Array phase recovery method and system based on frequency residual

Abstract

The application provides a frequency residual based array phase recovery method and system, and relates to the technical field of satellite navigation array signal processing. Frequency tracking vectors are obtained and time alignment is performed, normal geometric Doppler and modelable frequency items are stripped, frequency residuals are constructed, and dynamic changes of array additional phase are reflected. The frequency residuals are converted into phase increments, and a state recursive model is used to recover the phase dynamics. Through fine differential processing and joint estimation and deduction of the normal geometric Doppler and the modelable frequency items, the frequency residuals reflecting only the array additional phase dynamics are extracted from the mixed frequency tracking quantities. The current spatial processing weight and the calculated value of the array manifold are used to form an absolute anchor point, the anchor error vector is tested, and the long-term accuracy of the phase dynamic estimation is ensured. According to the frequency residual, the recovery state and the recovery quality mark, integrity control measures such as weight reduction, freezing and rollback are performed, and the reliability and robustness of the phase recovery result are improved.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation array signal processing technology, and more specifically, to an array phase recovery method and system based on frequency residuals. Background Technology

[0002] Array antennas rely on the coordinated operation of multiple array elements to improve angle measurement and positioning accuracy while suppressing interference. However, the element weights, carrier attitude, relative line of sight to satellites, element radiation patterns, inter-array coupling, and RF channel gain and phase all change over time, causing the complex space response phase of the array to each satellite to continuously drift. If the additional phase is obtained only through a single calibration without tracking its dynamic process, the calibration parameters will age rapidly, causing the array response model to deviate from reality.

[0003] In scenarios with strong interference, using the bypass signal of a single array element as the carrier phase reference is susceptible to interference contamination, making it difficult to maintain stable despreading and continuous phase tracking. In highly dynamic environments, phase prediction based on the offline array response model is limited in accuracy due to attitude estimation errors and channel time-varying drift. Although frequency-locked loop, phase-locked loop, carrier numerically controlled oscillator increments, and adjacent correlation results carry information about the phase change rate of the input carrier, the original frequency tracking quantities are mixed with the relative motion between the satellite and receiver, Doppler shift, clock drift, frequency reference error, channel drift, and tracking noise, and cannot be directly used as the derivative of the array's additional phase.

[0004] To obtain phase dynamics that reflect only changes in the array response, it is necessary to use inter-satellite differential, inter-station differential, and epoch differential, combined with a normal geometric model, to eliminate common geometric motion terms and construct a clean residual from the frequency tracking quantity. Especially after adaptive spatial filtering processes such as space-frequency power inversion, the time-varying additional phase introduced by the array complex response is coupled with the true geometric motion phase. In the absence of a continuous and reliable direct phase reference, existing technologies have not yet effectively solved the problem of accurately separating and recovering the array's additional phase dynamics from the frequency tracking residual while avoiding the elimination of the satellite's true geometric motion phase. Summary of the Invention

[0005] The problem to be solved by this invention is how to accurately separate and recover the array-added phase dynamics from the frequency tracking residual under the condition of lacking a continuous and reliable direct phase reference.

[0006] To address the aforementioned problems, in a first aspect, the present invention provides an array phase recovery method based on frequency residuals, comprising: After spatial processing, acquire the time-stamped frequency tracking vector, carrier phase observation vector, tracking quality vector, and covariance of at least two navigation satellites to form an observation information packet; Time alignment and interpolation are performed on the frequency quantities in the corresponding observation information packets of different satellites, antennas or receiving stations to form aligned observation packets; Based on the ephemeris, the motion state of the receiver and antenna reference point, and the reference satellite, the normal geometric Doppler vector, the modelable frequency term and its covariance are jointly estimated to form a normal frequency term data packet. Inter-satellite, inter-station, inter-antenna, and inter-epoch differential methods are used to subtract the normal frequency term from the normal frequency term data packet in the aligned observation packet to form a frequency residual packet. The frequency residual is converted into a phase increment, and the phase dynamics and covariance are recovered through state recursion to form a phase dynamic state packet. The absolute anchor point is formed by using the current spatial processing weights and the calculated values ​​of the array manifold, the working configuration and the reference configuration. Based on the candidate anchor point observation vector, the observation matrix corresponding to the anchor point and the prediction state, the anchor point error vector is analyzed and obtained. The validity of the anchor point error vector is checked according to the preset conditions, and the recovery state package composed of the recovery state and the recovery quality flag is obtained. Based on the frequency residual, recovery status, and recovery quality indicators, perform deterioration prevention operations to form an integrity control package; Based on the recovery status, integrity control packet, and observation information packet, the corresponding correction amount is subtracted to obtain the corrected carrier observation data packet.

[0007] Secondly, the present invention also provides an array phase recovery system based on frequency residuals, comprising: The array element signal acquisition module is used to acquire the time-stamped frequency tracking vector, carrier phase observation vector, tracking quality vector and covariance of at least two navigation satellites after spatial processing, and form an observation information packet. The time alignment module is used to perform time alignment and interpolation on the frequency quantities in the corresponding observation information packets of different satellites, antennas or receiving stations to form aligned observation packets; The normal frequency term estimation module is used to jointly estimate the normal geometric Doppler vector, the modelable frequency term and its covariance based on the ephemeris, the motion state of the receiver and antenna reference point and the reference satellite, and to form a normal frequency term data packet. The frequency residual construction module is used to extract the normal frequency items from the normal frequency data packets in the aligned observation packets by using inter-satellite, inter-station, inter-antenna, and inter-epoch differential methods to form frequency residual packets. The phase dynamic recovery module is used to convert the frequency residual into a phase increment, and recover the phase dynamics and covariance through state recursion to form a phase dynamic state package. The anchoring and re-anchoring module is used to form absolute anchor points by using the current spatial processing weights and the calculated values ​​of the array manifold, the working configuration and the reference configuration. Based on the candidate anchor point observation vector, the observation matrix corresponding to the anchor point and the prediction state, the module analyzes and obtains the anchor point error vector. The module then performs a validity check on the anchor point error vector according to preset conditions, and obtains a recovery state package consisting of the recovery state and the recovery quality flag. The integrity monitoring module is used to perform deterioration prevention operations based on frequency residuals, recovery status, and recovery quality indicators, forming an integrity control package; The carrier correction module is used to subtract the corresponding correction amount based on the recovery status, integrity control packet, and observation information packet to obtain the corrected carrier observation data packet.

[0008] This invention provides an array phase recovery method and system based on frequency residuals. Compared with existing technologies, it has the following advantages: By continuously acquiring and time-aligning the frequency tracking vector, and then stripping away the normal geometric Doppler and modelable frequency terms, a pure frequency residual is constructed. This frequency residual directly reflects the dynamic changes of the array's additional phase. Furthermore, by converting the frequency residual into phase increments and recovering the phase dynamics using a state recursive model, continuous and dynamic tracking of the array's additional phase is achieved. In addition, through refined differential processing and joint estimation and subtraction of the normal geometric Doppler and modelable frequency terms, the frequency residual reflecting only the array's additional phase dynamics is successfully extracted from the mixed frequency tracking quantities. Finally, absolute anchor point analysis and integrity control mechanisms are introduced. By forming an absolute anchor point using the current spatial processing weights and the calculated values ​​of the array manifold, and verifying the anchor point error vector, the long-term accuracy of the phase dynamic estimation is ensured. Simultaneously, integrity control measures such as weight reduction, freezing, and rollback are implemented based on the frequency residual, recovery state, and recovery quality indicators, significantly improving the reliability and robustness of the phase recovery results. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 A flowchart illustrating an array phase recovery method based on frequency residuals provided in an embodiment of the present invention; Figure 2 A simplified flowchart illustrating the array phase recovery method based on frequency residuals provided in this embodiment of the invention; Figure 3This is a schematic diagram of frequency tracking observation decomposition provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the construction of inter-satellite and inter-station differential operators provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of discrete phase state recursion provided in an embodiment of the present invention; Figure 6 The flowchart for initial anchoring and re-anchoring provided in the embodiments of the present invention; Figure 7 This is a schematic diagram of an array phase recovery system based on frequency residuals, provided as an embodiment of the present invention. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application are described clearly and completely. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0012] If these issues are not addressed, the array response model will continue to deviate from the actual state, leading to a decrease in interference suppression capability, accumulation of angle measurement errors, and ultimately, deterioration in positioning accuracy. In critical navigation missions, this could trigger positioning failures and increase the risk of system instability. Furthermore, inaccurate phase dynamic recovery will degrade the performance of adaptive spatial filtering, making it unable to effectively suppress strong interference.

[0013] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0014] like Figure 1 As shown in the embodiment of this application, an array phase recovery method based on frequency residuals is provided, comprising: S1. Obtain the time-stamped frequency tracking vector, carrier phase observation vector, tracking quality vector, and covariance of at least two navigation satellites after spatial processing to form an observation information packet.

[0015] Specifically, the frequency tracking vector is the set of frequency information output by the navigation receiver through a frequency-locked loop or phase-locked loop when tracking satellite signals. This vector reflects the change in the frequency of the received satellite signal over time, including various frequency components such as Doppler shift, clock drift, channel drift, and array-added phase changes. The carrier phase observation vector is the set of carrier phase measurements obtained by the navigation receiver after tracking the satellite carrier signal. This vector is usually measured in cycles and reflects the cumulative carrier phase experienced by the satellite signal from transmission to reception. The tracking quality vector is a set of indicators describing the quality of satellite signal tracking by the navigation receiver. This vector may include information such as signal-to-noise ratio, carrier lock-in status, and cycle slip indication, used to evaluate the reliability of the observation data. Covariance is used to characterize the uncertainty or error propagation characteristics of observation data such as the frequency tracking vector and carrier phase observation vector. Observation information includes encapsulating relevant observation data such as the frequency tracking vector, carrier phase observation vector, tracking quality vector, and covariance for a specific epoch, satellite, antenna, or receiving station into a data unit that is easy to process.

[0016] Satellite signals can be captured and tracked using a navigation receiver to obtain raw frequency and phase measurements. These measurements typically include timestamps, satellite identifiers, frequency information, and the corresponding measurement error covariance. For easier subsequent processing, this raw data can be packaged according to a pre-defined data structure to form a unified observation information package. In practice, standard data interfaces or custom data formats can be used to organize this information.

[0017] S2. Perform time alignment and interpolation on the frequency quantities in the corresponding observation information packets of different satellites, antennas or receiving stations to form aligned observation packets.

[0018] Specifically, since different observation sources may have inconsistent sampling times or missing data, time-homogeneous processing is required. For example, a common reference epoch sequence can be established, and then the frequency tracking vector in each observation packet can be resampled. For missing data at a certain epoch, linear interpolation or polynomial interpolation methods can be used for estimation. For data with incompletely aligned timestamps, adjustments can be made using time synchronization algorithms. This process ensures the consistency of all frequency observation data in the time dimension, laying the foundation for subsequent differential processing.

[0019] S3. Based on the ephemeris, the motion state of the receiver and antenna reference point, and the reference satellite, jointly estimate the normal geometric Doppler vector, the modelable frequency term, and its covariance to form a normal frequency term data packet.

[0020] Specifically, the normal geometric Doppler vector is the theoretical Doppler frequency shift caused by the relative motion between the satellite and the receiver, calculated through a geometric model based on the precise motion states of the satellite ephemeris, receiver, and antenna reference points. This vector reflects the pure geometric motion effect and does not contain other error terms. Modelable frequency terms are frequency error terms in the system that can be accurately modeled and estimated, in addition to the normal geometric Doppler, such as receiver clock drift, frequency reference drift, channel frequency offset, satellite clock drift, and modelable propagation rate of change.

[0021] Predictable frequency components, independent of the array's additional phase, are extracted from raw frequency observations. The satellite's precise position and velocity can be calculated using broadcast or precise ephemeris data. Combined with the trajectory of the receiver and antenna reference points (e.g., obtained through an inertial navigation system or external positioning system), the theoretical Doppler shift caused by the relative motion between the satellite and receiver, i.e., the normal geometric Doppler vector, can be calculated. Simultaneously, modelable frequency terms such as receiver clock drift, frequency reference drift, and channel frequency offset can be estimated based on the receiver's internal clock model, frequency reference source characteristics, and channel calibration parameters. These estimates and their uncertainties (covariance) are encapsulated into normal frequency term data packets.

[0022] S4. Using inter-satellite, inter-station, inter-antenna, and inter-epoch differential methods, the normal frequency items in the normal frequency data packets are deducted from the aligned observation packets to form frequency residual packets.

[0023] Specifically, a reference satellite can be selected, and the frequency observations from other satellites can be differentially compared with those of the reference satellite to eliminate common errors such as receiver clock bias. Similarly, inter-station differential (between different receiving stations), inter-antenna differential (between different antennas of the same receiver), or inter-epoch differential (between adjacent epochs) can be performed. After performing the differential operation, the frequency quantity in the aligned observation packet is subtracted from the corresponding normal frequency item in the normal frequency item data packet to eliminate frequency components unrelated to the array's additional phase to the greatest extent possible, thereby obtaining the frequency residual that mainly reflects the dynamics of the array's additional phase.

[0024] S5. Convert the frequency residual into a phase increment, and recover the phase dynamics and covariance through state recursion to form a phase dynamic state packet.

[0025] Specifically, the state recursion employs a state estimation algorithm based on Kalman filtering or similar methods, which uses the current observation and the state estimate from the previous time step to predict and update the current system state (such as additional phase dynamics) and its covariance.

[0026] The frequency residual can be multiplied by the sampling interval to obtain the phase change between two epochs, i.e., the phase increment. This phase increment, as an observation, is input into a discrete phase retrieval model based on state estimation algorithms such as Kalman filtering. This model uses the additional phase state and its covariance from the previous epoch, combined with the phase increment observation from the current epoch, to estimate the additional phase dynamics and its covariance at the current epoch through a state recursion process. This estimation result, along with the difference operator and reference star information, is encapsulated into a phase dynamics state package.

[0027] S6. Using the current spatial processing weights and the calculated values ​​of the array manifold, the working configuration and the reference configuration, an absolute anchor point is formed. Based on the candidate anchor point observation vector, the observation matrix corresponding to the anchor point and the prediction state, the anchor point error vector is analyzed and obtained. The validity of the anchor point error vector is checked according to the preset conditions, and a recovery state package consisting of the recovery state and the recovery quality flag is obtained.

[0028] Specifically, an absolute anchor point is an absolute reference point for the phase dynamics of an array, using known or reliable phase information (such as source phase measurements, reference antenna observations, fixed integer inverse calculations, etc.); this anchor point is used to calibrate or correct the cumulative error of the phase dynamics.

[0029] The theoretical phase response under a specific operating configuration can be calculated using the array's calibration data, current spatial processing weights, and the array manifold model, and this calculation serves as the absolute phase anchor point. This anchor point is compared with the phase dynamic prediction value obtained through state recursion, forming an anchor point error vector. This error vector undergoes statistical testing to determine if it is within a reasonable range. If it passes the test, the phase dynamics are updated using the anchor point information to obtain a more accurate recovery state, and a corresponding recovery quality indicator is generated.

[0030] S7. Based on the frequency residual, recovery status, and recovery quality indicators, perform deterioration prevention operations to form an integrity control package.

[0031] Specifically, an integrity criterion can be constructed based on the magnitude of the frequency residual, the stability of the recovered state, and recovery quality indicators (such as cycle slips, loss of lock, etc.). When the criterion indicates an anomaly, the system can take corresponding control measures. For example, if the frequency residual of a satellite is too large, its observation data may be downweighted; if the phase dynamic estimation diverges, the current state can be frozen or rolled back to a previous reliable state; in extreme cases, the reference satellite can be changed or the local state can be reinitialized to re-establish a reliable phase recovery process. These control decisions and related indicator information are encapsulated into an integrity control package.

[0032] S8. Based on the recovery status, integrity control packet, and observation information packet, subtract the corresponding correction amount to obtain the corrected carrier observation data packet.

[0033] Specifically, the estimated inter-satellite additional phase difference obtained in the recovered state is converted into corresponding carrier correction values ​​according to the carrier wavelength. Then, these correction values ​​are subtracted from the carrier phase observation vector in the original observation packet. This eliminates the influence of array additional phase on carrier phase observations, thereby obtaining clean, corrected carrier observation data that can be used for high-precision positioning or angle measurement applications. This corrected data, along with its corrected covariance, is encapsulated into a corrected carrier observation data packet.

[0034] In this optional embodiment, a clean frequency residual is constructed by continuously acquiring and time-aligning the frequency tracking vector, followed by stripping away the normal geometric Doppler and modelable frequency terms. This frequency residual directly reflects the dynamic changes in the array's additional phase. For example, in an urban canyon environment, the array phase drifts due to environmental changes as vehicles move; this method can capture these drifts in real time, rather than relying on static calibration. Furthermore, by converting the frequency residual into phase increments and recovering phase dynamics using a state recursive model, continuous and dynamic tracking of the array's additional phase is achieved. For example, even when harsh signal environments render single-element references unreliable, this method can still perform dynamic phase estimation based on the continuity of the frequency residual and perform periodic calibration using absolute anchor points, effectively overcoming the problem of insufficient prediction accuracy in offline models. Moreover, through refined differential processing (inter-satellite, inter-station, inter-antenna, and inter-epoch differentials) and joint estimation and subtraction of the normal geometric Doppler and modelable frequency terms, the method successfully extracts the frequency residual reflecting only the array's additional phase dynamics from the mixed frequency tracking quantities. For example, in the vehicle positioning example, factors such as receiver clock drift and satellite Doppler are effectively eliminated, allowing the frequency residual to be accurately used to derive the array's additional phase changes, avoiding the problem of erroneously eliminating the phase of the true geometric motion. Finally, absolute anchor point analysis and integrity control mechanisms are introduced. By using the current spatial processing weights and the calculated values ​​of the array manifold to form absolute anchor points, and verifying the anchor point error vector, the long-term accuracy of dynamic phase estimation is ensured. Simultaneously, integrity control measures such as weight reduction, freezing, and rollback are implemented based on the frequency residual, recovery status, and recovery quality flags, significantly improving the reliability and robustness of the phase recovery results. For example, when an anomaly is detected, the system can adjust its strategy promptly to prevent the propagation of erroneous phase estimates, thereby ensuring the quality of the final output corrected carrier observation data packet and providing a solid guarantee for high-precision positioning.

[0035] The following is a detailed description of each step.

[0036] In a preferred embodiment of this application, step S1 is as follows.

[0037] S11: Receive Era Multi-element complex baseband sampling vector and spatial processing of complex weight vectors .

[0038] Specifically, the multi-element complex baseband sampling vector refers to the set of raw digital signals obtained by down-converting and digitizing the received navigation satellite signals at each specific epoch, processed by the multi-element receiver front-end. This vector contains the amplitude and phase information of the signals captured by each antenna element at a specific time point, serving as the foundational data for subsequent space processing and signal tracking. The space processing weighted vector refers to a set of complex weights applied to the multi-element complex baseband sampling vector. These weights are used to weight and combine the signals received by different elements to achieve specific space filtering effects, such as forming a main beam pointing in a desired direction or suppressing interference signals. This vector can be statically configured according to a preset array pattern or dynamically calculated using adaptive algorithms (such as the Minimum Variance Distortionless Response (MVDR) algorithm or the Linear Constrained Minimum Variance (LCMV) algorithm) to cope with changing interference environments.

[0039] S12: Apply the spatial processing weighted vector to the multi-element complex baseband sampling vector of the same epoch to obtain the array synthesized signal. .

[0040] Specifically, ,in, Represents the epoch The array synthesizes complex baseband signals. This represents a multi-element complex baseband sampling vector. Represents a spatially processed complex weighted vector, with superscripts. This indicates the conjugate transpose.

[0041] S13: Perform multi-satellite carrier tracking on the array synthesized signal to obtain frequency tracking vectors arranged in a uniform satellite order. Carrier phase observation vector Frequency observation covariance Carrier observation covariance and tracking quality vector ;like Figure 3 As shown, the frequency tracking vector includes at least one of the following: frequency-locked loop (FLL) output, phase-locked loop (PLL) auxiliary frequency, carrier NCO (numerically controlled oscillator) increment, Doppler estimation, or adjacent epoch complex correlation phase difference.

[0042] S14: Set up satellite indexes Frequency identifier L (i.e., epoch code), time stamp vector The frequency tracking vector, carrier phase observation vector, frequency observation covariance, carrier observation covariance, and tracking quality vector are encapsulated into an observation information packet.

[0043] Specifically, the observation information package ,in, Indicating the first in space frequency processing One frequency unit.

[0044] By spatially processing and weighting the multi-element complex baseband sampling vectors, interference can be effectively suppressed and the signal-to-noise ratio of the target satellite signal can be improved, thus providing a cleaner signal source for subsequent carrier tracking. This optimized signal input makes the multi-satellite carrier tracking process more stable and accurate, and can reliably acquire the frequency tracking vector, carrier phase observation vector, and their corresponding covariance and tracking quality vector.

[0045] In a preferred embodiment of this application, step S2 is as follows.

[0046] S21: Read frequency tracking vector Each time stamp vector Frequency observation covariance and tracking quality vector Frequency observations that are out of lock, cycle slip, or whose quality does not meet the threshold are excluded.

[0047] Specifically, the tracking quality vector indicates the reliability of frequency tracking, such as signal strength, signal-to-noise ratio (SNR), and lock status, and is an important basis for determining data usability. Removing frequency observations that have lost lock, cycle slips, or whose quality does not meet a threshold ensures that subsequent data processing is of high quality and reliability, preventing abnormal data from contaminating the phase recovery process. This removal operation can be performed by analyzing the tracking quality vector and setting a preset quality threshold, such as an SNR below a certain threshold or a signal lock indication of an unlocked state, marking observations that do not meet the threshold as invalid and removing them; or by utilizing the continuity of the frequency tracking vector for cycle slip detection, for example, by comparing the rate of frequency change between adjacent epochs, if it exceeds a preset dynamic range, it is determined that a cycle slip has occurred, and the relevant observation data before and after the cycle slip is removed.

[0048] S22: Select a common epoch , for the Observations of retained frequencies Perform interpolation to obtain ,in, Represents the epoch Frequency observations.

[0049] Specifically, , in, Indicates the first The original time stamp of each frequency observation, This represents the rate of frequency change estimated from adjacent frequency observations or motion models; or it can be used to jointly solve for the relative time deviation as the state to be estimated.

[0050] S23: Arrange all aligned components in a unified order of satellite, receiving station, antenna, and frequency point to obtain... ,in, This represents a frequency tracking vector aligned to a common epoch but not yet differentiated and without subtracting the normal frequency term.

[0051] Specifically, , in, Alignment to common epoch However, the frequency tracking vector has not yet been differentially analyzed and the normal frequency term has not yet been subtracted. express The first in There are 1 element, and the superscript T indicates transpose.

[0052] S24: Propagate the original frequency noise, interpolation or extrapolation error, and relative time deviation estimation error into the aligned frequency covariance, and finally obtain the aligned observation package.

[0053] Specifically, alignment frequency covariance , In the formula, Indicates the transition from the original observed epoch to the common epoch. The time alignment matrix of the mapping, This indicates the additional error covariance in the time alignment model. This represents the frequency observation covariance.

[0054] Alignment observation package , In the formula, This represents the effective observation sequence obtained by aligning the satellites, receiving stations, antennas, and frequency points corresponding to each component in the frequency vector.

[0055] This application ensures that the frequency data used for subsequent processing is rigorously quality-controlled and time-synchronized, effectively avoiding errors introduced by time inconsistencies or quality issues in the original observation data. This allows subsequent normal frequency term estimation and frequency residual calculation to be based on more accurate and reliable data, thereby significantly improving the accuracy and stability of the frequency residuals. Ultimately, this provides high-quality input for the array phase recovery process, greatly enhancing the accuracy and reliability of phase recovery and avoiding phase estimation bias or divergence caused by data quality issues.

[0056] In a preferred embodiment of this application, step S3 is as follows.

[0057] S31: Align the valid observation sequences in the observation package Determine the reference satellite Sum and difference structures.

[0058] Specifically, the reference satellite can be dynamically selected from the valid observation sequence based on criteria such as signal quality, visibility, geometric distribution, or preset priority. For example, the satellite with the highest signal strength or the smallest geometrical precision factor (GDOP) can be selected as the reference satellite. The differential structure can be preset as inter-satellite single difference, that is, all satellites are differentially differentiated relative to the reference satellite, or it can be inter-station differential or inter-antenna differential to eliminate or reduce common error sources.

[0059] S32: By valid observation sequence The same undifferentiated dimension and order of calculation of normal geometric Doppler vectors The components of the normal geometric Doppler vector represent the predicted carrier frequency generated by the actual relative motion between the satellite and the receiver or antenna reference point.

[0060] Specifically, the prediction of the normal geometric Doppler vector can employ existing GNSS geometric Doppler prediction methods, and the receiver... The normal geometric Doppler vector is: , in, Frequency point The nominal wavelength of the carrier wave, For frequency identification, use L1, L2, etc.; The line-of-sight vector from the receiver to the reference satellite is given. and Receiver Speed ​​and reference satellite The speed.

[0061] S33: Estimating the modelable frequency term vectors in the same dimension and order Its components include at least one of receiver clock drift, frequency reference drift, channel frequency offset, satellite clock drift, and modelable propagation rate of change.

[0062] Specifically, receiver clock drift and frequency reference drift can be estimated using a characteristic model of the receiver's internal crystal oscillator or a drift model of an external high-precision clock. Channel frequency offset can be estimated using system calibration or adaptive filtering methods. Satellite clock drift information is typically contained in broadcast ephemeris or precise ephemeris, which can be read directly or obtained through interpolation. Modelable propagation rate of change can refer to the rate of frequency change caused by the ionosphere or troposphere, and can be calculated using empirical models or real-time estimation models.

[0063] S34: Construct the difference operator based on the effective observation sequence. Differential type and reference object determine the normal frequency item data packet.

[0064] Specifically, a common epoch is established to preserve Each satellite, with no discrepancy in frequency tracking vector. Arrange and select For reference satellite, Indicates satellite The frequency tracking vector, then the inter-satellite difference matrix Each line in the non-reference satellite Take the column In reference satellite Take the column All other elements are set to 0. For example... hour: .

[0065] If it also has a mobile station and base station First, form inter-station differential operators according to the same satellite order. ,in, Indicates mobile station The observation vector, Indicates the base station The observation vector.

[0066] Then form an inter-station-inter-satellite double difference operator. When only inter-satellite differences are performed When only station-to-station differences are used The same applies to inter-antenna differential. When the reference star or effective observation set changes, it should be based on the new... Regenerate . same It must act simultaneously on the alignment frequency, geometric Doppler, and modelable frequency terms.

[0067] and output ,in, It is a normal geometric Doppler vector; A vector of modelable frequency terms; and These are the covariance of the normal geometric Doppler vector and the covariance of the modelable frequency term vector, respectively. It is a difference operator; For reference satellite; Index mapping for effective observation of satellites, sites, or antennas.

[0068] By explicitly specifying the reference satellite and differential structure, and combining this with joint estimation of modelable frequency terms such as geometric Doppler, receiver clock drift, and satellite clock drift, it is ensured that all predictable frequency components are accurately stripped before the frequency residuals are formed. This significantly improves the purity of the frequency residuals, avoids misinterpreting modelable errors as array phase dynamics, and thus provides a more reliable input for subsequent phase increment conversion and phase dynamic recovery, ultimately improving the accuracy and stability of array phase recovery.

[0069] In a preferred embodiment of this application, step S4 is as follows.

[0070] S41: Based on the spatial processing complex weight vector, channel calibration state, and satellite-by-satellite array manifold, establish a phase dynamics model of the spatial processing complex response to obtain the equivalent frequency formed by the additional phase change in spatial processing.

[0071] Specifically, the spatial processing weights, channel calibration states, and satellite-by-satellite array manifolds from step S1 are read to establish a phase dynamics model of the spatial processing complex response. For example, in the non-zero response domain, the satellite-by-satellite complex response... The phase derivative satisfies: .

[0072] Ignoring channel deployment, satellite The additional phase is defined as Its phase index is further expanded as follows: , in, This indicates the additional phase of satellite s. This represents the additional phase rate of satellite s. For satellite Spatial processing of complex responses, For array weighted vectors, The channel amplitude and phase response matrix, For array guide vector, For the conjugate transpose, the function To take the imaginary part of the function, the dot sign indicates the time derivative; time t can also be replaced by epoch n. The phase derivative formula is only available when... The non-singular domain was established.

[0073] Therefore, the derivative of the inter-satellite additional phase difference is the difference between the individual phase derivatives of the two satellites. This derivative simultaneously incorporates weight dynamics, channel dynamics, and spatial manifold dynamics. This application does not require explicit separation of each term, as long as the composite result can be observed from the frequency residuals. The output consists of the satellite additional phase derivative and the inter-satellite additional phase difference derivative, which serve as the theoretical input for the following steps.

[0074] S42: Read the aligned observation packet, normal frequency term data packet, and difference operator, and calculate the observed frequency difference vector, normal geometric Doppler difference vector, and modelable frequency term difference vector, respectively.

[0075] Specifically, read the alignment observation package and normal frequency data packets Using the same difference operator output by S34 Calculate the observed frequency difference vector, the normal geometric Doppler difference vector, and the modelable frequency term difference vector, respectively: , In the formula, This represents the observation frequency difference vector after the aligned frequency observations have undergone inter-satellite, inter-station, inter-antenna, inter-epoch, or combinations thereof. This represents the true geometric Doppler (i.e., the normal geometric Doppler difference vector) that should be retained under the same difference operator. This represents the difference vectors of clock drift, channel frequency offset, and other modelable frequency terms under the same difference operator.

[0076] S43: The frequency residual is calculated based on the observed frequency difference vector, the normal geometric Doppler difference vector, and the modelable frequency term difference vector.

[0077] Specifically, the frequency residual is: , In the formula, This represents the frequency residuals attributable to the spatial processing complex response variation.

[0078] frequency residual ( , Indicates satellite The frequency residual between the satellite and the reference satellite (r) is expanded into a single-satellite observation decomposition and an inter-satellite scalar residual model: After spatial processing The actual frequency tracking observation of the satellite can be written as: , in, For actual frequency tracking observation after spatial processing; For geometric Doppler; For the receiver's common clock drift frequency term; For channel-dependent or frequency terms to be estimated; The equivalent frequency formed by the additional phase change in spatial processing; This includes frequency noise and unmodeled errors. (Based on a reference satellite.) Construct frequency residuals as a reference : , in, For satellite Relative reference star The frequency residual; and Satellites and reference stars The corresponding actual tracking frequency; and Satellites and reference stars The corresponding geometric Doppler; This represents the difference in the frequency terms of the modelable channels.

[0079] Under the condition of model consistency, the satellite Relative reference star Frequency residual for: .

[0080] in, Add phase difference to interstellar space. Indicates satellite Additional phase, Indicates reference star Additional phase, Used for converting radians per second to hertz. This represents the differential frequency noise and residual modeling error. The time t above can also be replaced by epoch n. Directly input step S5 to perform phase integration or state recursion; the single-star formula is the scalar expansion and theoretical basis of the above vector formula.

[0081] For two receiving stations or two antennas, inter-station-inter-satellite double-difference frequency residuals can be further formed to suppress common terms. Normal geometric Doppler can be predicted by ephemeris and navigation state, or it can be used as a joint state estimate; when it cannot be completely stripped away, its remainder is modeled together with the additional phase state instead of being ignored.

[0082] The scalar residuals and the vector frequency residuals output in step S43 have the same physical meaning; the inter-satellite scalar residuals are arranged and combined according to step S34 to form the frequency residual vector.

[0083] S44: Based on the difference operator, the aligned frequency covariance, the covariance of the normal geometric Doppler vector, and the covariance of the modelable frequency term, the frequency residual covariance is obtained, and a frequency residual packet is formed.

[0084] Specifically, frequency residual covariance , In the formula, Represents the frequency residual covariance. and These are the covariances of the normal geometric Doppler vector and the covariances of the modelable frequency term vector, respectively. This represents the alignment frequency covariance.

[0085] Frequency residual packet , Indicating the first in space frequency processing One frequency unit.

[0086] By establishing a phase dynamics model of the spatially processed complex response and incorporating it into the calculation of the frequency residuals, the influence of the array's own processing on phase observations is effectively eliminated, resulting in purer frequency residuals. Simultaneously, the use of multi-dimensional differential techniques significantly suppresses various common errors and systematic biases, improving the accuracy of the frequency residuals. Furthermore, the simultaneous calculation of the covariance of the frequency residuals provides a reliable error assessment for subsequent phase retrieval, enhancing the robustness and reliability of the entire phase retrieval process. This allows subsequent phase increment transformation and state recursive recovery to be based on more accurate and reliable input data, thereby significantly improving the accuracy and stability of array phase retrieval.

[0087] In a preferred embodiment of this application, step S5 is as follows.

[0088] S51: Based on frequency residual Frequency residual covariance epoch time interval By analyzing the phase increment observations and their covariance using the scaling factor, we can obtain the scale factor and the phase increment observations.

[0089] Specifically, according to the frequency tracking quantity unit to the scaling factor in radians per second. Generate phase increment observations and their covariance: , in, This represents the phase increment observation. This represents the covariance of the phase increment observations; This is a scaling factor for the frequency tracking quantity in radians per second; when the frequency tracking quantity is in cycles per second... . This indicates the epochal time interval.

[0090] S52: Input the frequency residual and the additional phase difference of the previous epoch into the discrete phase recovery model to obtain the additional phase difference of the current epoch.

[0091] Specifically, a discrete phase retrieval model is established and executed. This is done over an epoch time interval. The following can be adopted , in, and Encoding adjacent epochs, For epoch time intervals, The frequency residual at epoch n. This refers to noise in the discrete integration process. This represents the additional interstellar phase difference at epoch n. This represents the additional inter-satellite phase difference at epoch n+1.

[0092] If the frequency residual includes a slowly varying bias , can be established , in, The slowly varying bias in the frequency residual at epoch n; The slowly varying bias in the frequency residual at epoch n+1. If the unit is expressed in radians per second, then the phase coupling term is: ;like If the unit is expressed in Hertz, then it should be used. State equations according to The net contribution of the phase is modeled, meaning the sign has already been taken into account; if implemented using the residual deduction method, the corresponding coupling terms are taken as follows. The two are equivalent, only The conventions for positive and negative signs are different.

[0093] S53: Input the posterior state and its covariance of the previous epoch into the state transition model to obtain the predicted state of the current epoch.

[0094] Specifically, the a posteriori state of the previous epoch and its covariance Using the input as input, the current epoch prediction state is obtained through the state transition model. , , in, This indicates the prediction state at the current epoch. The prediction covariance for the current epoch. The covariance of the previous epoch. Here is the state transition matrix. Let be the process noise covariance.

[0095] use and Perform integral recursion, filtering update, robust smoothing, or factor graph incremental update; the state includes inter-satellite additional phase difference, frequency residual bias, frequency drift, channel phase drift, or phase branch integer; that is, the parameters contained in the state can all be updated and predicted by substituting them into the above state transition model.

[0096] The system can simultaneously estimate the phase state of multiple satellites relative to one or more reference satellites and maintain state consistency through a reference satellite switching matrix; the state and covariance after the reference satellite switching are components of the S54 output data packet.

[0097] S54: Forms a dynamic phase state package containing the updated phase prediction state, covariance, difference operator, and reference star.

[0098] Phase dynamic state packet ,in, Indicates the posterior state of the current epoch. This represents the covariance of the current epoch.

[0099] In this embodiment, the frequency residual can be accurately converted into phase increment observations, and historical information and current observations can be effectively fused using a discrete phase recovery model and a state transition model to achieve dynamic, continuous, and robust recovery of the array's additional phase difference. This state-recursive phase recovery mechanism not only smooths observation noise and improves the accuracy of phase estimation, but also effectively handles phase drift caused by dynamic changes in the system, ensuring the accuracy and reliability of array phase recovery in complex dynamic environments. Furthermore, by forming a dynamic phase state package that includes the predicted state, predicted covariance, differential operator, and reference star, a structured and comprehensive input is provided for subsequent anchoring, integrity monitoring, and carrier correction, greatly improving the systematicness and efficiency of the entire array phase recovery method.

[0100] In a preferred embodiment of this application, step S6 is as follows.

[0101] S61: The absolute phase anchor point and anchor point covariance are formed from at least one of the following: the calculated value of the current spatial processing weights and array manifold, the same source phase measurement value of the same batch of array samples in the working configuration and reference configuration, the reference antenna observation value, the fixed integer back-calculated value, the known baseline back-calculated value, the low interference calibration value or the historical reliable state. The anchor point error vector is then further analyzed.

[0102] Specifically, at least one anchor point source is selected from the calculated values ​​of the current spatial processing weights and array manifold, the same-source phase measurement results of the same batch of array samples in the working configuration and reference configuration, the reference antenna observation results, the fixed integer inverse calculation results, the known baseline inverse calculation results, the low-interference calibration results, or the historical reliable state; the first... The phase information from the various anchor points is converted to a unified reference star, unified phase symbol, and unified time base used in the phase state established in step S5, forming the observation model for the p-th candidate anchor point: ; in, For the first 1 candidate anchor point observation vector For the first Each candidate anchor point corresponds to a phase state. The observation matrix For anchor point observation error, The covariance of candidate anchor points is obtained by propagating from the measurement error, model error, integer fixed reliability, baseline error, or historical state covariance of the corresponding anchor point source.

[0103] When using multiple candidate anchor points, candidate anchor points with the same reference base and completed time alignment are stacked to obtain: ; ; ; in, This is the set of candidate anchor point indices for anchoring in the nth epoch. This indicates that the blocks are stacked line by line. This indicates the construction of a block-based diagonal matrix; when there are correlated errors between different candidate anchor points, the corresponding cross-covariance is written into... Off-diagonal blocks; This represents the total matrix of candidate anchor point observation vectors for the nth epoch. This represents the total observation matrix at the nth epoch. Let represent the total covariance matrix of the candidate anchor points in the nth epoch.

[0104] Based on the satellite-by-satellite complex response obtained in step S41 When the time is epoch n, it can be written as The normal state in the normal frequency data packet output in step S3, and the predicted state of the pre-anchoring phase output in step S5. and predicted covariance Calculate the anchor point error vector for: ; Calculate the anchor point prediction covariance matrix for: ; A candidate anchor point is deemed to have passed the validity test when it simultaneously meets the following preset conditions: ; ; ; ; Furthermore, none of the satellites involved in the anchoring process are in a state of lockout or have unrepaired cycle slips.

[0105] in, This indicates that satellite S processes the complex response in space at the nth epoch. For the set of satellites participating in the construction of the anchor point, Predict the covariance matrix for the anchor point. For complex response amplitude threshold, For anchor point statistics threshold, Represents the largest eigenvalue of the matrix. The upper limit of the anchor point covariance. This refers to the time alignment error between anchor point observations and phase state predictions. This is the time alignment error threshold.

[0106] The anchor point information that passes the validity check is encapsulated into an anchor information package. : , And As input for step S62 to perform phase state initialization, absolute observation update or weighted anchoring; when any validity condition is not met, the corresponding candidate anchor point is rejected and the phase dynamic state propagation result output in step S5 is maintained, or the process is switched to freeze, rollback or waiting for the next reliable anchor point.

[0107] S62: When the anchor point error vector passes the test, update the anchor point error vector according to the anchor point update model.

[0108] Specifically, when the anchor point error vector passes the magnitude and integrity checks, according to , Perform initialization, absolute observation update, or weighted anchoring; where, This represents the observation matrix corresponding to the anchor point. Indicates the predicted covariance The total covariance matrix corresponding to the anchor point Determined update gain.

[0109] S63: The recovery state is calibrated to obtain the recovery quality indicator. The inter-satellite additional phase difference estimate and its covariance are extracted from the updated anchor error vector to form the recovery state package.

[0110] Specifically, extract the inter-satellite additional phase difference estimate. and its covariance , forming a recovery state package In the formula, The recovery quality flag is an internal status label generated by the system based on frequency residuals, anchor point errors, response amplitude, lock status, and integral aging (0 for invalid, 1 for integral propagation only, 2 for trusted anchor point update, 3 for high-confidence fixed de-anchoring, and 4 for freeze or rollback). Enter the next step and save the posterior state and covariance as inputs for the next epoch steps S52 and S53.

[0111] The recovered phase and its covariance output in step S5 can also be mapped to the floating-point ambiguity mean and covariance, and used as a soft constraint in the integer least squares search. When the recovery reliability decreases, the constraint weight is automatically reduced or the constraint is removed. The integer search does not participate in the frequency residual integral recovery process from step S3 to step S5.

[0112] In this embodiment, the present application effectively solves the error accumulation and drift problems that may occur when performing phase dynamic recovery purely based on frequency residual integration. By introducing multi-source absolute phase anchors and rigorously verifying and updating the anchor error vectors, the absolute accuracy of the phase dynamic state can be periodically corrected, significantly improving the long-term stability and reliability of array phase recovery. This allows the accuracy of array phase recovery to be maintained over long periods or in dynamic environments, avoiding performance degradation due to error accumulation. Simultaneously, by calibrating the recovery state and generating recovery quality flags, reliable quality assessment information is provided for subsequent carrier observation data correction, ensuring the overall quality and availability of the corrected carrier observation data packets, thereby improving the accuracy and robustness of array-based navigation, positioning, or attitude determination.

[0113] In a preferred embodiment of this application, step S7 is as follows.

[0114] S71: Based on the frequency residual, recovery status and various recovery quality indicators, the integrity criterion is formed by combining the anchor point error vector, locking, cycle slip, time alignment error and integral aging.

[0115] Specifically, locking, cycle slips, time alignment errors, and integral aging are common factors affecting carrier phase observation quality. By combining this information, a multi-dimensional integrity criterion can be constructed to comprehensively assess the reliability of the current phase recovery result. For example, weighted summation, chi-square tests, or machine learning-based classifiers can be used to integrate this information, forming a unified criterion value or criterion vector.

[0116] S72: When the criterion is abnormal, perform a degrading operation, which includes one or more of the following: weight reduction, covariance increase, freezing, rollback, changing the reference star, removing the satellite, or local reinitialization.

[0117] Specifically, for example, if the final criterion is a single value, a threshold is set for that criterion. If the criterion value exceeds the corresponding threshold, it is considered an anomaly, triggering actions such as weight reduction, increasing covariance, freezing, rollback, changing the reference satellite, removing satellites, or partial reinitialization. Weight reduction refers to reducing the weight of anomalous observation data in subsequent processing to reduce its impact on the estimation results; increasing covariance directly increases the covariance of relevant states or observations, reflecting increased uncertainty; freezing refers to pausing updates to certain state variables or parameters, maintaining their last reliable values ​​before the anomaly occurred; rollback refers to restoring the system state to a previous reliable epoch state; changing the reference satellite refers to replacing the current reference satellite with another more reliable satellite in differential processing; removing satellites with severe anomalies refers to removing satellites from the set of satellites participating in phase recovery; partial reinitialization refers to reinitializing some or all state variables to eliminate the cumulative effects of anomalies. For the selection of deweighting, increasing covariance, freezing, rolling back, changing reference satellite, removing satellites, or local reinitialization, one or more degrade prevention operations can be adaptively set according to the actual key parameters.

[0118] S73: Output admission weights, state validity and integrity flags to form an integrity control package.

[0119] Specifically, the admission weight indicates the degree to which each observation data or state variable is accepted and used in subsequent processing; state validity indicates whether the currently estimated phase state is reliable and valid; and the integrity flag is a comprehensive indication of the reliability of the entire phase recovery process. By encapsulating this information into an integrity control packet, the necessary decision-making basis can be provided for the subsequent carrier correction module, ensuring that the final output corrected carrier observation data packet has high reliability.

[0120] Status validity and integrity flags , in, The integrity criterion statistic formed in step S71 is composed of frequency residual, recovery status, joint anchor point error vector of each recovery quality indicator, lock status, cycle slip, time alignment error and integral aging weighted sum. The larger the value, the lower the reliability of the current phase recovery result. This represents the integrity criterion threshold, which is a pre-set or calibrated threshold based on the false alarm probability. The status is considered valid if it does not exceed this threshold. Status validity and integrity flags. It also records the status of normal, downgraded, frozen, rollback, re-anchoring, and reference star switching.

[0121] In this embodiment, comprehensive and real-time monitoring and evaluation of various potential anomalies and uncertainties during the phase recovery process are possible. When an anomaly is detected, the system can flexibly adopt various control strategies based on the nature and severity of the anomaly, such as weight reduction, increasing covariance, freezing, rollback, changing the reference satellite, removing satellites, or local reinitialization, thereby effectively preventing the propagation and accumulation of erroneous phase states. This significantly improves the robustness and reliability of the phase recovery results, ensures the quality of subsequent corrected carrier observation data packets, and avoids a decrease in positioning or navigation accuracy due to unreliable phase estimation. Especially under complex electromagnetic environments or dynamic carrier motion conditions, it can maintain the system's high performance and high integrity.

[0122] In a preferred embodiment of this application, step S8 is as follows.

[0123] S81: The inter-satellite additional phase difference estimate and its covariance are used and converted into carrier correction and its covariance according to the carrier wavelength.

[0124] Specifically, ,in, Indicates the carrier correction amount. The nominal wavelength of the carrier wave at frequency L. This represents the estimated inter-satellite phase difference, expressed in radians. The covariance represents the carrier correction amount; This represents the covariance of the inter-satellite additional phase difference estimate.

[0125] S82: Based on the carrier phase observation vector, carrier observation covariance, and differential operator, form the carrier differential observation to be corrected and its covariance.

[0126] Specifically, the carrier differential observation to be corrected The covariance of the carrier differential observations to be corrected is .

[0127] S83: Based on the differential observations of the carrier to be corrected and their covariance, the corresponding carrier correction amount and correction covariance are subtracted to obtain the corrected carrier observations and their covariance, which are then further used to form the corrected carrier observation data packet as the final output.

[0128] Specifically, ,in, and These represent the corrected carrier observation and its covariance, respectively.

[0129] Correct carrier observation data packets .

[0130] Only the additional phase attributable to the complex response within the array in the frequency residual is used as the compensation amount, and the normal geometric Doppler integral is not used as the compensation amount. In dual-antenna or multi-antenna orientation, the geometric carrier phase generated by the translation of the real baseline and attitude change is retained in the carrier observation to be corrected, and only the additional phase within the array is deducted, thereby retaining the real position, heading, pitch and roll motion information.

[0131] This embodiment provides an effective way to transform complex phase dynamic recovery results into practically usable carrier observation corrections. This scheme can accurately apply the inter-satellite additional phase difference estimate obtained in the preceding steps to the original carrier phase observation data, thereby eliminating array-specific phase errors and significantly improving the accuracy and consistency of the carrier observation data. By converting the phase difference into a physical distance correction and combining it with differential operations, this scheme can effectively isolate and correct errors caused by array effects, making the corrected carrier observation data purer and more suitable for applications such as high-precision positioning and attitude determination, thus improving the practicality and performance of the entire array phase recovery system.

[0132] In one embodiment, a dual-element array with an element spacing no greater than half the wavelength of the operating frequency is used, with the array's geometric center serving as the rover antenna reference point. The two RF channels are divided into L frequency elements after synchronous sampling and amplitude / phase calibration; each frequency element performs space-frequency power inversion (PI) anti-interference processing, using the first element as the reference channel and the second element as the auxiliary channel. The base station uses a calibrated reference antenna. The execution steps of the method in this specific embodiment are as follows: Figure 2 As shown.

[0133] Step 1: Generate multi-satellite tracking observation data packets In a single continuous operation, four scenarios are integrated: single-station inter-satellite recovery is performed when the base station data is temporarily unavailable; inter-station-to-satellite double-difference recovery is performed when the base station data is available; asynchronous alignment is performed when the time stamps of the two stations are inconsistent; and fixed solution-assisted re-anchoring is performed when the integer is fixed and reliable.

[0134] No. The output of each frequency unit is ,in, For the first A multi-element complex sampling vector of frequency units For PI weighted vectors, For spatially weighted complex output.

[0135] like Figure 3 As shown, after synthesizing the frequency units, the inputs are the code loop, carrier loop, and frequency loop, and the output is the rover frequency vector. carrier phase Covariance, timestamp, and locking quality; synchronous reading of base station frequency vectors. and ,form And enter S2.

[0136] Step 2: Perform frequency observation time alignment In the asynchronous case, the observations from the two stations are interpolated or extrapolated to a common epoch; the time deviation uncertainty is included in the covariance, and observations exceeding the allowable extrapolation time are not included in the hard difference of the current epoch.

[0137] Interpolate or extrapolate the FLL values ​​of each star at both stations to a common epoch. Time alignment error formation Calculations were made based on ephemeris data, the positions and velocities of the two stations, and the motion of the antenna reference point: , in, Indicates site With satellite The normal geometric Doppler vectors between them For mobile stations or user stations, As a base station, For the site With satellite Rate of change of geometric distance between them The nominal wavelength of the carrier at frequency L.

[0138] Step 3: Establish normal frequency terms and difference structure Estimate clock drift, channel frequency offset, and modelable propagation rate of change, and select a reference satellite. And construct the difference matrix ,form Enter S4.

[0139] .

[0140] Step 4: Construct single-station or dual-station frequency residuals When only rover data is available, inter-satellite differential is used; when base station data is aligned via S2, inter-station-inter-satellite combined differential is used. Both modes share the same phase state and propagate continuously.

[0141] like Figure 4 As shown, the same difference operator is used to form , in, This refers to the frequency residuals between stations and between satellites, representing a double difference. The difference operator for the reference satellite, and These are the aligned frequency vectors of the rover and the base station, respectively. and Geometric Doppler for the rover and base station, respectively. This is the vector of modelable frequency terms that still need to be subtracted after differencing.

[0142] Frequency noise, time alignment error, geometric prediction error, and channel frequency offset error are propagated as ,form Enter S5.

[0143] Step 5: Integral recursion to recover phase dynamics like Figure 5 As shown, when FLL is measured in weeks per second, it generates... ; State take ,in, This represents the additional phase of the nth epoch. The residual frequency bias is predicted from the posterior state of the previous epoch, and then... Perform Kalman incremental update to obtain Enter S6.

[0144] Step 6: Initialization and Trusted Re-anchoring The fixed solution is used to form the anchor point only when the ratio, posterior residual, consecutive epoch consistency and integrity tests pass simultaneously; when the fixed test degenerates, the state is not reset, only the S5 increment propagation is retained and the covariance is increased.

[0145] During the startup phase, the model anchor points are calculated using space-frequency PI weights, channel calibration matrices, and satellite steering vectors. During the operational phase, the absolute anchor point observation vector total matrix is ​​formed only when measurements from the same source reference configuration or RTK fixed solutions simultaneously pass the ratio, residual, and integrity checks. and total covariance matrix Low-gain updates suppress integral drift; when anchor points are unreliable, only S4 increment propagation is retained. Output Up to S7.

[0146] Step 7: Integrity Monitoring and Access Control like Figure 6 As shown, the system jointly checks the normalized frequency residual, phase increment, anchor point error, compensated carrier residual, complex response amplitude, carrier lock, cycle slip, and integral aging. In case of anomalies, it performs freeze, increases covariance, changes the reference satellite, rolls back, or performs local reinitialization, without outputting untested hard compensation. When the test passes, it outputs corrected double-difference carrier, covariance, restored phase, reference satellite, satellite arrangement, weight version, and integrity flags for use in RTK floating-point calculations and integer fixed-point calculations.

[0147] Step 8: Correct the carrier wave and output. Convert the recovered phase to: ; And generate corrected carrier observations and their covariance: .

[0148] The correction only eliminates the additional phase of the spatial frequency PI converter; the true geometric distance, position, and attitude motion terms are retained. The final result is... It is then output to the Real-time Dynamic Positioning (RTK), Precision Point Positioning (PPP), and Orientation or Integrity Navigation Solving Modules.

[0149] like Figure 7 As shown in the figure, an array phase recovery system based on frequency residuals provided in this application includes: The array element signal acquisition module 10 is used to acquire the frequency tracking vector, carrier phase observation vector, tracking quality vector and covariance of at least two navigation satellites after spatial processing, forming an observation information packet.

[0150] The time alignment module 20 is used to perform time alignment and interpolation on the frequency quantities in the corresponding observation information packets of different satellites, antennas or receiving stations to form aligned observation packets.

[0151] The normal frequency term estimation module 30 is used to jointly estimate the normal geometric Doppler vector, the modelable frequency term and its covariance based on the ephemeris, the motion state of the receiver and antenna reference point and the reference satellite, and to form a normal frequency term data packet.

[0152] The frequency residual construction module 40 is used to extract the normal frequency items from the normal frequency data packets of the aligned observation packets by using inter-satellite, inter-station, inter-antenna, and inter-epoch differential methods to form frequency residual packets.

[0153] The phase dynamic recovery module 50 is used to convert the frequency residual into a phase increment, and recover the phase dynamics and covariance through state recursion to form a phase dynamic state package.

[0154] The anchoring and re-anchoring module 60 is used to form absolute anchor points by utilizing the current spatial processing weights and the calculated values ​​of the array manifold, the working configuration and the reference configuration. Based on the candidate anchor point observation vector, the observation matrix corresponding to the anchor point and the predicted state, the module analyzes and obtains the anchor point error vector. The module then performs a validity check on the anchor point error vector according to preset conditions, and obtains a recovery state package consisting of the recovery state and the recovery quality flag.

[0155] The integrity monitoring module 70 is used to perform deterioration prevention operations based on frequency residuals, recovery status, and recovery quality indicators to form an integrity control package.

[0156] The carrier correction module 80 is used to subtract the corresponding correction amount based on the recovery status, integrity control packet, and observation information packet to obtain the corrected carrier observation data packet.

[0157] By combining inter-satellite, inter-station, inter-antenna, and inter-epoch differential and state recursive recovery, and introducing absolute anchor point analysis and integrity control mechanisms, the array's additional phase dynamics can be accurately separated and recovered from the mixed frequency tracking quantities, while avoiding the elimination of the satellite's true geometric motion phase. This technical solution effectively solves the problems of single-element bypass signals being easily contaminated by interference in strong interference scenarios and the limited prediction accuracy of offline models in high dynamic environments. It also overcomes the limitation that the original frequency tracking quantities, mixed with multiple error sources, cannot be directly used as the array's additional phase derivative. Through the above technical means, continuous and reliable tracking of the array's additional phase dynamics is achieved, significantly improving the phase calibration accuracy and stability of the array antenna in complex environments, providing a solid guarantee for high-precision positioning and angle measurement applications.

[0158] In summary, compared with existing technologies, it has the following beneficial effects: (1) Improve the observability of additional phase dynamics under strong interference conditions. This invention uses the FLL and PLL auxiliary frequencies, carrier NCO increments or adjacent complex correlation phase differences that can be continuously obtained from the space frequency anti-interference output, without relying on single-element bypass carriers that may not be despread under strong interference; even if the absolute phase is unknown, its epoch changes can be observed first.

[0159] (2) Reduce the risk of false compensation of real Doppler. The original frequency quantity, normal geometric Doppler, common and channel frequency terms and final frequency residual are modeled separately. Only the part belonging to the complex response change of spatial processing is integrated, thus preserving the real navigation information carried by satellite motion, receiver motion and attitude motion.

[0160] (3) Solve the problems of unknown initial integral value and long-term drift. The frequency residual is used to recover the phase increment, and the array response model, the same source reference configuration, the low interference calibration, the reliable fixed integer or the known baseline are used to provide the absolute anchor point with covariance; the combination of the two can simultaneously handle dynamic recovery, initial constant and cumulative drift.

[0161] (4) Improve the consistency of asynchronous, multi-channel and multi-station processing. The frequency quantities of different satellites or receiving stations are first aligned to a common epoch, and the time alignment error is included in the covariance; the frequency observation, geometric terms and modelable terms use the same difference operator to avoid the formation of pseudo residuals due to inconsistencies in timestamps, satellite arrangement or reference stars.

[0162] (5) Reduce the risk of divergence caused by noise integration and error feedback. Implement integrity gating using frequency residual, phase recovery, anchor point error, compensated carrier residual, zero response, lockout and cycle slip state; in case of anomalies, perform weight reduction, freeze, rollback, change reference star or local reinitialization, and do not output untested hard compensation.

[0163] (6) Form a frequency residual-phase-carrier closed loop with uncertainty. Frequency noise, time alignment error and geometric prediction error propagate step by step to phase increment, recovery state and carrier correction covariance, so that downstream solvers can use, deweight or reject compensation based on recovery reliability.

[0164] An electronic device provided in this application includes a memory and a processor; the memory is used to store a computer program; the processor is used to implement the array phase recovery method based on frequency residuals as described above when the computer program is executed.

[0165] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the array phase recovery method based on frequency residuals as described above.

[0166] In this embodiment, the beneficial effects of the electronic device and the computer-readable storage medium are similar to those of the array phase recovery method based on frequency residuals described above, and will not be repeated here.

[0167] The present invention describes electronic devices that can serve as servers or clients of this application, which are examples of hardware devices that can be applied to various aspects of this application. Electronic devices are intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices can also represent various forms of mobile devices, such as personal digital assistant devices, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the application described and / or claimed herein.

[0168] Electronic devices include a computing unit that can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM can also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0169] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc. In this application, the separately described modules may or may not be physically separate. Some or all of the modules can be selected to achieve the purpose of the embodiments of this application according to actual needs. Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0170] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0171] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for array phase recovery based on frequency residuals, characterized in that, include: After spatial processing, acquire the time-stamped frequency tracking vector, carrier phase observation vector, tracking quality vector, and covariance of at least two navigation satellites to form an observation information packet; Time alignment and interpolation are performed on the frequency quantities in the corresponding observation information packets of different satellites, antennas or receiving stations to form aligned observation packets; Based on the ephemeris, the motion state of the receiver and antenna reference point, and the reference satellite, the normal geometric Doppler vector, the modelable frequency term and its covariance are jointly estimated to form a normal frequency term data packet. Inter-satellite, inter-station, inter-antenna, and inter-epoch differential methods are used to subtract the normal frequency term from the normal frequency term data packet in the aligned observation packet to form a frequency residual packet. The frequency residual is converted into a phase increment, and the phase dynamics and covariance are recovered through state recursion to form a phase dynamic state packet. The absolute anchor point is formed by using the current spatial processing weights and the calculated values ​​of the array manifold, the working configuration and the reference configuration. Based on the candidate anchor point observation vector, the observation matrix corresponding to the anchor point and the prediction state, the anchor point error vector is analyzed and obtained. The validity of the anchor point error vector is checked according to the preset conditions, and the recovery state package composed of the recovery state and the recovery quality flag is obtained. Based on the frequency residual, recovery status, and recovery quality indicators, perform deterioration prevention operations to form an integrity control package; Based on the recovery status, integrity control packet, and observation information packet, the corresponding correction amount is subtracted to obtain the corrected carrier observation data packet.

2. The array phase recovery method based on frequency residuals as described in claim 1, characterized in that, The process involves acquiring time-stamped frequency tracking vectors, carrier phase observation vectors, tracking quality vectors, and covariances from at least two navigation satellites after spatial processing, forming an observation information packet, including: Receive epoch Multi-element complex basis-band sampling vectors and spatially processed complex weight vectors; The spatial processing weighted vector is applied to the multi-element complex baseband sampling vector of the same epoch to obtain the array synthesized signal; Multi-satellite carrier tracking is performed on the array-synthesized signal to obtain a frequency tracking vector, a carrier phase observation vector, a frequency observation covariance, a carrier observation covariance, and a tracking quality vector arranged in a uniform satellite order; the frequency tracking vector includes at least one of the following: frequency-locked loop output, phase-locked loop auxiliary frequency, carrier NCO increment, Doppler estimation, or adjacent epoch complex correlation phase difference. The satellite index set, frequency point identifier, time stamp vector, frequency tracking vector, carrier phase observation vector, frequency observation covariance, carrier observation covariance, and tracking quality vector are encapsulated into an observation information packet.

3. The array phase recovery method based on frequency residuals as described in claim 2, characterized in that, The process of performing time alignment and interpolation on the frequency quantities in corresponding observation information packets from different satellites, antennas, or receiving stations to form aligned observation packets includes: Read the frequency tracking vector, time marker vectors, frequency observation covariance, and tracking quality vector, and remove frequency observations that are out of lock, cycle slip, or whose quality does not meet the threshold. Selecting a common epoch , for the Observations of retained frequencies Perform interpolation to obtain the epoch. Frequency observation; All aligned components are arranged in a unified order of satellite, receiving station, antenna and frequency point to obtain a frequency tracking vector aligned to a common epoch, but not yet differential and without deducting normal frequency terms; The original frequency noise, interpolation or extrapolation error, and relative time deviation estimation error are propagated into the aligned frequency covariance, ultimately yielding the aligned observation packet.

4. The array phase recovery method based on frequency residuals as described in claim 3, characterized in that, The process involves jointly ephemeris, receiver and antenna reference point motion state, and reference satellite data to estimate the normal geometric Doppler vector, modelable frequency term, and its covariance, forming a normal frequency term data packet, including: The reference satellite and differential structure are determined based on the valid observation sequences in the aligned observation package; The normal geometric Doppler vector is calculated based on the same undifferentiated dimension and order of the effective observation sequence. Each component of the vector represents the predicted carrier frequency generated by the actual relative motion between the satellite and the receiver or antenna reference point. The modelable frequency term vector is estimated using the same dimension and order, and its components include at least one of receiver clock drift, frequency reference drift, channel frequency offset, satellite clock drift, and modelable propagation rate of change. Construct a difference operator to determine the normal frequency term data packet based on the valid observation sequence, difference type, and reference object.

5. The array phase recovery method based on frequency residuals as described in claim 4, characterized in that, The method employs inter-satellite, inter-station, inter-antenna, and inter-epoch differential methods to subtract the normal frequency term from the normal frequency term data packet in the aligned observation packet, forming a frequency residual packet, including: Based on the space processing complex weight vector, channel calibration state, and satellite-by-satellite array manifold, a phase dynamics model of the space processing complex response is established to obtain the equivalent frequency formed by the additional phase change in space processing. Read the aligned observation packet, normal frequency term data packet, and difference operator, and calculate the observation frequency difference vector, normal geometric Doppler difference vector, and modelable frequency term difference vector, respectively; The frequency residuals are calculated based on the observed frequency difference vector, the normal geometric Doppler difference vector, and the modelable frequency term difference vector. Based on the difference operator, the aligned frequency covariance, the covariance of the normal geometric Doppler vector, and the covariance of the modelable frequency term, the frequency residual covariance is obtained, and a frequency residual packet is formed.

6. The array phase recovery method based on frequency residuals as described in claim 5, characterized in that, The process of converting frequency residuals into phase increments, recovering phase dynamics and covariance through state recursion, and forming a phase dynamic state package includes: Based on the frequency residual, frequency residual covariance, epoch time interval, and scaling factor, the phase increment observation and its covariance are obtained through analysis. Input the frequency residual and the additional phase difference of the previous epoch into the discrete phase recovery model to obtain the additional phase difference of the current epoch. Input the posterior state and its covariance of the previous epoch into the state transition model to obtain the predicted state of the current epoch. This generates a phase dynamic state package that includes the updated predicted state, predicted covariance, difference operators, and reference star.

7. The array phase recovery method based on frequency residuals as described in claim 1, characterized in that, The process involves forming absolute anchor points using the current spatial processing weights and the calculated values ​​of the array manifold, the working configuration, and the reference configuration. Based on the candidate anchor point observation vectors, the observation matrix corresponding to the anchor points, and the predicted state, an anchor point error vector is analyzed. The validity of the anchor point error vector is then verified according to preset conditions, resulting in a recovery state package composed of the recovery state and recovery quality indicators, including: The absolute phase anchor point and anchor point covariance are formed by at least one of the following: the calculated value of the current spatial processing weights and array manifold, the working configuration and the reference configuration, the source phase measurement value of the same batch of array samples, the reference antenna observation value, the fixed integer back-calculated value, the known baseline back-calculated value, the low interference calibration value or the historical reliable state; and the anchor point error vector is further analyzed. When the anchor point error vector passes the test, the anchor point error vector is updated according to the anchor point update model; The recovery state is calibrated to obtain the recovery quality indicator. The inter-satellite additional phase difference estimate and its covariance are extracted from the updated anchor error vector to form the recovery state package.

8. The array phase recovery method based on frequency residuals as described in claim 7, characterized in that, Based on the frequency residual, recovery status, and recovery quality indicators, the deterioration prevention operation is performed to form an integrity control package, including: Based on the frequency residual, recovery status and various recovery quality indicators, an integrity criterion is formed by combining the anchor point error vector, locking, cycle slip, time alignment error and integral aging. When the criteria are abnormal, a degrading operation is performed. The degrading operation includes one or more of the following: weight reduction, increasing covariance, freezing, rollback, changing the reference star, removing the satellite, or local reinitialization. Output the admission weights, status validity, and integrity flags to form an integrity control package.

9. The array phase recovery method based on frequency residuals as described in claim 8, characterized in that, The step of subtracting the corresponding correction amount based on the recovery status, integrity control packet, and observation information packet to obtain the corrected carrier observation data packet includes: The inter-satellite additional phase difference estimate and its covariance are used and converted into carrier correction and correction covariance according to the carrier wavelength. The carrier differential observation to be corrected and its covariance are formed based on the carrier phase observation vector, carrier observation covariance and differential operator; Based on the differential observations of the carrier to be corrected and their covariance, the corresponding carrier correction amount and the correction covariance are subtracted to obtain the corrected carrier observations and their covariance, which are then further used to form the corrected carrier observation data packet as the final output.

10. An array phase recovery system based on frequency residuals, characterized in that, include: The array element signal acquisition module is used to acquire the time-stamped frequency tracking vector, carrier phase observation vector, tracking quality vector and covariance of at least two navigation satellites after spatial processing, and form an observation information packet. The time alignment module is used to perform time alignment and interpolation on the frequency quantities in the corresponding observation information packets of different satellites, antennas or receiving stations to form aligned observation packets; The normal frequency term estimation module is used to jointly estimate the normal geometric Doppler vector, the modelable frequency term and its covariance based on the ephemeris, the motion state of the receiver and antenna reference point and the reference satellite, and to form a normal frequency term data packet. The frequency residual construction module is used to extract the normal frequency items from the normal frequency data packets in the aligned observation packets by using inter-satellite, inter-station, inter-antenna, and inter-epoch differential methods to form frequency residual packets. The phase dynamic recovery module is used to convert the frequency residual into a phase increment, and recover the phase dynamics and covariance through state recursion to form a phase dynamic state package. The anchoring and re-anchoring module is used to form absolute anchor points by using the current spatial processing weights and the calculated values ​​of the array manifold, the working configuration and the reference configuration. Based on the candidate anchor point observation vector, the observation matrix corresponding to the anchor point and the prediction state, the module analyzes and obtains the anchor point error vector. The module then performs a validity check on the anchor point error vector according to preset conditions, and obtains a recovery state package consisting of the recovery state and the recovery quality flag. The integrity monitoring module is used to perform deterioration prevention operations based on frequency residuals, recovery status, and recovery quality indicators, forming an integrity control package; The carrier correction module is used to subtract the corresponding correction amount based on the recovery status, integrity control packet, and observation information packet to obtain the corrected carrier observation data packet.

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