A partial integer ambiguity resolution method with additional known baseline constraints

Abstract

The present invention is a method for resolving partial integer ambiguities with additional known baseline constraints. The present invention relates to the field of satellite navigation technology. The present invention utilizes the optimal satellite selection strategy to retain the best number of available satellites to determine the subset of integer ambiguities to be fixed, utilizes pseudorange and phase double differences to construct a geometric correlation model, obtains the floating-point solution and corresponding covariance of the subset of integer ambiguities to be fixed through the optimal adjustment estimation theory, obtains the search benchmark of the subset of ambiguities to be fixed through the LAMBDA algorithm, expands the specified search range for each ambiguity, utilizes known baseline length constraint information to evaluate the correctness of the integer ambiguities in the set of alternative solutions, and finally determines the optimal alternative solution. The present invention not only expands the search range, but also utilizes known baseline length information to evaluate the correctness of the integer ambiguities, which can greatly improve the success rate of integer ambiguity resolution and has important development potential in high-precision satellite positioning or direction-finding application scenarios with known baseline constraints.

Description

Technical Field

[0001] The invention relates to the technical field of satellite navigation, and is a partial integer ambiguity resolution method with additional known baseline constraints. Background Art

[0002] Global Navigation Satellite Systems (GNSS) direction-finding technology has been widely used in navigation for dynamic platforms, including those at sea, on land, in the air, and in space. The essence of GNSS direction-finding can be summarized as GNSS short-baseline dynamic carrier phase differential positioning, the key to which lies in the rapid and accurate resolution of integer ambiguities. Because GNSS direction-finding typically involves attaching at least two receiving antennas to a rigid platform (such as a vehicle or ship), the baseline length between the receiving antennas, under the platform, can be pre-calibrated and measured. This known baseline length can be used as a constraint to improve the success rate of integer ambiguity resolution.

[0003] In GNSS direction finding technology, there are many methods for utilizing known baseline length information, but the main strategies can be categorized into the following three: Method 1: Linearize the known baseline length and directly introduce it into the function model as a virtual observation, thereby increasing the model observation redundancy and improving the floating-point accuracy of the integer ambiguity. Method 2: The known baseline length is only used as a basis for verifying the correctness of the integer ambiguity and does not directly participate in the integer ambiguity resolution, but rather ensures the correctness of the integer ambiguity resolution. Method 3: Incorporate the known baseline length into the integer ambiguity resolution process and modify the integer ambiguity search criteria. A typical method is the LAMBDA algorithm with a baseline length constraint (Constrained Least-squares AM Biguity Decorrelation Adjustment, C-LAMBDA algorithm).

[0004] Method 1 requires linearization of the known baseline length information. Since the initial receiving antenna position is unknown, single-point positioning must be used to provide an approximate value. The resulting positioning deviations exceeding the meter level can cause significant linearization errors. In severe cases, this may not even improve the model estimation strength, but instead introduce bias in the floating-point integer ambiguity solution, reducing the success rate of integer ambiguity resolution. Therefore, in practical applications with short known baseline lengths, such as less than 10 meters, this method does not substantially improve algorithm performance and may even lead to reduced performance of the integer ambiguity resolution model. Method 2 does not provide any additional information for integer ambiguity resolution. Instead, after obtaining a candidate set of integer ambiguities, it replaces them or combines them with a ratio test to determine the correctness of the integer ambiguities, thereby improving the accuracy of integer ambiguity fixation. This method has the advantage of requiring no modifications to the existing LAMBDA algorithm framework and a simple approach. However, in complex environments with poor observation quality, because it does not modify the LAMBDA algorithm's execution process for obtaining the candidate set, this method may not contain the true integer ambiguity solution, ultimately leading to failure in ambiguity fixation. Method 3 incorporates the known baseline length into the cost function for integer ambiguity resolution, which can effectively improve the success rate of integer ambiguity fixation to a certain extent. However, this method increases the algorithm search burden, causing the efficiency of the integer ambiguity search to decrease rapidly as the integer ambiguity search vector increases. Furthermore, this method is sensitive to poor observation quality and may cause the entire ambiguity fix to fail at some epochs.

[0005] In response to the above problems, the current integer ambiguity resolution method based on known baseline constraints still has a lot of room for improvement. The present invention proposes a partial integer ambiguity resolution method with additional known baseline constraints, which can effectively improve the success rate of integer ambiguity fixation. Summary of the Invention

[0006] The present invention aims to effectively improve the success rate of integer ambiguity fixation in high-precision satellite positioning or direction-finding applications with known baseline constraints. Based on this, the present invention provides a partial integer ambiguity resolution method with additional known baseline constraints.

[0007] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0008] The present invention provides a partial integer ambiguity resolution method with additional known baseline constraints. The present invention provides the following technical solutions:

[0009] A partial integer ambiguity resolution method with additional known baseline constraints, comprising the following steps:

[0010] Step 1: Determine the altitude and azimuth of all visible satellites based on the satellite ephemeris file and the user's approximate position;

[0011] Step 2: Based on the elevation and azimuth information of all visible satellites, determine the optimal satellite selection strategy according to the user's pre-set cutoff elevation and the number of selected satellites, and determine the column vector z of the subset of integer ambiguities to be fixed n ;

[0012] Step 3: Use pseudorange and carrier phase observations to build a geometric correlation model;

[0013] Step 4: Substitute the floating-point solution of the integer ambiguity subset to be fixed and the corresponding variance-covariance into the LAMBDA algorithm to obtain the optimal candidate solution column vector of the corresponding integer ambiguity subset to be fixed;

[0014] Step 5: Convert the column vector Each fuzziness element j∈[1,n], j is an integer, as a benchmark, expand ±m weeks to obtain the possible candidate set for the ambiguity element i∈[-m,m], i is an integer, and the alternative sets of all fuzzy elements are arranged and combined to form (2m+1) n Set of candidate solution vectors for the subset of integer ambiguities to be fixed k∈[1,(2m+1) n ], k is an integer;

[0015] Step 6: Using (2m+1) n The candidate solution vector of the subset of integer ambiguities to be fixed Get the geometric baseline fixed solution column vector corresponding to different alternative solutions

[0016] Step 7: Traverse (2m+1) n Group alternative solution column vector Calculate the geometric baseline solution according to step 6, and calculate the baseline length residual with the known baseline length. The optimal candidate solution column vector with the baseline length residual value not exceeding the fixed monitoring threshold and the smallest ambiguity residual is selected. As the final integer ambiguity fixed solution.

[0017] Preferably, the step 1 is specifically:

[0018] The position of each Beidou satellite is calculated using the Beidou satellite ephemeris file as r s , use the single point positioning algorithm to get the user's approximate location r r , get the station star projection vector for:

[0019]

[0020] Among them, * represents the norm; then the altitude angle of each satellite and azimuth It can be expressed as:

[0021]

[0022]

[0023]

[0024] Among them, E r It represents the transformation matrix from the Earth-centered Earth-fixed coordinate system to the local coordinate system; arctan(*) represents the inverse tangent operation; arcsin(*) represents the inverse sine operation.

[0025] Preferably, in step 2, the optimal star selection strategy is determined based on the principle of uniform distribution of satellites in the starry sky view and the geometric distribution factor as the measurement benchmark. If the total number of visible satellites is less than the preset number of selected satellites, the star selection strategy is not implemented, but all visible satellites are directly used for subsequent solution. The minimum number of visible satellites is 4.

[0026] Preferably, the step 3 is specifically:

[0027] The geometric correlation model is constructed using pseudorange and carrier phase observations.

[0028] E(y)=Hb+Fa+Bz, D(y)=Q yy

[0029] Where E(*) represents the expectation of the random variable; D(*) represents the variance of the random variable; y = [p T ,φ T ] T It represents the residual of the double-difference pseudorange observation p and the carrier phase observation φ, and the corresponding observation variance-covariance is expressed as Q yy b represents the geometric baseline vector, and the corresponding design matrix is ​​H; a represents the integer ambiguity subset that remains in a floating-point state, and the corresponding design matrix is ​​F; z represents the integer ambiguity subset to be fixed, and the corresponding design matrix is ​​B;

[0030] Using the least squares estimation method, the geometric baseline floating point solution column vector is obtained and the corresponding variance-covariance And the integer ambiguity fixed subset floating point solution column vector and the corresponding variance-covariance The variance-covariance between the geometric baseline and the integer ambiguity subset to be fixed is expressed as

[0031] Preferably, the step 7 is specifically as follows:

[0032] Optimal candidate solution vector Calculated by the following formula:

[0033]

[0034]

[0035] Among them, argmin(*) represents the variable value when the cost function reaches the minimum value, and |*| represents the absolute value; (*) T Indicates vector transpose; (*) -1 Indicates vector inversion; b 0 Indicates the known baseline length, T h Indicates the monitoring threshold, All index values ​​monitored to meet the monitoring threshold.

[0036] Preferably, when the integer ambiguity is correctly fixed, the residual error between the geometric baseline estimate and the known baseline length is generally no more than 1 cm, so the monitoring threshold T is set h When the carrier is in a dynamic and complex environment and the observation quality is poor, T h Relax to 2cm.

[0037] Preferably, the selection of the m value in step 5 is predetermined based on the application dynamic scenario, the quality of the observation quantity, the model error propagation characteristics, and the computational efficiency factor.

[0038] A partial integer ambiguity resolution system with additional known baseline constraints, the system comprising:

[0039] A data processing module, wherein the data processing module determines the elevation angles and azimuth angles of all visible satellites based on the satellite ephemeris file and the user's approximate position;

[0040] The strategy decision module determines the optimal satellite selection strategy based on the elevation and azimuth information of all visible satellites, the cutoff elevation and the number of selected satellites set by the user, and determines the column vector z of the subset of integer ambiguities to be fixed. n ;

[0041] A model building module, wherein the model building module uses pseudorange and carrier phase observations to build a geometric correlation model;

[0042] An integer ambiguity resolution module that feeds the floating-point solution and corresponding variance-covariance of the integer ambiguity subset to be fixed into the LAMBDA algorithm to obtain the optimal candidate solution column vector for the corresponding integer ambiguity subset to be fixed, thereby improving the success rate of integer ambiguity resolution.

[0043] A computer-readable storage medium stores a computer program, which is executed by a processor to implement a partial integer ambiguity resolution method with additional known baseline constraints.

[0044] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a partial integer ambiguity resolution method with additional known baseline constraints is implemented.

[0045] The present invention has the following beneficial effects:

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] The present invention utilizes the optimal satellite selection strategy to retain the best number of available satellites, thereby determining the subset of integer ambiguities to be fixed, reducing the computational burden of searching all integer ambiguities to a certain extent. Pseudorange and phase double differences are then used to construct a geometric correlation model. Floating-point solutions and corresponding covariances of the subset of integer ambiguities to be fixed are obtained through the optimal adjustment estimation theory. The search benchmark for the subset of ambiguities to be fixed is obtained through the LAMBDA algorithm. The specified search range is then expanded for each ambiguity. Known baseline length information is used to evaluate the correctness of the integer ambiguities in the set of alternative solutions, and the optimal alternative solution is determined, thereby effectively improving the success rate of integer ambiguity resolution.

[0048] The traditional LAMBDA method selects only two sets of optimal and suboptimal alternative solutions. In dynamic and complex environments, this method may not cover the entire set of correct integer ambiguity solutions, leading to integer ambiguity resolution failure. This method not only expands the search range but also utilizes known baseline length information to assess the correctness of integer ambiguities, significantly improving the success rate of integer ambiguity resolution. This method has significant potential for high-precision satellite positioning or direction-finding applications with known baseline constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 Flowchart of the partial integer ambiguity resolution method with additional known baseline constraints. DETAILED DESCRIPTION

[0051] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0052] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0053] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0054] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0055] The present invention is described in detail below with reference to specific embodiments. Specific embodiment one:

[0057] according to Figure 1As shown, the specific optimization technical solution adopted by the present invention to solve the above technical problems is: the present invention relates to a partial integer ambiguity resolution method with additional known baseline constraints.

[0058] A partial integer ambiguity resolution method with additional known baseline constraints, comprising the following steps:

[0059] Step 1: Determine the altitude and azimuth of all visible satellites based on the satellite ephemeris file and the user's approximate position;

[0060] The step 1 is specifically as follows:

[0061] The position of each Beidou satellite is calculated using the Beidou satellite ephemeris file as r s , use the single point positioning algorithm to get the user's approximate location r r , get the station star projection vector e r s for:

[0062]

[0063] Among them, * represents the norm; then the altitude angle of each satellite and azimuth It can be expressed as:

[0064]

[0065]

[0066]

[0067] Among them, E r It represents the transformation matrix from the Earth-centered Earth-fixed coordinate system to the local coordinate system; arctan(*) represents the inverse tangent operation; arcsin(*) represents the inverse sine operation.

[0068] Step 2: Based on the elevation and azimuth information of all visible satellites, determine the optimal satellite selection strategy according to the user's pre-set cutoff elevation and the number of satellites to be selected, and determine the column vector z of the subset of integer ambiguities to be fixed n ;

[0069] In step 2, the optimal star selection strategy is determined based on the principle of uniform distribution of satellites in the starry sky view and the geometric distribution factor. If the total number of visible satellites is less than the preset number of selected satellites, the star selection strategy is not implemented. Instead, all visible satellites are directly used in subsequent solutions. The minimum number of visible satellites is 4.

[0070] Step 3: Use pseudorange and carrier phase observations to build a geometric correlation model;

[0071] The step 3 is specifically as follows:

[0072] The geometric correlation model is constructed using pseudorange and carrier phase observations.

[0073] E(y)=Hb+Fa+Bz, D(y)=Q yy

[0074] Where E(*) represents the expectation of the random variable; D(*) represents the variance of the random variable; y = [p T ,φ T ] T It represents the residual of the double-difference pseudorange observation p and the carrier phase observation φ, and the corresponding observation variance-covariance is expressed as Q yy b represents the geometric baseline vector, and the corresponding design matrix is ​​H; a represents the integer ambiguity subset that remains in a floating-point state, and the corresponding design matrix is ​​F; z represents the integer ambiguity subset to be fixed, and the corresponding design matrix is ​​B;

[0075] Using the least squares estimation method, the geometric baseline floating point solution column vector is obtained and the corresponding variance-covariance And the integer ambiguity fixed subset floating point solution column vector and the corresponding variance-covariance The variance-covariance between the geometric baseline and the integer ambiguity subset to be fixed is expressed as

[0076] All integer ambiguities in the model are divided into two parts: the first part is the integer ambiguity subset that remains in a floating state, and the other part is the integer ambiguity subset to be fixed;

[0077] Step 4: Substitute the floating-point solution of the integer ambiguity subset to be fixed and the corresponding variance-covariance into the LAMBDA algorithm to obtain the optimal candidate solution column vector of the corresponding integer ambiguity subset to be fixed;

[0078] The LAMBDA (Least-squares AM Biguity Decorrelation Adjustment, LAMBDA) algorithm only needs to output one set of optimal alternative solutions, rather than the traditional algorithm which requires the output of two sets of alternative solutions, the optimal and the suboptimal.

[0079] Step 5: Convert the column vector Each fuzziness element j∈[1,n], j is an integer, as a benchmark, expand ±m weeks to obtain the possible candidate set for the ambiguity element i∈[-mm], i is an integer, and the alternative sets of all fuzzy elements are arranged and combined to form (2m+1) nSet of candidate solution vectors for the subset of integer ambiguities to be fixed k∈[1,(2m+1) n ], k is an integer;

[0080] The selection of the m value in step 5 will be predetermined based on the application dynamic scenario, observation quality, model error propagation characteristics, and computational efficiency factors.

[0081] Step 6: Using (2m+1) n The candidate solution vector of the subset of integer ambiguities to be fixed Get the geometric baseline fixed solution column vector corresponding to different alternative solutions

[0082] Step 7: Traverse (2m+1) n Group alternative solution column vector Calculate the geometric baseline solution according to step 6, and calculate the baseline length residual with the known baseline length. The optimal candidate solution column vector with the baseline length residual value not exceeding the fixed monitoring threshold and the smallest ambiguity residual is selected. As the final integer ambiguity fixed solution.

[0083] The step 7 is specifically as follows:

[0084] Optimal candidate solution vector Calculated by the following formula:

[0085]

[0086]

[0087] Among them, argmin(*) represents the variable value when the cost function reaches the minimum value, and |*| represents the absolute value; (*) T Indicates vector transpose; (*) -1 Indicates vector inversion; b 0 Indicates the known baseline length, T h Indicates the monitoring threshold, All index values ​​monitored to meet the monitoring threshold.

[0088] T h The selection of the value will be predetermined based on the application dynamic scenario, the quality of the observations, and the error propagation characteristics of the model.

[0089] When the integer ambiguity is correctly fixed, the residual error between the geometric baseline estimate and the known baseline length is generally no more than 1 cm, so the monitoring threshold T is set. h When the carrier is in a dynamic and complex environment and the observation quality is poor, T h Relax to 2cm.

[0090] The purpose of the present invention is to effectively improve the success rate of integer ambiguity fixation in satellite high-precision positioning or direction-finding application scenarios with known baseline constraints, and to provide a partial integer ambiguity resolution method with additional known baseline constraints. The present invention uses the optimal satellite selection strategy to retain the best number of available satellites, thereby determining the subset of integer ambiguities to be fixed, reducing the computational burden of searching all integer ambiguities to a certain extent. Then, a geometric correlation model is constructed using pseudorange and phase double differences. The floating-point solution and corresponding covariance of the subset of integer ambiguities to be fixed are obtained through the optimal adjustment estimation theory. The search benchmark for the subset of ambiguities to be fixed is obtained through the LAMBDA algorithm. Then, the specified search range is expanded for each ambiguity. The known baseline length information is used to evaluate the correctness of the integer ambiguity in the set of alternative solutions, and the optimal alternative solution is determined, thereby effectively improving the success rate of integer ambiguity resolution.

[0091] The present invention provides a partial integer ambiguity resolution system with additional known baseline constraints, the system comprising:

[0092] A data processing module, wherein the data processing module determines the elevation angles and azimuth angles of all visible satellites based on the satellite ephemeris file and the user's approximate position;

[0093] The strategy decision module determines the optimal satellite selection strategy based on the elevation and azimuth information of all visible satellites, the cutoff elevation and the number of selected satellites set by the user, and determines the column vector z of the subset of integer ambiguities to be fixed. n ;

[0094] A model building module, wherein the model building module uses pseudorange and carrier phase observations to build a geometric correlation model;

[0095] An integer ambiguity resolution module that feeds the floating-point solution and corresponding variance-covariance of the integer ambiguity subset to be fixed into the LAMBDA algorithm to obtain the optimal candidate solution column vector for the corresponding integer ambiguity subset to be fixed, thereby improving the success rate of integer ambiguity resolution.

[0096] The present invention provides a computer-readable storage medium having a computer program stored thereon. The program is executed by a processor to implement a partial integer ambiguity resolution method with additional known baseline constraints.

[0097] The present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a partial integer ambiguity resolution method with additional known baseline constraints is implemented. Specific embodiment two:

[0099] The difference between the second embodiment of the present application and the first embodiment is that:

[0100] A partial integer ambiguity resolution method with additional known baseline constraints is implemented using Beidou direction finding technology based on a known baseline length. The specific steps are as follows:

[0101] S1 uses the BeiDou satellite ephemeris file and the user's approximate position to calculate the elevation and azimuth angles of all visible satellites.

[0102] The position of each Beidou satellite is calculated using the Beidou satellite ephemeris file as r s , use the single point positioning algorithm to get the user's approximate location r r , get the station star projection vector for:

[0103]

[0104] Where * represents the norm; then the altitude angle of each satellite and azimuth It can be expressed as:

[0105]

[0106]

[0107]

[0108] Where E r It represents the transformation matrix from the Earth-centered Earth-fixed coordinate system to the local coordinate system; arctan(*) represents the inverse tangent operation; arcsin(*) represents the inverse sine operation.

[0109] S2 uses the elevation and azimuth information of all visible satellites to determine the optimal satellite selection strategy based on the user's pre-set cutoff elevation and the number of selected satellites, and determines the column vector z of the subset of ambiguities to be fixed for the entire cycle n , where n is the number of elements in the subset;

[0110] In this step, a cutoff height of 20° is set to prevent low-altitude observations from being susceptible to multipath interference. Six satellites are selected to ensure the model has a certain degree of redundancy and can identify faulty satellites. The six-satellite selection strategy is determined based on the principle of uniform satellite distribution within the sky view and the geometrical dilution of precision (GDOP) as a metric. First, the satellite with the highest elevation angle is selected as the first satellite. The remaining satellites are then divided into groups with elevation angles ranging from 20° to 40°, 40° to 70°, and 70° to 90°. If there are more than three satellites in the 20° to 40° elevation angle range, the system sorts them by azimuth from smallest to largest, selecting three satellites with evenly distributed azimuth angles. If there are fewer than three, the number is i (i < 3), and all are selected. The remaining 5-i satellites are selected from other ranges. If there are more than 5-i satellites in the 40° to 70° elevation angle range, the system sorts them by azimuth from smallest to largest, selecting 5-i satellites with evenly distributed azimuth angles. If there are fewer than 5-i satellites, the number is j (j < 5-i), and all are selected. The remaining satellites between 70° and 90° are selected based on evenly distributed azimuth angles. If there are fewer than six satellites, the system randomly selects from other ranges to make up the total number of six. If the total number of visible satellites is less than the preset number of satellites to be selected, the selection strategy is not implemented, and all visible satellites are directly used in the subsequent solution. The minimum number of visible satellites is 4. This embodiment is designed for single-frequency observations, so n is set to 6.

[0111] S3 uses pseudorange and carrier phase observations to build a geometric correlation model.

[0112] E(y)=Hb+Fa+Bz, D(y)=Q yy (5)

[0113] Where E(*) represents the expectation of the random variable; D(*) represents the variance of the random variable; y = [p T ,φ T ] T It represents the residual of the double-difference pseudorange observation p and the carrier phase observation φ, and the corresponding observation variance-covariance is expressed as Q yy ; b represents the geometric baseline vector, and the corresponding design matrix is ​​H; a represents the integer ambiguity subset that remains in a floating-point state, and the corresponding design matrix is ​​F; z represents the integer ambiguity subset to be fixed, and the corresponding design matrix is ​​B.

[0114] Based on the formula, the least squares estimation method is used to solve the geometric baseline floating point solution column vector and the corresponding variance-covariance And the integer ambiguity fixed subset floating point solution column vector and the corresponding variance-covariance The variance-covariance between the geometric baseline and the integer ambiguity subset to be fixed is expressed as

[0115] S4 brings the floating-point solution of the integer ambiguity subset to be fixed and the corresponding variance-covariance into the LAMBDA (Least-squares AM Biguity Decorrelation Adjustment, LAMBDA) algorithm to obtain the optimal candidate solution column vector of the corresponding integer ambiguity subset to be fixed

[0116] S5 will column vector Each fuzziness element (j∈[1,n], j is an integer) as a benchmark, expand ±m weeks to obtain the possible candidate set for the ambiguity element (i∈[-m,m], i is an integer). Then all possible candidate sets of fuzzy elements are arranged and combined to form (2m+1) n Set of candidate solution vectors for the subset of integer ambiguities to be fixed (k∈[1,(2m+1) n ], k is an integer);

[0117] In this step, considering that the pseudorange observation accuracy is approximately 1 meter and the phase wavelength is approximately 0.2 cm, m is set to 5 cycles, resulting in 1,771,561 alternative solutions. If the carrier is in a dynamic and complex environment and the observation quality is poor, the value of m can be appropriately relaxed, which will exponentially increase the number of alternative solutions.

[0118] S6 uses the above (2m+1) n The candidate solution vector of the subset of integer ambiguities to be fixed Get the geometric baseline fixed solution column vector corresponding to different alternative solutions

[0119] S7 traversal (2m+1) n Group alternative solution column vector Use S6 to calculate the geometric baseline solution and calculate the baseline length residual with the known baseline length. The optimal candidate solution column vector with the baseline length residual value not exceeding the fixed monitoring threshold and the smallest ambiguity residual is selected. As the final integer ambiguity fixation solution. If there is no optimal candidate column vector that satisfies the formula, it is determined that the integer ambiguity fixation has failed.

[0120]

[0121] In the formula, argmin(*) represents the variable value when the cost function reaches the minimum value. |*| represents the absolute value; (*)T Indicates vector transpose; (*) -1 Indicates vector inversion; b 0 Indicates the known baseline length. T h Indicates the monitoring threshold. All index values ​​monitored to meet the monitoring threshold. is the optimal alternative solution to be determined.

[0122] In this step, if the integer ambiguity is correctly fixed, the residual error between the geometric baseline estimate and the known baseline length is generally no more than 1 cm, so the monitoring threshold T is set. h The maximum value is 1 cm. If the carrier is in a dynamic and complex environment and the observation quality is poor, it can be relaxed to 2 cm.

[0123] The present invention belongs to the field of satellite navigation technology and relates to a method for resolving partial integer ambiguities with additional known baseline constraints. The method can be used in high-precision satellite positioning or direction-finding applications with known baseline constraints, effectively improving the success rate of integer ambiguity resolution. The present invention utilizes the optimal satellite selection strategy to retain the best number of available satellites, thereby determining a subset of integer ambiguities to be fixed, reducing the computational burden of searching all integer ambiguities to a certain extent. A geometric correlation model is then constructed using pseudorange and phase double differences. The floating-point solution and corresponding covariance of the subset of integer ambiguities to be fixed are obtained using the optimal adjustment estimation theory. The search benchmark for the subset of ambiguities to be fixed is obtained using the LAMBDA algorithm. The specified search range is then expanded for each ambiguity, and the correctness of the integer ambiguities in the set of alternative solutions is evaluated using the known baseline length constraint information, ultimately determining the optimal alternative solution. The traditional LAMBDA method only selects two sets of optimal and suboptimal alternative solutions. In dynamic and complex environments, it may not cover the correct set of integer ambiguity solutions, resulting in the failure of integer ambiguity resolution. The present invention not only expands the search range, but also uses the known baseline length information to evaluate the accuracy of the integer ambiguity resolution, which can greatly improve the success rate of integer ambiguity resolution. It has important development potential in satellite high-precision positioning or direction-finding application scenarios with known baseline constraints.

[0124] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in an appropriate manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples, unless otherwise clearly defined. In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, features defined as "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, "N" means at least two, such as two, three, etc., unless otherwise clearly defined. Any process or method description in a flowchart or otherwise described herein can be understood to represent a module, segment, or portion of code comprising one or more executable instructions for implementing a custom logic function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may be performed in a different order than shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which the embodiments of the present invention pertain. The logic and / or steps shown in a flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logic function, and can be embodied in any computer-readable medium for use by an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device), or for use in conjunction with such instruction execution systems, apparatuses, or devices. For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transmit a program for use by an instruction execution system, apparatus, or device, or in conjunction with such instruction execution systems, apparatuses, or devices. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection having one or N wirings (electronic devices), a portable computer disk cartridge (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and portable compact disc read-only memory (CDROM).In addition, the computer-readable medium may even be paper or other suitable medium on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, then editing, interpreting, or processing in other suitable ways as necessary, and then storing it in a computer memory. It should be understood that the various parts of the present invention can be implemented with hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented with software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented with hardware, as in another embodiment, any one of the following technologies known in the art or their combination can be used to implement: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0125] The above description is merely a preferred embodiment of a partial integer ambiguity resolution method with a known baseline constraint. The scope of protection for a partial integer ambiguity resolution method with a known baseline constraint is not limited to the aforementioned embodiment. All technical solutions based on this concept fall within the scope of protection of the present invention. It should be noted that improvements and variations that do not depart from the principles of the present invention, as readily apparent to those skilled in the art, should also be considered within the scope of protection of the present invention.

Claims

1. A partial integer ambiguity resolution method with additional known baseline constraints, characterized by: The method comprises the following steps: Step 1: Determine the altitude and azimuth of all visible satellites based on the satellite ephemeris file and the user's approximate position; Step 2: Based on the elevation and azimuth information of all visible satellites, determine the optimal satellite selection strategy according to the user's pre-set cutoff elevation and the number of satellites to be selected, and determine the column vector z of the subset of integer ambiguities to be fixed n ; Step 3: Use pseudorange and carrier phase observations to build a geometric correlation model; Step 4: Substitute the floating-point solution of the integer ambiguity subset to be fixed and the corresponding variance-covariance into the LAMBDA algorithm to obtain the optimal candidate solution column vector of the corresponding integer ambiguity subset to be fixed; Step 5: Convert the column vector Each fuzziness element j is an integer, which is used as a benchmark to expand ±m weeks to obtain the possible candidate set for the ambiguity element. i is an integer, and all the candidate sets of ambiguity elements are arranged and combined to form (2m+1) n Set of candidate solution vectors for the subset of integer ambiguities to be fixed k is an integer; Step 6: Utilize (2m+1) n The candidate solution vector of the subset of integer ambiguities to be fixed Get the geometric baseline fixed solution column vector corresponding to different alternative solutions Floating point solution column vector for the geometric baseline is the variance-covariance between the geometric baseline and the subset of integer ambiguities to be fixed, is the float solution column vector of the integer ambiguity subset to be fixed, is the corresponding variance-covariance; Step 7: Traverse (2m+1) n Group alternative solution column vector Calculate the geometric baseline solution according to step 6, and calculate the baseline length residual with the known baseline length. The optimal candidate solution column vector with the baseline length residual value not exceeding the fixed monitoring threshold and the smallest ambiguity residual is selected. As the final integer ambiguity fixed solution.

2. The method according to claim 1, wherein: The step 1 is specifically as follows: The position of each Beidou satellite is calculated using the Beidou satellite ephemeris file as r s , use the single point positioning algorithm to get the user's approximate location r r , get the station star projection vector for: Among them, ||*|| represents the norm; then the altitude angle of each satellite and azimuth It can be expressed as: Among them, E r It represents the transformation matrix from the Earth-centered Earth-fixed coordinate system to the local coordinate system; arctan(*) represents the inverse tangent operation; arcsin(*) represents the inverse sine operation.

3. The method according to claim 2, wherein: In step 2, the optimal star selection strategy is determined based on the principle of uniform distribution of satellites in the starry sky view and the geometric distribution factor. If the total number of visible satellites is less than the preset number of selected satellites, the star selection strategy is not implemented. Instead, all visible satellites are directly used in subsequent solutions. The minimum number of visible satellites is 4.

4. The method according to claim 3, wherein: The step 3 is specifically as follows: The geometric correlation model is constructed using pseudorange and carrier phase observations. E(y)=Hb+Fa+Bz,D(y)=Q yy Where E(*) represents the expectation of the random variable; D(*) represents the variance of the random variable; y = [p T ,φ T ] T It represents the residual of the double-difference pseudorange observation p and the carrier phase observation φ, and the corresponding observation variance-covariance is expressed as Q yy b represents the geometric baseline vector, and the corresponding design matrix is ​​H; a represents the integer ambiguity subset that remains in a floating-point state, and the corresponding design matrix is ​​F; z represents the integer ambiguity subset to be fixed, and the corresponding design matrix is ​​B; Using the least squares estimation method, the geometric baseline floating point solution column vector is obtained and the corresponding variance-covariance And the integer ambiguity fixed subset floating point solution column vector and the corresponding variance-covariance The variance-covariance between the geometric baseline and the integer ambiguity subset to be fixed is expressed as 5. The method according to claim 4, wherein: The step 7 is specifically as follows: Optimal candidate solution vector Calculated by the following formula: Among them, arg min (*) represents the variable value when the cost function reaches the minimum value, and |*| represents the absolute value; (*) T Indicates vector transpose; (*) -1 Indicates vector inversion; b 0 Indicates the known baseline length, T h Indicates the monitoring threshold, All index values ​​monitored to meet the monitoring threshold.

6. The method according to claim 5, wherein: When the integer ambiguity is correctly fixed, the residual difference between the geometric baseline estimate and the known baseline length does not exceed 1 cm, so the monitoring threshold T is set h When the carrier is in a dynamic and complex environment and the observation quality is poor, T h Relax to 2cm.

7. The method according to claim 6, wherein: The selection of the m value in step 5 will be predetermined based on the application dynamic scenario, observation quality, model error propagation characteristics, and computational efficiency factors.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the method according to any one of claims 1 to 7.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

Images