A method for calculating the integer ambiguity of single-difference carrier phase between short-baseline stations of dual-frequency single-epoch single-satellite
By eliminating errors through inter-frequency difference, the integer ambiguity calculation of a dual-antenna satellite navigation system with a short baseline arrangement in a complex satellite navigation environment is realized, which solves the difficulty in ambiguity calculation caused by the failure of pseudo-range information in the existing technology. Efficient and accurate ambiguity fixation is achieved.
Patent Information
- Application Number
- CN202411345586.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-26
- Publication Date
- 2025-01-21
- Estimated Expiration
- 2044-09-26
AI Technical Summary
In complex satellite navigation environments, a dual-antenna satellite navigation system with short baseline/ultra-short baseline arrangement cannot effectively calculate the ambiguity throughout the week, especially when the pseudorange measurement information is invalid or unreliable.
By performing inter-frequency difference on the single-difference carrier phase information between dual-antenna stations, the effects of satellite clock differences, ionospheric and tropospheric errors, and inter-station clock differences are eliminated to achieve reliable ambiguity calculations. The specific steps include establishing the single-difference ambiguity observation equation of the carrier phase, performing the difference between frequency points, simplifying the formula, converting it into the standard deviation form, and determining the integer ambiguity through the deviation function.
It achieves the rapid and reliable determination of integer ambiguity under single epoch conditions, with a theoretical success rate and accuracy of not less than 99%, without the need for multiple inter-satellite channels, and high computational efficiency.
Smart Images

Figure CN118859270B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of satellite navigation, and in particular to a method for calculating integer ambiguity of a dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase. Background Art
[0002] Satellite navigation is widely used for positioning and speed determination of low-cost carriers. When the carrier uses a two-antenna solution, the satellite navigation system can provide more complete navigation information such as attitude based on carrier phase differential information. At the same time, it can provide more sufficient observation information for low-cost unmanned aerial vehicles based on satellite navigation combined navigation. However, in a complex satellite navigation environment, when an unmanned small aircraft equipped with a dual-antenna satellite navigation system with a short baseline / ultra-short baseline arrangement determines the integer ambiguity, it is necessary to discard the pseudo-range measurement information with large errors. At the same time, the multipath effect appears and disappears with the sudden change of the carrier's maneuver. Therefore, it is impossible to use traditional methods to filter and solve the integer ambiguity. It is necessary to propose a method that does not rely on multi-epoch information cache and pseudo-range measurement information and can quickly determine the accurate station-to-station single-difference integer ambiguity of the current epoch.
[0003] The earliest integer ambiguity fixing algorithm was the integer least squares method, which used carrier phase observations and inter-station baseline constraints to limit the range of ambiguity search, but the search efficiency was low.
[0004] The traditional carrier phase ambiguity fixation method is mainly through multi-epoch filtering. The LAMBD algorithm proposed by Teunissen improves the efficiency of solution by using integer transformation to reduce the correlation between ambiguities. Since the integer characteristics of the integer ambiguity are ignored, solving the floating point solution only requires standard least squares solution, which is easy to calculate. However, the disadvantage is that it requires filtering calculations of the previous and next epochs to obtain highly reliable integer ambiguity results and requires cycle slip detection of the data at each moment.
[0005] The Three Carrier Ambiguity Resolution (TCAR) algorithm proposed by Forssell and the Cascading Integer Resolution (CIR) algorithm proposed by Jung et al. effectively fix the integer ambiguity solution by solving the ultra-wide lane, wide lane and single-frequency ambiguity step by step based on the Bootstrapping method. The advantage of these algorithms is that they can guarantee extremely high reliability. However, their disadvantage is that the amount of calculation is large, and a large number of complex calculations are often required to obtain ambiguity results.
[0006] In response to the method of single-epoch fast ambiguity fixation, Geng Jianghui et al. proposed PPP-WAR for Precise Point Positioning (PPP) fast single-point positioning based on full use of the single-epoch information of three-frequency points for ambiguity fixation. The availability under three-frequency conditions reached more than 90%. The single-epoch LAMBD algorithm can search for highly reliable single-epoch carrier phase ambiguities under a multi-satellite geometric configuration that obtains pseudorange information. The Ambiguity Function Method (AFM) algorithm proposed by Counselman completes the ambiguity solution by establishing an objective function and searching all grid points to determine the ambiguity solution. However, the disadvantage of the above method is that it is difficult to guarantee reliable ambiguity resolution. Summary of the invention
[0007] The technical problem to be solved by the present invention is to provide a dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase integer ambiguity calculation method in view of the shortcomings of the existing technology. By performing inter-frequency differentiation on the single-difference carrier phase information between dual-antenna stations, the influence of satellite clock error, ionosphere and troposphere errors and station-to-station clock error is eliminated, thereby achieving reliable ambiguity calculation.
[0008] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for calculating the integer ambiguity of a dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase, comprising the following steps:
[0009] S1. Establish the carrier phase single-difference ambiguity observation equation for the two frequency points of the two stations respectively:
[0010] ;
[0011] in, Respectively represent Two frequency wavelengths, , Respectively represent Single difference carrier phase between two frequency stations; , Respectively represent the position of satellite No. i corresponding to the signal received by antenna No. 1 and antenna No. 2; Respectively represent the real positions of antenna No. 1 and antenna No. 2; Respectively represent Two frequency points; Respectively represent The inter-station clock difference between the two frequency points at antenna No. 1 and antenna No. 2; Represents antenna No. 1 and antenna No. 2 respectively The single difference integer ambiguity of two frequency points relative to satellite i;
[0012] S2. Subtract the two equations of the observation equation to obtain the following equation: ;
[0013] in, ;
[0014] c is the speed of light, for Random error between two frequency points, Respectively represent The inter-station clock difference between the two frequency points at antenna No. 1 and antenna No. 2; Respectively represent The inter-station clock difference between the frequency points of antenna No. 1 and antenna No. 2, Respectively represent The inter-station clock difference between the frequency points of antenna No. 1 and antenna No. 2;
[0015] S3. Simplify the formula in step S2 to obtain: ;
[0016] in, ; L is the baseline length;
[0017] S4. Convert the formula in step S3 into the following form: ;
[0018] is the single difference carrier phase measurement error between antennas 1 and 2 The standard deviation of
[0019] S5. Define the deviation function f: ;
[0020] in, For collection The elements in , n is the number of integer solution points;
[0021] The deviations are aggregated The value closest to 0 in the deviation set D is mapped to the integer solution point under the condition of minimum error. , That is The single-difference integer ambiguity between two frequency points.
[0022] The present invention performs frequency difference on the single-difference carrier phase information between dual-antenna stations, eliminates the influence of satellite clock error, ionosphere and troposphere errors and inter-station clock error, and realizes reliable ambiguity calculation.
[0023] Before step S1, the method further includes:
[0024] The probability of an incorrect integer ambiguity solution is calculated using the following formula: : ;in, For collection The minimum value in , For The distance between two adjacent straight lines in the established parallel line cluster. The expression of the parallel line cluster is: , is the carrier phase distance information, .
[0025] From the above formula, it can be obtained that the error rate of the integer ambiguity solution of the present invention is only the distance between two adjacent straight lines in the parallel line cluster, and the number of parallel line clusters is related to the baseline length. When the baseline length is short, a higher accuracy integer ambiguity solution can be effectively obtained.
[0026] In the present invention, ,in, is a chi-square distribution with 2 degrees of freedom.
[0027] The present invention can also use the following formula to calculate the probability of wrong integer ambiguity solution: :
[0028] ;
[0029] For collection The minimum value in , For The distance between two adjacent straight lines in the established parallel line cluster is is the carrier phase distance information.
[0030] The calculation formula is:
[0031] ;
[0032] Among them, j=i+1.
[0033] As an inventive concept, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the above method.
[0034] As an inventive concept, the present invention also provides a computer-readable storage medium having a computer program / instruction stored thereon; the computer program / instruction implements the steps of the above method when executed by a processor.
[0035] As an inventive concept, the present invention also provides a computer program product, including a computer program / instruction; when the computer program / instruction is executed by a processor, the steps of the above method are implemented.
[0036] Compared with the prior art, the present invention has the following beneficial effects: the present invention can fix the ambiguity in a single epoch. The theoretical success rate and accuracy of the cycle time are not less than 99%; the present invention can complete ambiguity fixation when the dual-frequency points of a single satellite in a single epoch are complete, without the need for inter-satellite multi-channels, and has high calculation efficiency; the present invention solves the problem of carrier phase ambiguity fixation under the condition that the geometric configuration constraints between the antenna and the satellite cannot be used when the pseudo-range information is invalid or unreliable. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1 It is a principle diagram of the method of the embodiment of the present invention;
[0038] Figure 2 yes Schematic diagram of the single-difference integer ambiguity domain and standard points between frequency stations;
[0039] Figure 3 yes Schematic diagram of the single-difference integer ambiguity domain and observation line between frequency point stations;
[0040] Figure 4 yes Schematic diagram of the ambiguity line cluster of the single difference fractional part between frequency point stations;
[0041] Figure 5 yes Schematic diagram of the inter-epoch difference results of the single-difference ambiguity compensation values between frequency points of BeiDou-2 satellite stations;
[0042] Figure 6 yes Schematic diagram of the error results of the single-difference ambiguity compensation value between frequency points of BeiDou-2 satellite stations;
[0043] Figure 7 It is a schematic diagram of the time consumption ratio between the method of the embodiment of the present invention and the traditional LAMBD part. DETAILED DESCRIPTION
[0044] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0045] Example 1
[0046] like Figure 1As shown, this embodiment provides a method for quickly and accurately solving the integer ambiguity of the short baseline single-difference carrier phase between stations of a dual-frequency single-epoch single-satellite. The method eliminates the influence of the satellite clock error, ionospheric and tropospheric errors, and the clock error between stations by performing inter-frequency differentiation on the single-difference carrier phase information between stations. The ambiguity is solved in a single-epoch single-satellite dual-frequency through the integer constraint of the integer ambiguity and the short baseline geometric constraint conditions, and the error rate calculation formula based on the carrier phase random error variance value is used.
[0047] The implementation process of the method in this embodiment includes:
[0048] From the carrier phase observation equation:
[0049] (1)
[0050] In the formula, is the carrier phase wavelength, is the true value of the carrier phase, is the integer ambiguity of the carrier phase of satellite i, is the real position of star i, is the real position of antenna No. 1, is the receiver clock error of antenna No. 1, is the ionosphere-troposphere error, and f represents the frequency. The carrier phase single-difference ambiguity observation equation is established for the two frequency points of the two stations:
[0051] (2)
[0052] In the formula Respectively represent Single difference carrier phase between two frequency stations; Respectively represent the satellite positions corresponding to the signals received by antenna No. 1 and antenna No. 2; , Represent the true positions of antennas 1 and 2 respectively; Respectively represent Two frequency points; Respectively represent The inter-station clock difference between the two frequency points at antennas 1 and 2; Represents antenna No. 1 and No. 2 respectively The single-difference integer ambiguity of two frequency points relative to satellite i.
[0053] Considering the short distance between stations, the ionosphere and troposphere errors of the two stations are approximately the same, so they can be eliminated in the difference, but the clock error between the receiver stations still exists in equation (2).
[0054] Since there is still the influence of the clock difference between the two antenna stations in equation (2), we can obtain the following by subtracting the upper and lower equations of equation (2): (3)
[0055] In the formula
[0056] (4)
[0057] Considering the same receiver The error between frequency points is smaller than the random error of noise and can be ignored. Therefore, equation (3) can be transformed into
[0058] (5)
[0059] The single difference carrier phase between frequency points represents the same distance, and the distance does not exceed the baseline length L, that is,
[0060] (6)
[0061] (7)
[0062] See also Figure 3 , the points in the range of formula (6) represent different Frequency integer ambiguity group .
[0063] Accounting for accidental measurement errors and its standard deviation , equation (6) and equation (7) can be converted into the following equation:
[0064] (8)
[0065] The first formula is a straight line, see Figure 3 As shown in Figure They are the lower and upper bounds of the second and third inequalities in equation (8), respectively.
[0066] Considering is an integer, so after adding this constraint, there are only a limited number of solutions available within the rectangular dashed box, so there is a finite set.
[0067] Select the integer solution point closest to the oblique straight line to obtain the integer ambiguity solution.
[0068] See also Figure 3 , We have determined n integer solution points, that is, there exists a set: .
[0069] definition is the distance from the ith integer solution point to the oblique straight line, with positive and negative signs. It is positive when the integer solution point is at the upper left of the oblique straight line, and negative when it is at the lower right.
[0070] Define the deviation function f:
[0071] (9)
[0072] So it exists in the deviation set The function f corresponds to the set N one by one, where the mapping of the value closest to 0 in set D to set N is the integer solution point under the condition of minimum error. .in That is what you want Two-frequency single-difference ambiguity.
[0073] To determine the error rate of the above dual-frequency single-epoch single-satellite short baseline inter-station single-difference carrier phase integer ambiguity method, define the carrier phase distance information They represent: .
[0074] remember represents a two-dimensional space. Convert to , we can get:
[0075] (10)
[0076] You can see that for The choice space of is still the set described above:
[0077]
[0078] See also Figure 5 Established with The value of the product of the frequency point carrier phase and the respective wavelength is the rectangular system of the X / Y axis. Create clusters of parallel lines:
[0079] (11)
[0080] The distance between two parallel lines in a parallel line cluster can be expressed as:
[0081] (12)
[0082] Introducing the error term into formula (11) yields:
[0083] (13)
[0084] Considering the existence of random error terms in formula (13) , so the actual measurement is It does not completely fall on the cluster of parallel lines, that is, there is Make the point It falls at a position equidistant from two parallel lines in the cluster of parallel lines. In this case, the proposed method obtains an incorrect integer solution. Define the set , where i and i + 1 The distance between two straight lines is simply expressed as . Take the collection The minimum value is .
[0085] remember is the single difference carrier phase measurement error between antennas, and they all obey the normal distribution , is the standard deviation. Also d is the point The vertical distance to the true value constraint line of the single difference carrier phase between the dual-frequency antennas corresponding to the correct integer ambiguity solution is:
[0086] (14)
[0087] remember The probability of getting an incorrect integer ambiguity solution is:
[0088] (15)
[0089] Introducing the error term, equation (15) can be transformed into:
[0090] (16)
[0091] Considering that the probability calculation in formula (16) is difficult, we can scale formula (16) to obtain:
[0092] (17)
[0093] Where:
[0094] (18)
[0095] By threshold The probability on the right side of the last equal sign in equation (17) can be calculated.
[0096] in for The error rate calculation can be calibrated before the test after determining the baseline length and the standard deviation of the single-difference carrier phase between antennas.
[0097] The following is the application scenario of this embodiment.
[0098] BeiDou-2 Satellite Station 1 Dual Frequency The observed values are: 198574101.289, 153550091.328 respectively.
[0099] BeiDou-2 Satellite Station 2 Dual Frequency The observed values are: 198574023.192, 153550049.578 respectively.
[0100] See also Figure 2 , Figure 3 Establish dual antenna baseline for target The single-difference integer ambiguity domain and its observation line between frequency stations.
[0101] See also Figure 4 Establish dual antenna baseline for target Cluster of single-difference fractional ambiguity lines between frequency stations.
[0102] In order to quantitatively evaluate the proposed method and minimize the impact of the clock difference between receiver stations on the aforementioned evaluation indicators, this embodiment uses a common clock receiver and calibrates the distance between dual antenna stations to determine the constraint conditions for subsequent calculations. In the test sample, it is 0.5m, and the carrier phase random noise The value is 0.1 week.
[0103] Create a collection ,
[0104] ;
[0105] Search for the smallest value , the corresponding value is 5, corresponding to the dual-frequency ambiguity compensation The carrier phase values are 2.097 and 1.750.
[0106] Therefore, this embodiment adopts two indicators, namely:
[0107] 1. The inter-epoch stability of the fixed ambiguity solution of the single-difference single-epoch single-satellite dual-frequency linear matching ambiguity method;
[0108] 2. The error between the carrier phase after fixed ambiguity solution compensation and the calculated true value of the single-difference single-epoch single-satellite dual-frequency linear matching ambiguity method.
[0109] The accuracy and stability of the single-difference single-epoch single-satellite dual-frequency linear matching ambiguity determination method are evaluated, and the effectiveness of the method of this embodiment is evaluated. At the same time, in order to quantitatively evaluate the embodiment method, the influence of the clock difference between the receiver stations on the aforementioned evaluation indicators is minimized as much as possible. For this reason, this embodiment uses a common clock receiver and calibrates the distance between the dual antenna stations to determine the constraint conditions for subsequent calculations. In the test sample, it is 0.5m, and the carrier phase random noise The value is 0.1 week. The error probability can be calculated. Among them:
[0110]
[0111] in , then
[0112]
[0113] From the table, we can see that:
[0114]
[0115] That is, under the above conditions, the error rate of the single-difference single-epoch dual-frequency single-epoch single-satellite short baseline inter-station single-difference carrier phase integer ambiguity method should be less than 1%.
[0116] Select the synchronous orbit satellite and the satellite position Approximate value, considering the dual antennas as static short baselines, then , No change. Then:
[0117] (19)
[0118] Considering random noise error and receiver epoch clock error The value is less than 0.1 week. Therefore, when the difference result of the carrier phase ambiguity compensation value between epochs is less than 0.1 week, it can be regarded that the single-difference carrier phase ambiguity fixed solution is in a stable state.
[0119] Reference Figure 5 The results clearly show that the ambiguity fixed by the single-difference single-epoch single-satellite dual-frequency linear matching ambiguity method is resolved after the inter-epoch difference Values less than 0.1 weeks are consistent with single-difference ambiguity errors The characterization shows that there is no jump value over time, which is consistent with the expected analysis value of the error rate. Therefore, it can be regarded as that the single-difference carrier phase ambiguity fixed solution is in a stable state. At the same time, the error rate conforms to the error rate characteristics of the linear matching ambiguity of the two-frequency points between frequencies, that is, the method of this embodiment can obtain a stable inter-station carrier phase ambiguity solution.
[0120] Depend on:
[0121] (20)
[0122] However, considering that even if the receivers share the same clock, there is still a small clock difference between stations, that is, It is not strictly 0. Therefore, the clock error of the common clock receiver is assumed to be no more than 0.5 weeks, that is, when the carrier phase ambiguity compensation value is basically consistent, the ambiguity solution fixed by the single-difference single-epoch single-satellite dual-frequency point linear matching ambiguity method is considered to be the true single-difference carrier phase solution.
[0123] (twenty one)
[0124] Reference Figure 6The results clearly show that the carrier phase after ambiguity solution compensation fixed by the single-difference single-epoch single-satellite dual-frequency linear matching ambiguity method is within 0.5 weeks of the calculated true value, and the fluctuation around the center is within 0.1 weeks, which is in line with the single-difference ambiguity error. The characteristic of the value being about 0.1 cycle is consistent with the expectation of the carrier phase error after the single difference ambiguity fixed value compensation. Therefore, it can be considered that the single difference carrier phase ambiguity fixed solution is in an accurate state. That is, the method of this embodiment can obtain the correct inter-station single difference carrier phase ambiguity solution.
[0125] The operation time of the traditional algorithm LAMBD is compared with that of the method proposed in this embodiment. Considering that the ambiguity resolved by the LAMBD algorithm is the ambiguity of all stars, and the ambiguity resolved by the method of this embodiment is the dual-frequency ambiguity of a single star, the ambiguity determination method described in this embodiment is set to perform 20 times of cycles to simulate the number of observable stars. At the same time, in order to reduce the random influence of the operation, 1000 cycles of calculation and timing are performed for each epoch, so as to obtain a more accurate and reliable calculation time.
[0126] Reference Figure 7 The results clearly show that the running time ratio of the LAMBD part of the ambiguity solution fixed by the short baseline single-difference single-epoch single-satellite dual-frequency linear matching ambiguity method and the traditional pseudo-range carrier phase joint geometrically constrained single-epoch multi-satellite ambiguity fixation method is about 1%, which effectively reduces the computational complexity under short baseline conditions and achieves the expected indicators.
[0127] Example 2
[0128] Embodiment 2 of the present invention provides a terminal device corresponding to the above-mentioned embodiment 1. The terminal device may be a processing device for a client, such as a mobile phone, a laptop computer, a tablet computer, a desktop computer, etc., to execute the method of the above-mentioned embodiment.
[0129] The terminal device of this embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in the above-mentioned embodiment 1.
[0130] In some implementations, the memory may be a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk memory.
[0131] In some other implementations, the processor may be a central processing unit (CPU), a digital signal processor (DSP), or other general-purpose processors of various types, which are not limited herein.
[0132] Example 3
[0133] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to the above embodiment 1, on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps of the method of the above embodiment 1 are implemented.
[0134] Computer readable storage media can be tangible devices that hold and store instructions used by instruction execution devices. Computer readable storage media can be, for example, but not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any combination thereof.
[0135] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The schemes in the embodiments of the present application may be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.
[0136] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.
[0137] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.
[0138] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.
[0139] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.
Claims
1. A dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase integer ambiguity calculation method, characterized in that: The following steps are involved: S1. Establish the carrier phase single-difference ambiguity observation equation for the two frequency points of the two stations respectively: ; in, Respectively represent Two frequency wavelengths, Respectively represent Single difference carrier phase between two frequency stations; , Respectively represent the position of satellite No. i corresponding to the signal received by antenna No. 1 and antenna No. 2; Respectively represent the real positions of antenna No. 1 and antenna No. 2; Respectively represent Two frequency points; Respectively represent The inter-station clock difference between the two frequency points at antenna No. 1 and antenna No. 2; Represents antenna No. 1 and antenna No. 2 respectively The single difference integer ambiguity of two frequency points relative to satellite i; S2. Subtract the two equations of the observation equation to obtain the following equation: ; in, ; c is the speed of light, for Random error between two frequency points, Respectively represent The inter-station clock difference between the two frequency points at antenna No. 1 and antenna No. 2; Respectively represent The inter-station clock difference between the frequency points of antenna No. 1 and antenna No. 2, Respectively represent The inter-station clock difference between the frequency points of antenna No. 1 and antenna No. 2; S3. Simplify the formula in step S2 to obtain: ; in, ; L is the baseline length; S4. Convert the formula in step S3 into the following form: ; is the single difference carrier phase measurement error between antennas 1 and 2 The standard deviation of S5. Define the deviation function f: ; in, For collection The elements in , n is the number of integer solution points; The deviations are aggregated The value closest to 0 in the deviation set D is mapped to the integer solution point under the condition of minimum error. , That is The single-difference integer ambiguity between two frequency points.
2. The dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase integer ambiguity calculation method according to claim 1 is characterized in that: Before step S1, the method further includes: The probability of an incorrect integer ambiguity solution is calculated using the following formula: : ; in, For collection The minimum value in , For The distance between two adjacent straight lines in the established parallel line cluster. The expression of the parallel line cluster is: , is the carrier phase distance information, .
3. The dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase integer ambiguity calculation method according to claim 2 is characterized in that: ,in, is a chi-square distribution with 2 degrees of freedom.
4. The dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase integer ambiguity calculation method according to claim 1 is characterized in that: The probability of an incorrect integer ambiguity solution is calculated using the following formula: : ; For collection The minimum value in , For The distance between two adjacent straight lines in the established parallel line cluster is is the carrier phase distance information.
5. The dual-frequency single-epoch single-satellite short baseline station-to-station single-difference carrier phase integer ambiguity calculation method according to any one of claims 2 to 4, characterized in that: The calculation formula is: ; Among them, j=i+1.
6. A computer device comprising a memory, a processor and a computer program stored in the memory; characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.
7. A computer-readable storage medium having a computer program or instruction stored thereon; characterized in that: When the computer program or instruction is executed by a processor, the steps of the method described in any one of claims 1 to 5 are implemented.
8. A computer program product comprising a computer program or instructions; characterized in that: When the computer program or instruction is executed by a processor, the steps of the method of any one of claims 1 to 5 are implemented.
Citation Information
Patent Citations
GNSS double-frequency carrier phase integer ambiguity resolving method
CN111751853A
GLONASS inter-frequency deviation real-time estimation method based on BDS assistance
CN117289318A
Cited By
Satellite deception signal source positioning method based on double-antenna satellite-inertia combination
CN121878727A
A satellite spoofing signal source localization method based on dual-antenna satellite-inertial combination.
CN121878727B