A precise orientation method based on Beidou PPP-B2b signal and rigid array self-calibration

Abstract

The application belongs to the technical field of satellite navigation and attitude measurement, and specifically discloses a precise orientation method based on Beidou PPP-B2b signals and rigid array self-calibration.The method uses a main antenna to receive Beidou PPP-B2b satellite-based precise correction information to obtain absolute position and speed prior, uses a three-antenna rigid array to construct a double-difference observation model, and introduces baseline length constraints, baseline closure constraints and online self-calibration constraints to sequentially complete multi-baseline integer ambiguity solution, consistency checking, heading installation angle recursive correction and carrier heading angle calculation.The application can output pitch angle, roll angle and length residual, closure difference and temperature information corresponding to the orientation result, has the advantages of not depending on ground RTK base stations, clear implementation process, stable orientation result and strong long-term use precision maintaining capability, and is especially suitable for scenes such as unmanned systems, engineering machinery, ships and orientation platforms.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and attitude measurement technology, and specifically relates to a precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration. Background Technology

[0002] Currently, high-precision orientation mainly employs the GNSS multi-antenna carrier phase technology approach. International research has widely adopted dual-antenna or triple-antenna structures, using short-baseline double-difference carrier phase to calculate the baseline vector between antennas, and then inverting the vehicle's heading, pitch, and roll angles from the baseline vectors. This method has advantages such as independence from magnetic fields and good long-term stability; however, existing engineering solutions often rely on GPS or multi-GNSS joint calculations and frequently require ground-based RTK corrections or strong inertial navigation assistance.

[0003] With the rapid development of the BeiDou-3 system, especially the formation of the BeiDou PPP-B2b satellite-based precision correction service, domestic BeiDou orientation technology has made it possible for terminals to obtain high-precision absolute positions without relying on ground RTK base stations, providing new technical conditions for independent orientation using a single BeiDou system. Current domestic research mainly focuses on dual-antenna heading measurement, short baseline ambiguity fixing, and BeiDou / inertial navigation fusion. However, existing technologies still have the following problems: Independent high-precision orientation methods are not yet mature enough for single BeiDou systems without ground-based RTK base stations. Existing methods often treat the antenna array as an ideal rigid body, failing to adequately compensate for baseline geometric deviations caused by temperature changes, minor deformations of the support structure, and installation errors. While many methods can output heading results, they lack stable orientation procedures and implementation steps suitable for engineering applications.

[0004] In summary, existing BeiDou / GNSS orientation methods suffer from the following main problems in engineering implementation: they are highly dependent on external differential sources, making it difficult to fully utilize the BeiDou system's own satellite-based precision correction capabilities in the absence of ground-based RTK base stations; and the antenna array's actual baseline length and geometric relationship deviate from nominal values ​​due to temperature, vibration, and mechanical stress during long-term use, thus affecting orientation accuracy. Therefore, it is necessary to propose a precision orientation method for BeiDou PPP-B2b signals that can be implemented independently and has strong engineering operability.

[0005] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art. Summary of the Invention

[0006] The purpose of this invention is to propose a precision orientation method based on BeiDou PPP-B2b signal and rigid array self-calibration. This method utilizes the three-antenna rigid body installation to form a stable array geometry, and achieves high-precision solution of the carrier heading angle and related attitude information through multi-antenna carrier phase observation, short baseline calculation, array parameter calibration and baseline constraint combined.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A precise orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration includes the following steps: Step 1. Complete the installation of the three-antenna rigid antenna array and calibrate the initial array geometry parameters; Step 2. Based on the initial array geometry parameters, establish a temperature compensation model for the lengths of the three baselines; Step 3. Synchronously acquire the BeiDou carrier phase, pseudorange, PPP-B2b satellite-based precision correction information received by the main antenna, and array temperature information from the three antennas, and perform time alignment to form an effective satellite observation set; Step 4. Based on the effective satellite observation set of the main antenna, PPP-B2b correction information and temperature information at the same moment, perform PPP precise position calculation and state estimation of the main antenna to obtain the absolute position and velocity of the main antenna as the geometric prior of the main antenna; Step 5. Based on the array geometric parameter calibration results, the effective satellite observation set and the geometric prior of the main antenna, first take the main antenna A0 as the reference antenna, and establish double-difference observation models based on the two directional baselines A0-A1 and A0-A2 respectively; The baseline length parameter after temperature compensation in step 2 is introduced into the double-difference observation model as a baseline length constraint, and further baseline closure constraints between the three baselines are introduced based on the geometric relationship of the rigid body array, thereby constructing a joint orientation model; Step 6. Based on the joint orientation model, use multi-baseline joint solution and rigid body consistency check to perform unified solution on the three baselines A0-A1, A0-A2 and A1-A2, and select the baseline results of high confidence epochs; Step 7. Based on the baseline results of the high-confidence epochs selected in Step 6, online self-calibration updates are performed on the array baseline length parameters and heading installation angle parameters using a combination of sliding window statistics and recursive updates. Step 8. Based on the valid main orientation baseline vector confirmed in Step 6, calculate the vehicle heading angle and optional extended attitude angle;

[0008] Step 9. Output the orientation results and the quality information corresponding to the current orientation results.

[0009] The present invention has the following advantages: 1. The present invention forms a complete processing chain from array calibration, temperature compensation, synchronous observation preprocessing, PPP prior construction, multi-baseline joint orientation, online self-calibration to result output by following the processing sequence of steps 1 to 9. The input and output relationships of each step are clear and the parameter calling relationships are clear, so it is easy to form an engineering implementation scheme that can be directly deployed.

[0010] 2. In step 2, the present invention pre-establishes a baseline length temperature compensation model, aligns the temperature information with the GNSS epoch in step 3, and calls the baseline length parameters compensated by the temperature compensation model in step 2 in real time in steps 5 and 6. Therefore, it can reduce the influence of temperature changes on the geometric relationship of non-collinear rigid body antenna arrays, effectively avoid the length constraint mismatch caused by thermal expansion and contraction of the support, and thus improve the consistency of multi-baseline solution and long-term operational stability.

[0011] 3. In step 4, this invention uses the BeiDou PPP-B2b satellite-based precise correction information received by the main antenna to perform precise PPP position calculation and state estimation of the main antenna, providing a unified absolute position and velocity prior for subsequent dual-difference orientation. Therefore, single BeiDou precise orientation can be achieved without relying on ground RTK base stations, expanding the applicability of the system under ground-less differential conditions.

[0012] 4. In step 5, the present invention jointly models the double-difference observation model with the three baseline length constraints and baseline closure constraints, and in step 6, performs unified integer ambiguity solving and consistency verification on the main orientation baseline, the lateral check baseline and the closed baseline. Therefore, it not only utilizes the orientation information of the main baseline, but also utilizes the geometric redundancy relationship between the lateral check baseline and the closed baseline to cross-validate the fixed results, thereby improving the reliability of performance heading calculation and the ability to identify incorrect fixed points.

[0013] 5. In step 7, this invention constructs a calibration window only for high-confidence epochs and uses methods such as sliding window statistics, recursive least squares estimation, single correction amount limiting, and continuous over-limit freezing of closure error to update the baseline length additional deviation and heading installation angle correction in a controlled manner. This suppresses the cumulative effects of long-term thermal deformation, installation loosening, and minor mechanical drift on the orientation results without destroying the basic geometric relationship of the array, thereby improving the orientation stability and repeatability of the array during long-term use.

[0014] 6. In step 8, this invention not only solves the vehicle heading angle based on the fixed vector of the main baseline, but also constructs the vehicle coordinate axis by combining the lateral check baseline and lateral sign parameters, and then solves the pitch angle and roll angle as needed; at the same time, in step 9, the heading angle, extended attitude angle, closure error, length residual, temperature and result quality information are output in a unified manner. Therefore, it can output both the core orientation value and the quality information directly corresponding to the result, which is convenient for engineering monitoring, result verification and subsequent traceability. Attached Figure Description

[0015] Figure 1 This is a structural block diagram of the precision orientation system based on BeiDou PPP-B2b signal and rigid body array self-calibration in this invention; Figure 2 This is a diagram showing the geometric arrangement of the three antennas on the carrier in this invention; Figure 3 This is a flowchart of the precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration in this invention; Figure 4 This is a flowchart of the multi-baseline integer ambiguity solution and consistency verification process in this invention; Figure 5 This is a schematic diagram of the online correction process of array geometric parameters under high-confidence epoch conditions in this invention. Detailed Implementation

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment 1 describes a precise orientation method based on BeiDou PPP-B2b signals and rigid array self-calibration. This method utilizes the BeiDou Navigation Satellite System PPP-B2b precise single-point positioning correction signal, three-antenna rigid array observations, and online self-calibration constraints of the array for precise orientation. First, in step 1, the three-antenna rigid antenna array is installed, and initial geometric parameters such as the lengths of the three baselines, the initial heading angle of the main baseline, the lateral sign definition of the lateral check baseline, and the reference temperature are calibrated. Then, in step 2, a temperature compensation model is established to adapt the lengths of the three baselines to temperature variations, allowing subsequent epochs to use the temperature-compensated baseline length parameters as length constraints. In step 3, the BeiDou carrier phase, pseudorange, PPP-B2b satellite-based precise correction information received by the main antenna, and array temperature information are simultaneously acquired from the three antennas. Time alignment, cycle slip detection, and abnormal observation removal are performed in the same step, forming an effective observation set that can be used for subsequent orientation processing. After the observation data preparation is completed, step 4 performs precise PPP position calculation and state estimation of the main antenna based on the BeiDou PPP-B2b correction information received by the main antenna A0, obtaining the absolute position and velocity of the main antenna. The absolute position of the main antenna is used for the unified satellite geometry calculation and line-of-sight direction determination in step 5, while the velocity direction of the main antenna serves as a coarse prior for the subsequent main baseline fixing results and heading result rationality verification. Subsequently, step 5 uses A0 as the reference antenna to establish double-difference observation models for A0-A1 and A0-A2 respectively, and introduces the temperature-compensated baseline length parameter obtained in step 2 into the double-difference observation model as a baseline length constraint. Simultaneously, the rigid body array closure relationship between the three baselines is introduced into the double-difference observation model as a baseline closure constraint, thereby constructing a joint orientation model. Based on the joint orientation model, step 6 performs unified multi-baseline integer ambiguity solving and consistency verification on the main orientation baseline A0-A1, the lateral verification baseline A0-A2, and the closed baseline A1-A2, and combines the baseline length constraint and baseline closure constraint to determine whether the current epoch calculation result is reliable. Step 7 only uses the current epoch as a high-confidence epoch if the preset conditions in step 6 are met, and then performs online self-calibration updates on the array baseline length parameters and heading installation angle parameters. The updated parameters are then fed back to steps 5 and 6 in subsequent epochs, used to construct length constraints and perform consistency checks, respectively. Finally, step 8 calculates the carrier heading angle and optional extended attitude angle based on the valid main orientation baseline vector confirmed in step 6, and step 9 outputs the orientation results and the corresponding mass information.

[0017] Before formally introducing the method of this invention, the precision orientation system based on BeiDou PPP-B2b signal and rigid array self-calibration corresponding to the method of this invention will be specifically described, and its overall structure is as follows: Figure 1 As shown.

[0018] The precision orientation system described in this invention includes at least a main antenna A0, a first slave antenna A1, a second slave antenna A2, a Beidou multi-channel receiver, a processing unit, a temperature sensor, and a storage unit.

[0019] The main antenna A0, the first slave antenna A1, and the second slave antenna A2 constitute a non-collinear rigid body antenna array.

[0020] The BeiDou multi-channel receiver is used to synchronously acquire BeiDou observation data output from the main antenna A0, the first slave antenna A1, and the second slave antenna A2, and to receive BeiDou PPP-B2b satellite correction information.

[0021] Temperature sensors are used to collect temperature information at relevant locations on the support frame of a non-collinear rigid antenna array.

[0022] The storage unit is used to store the array's initial calibration parameters, temperature compensation parameters, and online self-calibration update parameters.

[0023] The processing unit is connected to the BeiDou multi-channel receiver, temperature sensor, and storage unit, respectively.

[0024] The processing unit is the core part of the precision orientation system of the present invention. It is used to perform observation data preprocessing, main antenna PPP precision position calculation and state estimation based on Beidou PPP-B2b correction, multi-baseline joint orientation calculation, multi-baseline integer ambiguity solution and consistency verification, online self-calibration, and orientation result and quality information output.

[0025] like Figure 2 As shown, the main antenna A0 and the first slave antenna A1 form a main directional baseline. Specifically, the distance between the main antenna A0 and the first slave antenna A1 is 0.6 m to 1.5 m, preferably 0.8 m, to form the main directional baseline.

[0026] The main antenna A0 and the second slave antenna A2 form a lateral verification baseline. Specifically, the distance between the main antenna A0 and the second slave antenna A2 is 0.3 m to 1.0 m, preferably 0.55 m, to form a lateral verification baseline.

[0027] The first slave antenna A1 and the second slave antenna A2 form a closed verification baseline.

[0028] In this embodiment, the main antenna A0, the first slave antenna A1, and the second slave antenna A2 are fixedly mounted on the same rigid body support to ensure the stability of the geometric relationship of the non-collinear rigid body antenna array.

[0029] Since the rigid support is not the focus of this application, the present invention does not impose specific structural limitations on the structure.

[0030] Temperature sensors are installed at critical stress points on the rigid support or near the main orientation baseline connection point, such as... Figure 2 As shown, this temperature sensor is used to reflect the structural temperature changes of a non-collinear rigid body antenna array.

[0031] After the installation of the non-collinear rigid body antenna array is completed, the initial geometric parameters of the non-collinear rigid body antenna array are obtained through static calibration, which serve as the initial basis for subsequent temperature compensation and online self-calibration.

[0032] The initial geometric parameters include at least the lengths of three baselines (main orientation baseline, lateral check baseline, and closed check baseline), the initial heading installation angle of the main baseline, the lateral sign parameter of the lateral check baseline, and the reference temperature.

[0033] The following is a detailed implementation process of the precision orientation method based on BeiDou PPP-B2b signal and rigid array self-calibration according to the present invention, such as... Figure 3 As shown. In this section, for ease of explanation and understanding, the following definitions are used: The main antenna is denoted as A0, the first slave antenna as A1, and the second slave antenna as A2; the baseline vector from A0 to A1 is denoted as... The baseline vector pointing from A0 to A2 is denoted as... The baseline vector pointing from A1 to A2 is denoted as... .

[0034] Baseline vector , as well as The corresponding nominal baseline lengths are denoted as follows: , and The baseline length parameters after temperature compensation are denoted as follows: , and .

[0035] in Given the current temperature of the rigid body support, The initial calibration temperature is set. The main baselines A0-A1 are used for heading output, the check baselines A0-A2 are used for result verification and attitude-aided calculation, and the closed baselines A1-A2 are used for array rigid body closure verification.

[0036] In this invention, the heading angle refers to the final output heading angle of the carrier. Initial heading installation angle refers to The heading installation angle correction refers to... Total heading angle refers to .

[0037] Both velocity and heading angle refer to the velocity prior given in step 4. This is only used in step 7 to construct the heading installation angle observation and is not used as the final output heading angle. The carrier coordinate system, rigidly connected to the carrier, is defined as follows: .

[0038] origin A carrier mounting reference point is set at the phase center of the main antenna A0 or fixed to A0 and remains unchanged throughout the entire process. The axis is defined as the forward direction of the carrier. The axis is defined as the rightward direction of the carrier. The axis is defined as the upward axis of the carrier, and the three axes satisfy the right-hand coordinate system relationship.

[0039] This carrier coordinate system facilitates the unification of array installation geometry and the physical meaning of heading output.

[0040] When A0-A1 is defined as the primary orientation baseline, it is preferable to make The nominal direction is positively correlated with the carrier coordinate system. The axis is consistent and relative to it. The initial heading installation angle is denoted as .

[0041] When A0-A2 is defined as the lateral check baseline, it is preferable to make The nominal direction is positively correlated with the carrier coordinate system. The axis is consistent, and its lateral sign parameter (i.e., the lateral sign parameter of the lateral check baseline) is denoted as... .

[0042] If installation constraints cause A0-A2 to actually point to the left of the carrier, then in step 1, it should be clearly stated that... And this symbol definition remains unchanged in subsequent attitude calculations and heading angle corrections.

[0043] In subsequent epochs, whenever length constraints are involved, the initial array geometric parameter calibration results obtained in step 1 are called; whenever a joint orientation model is involved, the effective satellite observation set and the primary antenna prior information output in steps 3 and 4 are called.

[0044] like Figure 3 As shown, the precise orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration includes the following steps: Step 1. Complete the installation of the three-antenna rigid body antenna array and calibrate the initial array geometry parameters.

[0045] Step 1 first employs a three-antenna rigid body antenna array installation and static calibration method. To address the issues of unclear geometric relationships in multi-antenna arrays and the lack of reliable priors for subsequent double-difference models, the spatial relative positional relationships of the main antenna A0, the first slave antenna A1, and the second slave antenna A2 are initialized to obtain the initial array geometric parameters.

[0046] The initial array geometry parameters include the initial baseline length parameter, the initial heading installation angle of the main baseline, the lateral sign parameter of the lateral check baseline, the antenna phase center installation deviation, and the reference temperature parameter, which can be directly called upon in subsequent steps.

[0047] Step 1.1. Installation of the three-antenna rigid body antenna array.

[0048] Install the main antenna A0 in an unobstructed position on the top of the carrier or above the platform to ensure that the main antenna A0 obtains stable and continuous BeiDou observation and PPP-B2b corrected reception conditions as much as possible.

[0049] The first slave antenna A1 is installed in the forward direction of the carrier or in the predetermined heading direction, so that A0-A1 form the main orientation baseline, which is used as the core baseline for joint solution in subsequent step 6 and outputting the heading angle in step 8.

[0050] The second slave antenna A2 is installed on the side of A0, so that A0-A2 form a lateral verification baseline for step 6 to perform multi-baseline consistency verification, and participates in the pitch angle and roll angle calculation when the attitude calculation needs to be extended in step 8.

[0051] At the same time, it is necessary to ensure that A0, A1, and A2 are fixed on the same rigid body support to avoid relative loosening, slippage, or significant elastic deformation of the array during operation; otherwise, the subsequent baseline length constraint and baseline closure constraint will lose their physical basis.

[0052] Step 1.2. Initial array geometry parameter calibration.

[0053] Measure the actual lengths of the three baselines A0-A1, A0-A2, and A1-A2, and record them as the nominal baseline lengths. , and , as the initial baseline length parameter. , and Used for length constraints, checks, and closure verification in steps 5 and 6.

[0054] Recording array relative to carrier coordinate system The installation geometry requirements should be clarified, specifying whether A0-A1 correspond to the forward direction of the carrier. Direction, and clearly define the rightward direction of the carriers corresponding to A0-A2. The direction is still left of the carrier. direction.

[0055] This invention specifies that A0-A1 correspond to A0-A2 correspond to .

[0056] Relative to the positive forward axis of the carrier, A0-A1 The initial heading installation angle is denoted as .

[0057] When A0-A1 and When strictly aligned, take the initial heading installation angle. When there is a fixed angle between the two, record the sign and value of the angle according to the heading positive direction convention adopted in step 8.

[0058] For A0-A2, record their lateral sign parameters. .

[0059] in Indicates A0-A2 correspondence direction, Indicates A0-A2 correspondence direction.

[0060] In a static, open, and unobstructed environment, BeiDou observation data was continuously collected for no less than 20 minutes using a BeiDou multi-channel receiver, and the initial baseline vector between the three antennas was calculated using high-stability observation conditions.

[0061] The static observation results are averaged to obtain the average principal orientation baseline vector. Average verification baseline vector Average closed-loop verification baseline vector and antenna phase center installation deviation. (Superscript) This indicates the northeast-central coordinate system.

[0062] Then, based on the forward axis of the carrier recorded in step 1... Right axis The installation geometry convention involves projecting the average principal orientation baseline vector and transforming it to the carrier coordinate system. Below, get And calculate the initial heading installation angle accordingly: (1) in and These are the average principal orientation baseline vectors. In the carrier coordinate system Down shaft and Axial components. Simultaneously, lateral symbol parameters are written according to the carrier coordinate system definition. The parameters were written into the storage unit as initial array geometry calibration parameters, and the ambient temperature during calibration was recorded simultaneously. This serves as the reference temperature for establishing the temperature compensation model in step 2.

[0063] The output of step 1 should include at least the initial baseline length parameter. , , Initial heading angle of the main baseline Lateral verification of baseline lateral sign parameters and reference temperature .

[0064] The above outputs will be directly used in step 2 to establish the temperature compensation model, in step 5 to establish baseline length constraints and baseline closure constraints, and in steps 7 and 8 to perform recursive updates of the heading installation angle and call the heading output.

[0065] Step 2. To address the issue that temperature changes in the stent may cause the lengths of the three baselines to drift slowly, thereby compromising the consistency of the fixation results, a baseline length temperature compensation model is established, and temperature compensation parameters are obtained.

[0066] Based on the initial array geometric parameters obtained in step 1, a temperature compensation model for the baseline length as a function of temperature is established for the three baselines A0-A1, A0-A2 and A1-A2 using static observation under multiple temperature conditions and parameter fitting.

[0067] The temperature compensation parameters corresponding to each baseline are calibrated to obtain the temperature compensation model that can be called in real time at subsequent epochs, as well as the temperature compensation parameters corresponding to the corresponding temperature compensation model.

[0068] Static short-time observations were repeatedly conducted under different ambient temperature conditions to collect sample data on the variation of three baseline lengths with temperature. Temperature compensation models for the baseline length variation with temperature were established for the three baselines A0-A1, A0-A2, and A1-A2 respectively. (2) in Indicates the current temperature Lower baseline The length after compensation, Indicates reference temperature The calibration length of the baseline is set below. This represents the primary temperature sensitivity coefficient. This represents the secondary temperature sensitivity coefficient. and .

[0069] The calibration length here is a constant of a formula after fitting formula (2). For example, if the baseline lengths at 20 degrees, 25 degrees and 32 degrees are measured, the calibration length after fitting formula (2) may be the baseline length at 18.8 degrees.

[0070] Residual analysis was performed on the fitting results to remove obvious outliers, ensuring that the established temperature compensation model reflects the true changes of the array under the influence of thermal expansion and contraction or slow material deformation, rather than occasional observation errors.

[0071] The result , and and its corresponding , Write to the storage unit and output temperature compensation parameters. , , This serves as the baseline length constraint input in the joint orientation model in step 5 and the basis for the multi-baseline consistency verification in step 6.

[0072] Step 3. Synchronous acquisition and preprocessing of observation data.

[0073] Step 3 adopts the method of "integrated synchronous acquisition and co-epoch preprocessing". To address the problem that multi-antenna precision orientation must rely on synchronous observation and quality control must be completed before the solution, GNSS observation data, PPP-B2b correction information and temperature data are uniformly acquired, aligned and filtered to obtain an effective satellite observation set.

[0074] The main antenna A0, the first slave antenna A1, and the second slave antenna A2 synchronously acquire BeiDou carrier phase observations and pseudorange observations. The main antenna A0 synchronously receives PPP-B2b satellite-based precision correction information.

[0075] In addition, the temperature sensor synchronously collects temperature values ​​from the array bracket or key installation locations. .

[0076] The processing unit matches and aligns the observations from the three antennas, PPP-B2b correction information, and temperature information according to a unified epoch time label, forming original multi-source observation records that can be matched one-to-one under the same epoch.

[0077] A Melbourne-Wubbena combination is used for cycle slip detection of carrier observations, followed by a geometric free combination for secondary cycle slip detection. Cross-checking is performed on observations at the same epoch to identify satellite signals with abrupt changes in integer ambiguity, thus completing data quality control. In this embodiment, a GNSS observation update rate of 10 Hz and a temperature observation update rate of 1 Hz are preferred.

[0078] When the update rates of the two are not synchronized, the temperature value is mapped to the GNSS epoch using nearest neighbor or interpolation methods to ensure that the temperature compensation parameters called in subsequent steps 5, 6 and 7 are consistent with the current epoch.

[0079] This invention performs strict time alignment on the frequency observations of the three antennas (A0, A1, and A2) within the same epoch, and uniformly corrects receiver channel delay, time stamp deviation, or other known hardware delays. This eliminates systematic errors caused by inconsistent sampling times or hardware delays, and forms a valid satellite observation set for the current epoch. This set includes, after filtering, valid pseudorange and carrier phase observations of different satellites for the main antenna, valid pseudorange and carrier phase observations of multiple antennas, PPP-B2b correction information, and temperature values ​​at the current array support or key installation locations. Step 3 outputs a set of valid satellite observations with a unified time stamp and complete quality control, along with quality indicators for each satellite observation.

[0080] Step 4. Calculate the precise PPP position and state of the main antenna based on the BeiDou PPP_B2b correction.

[0081] This invention uses the BeiDou PPP-B2b correction information received by the main antenna A0 to perform precise PPP position calculation and state estimation of the main antenna, and obtains the absolute position and velocity of the main antenna as the geometric prior of the main antenna.

[0082] Step 4: Based on the effective satellite observation set of the main antenna, PPP-B2b correction information, and temperature information at the same moment, to address the problem of lack of unified absolute geometric prior and unstable reference direction in multi-antenna orientation, the absolute position of A0 is estimated by using the PPP epoch-by-epoch solution method of the main antenna based on Beidou PPP-B2b correction, thus obtaining a unified spatial geometric prior.

[0083] Using A0 as the main antenna, read the real-time carrier phase and pseudorange observations after filtering in step 3. Read the PPP-B2b correction information, which includes at least real-time precise satellite orbit information and real-time precise satellite clock bias information.

[0084] Real-time precise satellite orbit information is used to correct the satellite's spatial position and participate in the geometric distance between the main antenna and the satellite. The calculations, using real-time precise satellite clock bias information, are used to correct the satellite clock bias term in the observation equations. It can also combine broadcast ephemeris, system time parameters and other auxiliary correction information to restore the precise satellite position and precise clock error of the current epoch.

[0085] The main antenna PPP observation model is established, and its pseudorange observation equation and carrier phase observation equation are as follows: (3) (4) in Main antenna to satellite pseudorange observations, This corresponds to the carrier phase observation value.

[0086] Main antenna and satellite The geometric distance between them is calculated by combining broadcast ephemeris data with real-time precise satellite orbit information provided by PPP-B2b. At the speed of light, This refers to the receiver clock bias. This is the satellite clock bias, corrected by real-time precise satellite clock bias information provided by PPP-B2b or directly given. For tropospheric delay, For ionospheric delay, and These are pseudorange and carrier hardware bias, respectively. Auxiliary corrections related to code bias, phase bias, etc., can be incorporated. and Or correct it separately during observation preprocessing. For carrier wavelength, For integer ambiguity, and These are pseudorange and carrier observation noise, respectively.

[0087] The state parameters of the main antenna PPP solution Written as: (5) in, The three-dimensional coordinates of the main antenna A0 in the geocentric coordinate system. For the total zenith delay in the troposphere, This represents the carrier ambiguity state corresponding to each visible satellite.

[0088] Based on real-time precise satellite orbit information and real-time precise satellite clock bias information, the state parameters are estimated epoch by epoch using Kalman filtering, the absolute position of the main antenna in the current epoch is calculated, and the velocity is obtained by epoch-to-epoch difference.

[0089] The output of step 4 includes the absolute position and velocity of the main antenna, which serve as the geometric prior of the main antenna.

[0090] The absolute position of the main antenna is used for the calculation of the unified satellite geometry and the determination of the line of sight in step 5, while the velocity direction of the main antenna serves as a coarse prior for the subsequent main baseline fixing result and the rationality verification of the heading result.

[0091] Step 5. Construction of multi-baseline double-difference observation model and joint modeling of rigid body constraints.

[0092] Based on the array geometric parameter calibration results, the effective satellite observation set, and the geometric prior of the main antenna, the main antenna A0 is used as the reference antenna, and a double-difference observation model is established based on the two directional baselines A0-A1 and A0-A2 respectively.

[0093] The baseline length parameter after temperature compensation in step 2 is introduced into the double-difference observation model as a baseline length constraint, and further baseline closure constraints between the three baselines are introduced based on the geometric relationship of the rigid body array, thereby constructing a joint orientation model.

[0094] Step 5, based on the initial array geometric parameter calibration results of Step 1, the baseline length parameters after temperature compensation in Step 2, the effective satellite observation set in Step 3, and the main antenna geometric prior in Step 4, addresses the problem that it is difficult to balance the success rate and reliability by relying solely on single-baseline observations. It adopts a joint modeling approach of multi-baseline double-difference observation modeling and rigid body constraint modeling to construct a joint orientation model for subsequent multi-baseline integer ambiguity solving and consistency verification.

[0095] Step 5.1. Using the main antenna A0 as the reference antenna, and considering A1 and A2 as slave antennas respectively, construct two sets of directional baselines: A0-A1 and A0-A2. Establish a double-difference observation model for each set of directional baselines, as shown in formula (6): (6) Formula (6) The first equation and the second equation are the double-difference pseudorange observation equation and the double-difference carrier phase observation equation, respectively.

[0096] in, Indicates baseline A0-Ai for satellite With reference satellite The resulting double-difference pseudorange observations, This represents the corresponding double-difference carrier phase observation. This represents the baseline vector from A0 to Ai. and They represent satellites and reference satellite The unit vector of the line of sight at the location of the main antenna. This indicates the integer ambiguity corresponding to the double-difference observation.

[0097] At each epoch, the satellite with the best observation conditions is selected from the valid satellite observation set output in step 3 as the reference satellite. The optimal observation conditions refer to the selection of satellites with higher elevation angles, better signal-to-noise ratios, and higher observation continuity.

[0098] Two sets of double-difference observation models, A0-A1 and A0-A2, were constructed based on all available satellites.

[0099] Step 5.2. Based on the double-difference observation model, the baseline length parameter after temperature compensation in Step 2 is introduced into the double-difference observation model as a baseline length constraint, as shown in Equation (7): (7) At the same time, a baseline closure constraint determined by the geometric relationship of the rigid body array is introduced, as shown in equation (8): (8) in The main orientation baseline vector, For the horizontal verification baseline vector, The closed-loop verification baseline vector; when all three conditions are met, it indicates that the current solution result is consistent with the physical structure of the rigid body array.

[0100] This establishes a joint orientation model that simultaneously incorporates a double-difference observation model, baseline length constraints, and baseline closure constraints. Step 5 provides a unified solution basis for step 6 to perform multi-baseline integer ambiguity solving and consistency verification.

[0101] Step 6. Solve for multi-baseline integer ambiguity and verify consistency, such as... Figure 4 As shown.

[0102] This invention is based on a joint orientation model and employs multi-baseline joint solution and rigid body consistency verification to perform unified solution on A0-A1, A0-A2 and A1-A2, obtaining high-reliability epoch baseline results that can be directly used for heading solution and online self-calibration screening.

[0103] Step 6.1. This step is based on the joint orientation model constructed in step 5. Taking into account the characteristics of the three-antenna rigid body array being short baselines and relatively easy integer ambiguity solution, a method combining multi-baseline joint solution and rigid body consistency verification is adopted to uniformly solve the A0-A1 main orientation baseline, the A0-A2 lateral verification baseline, and the A1-A2 closed baseline.

[0104] Through unified solution, high-reliability epoch baseline results are obtained that can be directly used for heading calculation and online self-calibration screening.

[0105] Using the joint orientation model consisting of the double-difference observation model, baseline length constraint, and baseline closure constraint output from step 5 as a unified input, the main orientation baseline vector is... Lateral verification baseline vector The ambiguity of the integers and their corresponding integer ambiguities are jointly estimated.

[0106] For integer ambiguity resolution, the conventional fixed strategy in short-baseline GNSS orientation can be used to determine the integer ambiguity within the current epoch or short time window; this invention does not elaborate on this. After the ambiguity resolution is completed, the main baseline fixed vector is obtained. and lateral verification baseline fixed vector And by combining the baseline closure constraint in step 5, the closure check baseline vector is obtained. Or their equivalent calculated values, calculate the length residuals of the three baselines respectively: (9) in , as well as The length residuals of the main orientation baseline (A0-A1), the lateral check baseline (A0-A2), and the closed baseline (A1-A2) are respectively used. Then, the closure difference vector of the three baselines is calculated. As shown in formula (10): (10) in, Used to characterize the consistency between the current epoch multi-baseline solution results and the physical geometry of the rigid body array.

[0107] Step 6.2. Further verify the continuity and rationality of the main baseline direction. If the following conditions are met: The difference between the main baseline direction and the main baseline direction of the previous valid epoch does not exceed the first preset threshold, the residual lengths of the three baselines are all less than the first preset threshold, and the closure difference modulus value... Less than the first preset threshold; If the multi-baseline solution result for the current epoch is deemed valid, the epoch will be marked as a high-confidence epoch.

[0108] Output the fixed principal baseline vector at this high-confidence epoch. Lateral verification baseline fixed vector Closed-loop verification baseline vector The data includes baseline length residuals, closure error indices, and a marker indicating whether the current epoch is highly reliable.

[0109] The preferred value for the first preset threshold is 0.010m or 0.005m. Otherwise, the solution result for the current epoch is rejected, and the stable heading result of the previous epoch is retained in the output stage, while the current epoch is marked as a restricted state.

[0110] Step 7. Online self-calibration and recursive update of array geometry parameters, such as... Figure 5 As shown.

[0111] To address the potential issues of localized thermal deformation, slight deviations in the heading and installation angles, and long-term drift of the mechanical structure during long-term array operation, the baseline results of the high-confidence epochs selected in step 6 are used to perform small-scale, controlled online corrections to the array geometric parameters using a combination of sliding window statistics and recursive updates, resulting in new array parameters that are fed back into subsequent epochs.

[0112] Only when the current epoch meets the requirements of valid multi-baseline solution, the length residuals and closure errors of the three baselines not exceeding the first preset threshold, and the temperature sensor is working properly, will the epoch be used as a high-confidence epoch for online self-calibration.

[0113] Step 7 is used to perform online tracking and controlled correction of slow-changing deviations in array geometric parameters using the high-confidence epochs selected in Step 6, without changing the basic conclusions of the fixed solution at the current epoch. The basic idea is as follows: First, using the baseline results, length residuals, closure errors, and velocity priors from the high-confidence epochs output in Step 6 as input, a calibration window is constructed only at epochs that meet the consistency conditions. Then, within the calibration window, statistical estimation and recursive updates are performed on the additional length deviations of the three baselines relative to the temperature compensation model and the heading and mounting angle corrections of the main baseline relative to the forward axis of the carrier. Finally, the updated baseline length parameters and heading and mounting angle parameters are fed back to Steps 5 and 6 of subsequent epochs, respectively, to construct length constraints that are closer to the current array state and to perform more stable consistency checks, thereby suppressing the cumulative effects of local thermal deformation, installation micro-deviations, and long-term drift of the mechanical structure on long-term orientation accuracy.

[0114] Step 7.1. Record the current update time as Define calibration windows for high-confidence epochs in the recent period: (11) in Indicates the first Each epoch is determined to be a high-confidence epoch in step 6. To calibrate the window duration.

[0115] Preferred Pick s, more preferred s; When the GNSS update rate is 10Hz, the preferred method is to use A highly reliable epoch, a better one A high-confidence epoch. Definition The number of valid epochs within the window, only when Online updates will only be performed at certain times. For GNSS update rate, The effective epoch percentage threshold, i.e., the minimum percentage of effective epochs relative to the theoretical number of epochs, is preferably selected as follows: If a high-confidence epoch interruption, continuous exceeding of closure error limit, or abnormal freezing event occurs within the window, the current window is discarded and rebuilt.

[0116] Step 7.2. For the window Main orientation baseline vector within Lateral verification baseline vector Closed-loop verification baseline vector and corresponding temperature Perform statistical analysis and calculate the window average: (12) in Indicates the first Baseline within the next update window The average vector, This represents the average observation length obtained by statistically analyzing the fixed baseline vector magnitude within the same window. This indicates the average temperature of the window.

[0117] Indicates the first in the window High-reliability epoch baseline The baseline vector, This represents the magnitude of the corresponding baseline vector. Indicates the first The array temperature corresponding to each epoch; .

[0118] Will Baseline length after temperature compensation Define the slowly varying deviation observations for the lengths of the three baselines. for: (13) Indicates the average temperature The baseline length parameter is calculated by the temperature compensation model in step 2.

[0119] Indicates the first Baseline at the next update The length deviation observation is used to characterize the additional length deviation caused by slow structural drift, loose installation, or local thermal deformation outside of the temperature compensation model.

[0120] The heading installation angle correction is defined as the principal baseline A0-A1 relative to the forward axis of the carrier. The correction amount.

[0121] When the velocity direction output in step 4 can be used as a forward reference for the carrier, and the carrier is in a straight line or a small turn with negligible sideslip, the heading installation angle deviation observation within the construction window is calculated. : (14) in The horizontal velocity component of the main antenna output in step 4. The east and north components of the main baseline fixed vector. Indicates speed and heading angle. Indicates the azimuth of the main baseline.

[0122] This indicates that the angle is reduced to... The interval. This information is used only as a priori reference for constructing the heading installation angle deviation observation, and is not used as the final heading output for steps 8 and 9. If the current window does not meet the condition for the availability of the prior velocity, only the array baseline length parameter is updated, and the heading installation angle correction remains unchanged from the previous time step.

[0123] The available conditions for velocity priors must include at least the following: The horizontal velocity component output from step 4 within the current calibration window is continuously valid and has not experienced any loss of lock or abnormal jump; The velocity modulus within the window is greater than the preset minimum velocity threshold. To avoid noise dominating the velocity direction at low speeds or near standstill; The vehicle is traveling in a straight line or making a slight turn within the window, so that the velocity direction can approximately represent the forward direction of the vehicle; and the lateral sideslip angle of the vehicle is less than a preset sideslip threshold. The effect of sideslip can be considered negligible.

[0124] The slowly varying deviations of the array geometry parameters are modeled as random walks or low-dynamic recursive models, defining the state vector to be updated. for: (15) in, , and These represent the additional length corrections for the three baselines relative to the temperature compensation model in step 2. This represents the heading angle correction. Its state evolution model can be written as: (16) in, This represents noise in a zero-mean, small-variance process. The corresponding observation vector... Defined as: (17) in, Indicates the first The observation vector corresponding to the next update, the first three items , , The fourth item corresponds to the length deviation observations of the three baselines respectively. Observations of the corresponding heading installation angle deviation.

[0125] The observation model is then written as: (18) in, It is the identity matrix. To observe noise.

[0126] Equations (17) and (18) are updated using recursive least squares or equivalent recursive estimation methods, as shown in equation (19): (19) in, For the first The recursive gain matrix updated every time; and These are the state covariance matrices before and after the update, respectively. and These are the state estimates before and after the update, respectively. To observe the residual vector.

[0127] This is a forgetting factor used to increase the weight of the influence of new observations on the current state estimate; the optimal value is [missing value]. .

[0128] Based on this, the expression for the baseline length parameter after online update is obtained: (20) in Indicates the first The baseline obtained after the second online update Additional length correction estimate, This indicates the online updated baseline length parameter after the overlay correction.

[0129] Indicates the first The estimated heading installation angle correction value obtained after the second online update Indicates the total heading installation angle parameter. The initial heading installation angle obtained in step 1.

[0130] When the heading angle needs to be output, it is calculated using formula (21): (twenty one) in and The first The eastward and northward components of the fixed vector of the principal baseline of each epoch in the northeast-northeast coordinate system. The current epoch carrier heading angle is obtained by combining the online calibration results.

[0131] To prevent over-correction, each update should meet preset limits, preferably: ; in, Indicates the baseline between two adjacent updates The increment of the additional length correction, This indicates the increment of the heading installation angle correction between two consecutive updates.

[0132] For single length update limiting, the preferred option is... m, more preferred m.

[0133] For single-trip installation angle update limit, the preferred option is... , better .

[0134] The freeze criterion for continuous exceeding of the closed differential modulus value is defined as: when the continuous... Each epoch satisfies Immediately freeze the online self-calibration; among which The closure difference threshold is used for freezing; where, The closed difference vector obtained in step 6, For its modulus length, For the closure difference threshold used in freezing, the preferred value is... m, more preferred m.

[0135] For consecutive out-of-limit epochs, the preferred choice is... Each epoch, a better selection Each calendar unit.

[0136] When the single correction exceeds the above-mentioned preset limit, the closure error exceeds the limit continuously, the temperature sensor malfunctions, or the carrier is involved in a collision or severe vibration, the online self-calibration is immediately frozen, and only the last valid parameter before freezing is retained.

[0137] Step 7.3. After the online self-calibration is complete, update the baseline length parameter. , , Heading installation angle correction The update time and corresponding temperature information are written to the storage unit and fed back to steps 5 and 6 of subsequent epochs to construct new length constraints and perform new multi-baseline consistency checks.

[0138] Step 8. Inverse calculation of the main orientation baseline vector heading angle and solution of extended attitude. This step 8 is based on the main baseline fixed vector result output in step 6, which has completed integer ambiguity fixation and passed baseline length constraints and baseline closure constraints. For the problem of converting the baseline vector into intuitive heading information in engineering applications, coordinate transformation and geometric inverse calculation are used to solve the carrier heading angle in the current epoch, and the extended attitude angle is further solved when necessary.

[0139] Read the main baseline output from step 6 If necessary, the horizontal verification baseline should be read simultaneously. .

[0140] Transform the principal baseline fixed vector from the solution coordinate system to the northeast-sky coordinate system to obtain its eastward, northward, and celestial components, denoted as follows: , and First, calculate the principal baseline azimuth angle for the current epoch based on the principal baseline fixed vector: (twenty two)

[0141] Combined with the total heading installation angle parameters obtained from online updates The current epoch carrier heading angle is calculated using the following formula: (twenty three) in The current epoch is the carrier's heading angle, i.e., the positive coordinate angle of the carrier coordinate system. The azimuth of the axis relative to true north; The sum of the initial heading angle in step 1 and the online estimated heading angle correction in step 7 is given by the following formula; ; When step 1 has specified that A0-A1 is aligned with the forward direction of the carrier When strictly aligned, let And when there is no significant installation deviation The convergence to 0 means that the azimuth of the main baseline can be directly used as the heading angle of the carrier. When step 1 has specified that A0-A1 is aligned with the forward direction of the carrier When strictly aligned, it can be made And when there is no significant installation deviation It converges to 0, at which point the azimuth of the main baseline can be directly used as the heading angle of the carrier.

[0142] If pitch and roll angles need to be output, confirm the valid lateral check baseline in step 6. Perform attitude calculation.

[0143] Specifically, first Transform to the northeast-north-sky coordinate system to obtain its east, north, and sky components. , and Then construct the unit axis vector corresponding to the array: (twenty four) in, Indicates the forward axis of the carrier The unit direction vector in the northeast-northeast coordinate system Indicates the rightward axis of the carrier The unit direction vector, Indicates the upward axis of the carrier The unit direction vector.

[0144] As given in step 1, it is used to unify the correspondence between A0 and A2. or The symbol definition, further noted: (25) in , , They represent The three components of the direction vector in the E, N, and U directions; , , express The direction vector has three components in the E, N, and U directions.

[0145] , , express The direction vector has three components in the E, N, and U directions.

[0146] The pitch angle and roll angle are calculated using the following formulas: (26) in, The pitch angle for the current epoch is preferably defined as positive; The current epoch's roll angle is defined, preferably with the right side of the carrier tilted downwards as positive. If... If the value is less than the second preset threshold (the second preset threshold here is, for example, 0.01°), it indicates that the two baselines are nearly collinear or the current verification baseline is invalid. In this case, only the heading angle is output, and the pitch angle and roll angle are not output.

[0147] In addition, the continuity and rationality of the course results for each epoch were checked.

[0148] When the abrupt change in heading of an adjacent epoch exceeds the third preset threshold (the third preset threshold here is 0.005°), the epoch result is marked as restricted based on the velocity direction prior in step 4 and the consistency check result in step 6.

[0149] Step 8 outputs the heading angle at the current epoch. And optional extended attitude angle , Output 8 will be the final output of step 9 and can be used as one of the continuity criteria for subsequent high-confidence epoch screening.

[0150] Step 9. Output the orientation result and the corresponding quality information as the final orientation output.

[0151] Step 9, based on the heading angle and optional extended attitude angle obtained in Step 8, uses structured result encapsulation to uniformly release the current epoch solution results and related auxiliary indicators.

[0152] Output the heading angle at the current epoch. Pitch angle can be output synchronously when necessary. Roll angle Or the main orientation baseline vector.

[0153] Output the quality identifier of the current epoch result, preferably including at least two categories: "fixed availability" and "restricted availability". Specifically, if step 6 determines that the current epoch is a high-confidence epoch, it is marked as "fixed availability"; otherwise, it is marked as "restricted availability".

[0154] When the current epoch is marked as "restricted," the stable heading result from the previous epoch is preferably used as the output value, and the corresponding mass information for the current epoch is output simultaneously. The output mass information corresponding to the current heading result includes: Main baseline length residual Lateral verification baseline length residual Closed baseline length residual closure difference or Current temperature Valid epochs in the current window And information such as whether to perform step 7 online update.

[0155] Compared with existing technologies, this invention directly incorporates the BeiDou PPP-B2b satellite-based precision correction signal into the precision orientation process. Without relying on ground-based RTK base stations, it provides stable absolute position and velocity priors for the main antenna, thus supporting independent high-precision orientation for a single BeiDou system. Furthermore, this invention introduces an online self-calibration mechanism for rigid arrays in multi-antenna short-baseline orientation. It utilizes high-confidence epochs to recursively correct the array baseline geometry and heading installation angle parameters, reducing the impact of temperature variations, support micro-deformation, and installation deviations on orientation accuracy. In addition, based on heading calculation, this invention further constructs a unified output mechanism for extended attitude angles and mass information. This allows the system to output not only the carrier heading angle but also selectable pitch angles, roll angles, closure error, and length residuals simultaneously, facilitating engineering use and result verification. The present invention relates to the application of BeiDou PPP-B2b satellite-based precision correction information in carrier orientation, which can be applied to highly reliable heading determination of UAVs, unmanned vehicles, ships, engineering machinery, surveying and mapping equipment, directional antenna platforms and other mobile platforms. It is particularly suitable for high-precision orientation application scenarios that require consideration of independent BeiDou signal system, PPP-B2b wide-area correction service, rigid array configuration stability and long-term online calibration capability.

[0156] Example 2 This embodiment 2 describes a computer device, which includes a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration in embodiment 1 above.

[0157] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0158] Example 3 This embodiment 3 describes a computer-readable storage medium storing a program that, when executed by a processor, is used to implement the steps of the precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration in embodiment 1 above.

[0159] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0160] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A precise orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration, characterized in that, Includes the following steps: Step 1. Complete the installation of the three-antenna rigid antenna array and calibrate the initial array geometry parameters; Step 2. Based on the initial array geometry parameters, establish a temperature compensation model for the lengths of the three baselines; Step 3. Synchronously acquire the BeiDou carrier phase, pseudorange, PPP-B2b satellite-based precision correction information received by the main antenna, and array temperature information from the three antennas, and perform time alignment to form an effective satellite observation set; Step 4. Based on the effective satellite observation set of the main antenna, PPP-B2b correction information and temperature information at the same moment, perform PPP precise position calculation and state estimation of the main antenna to obtain the absolute position and velocity of the main antenna as the geometric prior of the main antenna; Step 5. Based on the array geometric parameter calibration results, the effective satellite observation set and the geometric prior of the main antenna, first take the main antenna A0 as the reference antenna, and establish double-difference observation models based on the two directional baselines A0-A1 and A0-A2 respectively; The baseline length parameter after temperature compensation in step 2 is introduced into the double-difference observation model as a baseline length constraint, and further baseline closure constraints between the three baselines are introduced based on the geometric relationship of the rigid body array, thereby constructing a joint orientation model; Step 6. Based on the joint orientation model, use multi-baseline joint solution and rigid body consistency check to perform unified solution on the three baselines A0-A1, A0-A2 and A1-A2, and select the baseline results of high confidence epochs; Step 7. Based on the baseline results of the selected high-confidence epochs, online self-calibration updates are performed on the array baseline length parameters and heading installation angle parameters using a combination of sliding window statistics and recursive updates. Step 8. Based on the valid main orientation baseline vector confirmed in Step 6, calculate the vehicle heading angle and optional extended attitude angle; Step 9. Output the orientation results and the quality information corresponding to the current orientation results.

2. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 1, characterized in that, In step 1, the initial array geometric parameters include the initial baseline length parameter, the initial heading installation angle of the main baseline, the lateral sign parameter of the lateral check baseline, and the reference temperature parameter. Step 1 specifically involves: Step 1.

1. Installation of the three-antenna rigid antenna array; The main antenna A0 is installed on the top of the carrier or above the platform in an unobstructed position so that the main antenna A0 can obtain stable and continuous BeiDou observation and PPP-B2b corrected reception conditions. The first slave antenna A1 is installed in the forward direction or the predetermined heading direction of the carrier, so that A0-A1 form the main directional baseline; the second slave antenna A2 is installed in the lateral position of A0, so that A0-A2 form the lateral check baseline. The main antenna A0, the first slave antenna A1 and the second slave antenna A2 constitute a non-collinear rigid body antenna array, and the main antenna A0, the first slave antenna A1 and the second slave antenna A2 are fixed on the same rigid body support. Step 1.

2. Initial array geometry parameter calibration; Measure the actual lengths of the three baselines A0-A1, A0-A2, and A1-A2, and record them as the nominal baseline lengths. , and ; Recording array relative to carrier coordinate system Based on the installation geometry requirements, determine whether A0-A1 correspond to the forward direction of the carrier. Direction, and determine the rightward direction of the carriers corresponding to A0-A2. The direction is still left of the carrier. direction; Relative to the positive forward axis of the carrier, A0-A1 The initial heading installation angle is denoted as ; For A0-A2, record their lateral sign parameters. ;in Lateral sign parameters for cross-sectional verification of baseline; Indicates the correspondence between A0 and A2 direction, Indicates the correspondence between A0 and A2 direction; In a static, open, and unobstructed environment, BeiDou observation data was continuously collected for no less than 20 minutes using a BeiDou multi-channel receiver, and the initial baseline vector between the three antennas was calculated using high-stability observation conditions. The static observation results are averaged to obtain the average principal orientation baseline vector. Average verification baseline vector, average closed verification baseline vector, and antenna phase center installation deviation, superscript Indicates the northeast-central coordinate system; Then, based on the recorded forward axis of the carrier Right axis The installation geometry convention involves projecting the average principal orientation baseline vector and transforming it to the carrier coordinate system. Below, get And calculate the initial heading angle accordingly. : （1） in and for In the carrier coordinate system Below shaft and Axial components; At the same time, record the ambient temperature during calibration. , which serves as the reference temperature for establishing the temperature compensation model.

3. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 1, characterized in that, Step 2 specifically involves: Static short-time observations were repeatedly conducted under different ambient temperature conditions to collect sample data on the variation of three baseline lengths with temperature. Temperature compensation models for the three baseline lengths (A0-A1, A0-A2, and A1-A2) were established, as shown in the following formula: （2） in Indicates the current temperature Lower baseline The length after compensation; Indicates reference temperature The calibration length of the lower baseline, This represents the primary temperature sensitivity coefficient. This represents the secondary temperature sensitivity coefficient. and Output temperature compensation parameters , , .

4. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 1, characterized in that, Step 3 specifically involves: The main antenna A0, the first slave antenna A1, and the second slave antenna A2 synchronously acquire BeiDou carrier phase observations and pseudorange observations; the main antenna A0 synchronously receives PPP-B2b satellite-based precision correction information. In addition, the temperature sensor synchronously collects temperature values ​​from the array bracket or key installation locations. ; The observations from the three antennas, PPP-B2b correction information, and temperature information were matched and aligned according to the unified epoch time label to form original multi-source observation records that can be matched one by one under the same epoch. Time alignment is performed on the frequency observations of the three antennas A0, A1, and A2 within the same epoch, and receiver channel delay, time stamp bias, or other known hardware delays are uniformly corrected to form the effective satellite observation set for the current epoch. The effective satellite observation set includes: effective pseudorange and carrier phase observations from different satellites with the main antenna after screening; effective pseudorange and carrier phase observations from multiple antennas; PPP-B2b correction information; and temperature values. .

5. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 1, characterized in that, Step 4 specifically involves: Using A0 as the main antenna, read the real-time carrier phase, pseudorange observations and PPP-B2b correction information after filtering in step 3. The PPP-B2b correction information includes at least real-time precise satellite orbit information and real-time precise satellite clock error information. The main antenna PPP observation model is established, and its pseudorange observation equation and carrier phase observation equation are as follows: （3） （4） in Main antenna to satellite pseudorange observations; These are the corresponding carrier phase observations; Main antenna and satellite The geometric distance between them is calculated after correction by combining the broadcast ephemeris with the real-time precise satellite orbit information provided by PPP-B2b; The speed of light; For receiver clock bias; It is a satellite clock bias, corrected by real-time precise satellite clock bias information provided by PPP-B2b or given directly; For tropospheric delay; For ionospheric delay, and These are pseudorange and carrier hardware offset, respectively; The carrier wavelength; For integer ambiguity; and These are pseudorange and carrier observation noise, respectively. The state parameters of the main antenna PPP solution Written as: （5） in, The three-dimensional coordinates of the main antenna A0 in the geocentric coordinate system. For the total zenith delay in the troposphere, The carrier ambiguity status corresponding to each visible satellite; Based on real-time precise satellite orbit information and real-time precise satellite clock error information, Kalman filtering is used to estimate Equation (5) epoch by epoch, the absolute position of the main antenna in the current epoch is calculated, and the velocity is obtained by epoch-to-epoch difference.

6. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 5, characterized in that, Step 5 specifically involves: Step 5.

1. Using the main antenna A0 as the reference antenna, construct two sets of directional baselines, A0-A1 and A0-A2; For each set of directional baselines, a double-difference observation model is established, as shown in formula (6): （6） in Indicates baseline A0-Ai for satellite With reference satellite The resulting double-difference pseudorange observations; Indicates baseline A0-Ai for satellite With reference satellite The resulting double-difference carrier phase observations; This represents the baseline vector from A0 to Ai. and They represent satellites and reference satellite The unit vector of the line of sight at the location of the main antenna. This indicates the integer ambiguity corresponding to the double-difference observation; At each epoch, select the satellite with the best observation conditions from the valid satellite observation set output in step 3 as the reference satellite. Two sets of double-difference observation models, A0-A1 and A0-A2, were constructed based on all available satellites; Step 5.

2. Based on the double-difference observation model, the baseline length parameter after temperature compensation in step 2 is introduced into the double-difference observation model as a baseline length constraint, as shown in equation (7); （7） At the same time, a baseline closure constraint determined by the geometric relationship of the rigid body array is introduced, as shown in equation (8): （8） in The main orientation baseline vector, For the horizontal verification baseline vector, The closed-loop verification baseline vector; when formulas (6) to (8) are satisfied simultaneously, it indicates that the current solution result is consistent with the physical structure of the rigid body array; This leads to the establishment of a joint orientation model that simultaneously incorporates a double-difference observation model, baseline length constraints, and baseline closure constraints.

7. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 6, characterized in that, Step 6 specifically involves: Using the joint orientation model output from step 5 as input, for , The ambiguity of the integers and their corresponding integer ambiguities are jointly estimated; For integer ambiguity resolution, the conventional fixed strategy in short baseline GNSS orientation is adopted to determine the integer ambiguity within the current epoch or short time window. After the ambiguity is resolved, the fixed vector of the principal baseline is obtained. and lateral verification baseline fixed vector And by combining the baseline closure constraint in step 5, the closure check baseline vector is obtained. Calculate the length residuals of the three baselines respectively: （9） in , as well as The length residuals of the A0-A1 main orientation baseline, the A0-A2 lateral check baseline, and the A1-A2 closed baseline are respectively used. Then, the closure difference vector of the three baselines is calculated. As shown in formula (10): （10） Step 6.

2. Further verify the continuity and rationality of the main baseline direction, including: The difference between the main baseline direction and the main baseline direction of the previous valid epoch does not exceed the first preset threshold, the length residuals of the three baselines are all less than the first preset threshold, and the closure difference modulus value is... Less than the first preset threshold; The multi-baseline solution result for the current epoch is then determined to be valid, and the epoch is marked as a high-confidence epoch. Output the fixed principal baseline vector at this high-confidence epoch. Lateral verification baseline fixed vector Closed-loop verification baseline vector Baseline length residuals, closure error indices, and a marker indicating whether the current epoch is highly reliable; Otherwise, the solution result for the current epoch is rejected, and the stable heading result of the previous epoch is retained in the output stage, and the current epoch is marked as a restricted state.

8. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 7, characterized in that, Step 7 specifically involves: Let the current update time be denoted as Define a calibration window for the high-confidence epoch within the current time window. : （11） in Indicates the first Each epoch was determined to be a high-confidence epoch, and This indicates that it was determined to be a high-confidence epoch in step 6; To calibrate the window duration, The number of valid epochs within the window, only when Perform online updates in a timely manner; in For GNSS update rate, The effective epoch percentage threshold is the minimum percentage of effective epochs relative to the theoretical number of epochs. Aim at the window Main orientation baseline vector within Lateral verification baseline vector Closed-loop verification baseline vector and corresponding temperature To perform statistical analysis, calculate the window average using the following formula: （12） in Indicates the first Baseline within the next update window The average vector, This represents the average observation length obtained by statistically analyzing the fixed baseline vector magnitude within the same window. Indicates the average temperature of the window; Indicates the first in the window High-reliability epoch baseline The baseline vector, This represents the magnitude of the corresponding baseline vector. Indicates the first The array temperature corresponding to each epoch; ; Slowly varying deviation observations defined by three baseline lengths for: （13） in Indicates the first Baseline at the next update The length deviation observation is used to characterize the additional length deviation caused by slow structural drift, loose installation, or local thermal deformation outside the temperature compensation model; Indicates the average temperature The baseline length parameter is calculated by the temperature compensation model. The heading installation angle correction is defined as the principal baseline A0-A1 relative to the forward axis of the carrier. The amount of correction; When the velocity direction output in step 4 is used as the forward reference of the carrier, the heading installation angle deviation observation within the construction window is determined. : （14） in The horizontal velocity component of the main antenna output in step 4. The east and north components of the main baseline fixed vector. Indicates speed and heading angle. Indicates the azimuth of the principal baseline; This indicates that the angle is reduced to... If the current window does not meet the a priori availability condition for velocity, only the array baseline length parameter is updated, and the heading installation angle correction remains unchanged from the previous time step. Define the state vector to be updated for: （15） in, , and These represent the additional length corrections for the three baselines relative to the temperature compensation model in step 2. This represents the heading installation angle correction; its state evolution model is written as: （16） in, This represents noise in a zero-mean, small-variance process; the corresponding observation vector. Defined as: （17） in, Indicates the first The observation vector corresponding to the next update, the first three items , , The fourth item corresponds to the length deviation observations of the three baselines respectively. Corresponding heading installation angle deviation observation; The observation model is then written as: （18） in, It is the identity matrix. To observe noise; Equations (17) and (18) are updated using recursive least squares or equivalent recursive estimation methods, as shown in equation (19): （19） in, For the first The recursive gain matrix updated every time; and These are the state covariance matrices before and after the update, respectively. and These are the state estimates before and after the update, respectively. To observe the residual vector; This is a forgetting factor used to increase the weight of the influence of new observations on the current state estimate; Therefore, the parameter expression for the baseline length after online update is obtained: （20） in, Indicates the first The baseline obtained after the second online update Additional length correction estimate, This indicates the online updated baseline length parameter after the overlay correction. The initial heading installation angle obtained in step 1; Indicates the first The estimated heading installation angle correction value obtained after the second online update Indicates the total heading installation angle parameter; When the heading angle needs to be output, it is calculated using formula (21): （21） in and The first The eastward and northward components of the fixed vector of the principal baseline of each epoch in the northeast-northeast coordinate system. The current epoch carrier heading angle is obtained by combining the online calibration results; To prevent over-correction, each update should meet preset limits, namely: ； in, Limiting the length update for a single time. Update the amplitude limit for a single heading installation angle; in, Indicates the baseline between two adjacent updates The increment of the additional length correction, This indicates the increment of the heading installation angle correction between two consecutive updates; Limiting the length update for a single time. Update the amplitude limit for a single heading installation angle; The freeze criterion for continuous exceeding of the closed differential modulus value is defined as: when the continuous... Each epoch satisfies Immediately freeze the online self-calibration; among which Use the closure difference threshold for freezing; For consecutive out-of-limit epochs; in, The closed difference vector obtained in step 6, For its modulus length, Use the closure difference threshold for freezing; When the single correction exceeds the above-mentioned preset limit, the closure error exceeds the limit continuously, the temperature sensor is abnormal, or the carrier is involved in a collision or severe vibration, the online self-calibration is immediately frozen, and only the last valid parameter before freezing is retained. After online self-calibration is completed, the updated baseline length parameter is obtained. , , Heading installation angle correction And update the time and corresponding temperature information.

9. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 8, characterized in that, Step 8 specifically involves: Read the main baseline fixed vector output in step 6 The principal baseline fixed vector is transformed from the solution coordinate system to the northeast-sky coordinate system to obtain its eastward, northward, and celestial components, which are denoted as follows: , and ; First, calculate the principal baseline azimuth of the current epoch based on the principal baseline fixed vector: （22） Combined with the total heading installation angle parameters obtained from online updates The current epoch carrier heading angle is calculated using the following formula: （23） in The current epoch is the carrier's heading angle, i.e., the positive coordinate angle of the carrier coordinate system. The azimuth of the axis relative to true north; The sum of the initial heading angle in step 1 and the online estimated heading angle correction in step 7 is given by the following formula; ； When step 1 has specified that A0-A1 is aligned with the forward direction of the carrier When strictly aligned, let And when there is no significant installation deviation The convergence to 0 means that the azimuth of the main baseline is directly used as the heading angle of the carrier. If the pitch and roll angles are output, then confirm the valid lateral check baseline in step 6. Perform attitude calculation; Specifically, first check the horizontal baseline. Transform to the northeast-north-sky coordinate system to obtain its east, north, and sky components. , and Then construct the unit axis vector corresponding to the array: （24） in, Indicates the forward axis of the carrier The unit direction vector in the northeast-northeast coordinate system Indicates the rightward axis of the carrier The unit direction vector, Indicates the upward axis of the carrier The unit direction vector; As given in step 1, it is used to unify the correspondence between A0 and A2. or The symbol definition, further noted: （25） in , , They represent The three components of the direction vector in the E, N, and U directions; , , express The three components of the direction vector in the E, N, and U directions; , , express The three components of the direction vector in the E, N, and U directions; The pitch angle and roll angle are calculated using the following formulas: （26） The pitch angle for the current epoch is defined as positive (head up). The current epoch is the roll angle, with the right-side tilt of the carrier defined as positive.

10. The precision orientation method based on BeiDou PPP-B2b signal and rigid body array self-calibration according to claim 9, characterized in that, In step 9, the quality information corresponding to the current orientation result includes: Main baseline length residual Lateral verification baseline length residual Closed baseline length residual closure difference or Current temperature Valid epochs in the current window And whether to perform step 7 to update information online.

Images