target observation value; the step of searching for each observation value satisfying a preset residual condition from the first observation set through a least square residual checking method according to the least square observation vector, the observation matrix and the observation weight matrix to obtain a second observation set composed of the searched observation values comprises: Step 1: determining an accuracy factor corresponding to a current constellation configuration of the observation satellite; if the accuracy factor is higher than a preset first threshold, ending, if not higher than the first threshold, turning to Step 2; Step 2: performing weighted least square estimation on a to-be-estimated vector, and generating a residual vector according to the estimation result; the to-be-estimated vector is composed of a position increment and a clock difference increment of the receiver; Step 3: determining whether the residuals corresponding to each observation value in the current residual observation set in the residual vector all satisfy the preset residual condition; if not, turning to Step 4, if yes, turning to Step 5; wherein the initial value of the residual observation set is the first observation set; Step 4: determining the current number of observation satellites, and deleting a corresponding number of observation values from the residual observation set based on a preset deletion strategy under the condition that the current number of observation satellites is higher than a preset number, so as to update the residual observation set; returning to Step 1 after the deletion is completed, until the residuals corresponding to each observation value in the obtained residual observation set all satisfy the preset residual condition, and then turning to Step 5; wherein the number of observation satellites remaining after the deletion is completed is not less than the preset number; Step 5: if the current accuracy factor is lower than a preset second threshold, taking the current residual observation set as the second observation set; if the current accuracy factor is not lower than the second threshold, adding the deleted observation values one by one to the current residual observation set, and returning to Step 3 after the residual observation set is updated each time an observation value is added; if the updated residual observation set satisfies the condition in Step 3, retaining the added observation value in the residual observation set, until the traversal of each deleted observation value is completed, and then taking the current obtained residual observation set as the second observation set; wherein the second threshold is lower than the first threshold.

2. The method of claim 1, wherein, the step of performing a preset cycle slip detection preparation process comprises: Collect multiple carrier phase observations of adjacent epochs of an observation satellite, and prepare broadcast ephemeris.

3. The method of claim 2, wherein, The generating of the least square observation vector and the observation matrix corresponding to each observation value in the first observation set, and the generating of the observation weight matrix through observation weighting processing, comprises: In the case that the number of observation satellites corresponding to the first observation set is not less than a preset number: Determine the carrier phase increment according to the carrier phase observations of adjacent epochs in the first observation set, and compensate the satellite position increment and the satellite clock error increment in the carrier phase increment using the broadcast ephemeris, to generate the least square observation vector through compensation processing; Determine the observation matrix according to the receiver position and the satellite position; Weight each observation corresponding to the first observation set using prior information to obtain the observation weight matrix; The preset number is the minimum number of satellites required to ensure the effectiveness of the least square residual check.

4. The method of claim 1, wherein, The deleting of a corresponding number of observation values from the residual observation set based on a preset deletion strategy, comprises: Determine the sum of squares of residuals corresponding to each observation value in the current residual observation set respectively; According to the sum of squares, delete a corresponding number of high residual observation values in descending order of the corresponding residuals, and make the number of observation satellites remaining after deletion not less than the preset number.

5. The method according to claim 1 or 4, characterized in that, The preset number is 5.

6. The method of claim 1, wherein, The determining of the target observation value in the first observation set in which cycle slip occurs according to the second observation set, and the cycle slip repair processing of the target observation value, comprises: Determine each observation value in the first observation set which is deleted compared with the second observation set as each target observation value in which cycle slip occurs; Determine whether the current precision factor is lower than the second threshold; If lower, perform cycle slip repair on each target observation value according to the optimal estimation value of the estimated vector; the optimal estimation value of the estimated vector is the last least square estimation result of the estimated vector; If not lower, do not perform cycle slip repair operation on the target observation value.

7. The method of claim 6, wherein, The cycle slip repair of the target observation value according to the optimal estimation value of the estimated vector, comprises: Determine the residual of each target observation value according to the optimal estimation value of the estimated vector; Perform cycle slip repair on each target observation value according to the residual of each target observation value and the corresponding carrier wavelength.

8. The method of claim 6, wherein, Further comprising: Determine whether the number of successful repairs is zero; If not zero, return to step one to perform the cycle slip detection and repair process based on least square estimation in a loop until the number of successful repairs in the current round is zero; If zero, end.

9. A carrier phase cycle slip detection and repair apparatus, characterized by, Comprise: A preparation processing unit is configured to perform a preset cycle slip detection preparation processing to obtain at least a plurality of carrier phase observations of an observation satellite through the cycle slip detection preparation processing, and obtain a first observation set; A generating unit is configured to generate a least square observation vector and an observation matrix corresponding to each carrier phase observation, and generate an observation weight matrix through observation weighting processing; The generating unit is further configured to: The searching unit searches each observation value satisfying a preset residual condition from the first observation set by a least square residual checking manner according to the least square observation vector, the observation matrix and the observation weight matrix, and obtains a second observation set composed of the searched each observation value. The detecting and repairing unit determines a target observation value in the first observation set in which cycle slip occurs according to the second observation set, and performs cycle slip repairing processing on the target observation value. The searching unit searches each observation value satisfying a preset residual condition from the first observation set by a least square residual checking manner according to the least square observation vector, the observation matrix and the observation weight matrix, and obtains a second observation set composed of the searched each observation value, including: Step one: determining an accuracy factor corresponding to a current constellation configuration of an observation satellite; if the accuracy factor is higher than a preset first threshold, ending, if not higher than the first threshold, turning to step two; Step two: performing weighted least square estimation on a to-be-estimated vector, and generating a residual vector according to an estimation result; the to-be-estimated vector is composed of a position increment and a clock difference increment of a receiver; Step three: determining whether each residual corresponding to each observation value in a current residual observation set in the residual vector satisfies the preset residual condition; if not, turning to step four, if yes, turning to step five; wherein an initial value of the residual observation set is the first observation set; Step four: determining a current number of observation satellites, and deleting a corresponding number of observation values from the residual observation set based on a preset deletion strategy in a case that the current number of observation satellites is higher than a preset number, so as to update the residual observation set; returning to step one after the deletion is completed, until each residual corresponding to each observation value in the obtained residual observation set satisfies the preset residual condition, and turning to step five; wherein a number of observation satellites remaining after the deletion is completed is not lower than the preset number; Step five: if the current accuracy factor is lower than a preset second threshold, taking the current residual observation set as the second observation set; if the current accuracy factor is not lower than the second threshold, adding the deleted observation values to the current residual observation set one by one, and returning to step three after the residual observation set is updated each time an observation value is added; if the updated residual observation set satisfies the condition in step three, retaining the added observation value in the residual observation set, until the iteration of each deleted observation value is completed, and taking the current obtained residual observation set as the second observation set; The second threshold is lower than the first threshold.

10. A computer readable medium characterized by A computer program is stored thereon, and the computer program contains program codes for executing the method according to any one of claims 1-8.

11. A computer program product, characterised in that, The computer program is carried on a non-transitory computer readable medium, and the computer program contains program codes for executing the method according to any one of claims 1-8.

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