Mobile terminal high-precision satellite track processing method based on kalman filtering algorithm

Abstract

The application discloses a mobile terminal high-precision satellite trajectory processing method based on a Kalman filtering algorithm, relates to the technical field of satellite navigation and positioning, and comprises the following steps: receiving and buffering broadcast ephemeris and high-precision correction information in a terminal, and generating a correction candidate set and a state label according to a satellite; a correction state filter is established according to the state label, and version transition bridging correction, late measurement backfilling and forward repropagation are performed, time lag smoothing equivalent correction and uncertainty description quantity are output, terminal precise satellite trajectory and clock difference products are formed; and the output is conservatively fused in a correction layer, is mapped into operation indexes and a prediction upper bound to drive an operation state machine to degrade and recover. According to the method, the trajectory continuity is improved in a weak network and an ephemeris update asynchronous scene, sudden jumps and re-convergence are reduced, the agricultural automatic operation availability and operation quality are improved, and the risk of missing spraying, re-spraying and rework is reduced.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, specifically to a high-precision satellite trajectory processing method for mobile terminals based on the Kalman filter algorithm. Background Technology

[0002] In precision agriculture and automated agricultural machinery operations, tractors, rice transplanters, sprayers, harvesters, and other machinery typically require the installation of onboard controllers, tablet terminals, or mobile terminals. These systems utilize satellite navigation and raw observation to achieve automatic steering, row tracking, plot boundary constraints, variable-rate fertilization and pesticide application, and repetitive operation paths. These operations often occur in open fields, orchards, hilly terraces, forest edges, and areas covered by facility agriculture. These operations are characterized by long operating times, low speeds, and high requirements for the stability of lateral offset, heading continuity, and the spacing between adjacent operation trajectories in the control closed loop. Furthermore, the operation areas are often located at the edge of communication base station coverage or in areas undergoing cross-carrier handover. Additionally, factors such as metal structures of agricultural machinery obstructing view, trellis reflections, and tree canopy attenuation exist. Therefore, the continuous availability of high-precision positioning services directly impacts swath utilization, input utilization, and operational safety.

[0003] Existing high-precision positioning terminals are generally based on broadcast ephemeris superimposed with external corrections (orbit correction, clock error correction, signal deviation correction), and Kalman filtering is used to achieve state estimation and smoothing.

[0004] Correction information can originate from cellular networks or satellite broadcast links. During periods of weak network or link failure, correction messages are often delayed, intermittently missing, or arrive out of order. Furthermore, different types of corrections may experience asynchronous updates in terms of time and content. Broadcast ephemeris is updated periodically and has version identifiers, while correction information is often associated with specific ephemeris versions. When ephemeris updates and correction updates are inconsistent, the terminal may obtain a combination of the new ephemeris and the old correction, or the old ephemeris and the new correction, at the same epoch. This introduces systematic biases into satellite position and clock error calculations, leading to abnormal filtering innovations, weight mismatches, or reinitialization. To ensure operation, some terminals may use corrections from the previous epoch or short-term predictions during short-term gaps, switching to a lower-level positioning mode after failure. However, when ephemeris version switching, delayed message replenishment, and link jitter coexist, the time and version consistency of correction inputs are also compromised. If such discontinuities or mismatches occur during operation, it can lead to positioning solution jumps, trajectory drift, autopilot disengagement, or prolonged reconvergence, resulting in missed spraying and respraying, row spacing deviation, plot boundary crossing, rework, and machine downtime.

[0005] Therefore, the current technical problem is that when there are weak agricultural networks, broken links, and inconsistencies between ephemeris and correction information updates, resulting in delayed, missing, out-of-order, and version-inconsistent correction messages, the terminal side cannot continuously provide satellite trajectory correction inputs with consistent time and version to the high-precision solution, leading to discontinuous positioning and repeated convergence during the operation. Summary of the Invention

[0006] (a) Technical problems to be solved:

[0007] To address the shortcomings of existing technologies, this invention provides a high-precision satellite trajectory processing method for mobile terminals based on the Kalman filter algorithm. By performing version transition bridging correction, late measurement backfilling, and forward repropagation, it outputs time-delay smoothing equivalent corrections and uncertainty descriptors, forming a precise satellite trajectory and clock error product for the terminal. The output is conservatively fused at the correction layer and mapped to operational indicators and prediction upper bounds to drive the operational state machine's degradation and recovery. This method improves trajectory continuity in scenarios with weak networks and asynchronous ephemeris updates, reduces abrupt jumps and reconvergence, and enhances the availability and quality of automated agricultural operations; it also solves the technical problems described in the background art.

[0008] (II) Technical Solution:

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A high-precision satellite trajectory processing method for mobile terminals based on Kalman filtering algorithm includes receiving broadcast ephemeris and high-precision correction information, writing the broadcast ephemeris version identifier, the message timestamp of the high-precision correction information, the associated version identifier and the field integrity flag into the correction record library and caching it according to satellite, forming a satellite-by-satellite correction candidate set and status label;

[0011] A correction state filter is established for each satellite based on the status label. Kalman filtering is used for prediction and updating. During version transition, a bridging correction vector is generated by the difference between the precise satellite status anchor point and the broadcast ephemeris. When the satellite is late or out of order, the correction is backfilled and propagated forward. The output is a fixed-delay smooth equivalent correction vector and an equivalent uncertainty description matrix.

[0012] The terminal's precise satellite trajectory and clock error products are generated using the equivalent correction vector and equivalent uncertainty description matrix. These are then mapped to the operation index vector and prediction upper bound. The operation index vector and prediction upper bound are compared with the operation threshold coefficient and recovery threshold coefficient to drive the operation state machine to output the operation level and downgrade or recovery instructions.

[0013] Furthermore, the correction record library establishes a circular buffer based on satellite number and a time index based on message timestamp. When receiving high-precision correction information, it inserts it into the corresponding position according to the time index and writes the broadcast ephemeris version identifier, associated version identifier, field integrity flag, delay duration, and correction category into the corresponding correction record. Correction records that exceed the cache window are eliminated according to time.

[0014] Furthermore, for each satellite at each epoch, correction records are selected from the satellite-by-satellite correction candidate set and status labels are generated. Among them, version consistency means that the associated version identifier is consistent with the broadcast ephemeris version identifier and the fields are complete; version transition means that the broadcast ephemeris version identifier has been updated and the correction record corresponds to the old version; late or out of order means that the message timestamp is behind the current epoch and is within the backfill window; and real interruption means that there are no available correction records for several consecutive epochs.

[0015] Furthermore, the determination of version transition is based on the version difference, which is determined according to the minimum difference between the broadcast ephemeris version identifier and the associated version identifier. When the associated version identifier is missing, the corresponding correction record is marked as missing version identifier and its priority in the satellite-by-satellite correction candidate set is reduced.

[0016] Furthermore, the state variables of the corrected state filter include orbital triaxial correction, clock error correction and its drift term. When the version is consistent and available, the correction record is used as the measurement input to perform the update. When there is a real interruption, only the prediction is performed and the equivalent uncertainty description matrix is ​​expanded. The update process introduces measurement injection coefficients based on the state label to adjust the measurement update intensity.

[0017] Furthermore, the precise satellite state anchor point is determined by the precise satellite trajectory and clock error product of the previous epoch terminal, and the bridging correction vector is formed by the difference between the precise satellite state anchor point and the satellite position and clock error obtained from the broadcast ephemeris. The position difference is then projected into radial, tangential, and normal unit vectors to generate a three-dimensional orbital bridging correction.

[0018] Furthermore, when a correction is late or out of order, the historical state of the correction status filter is saved in the cache window of the correction record library. After receiving a late correction record, the historical epoch is located according to the message timestamp to perform backfilling and updating, and the recorded status label is propagated forward to the current epoch.

[0019] Furthermore, when the terminal receives multi-source corrections, it first performs compatibility screening based on the differential sequence of the terminal's precise satellite trajectory and clock error products. Then, at the correction layer, it uses the covariance intersection method to obtain the fusion result for the equivalent correction vector and equivalent uncertainty description matrix that have passed the screening. The intersection weight is determined by one-dimensional search and the fusion matrix is ​​positive definite.

[0020] Furthermore, the operation index vector is calculated based on the terminal's precise satellite trajectory and clock difference product in the operation line coordinate system. The upper bound of the prediction is determined by the operation uncertainty obtained by the equivalent uncertainty description matrix through sensitivity mapping. The maximum eigenvalue of the operation uncertainty is obtained by power iteration as the upper bound of the prediction. The sensitivity mapping is obtained by perturbing each component of the equivalent correction vector according to a preset perturbation step size and recalculating the operation index vector.

[0021] Furthermore, the job state machine is set to four states: hold, degrade preparation, degrade execution, and recovery preparation. State transitions are triggered by the comparison results of the predicted upper bound with the job threshold coefficient and the recovery threshold coefficient, and the transition is required to be executed after several consecutive epochs meet the same triggering conditions. The job state machine outputs the job level, the expected continuous job time, and the instructions corresponding to the current state. The instructions include degrade instructions and recovery instructions and are written to the job log.

[0022] (III) Beneficial Effects:

[0023] This invention provides a high-precision satellite trajectory processing method for mobile terminals based on the Kalman filter algorithm, which has the following advantages:

[0024] By versioning and caching broadcast ephemeris and high-precision correction information, a satellite-by-satellite correction candidate set and status tags are generated. This ensures consistent version availability, separates version transitions, delays or out-of-order delivery from actual interruptions, and provides traceable input and verification for subsequent processing, unaffected by message arrival order. A correction status filter is established based on the status tags. During version transitions, the precise satellite status anchor point and broadcast ephemeris are differentially used to generate a bridging correction vector. This ensures the continuity of the terminal's precise satellite trajectory and clock difference products during ephemeris desynchronization, avoiding trajectory abrupt changes and resets caused by correction mismatch.

[0025] For late or out-of-order correction records, the message timestamp is used to backfill the historical epoch and retransmit it forward to the current epoch. The output is a fixed-delay smooth equivalent correction vector. The weak network backfill information is entered into the output in a consistent manner to avoid transient jumps in the control side input.

[0026] Output the equivalent correction vector and the equivalent uncertainty description matrix. Adjust the uncertainty growth according to the path semantics during actual interruption or version transition. While downstream judges the reliability based on upstream, avoid over-confidence in the output during bridging, backfilling or prediction stages.

[0027] When multiple corrections coexist, the differential sequences of the terminal precision satellite trajectory and clock error products are first screened for compatibility based on compatibility. Then, the equivalent correction vector and the equivalent uncertainty description matrix are conservatively fused at the correction layer to avoid breakage jitter caused by hard switching at the result layer.

[0028] The terminal's precise satellite trajectory is mapped to clock error products and equivalent uncertainty description matrix as an operation index vector and prediction upper bound. Then, it is compared with the operation threshold coefficient and recovery threshold coefficient to drive the operation state machine to output the operation level and downgrade or recovery instructions, and record the operation log, so that the status label, bridging backfill and conservative fusion work together in the operation closed loop. Attached Figure Description

[0029] Figure 1This is a schematic diagram of the high-precision satellite trajectory processing method for mobile terminals according to the present invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] Please see Figure 1 This invention provides a high-precision satellite trajectory processing method for mobile terminals based on the Kalman filter algorithm, including: Step 1: On the mobile terminal side, the broadcast ephemeris and high-precision correction information are organized into traceable records with version, time and integrity, and a satellite-by-satellite correction candidate set and status label are formed at each epoch that can directly trigger subsequent processing, so as to decompose the weak network phenomenon into a manageable state rather than classifying it as an interruption.

[0032] In automated agricultural operations, the transmission link for correction information may experience short-term downtime, intermittent availability, or message congestion and rework. This can cause correction information from the same satellite to arrive at the terminal with delays, out-of-order arrival, or missing segments. Meanwhile, broadcast ephemeris is updated periodically, and correction information often carries its associated ephemeris version identifier. When the ephemeris update and correction update are not synchronized, the terminal may simultaneously hold input combinations with inconsistent broadcast ephemeris version identifiers and correction-associated ephemeris version identifiers within the same epoch.

[0033] If the terminal only uses whether a correction has been received as the criterion, it will misjudge the version transition period and the late patching period as interruptions, thereby introducing unnecessary resets and switches in the subsequent filtering and control links. Therefore, step one needs to first name the input objects uniformly and solidify them into traceable records, and then use the consistency diagnosis output status label as the trigger condition for step two to select cross-version bridging, late patching update or pure prediction.

[0034] At the beginning of each epoch, the mobile terminal first establishes a broadcast ephemeris ledger at the satellite level, which serves as a reference benchmark for subsequent consistency diagnostics. This ledger does not aim to expand into a complex model, but rather explicitly archives the broadcast ephemeris of each satellite as a currently available reference object, ensuring that all correction records within the same epoch can be traced back to the same reference version.

[0035] If the reference benchmark is not fixed first, the difference in decoding order within the same epoch may cause the reference ephemeris to drift, which in turn may lead to different conclusions for the same correction record at different decision times, thus undermining the stability of the state tag from the source.

[0036] After receiving the broadcast ephemeris, the mobile terminal first performs verification and field extraction, then writes the satellite identifier, broadcast ephemeris version identifier, applicable time period of the broadcast ephemeris, and broadcast ephemeris generation time into the broadcast ephemeris ledger, and generates a unique reference pointer within an epoch for the satellite. This pointer is only replaced when the ephemeris version is updated.

[0037] The mobile terminal uses a fixed-length record area indexed by satellite identifier to store the broadcast ephemeris log, and uses a version identifier change-triggered write method to avoid duplicate overwriting; at the same time, the broadcast ephemeris log is bound to the epoch time, so that all subsequent diagnoses are based on the broadcast ephemeris log of that epoch.

[0038] When using this system, the broadcast ephemeris log is first solidified at the satellite level, and then reference consistency within an epoch is maintained by triggering version identifier changes. The broadcast ephemeris forms a stable reference within each epoch, facilitating subsequent consistency comparisons between correction records and reference versions; and avoiding contradictory diagnostic conclusions arising from changes in the reference object due to changes in the same reference object within the same epoch for the same correction record.

[0039] After the broadcast ephemeris log is solidified, the mobile terminal will write the high-precision correction information into the correction record library and establish a circular buffer with satellite as the granularity, so that the correction information can be written to the corresponding time position even if it arrives out of order.

[0040] In weak networks, packet backlog and concentrated arrival can lead to terminals receiving multiple correction records from the same satellite within a short period. If these records are overwritten in the order they are received, historical corrections will be erased, making it impossible to determine whether a particular epoch can be effectively corrected through backfilling. When parsing each correction message, the mobile terminal extracts the satellite identifier, correction category, correction record message time, correction-related ephemeris version identifier, field integrity flag, and latency, and writes these into a single correction record. The latency characterizes the time offset of the correction record relative to the current epoch, and is taken as the absolute value of the difference between the epoch time and the correction record message time.

[0041] The mobile terminal establishes a circular buffer based on a first index, and a second index, a time index structure based on the message time of the correction record. When out-of-order arrivals occur, the correction record is inserted at the second message time. The time index structure can use a balanced binary search tree or skip list to provide an upper bound for insertion and searching, while also eliminating excessively long records during the circular buffer wrap-around process. A circular buffer is established at the time-satellite level, and a time index structure is built based on the message time of the correction record, supporting out-of-order insertion and windowed elimination. Correction records retain temporal semantics after weak network patching, subsequently distinguishing between late patching and genuine missing records. Correction record writing rules are in place to avoid overwriting historical information and misjudging errors.

[0042] Once the broadcast ephemeris log and correction record library have traceable input, the mobile terminal needs to establish a satellite-by-satellite correction candidate set for each satellite and assign a continuously comparable reliability metric to all correction records in each candidate set to avoid using binary logic for availability / unavailability switching. The reliability metric is used for sorting and filtering, ensuring that subsequent status label generation has stable input rather than random arrival order. Multiple available correction records may exist in the same epoch: some records may have the same version but excessive latency, while others may have insufficient latency but missing fields. Without continuous quantization, status labels will frequently flip according to the arrival order of records, thus propagating input fluctuations to subsequent filtering and control links.

[0043] The mobile terminal uses the broadcast ephemeris version identifier in the broadcast ephemeris ledger as a reference to calculate the version difference of each correction record. This is combined with a field integrity flag to obtain the completeness score. The latency is then mapped to a monotonically decreasing weight, ultimately forming a version consistency index for ranking. The version consistency index uses the form of completeness × exponential decay × soft penalty, which non-linearly suppresses the exponent by the version difference. This keeps records with inconsistent versions but still usable for transitional judgment in the candidate set instead of discarding them directly, facilitating the generation of version transitional state labels. Specifically:

[0044] ;

[0045] Where: Version consistency index : A continuous quantity used to rank the reliability of similar correction records from the same satellite. Completeness : A continuous quantity obtained by mapping from the field integrity flag. When all fields are present, the highest value is used; when fields are missing, the value is reduced according to the missing category; latency. : The time offset between the epoch time and the time of the correction record message, with a value range of . ;

[0046] Delay penalty coefficient : Exponential decay intensity parameter, values The larger the value, the faster the weight decreases for the same amount of latency; version difference : A measure of the difference between the broadcast ephemeris version identifier and the corrected associated ephemeris version identifier, expressed as a non-negative integer. A value of 0 indicates version consistency, while a larger value indicates a larger deviation. Version penalty coefficient. : Soft penalty intensity parameter, value The soft penalty mapping is defined as:

[0047] ;

[0048] Soft penalty mapping The range of values ​​is This is used to map version differences to inhibition factors; version penalty coefficient. The range of values ​​is Version difference The value range is the set of non-negative integers; boundary handling can be added during implementation: when Exceeding the preset upper limit At that time, directly ordered This avoids exponential overflow; a preset upper bound is used. It is a positive real number, which can be determined by the range of terminal values.

[0049] When sorting the candidate set, the mobile terminal arranges the correction records of the same satellite and the same correction category from largest to smallest according to the version consistency index, and encapsulates the sorting result together with its field integrity flag and latency into a satellite-by-satellite correction candidate set.

[0050] When in use, the version consistency index is calculated and the correction records are sorted and encapsulated to form a stable input for the satellite-by-satellite correction candidate set; the candidate set sorting is driven by continuous quantities, reducing the state label flipping caused by changes in the order of record arrival; version inconsistency records are retained in the candidate set but their weights are suppressed, providing a traceable basis for subsequent determination of version transition.

[0051] After obtaining the satellite-by-satellite correction candidate set, the mobile terminal needs to compress the input state of each satellite at the current epoch into a single state label, and ensure that this label maintains temporal continuity under weak network jitter. The challenge lies in distinguishing between late or out-of-order arrivals and genuine interruptions: the former may still have records in the correction record library that cover the current epoch or historical records that can be backfilled, while the latter means that there are indeed no usable records in the window.

[0052] If all corrections not arriving in the current epoch are judged as interruptions, late-arrival corrections will be misjudged as interruptions, forcing subsequent continuous correction generation to follow a pure prediction path. Conversely, if all delays are judged as fillable, expired records may be misused as current input. The mobile terminal first maps the delay amount to a late availability coefficient, and then combines the sorting result of the version consistency index with the field integrity flag to generate four types of status labels: version consistent and available, version transition, late or out-of-order, and real interruption. The late availability coefficient adopts a piecewise function with full availability within the window, exponential decay outside the window, and zeroing after exceeding the upper limit, so that late-arrival corrections have clear availability semantics within a reasonable window and naturally become invalid after exceeding the upper limit. At the same time, a hysteresis judgment rule is introduced, so that when the status label changes from version consistent and available to late, out-of-order, or real interruption, it needs to satisfy consistent evidence for several consecutive epochs to avoid label jitter caused by link jitter.

[0053] ;

[0054] Where: Late arrival availability coefficient : A continuous quantity used to characterize whether a late correction record still possesses backfill semantics in the current epoch; its value range is . Delay : The time offset between the epoch time and the time of the correction record message, with a value range of . In this function, it is used as an independent variable to determine the degree of lateness.

[0055] Backfilling limit The time threshold for ensuring availability even for late arrivals, with a specified value. When the delay does not exceed the backfill limit, the available lateness coefficient is taken as follows: Discard the upper limit The time threshold for discarding late arrivals, with a specified value. When the delay exceeds the discard limit, the late availability factor is taken as... attenuation coefficient : Exponential decay intensity parameter, values Its function is to continuously reduce the late availability coefficient between the backfill limit and the discard limit;

[0056] Delay Take as epoch time With the correction log message time The absolute difference:

[0057] ;

[0058] epochal time : Measurement time marker from receiver observation epoch; message time The reference time is derived from the correction message; if the message does not contain a reference time, the message arrival time is taken and the time source type is written to the record header field; at the same time, the backfill threshold is constrained: the upper limit is discarded. Not greater than the window length of the corrected record circular buffer This ensures that records that are allowed to be backfilled can be found in the cache.

[0059] When generating status labels, the mobile terminal uses the first record in the satellite-by-satellite correction candidate set as the current preferred record and reads its version consistency index and late availability coefficient: when the version difference of the preferred record is 0 and the field integrity flag meets the requirements, it is marked as version consistent and available; when the version difference is not 0 but the version consistency index is still non-zero and the late availability coefficient is not 0, it is marked as version transition; when the version difference is 0 but the late availability coefficient is significantly less than 1 and the preferred record message time lags behind the epoch time, it is marked as late or out of order; when there is no record in the candidate set that meets the requirements of a non-zero late availability coefficient and a field integrity flag, and the status continuously crosses the preset epoch count threshold, it is marked as a real interruption. The preset epoch count threshold is used to implement hysteresis, so that the status label does not frequently flip due to the loss of a single epoch under link jitter.

[0060] Finally, the mobile terminal encapsulates and outputs the status label of each satellite along with the satellite-by-satellite correction candidate set. The output object includes the satellite identifier, correction category, preferred record, alternative record, delay amount, field integrity flag, version consistency index, late availability coefficient, and status label body.

[0061] In use, the late availability coefficient characterizes the backfill semantics, and the stable state label is generated by combining the version consistency index and hysteresis judgment before outputting the encapsulated object. Late and expired records are clearly distinguished by the segmentation function to avoid expired records being mistakenly included in the current epoch input semantics. The state label has hysteresis characteristics, maintaining continuity even under link jitter, which facilitates subsequent steps to trigger fixed paths according to the label.

[0062] Step 2: Based on the satellite-by-satellite correction candidate set and status label, establish a correction status filter for each satellite, and still form continuous equivalent corrections and uncertainty descriptions under version transition, late arrival or out-of-order conditions, and then output continuous terminal precision satellite trajectory and clock error products.

[0063] The target is the satellite-by-satellite correction candidate set and status tags output from step one. The mobile terminal no longer uses whether a correction message has been received as the sole criterion, but uses the status tags as the action switch for the correction status filter. To avoid abrupt changes in update intensity caused by the alternation of fresh and late records in boundary epochs, a measurement injection coefficient is introduced and linked to the version consistency index and the late availability coefficient, so that the measurement update presents a continuous change in intensity over time.

[0064] Link jitter in agricultural operations can cause correction records from the same satellite to exhibit varying freshness and version consistency across adjacent epochs. If the filter updates each record with the same intensity of measurement, it can easily mix up version-consistent but late records with version-inconsistent but transitional records, thus transferring input fluctuations into correction estimation fluctuations. Therefore, it is necessary to incorporate the version consistency index and late availability coefficient from step one into the update rhythm to form a verifiable injection rule.

[0065] The mobile terminal reads the status label of each satellite: when the status label is "Version Consistent and Available," the corrected status filter performs measurement updates; when the status label is "True Interruption," the corrected status filter only performs predictions and keeps measurement updates off; when the status label is "Version Transition," "Late," or "Out of Order," the corrected status filter does not directly reject candidate records, but instead scales the measurement information using measurement injection coefficients, so that the update intensity changes continuously with the version consistency index and the late availability coefficient. Therefore, the measurement injection coefficients do not change the semantics of the status label in step one, nor do they change the candidate record itself, but rather change the intensity at which candidate records enter the filter.

[0066] The mobile terminal retrieves the preferred record from the satellite-by-satellite correction candidate set, and then reads the version consistency index and late availability coefficient corresponding to the preferred record. The two are then combined into a measurement injection coefficient. This ensures that the injection strength changes in the same direction as the version and its freshness. The specific form of the measured injection coefficients uses logarithmic compression to avoid excessively abrupt changes in injection strength when approaching a certain value, thus maintaining a continuous filter update rhythm.

[0067] ;

[0068] Where: Measurement injection coefficient : A continuity coefficient used to scale the injection force of measurement information, with a value range of Used to scale measurement information increments; or, equivalently, to increase measurement noise, enabling soft injection; version consistency index. : A continuous measure used to assess the degree of match between corrected records and broadcast ephemeris versions, the completeness of fields, and their freshness; its value ranges from [value range missing]. ;

[0069] Late arrival availability factor : A continuous quantity used to measure whether a corrected record still possesses backfill semantics under a given delay condition; its value range is . Delay : The time offset between the epoch time and the time of the correction record message, with a value range of . After the measurement injection coefficients are formed, the mobile terminal enters the high range and uses the preferred record as the measurement update input when the version is consistent and available. When the version is interrupted, the value is set to 0 and the measurement update is turned off. When the version is transitioning, delayed or out of order, the measurement information is scaled so that the strength of the measurement update changes continuously with the quality of the candidate record.

[0070] To reduce numerical instability, the corrected state filter can employ information-form Kalman filtering or square root information filtering. The measurement injection coefficients directly affect the scaling of the information increment, keeping the condition number of matrix decomposition controllable during the update process.

[0071] In practice, status labels determine the on / off state of measurement updates, and measurement injection coefficients incorporate version consistency indices and late availability coefficients into the measurement information injection strength, thus forming a continuous update rhythm. The four semantic categories of status labels are retained as action trigger entry points, ensuring that the filter update path remains consistent across epochs, reducing action sway caused by link jitter. The measurement injection coefficients ensure that the strength of late and transitional versions entering the filter changes continuously, avoiding abrupt updates caused by forced full injection or full rejection within a single epoch.

[0072] For satellites with a status label indicating version transition, mobile terminals need to continuously generate usable correction inputs during the phase of broadcast ephemeris version switching and subsequent synchronization correction, ensuring continuity between the terminal's precise satellite trajectory and clock bias products at version boundaries. Instead of directly equating version transition with actual interruption, a cross-version bridging correction is constructed and a correction status filter is injected, using the precise satellite status anchor point as a reference.

[0073] Version transition is essentially an input semantic misalignment where the reference model switch precedes the correction switch. The mechanism manifests as follows: the broadcast ephemeris version identifier for the same satellite changes within adjacent epochs, while the available correction records in the satellite-by-satellite correction candidate set still point to the old version identifier. If the old correction is still overlaid with the new ephemeris at this point, it will introduce systematic bias and drive filter innovation anomalies; if the correction is directly rejected and pure prediction is entered, the version transition will be mistaken for a link interruption, leading to unnecessary prediction drift.

[0074] Therefore, it is necessary to use the terminal precision satellite trajectory and clock bias products already formed in the previous epoch as anchor points, and to re-express these anchor points under the new version of the ephemeris framework, thereby forming an injectable bridging correction.

[0075] At the end of each epoch, the mobile terminal solidifies the terminal's precise satellite trajectory and clock error product used for output in that epoch into a precise satellite state anchor point. This includes the satellite's position components and clock bias components in the Earth-fixed coordinate system; when the next epoch arrives and the status label is determined to be a version transition, the mobile terminal uses the current broadcast ephemeris ledger to calculate the broadcast satellite status of the same satellite. Then, the bridging correction vector is generated by the difference between the two. The bridging correction vector is written back to the first position of the satellite-by-satellite correction candidate set and participates in the correction state filter update as the preferred record under the version transition condition.

[0076] Since bridging corrections originate from differential construction rather than the original correction message, their injection strength must be controlled by the measurement injection coefficient, and their uncertainty description quantity must monotonically tighten with the duration of the version transition to avoid the backend becoming overly dependent on bridging corrections during the transition period.

[0077] The bridging correction vector is constructed using the difference method, and its specific representation is as follows:

[0078] ;

[0079] Where: bridging correction vector : A correction vector used during version transitions to express the difference between the anchor point and the new broadcast ephemeris. It includes position difference components and clock difference components, and its value range is constrained by the satellite orbit scale and clock difference scale; epoch time : A time parameter used to identify the current processing time, with a value range covering the continuous operation period of the terminal; Precision satellite status anchor point The satellite state vector, which is solidified from the terminal output of the previous epoch, contains at least the satellite position component and the clock error component.

[0080] Broadcast satellite status The satellite state vector, calculated from the current broadcast ephemeris at an epoch, contains at least the satellite position component and the clock error component.

[0081] The precise satellite status anchor point is solidified from the terminal precise satellite trajectory and clock bias product output from the previous epoch, and includes at least the satellite ground-fixed coordinate position component and the clock bias component. When there is no anchor point after system startup, the anchor point is initialized with the satellite status calculated from the broadcast ephemeris, and the anchor point source flag is set to broadcast initialization; when the first version is consistent and a correction update is available, the anchor point source is switched to the correction overlay output. In this way, cross-version bridging has an anchor point source before the first version transition.

[0082] The epoch time is taken from the system time of the receiver's observation epoch (e.g., the measurement time marker), and the message time is taken from the reference time carried in the correction message. When the correction message does not provide a reference time, the message arrival time can be used as a substitute message time, and the time source type is marked in the correction record so that different processing paths can be selected in subsequent steps.

[0083] After the differential construction is completed, the mobile terminal adds the bridging correction vector as the preferred record to the satellite-by-satellite correction candidate set, and sets the version consistency index of this record to a transitional value that can be distinguished from version-consistent records, so that the measurement injection coefficient is in the soft injection range during the transition period. The broadcast satellite state solution uses the standard solution process of broadcast ephemeris to obtain the satellite position and clock bias. The precise satellite state anchor point is derived from the terminal's output of the previous epoch without the need for a station. The position component can be smoothly aligned with the solution value within the epoch using cubic Lagrange interpolation, and the clock bias component can use the same interpolation time to ensure consistency of the differential construction time.

[0084] For example, on a tractor working between rows in an orchard, when the on-board terminal makes a U-turn at the edge of the field, the cellular link becomes congested. Subsequently, the broadcast ephemeris is updated, but the network correction is still the old version. The terminal marks the satellite as an interim version in the screen log, retrieves the precise satellite state anchor point from the previous epoch output, calculates the broadcast satellite state using the new broadcast ephemeris, forms a bridging correction vector, and writes it to the candidate set. The driver does not notice the sudden change in the trajectory line, and the controller turns along the predetermined row line. Several epochs later, the correction message is synchronized, the terminal restores the status label to be consistent with the version and available, and the bridging correction record naturally exits the preferred position.

[0085] Precision satellite status anchor points are fixed by terminal output. The broadcast satellite status is calculated using the new broadcast ephemeris. A bridging correction vector is constructed using differential methods and written back to the satellite-by-satellite correction candidate set, participating in filter updates via soft injection. Version transitions are represented as injectable bridging corrections rather than direct interruptions, maintaining continuous input semantics between the terminal's precise satellite trajectory and clock products at version boundaries. The bridging correction vector is constructed with anchor points as references and controlled by measurement injection coefficients, ensuring controllable injection intensity during the transition period and preventing the differentially constructed vector from being used as a highly reliable original correction.

[0086] For satellites with status labels of late or out of order, mobile terminals need to convert the late arrival correction records into continuous correction estimates that are still meaningful at the current time, rather than simply overlaying the late records directly onto the current broadcast ephemeris.

[0087] By preserving historical filtering states, backfilling and updating late epochs, and forward repropagation after backfilling, a time-series closed loop is formed, making the corrected estimation sequence self-consistent on the time axis.

[0088] Weak network backfilling often manifests as correction records arriving simultaneously from multiple epochs. If only the latest arriving record is considered the current measurement, records with earlier timestamps will be mistakenly used for the current epoch, disrupting the temporal consistency of the correction. If all late records are discarded, valuable backfillable information will be lost, causing the correction state filter to remain in pure prediction for an extended period and progressively tightening the uncertainty description. To balance temporal consistency and information utilization, backfilling updates need to be completed at the message time of late records, and then the update effects need to be propagated along the time axis to the current epoch.

[0089] The mobile terminal saves the historical state of the correction state filter at each epoch. The historical state includes the correction estimate, uncertainty descriptor, and trigger path marker for that epoch. When a late record is received, the terminal locates the corresponding epoch in the historical state sequence based on the message time of the late record, uses the late record as the measurement update input, and scales the update intensity using the measurement injection coefficient. After the update is completed, the terminal performs prediction and necessary bridging injection for each subsequent epoch in epoch order until it pushes to the current epoch, so that the current output reflects the information increment brought by the late record.

[0090] During the backfilling process, a late step-one delay can be used to limit the backfilling window. If the delay exceeds the discard limit, the device will not enter the backfilling chain, thus ensuring the boundary of the time-series closed loop from the source. The mobile terminal is implemented according to a circular sequence of relatively independent historical states of the satellites. Its index is determined by the message time in the step-one correction record library. The positioning process obtains the historical epoch position through the time index structure and then performs backfilling updates. The forward repropagation after backfilling updates does not save all observation information for each epoch, but it does save the trigger input summary, including the epoch's state label, preferred record identifier, and measurement injection coefficients. Repropagation uses the trigger semantics at that time without relying on re-diagnosis.

[0091] The state transition during repropagation can be implemented using a constant velocity discretization form (using a constant value or constant drift discretization model, with the discretization interval given by the epoch interval). The discretization coefficients are implemented through matrix exponentiation or first-order Taylor expansion. The engineering implementation of the matrix exponentiation can use Pad approximation and square exponentiation process, so that the terminal can still execute under the condition of limited computing power.

[0092] In practice, a separate historical filtering state sequence for each satellite is saved. Upon arrival of a late record, the epoch is located and backfilled according to the message time, and a measurement update is performed. Then, the sequence is forward-propagated to the current epoch, ensuring that late information enters the current corrected output in a time-consistent manner. Late records are not directly applied to the current epoch; backfilling and updating occur at their message time, guaranteeing the temporal consistency and traceability of the corrected estimation sequence. Forward repropagation reuses the state label and measurement injection coefficients from the previous epoch, preventing late backfilling from introducing update paths inconsistent with the previous semantics and avoiding abrupt jumps in the output.

[0093] After completing cross-version bridging and late backfilling, the output of the corrected state filter is organized into a fixed-delay smoothed output, which is then superimposed and encapsulated with the broadcast ephemeris calculation results to form a terminal precision satellite trajectory and clock bias product. The fixed-delay smoothed output does not change the internal timing update of the filter, but only changes the timing and method of the external output value, so that the control closed loop obtains a smoother input semantics.

[0094] Agricultural automated operation control typically relies on continuous trajectory input. If the corrected estimate for the current epoch is directly output, the information replenishment triggered by delayed backfilling may cause a significant change in the update magnitude at the current epoch, which then manifests as transient changes in lateral commands on the control side. Fixed-delay output shifts the output point forward by a defined time delay and performs kernel smoothing on the corrected estimate sequence within that time delay window, making the output more consistent with the control system's requirement for smooth input while retaining the information increment brought by delayed backfilling.

[0095] The mobile terminal generates a correction estimate sequence at each epoch and sets the output time to the current epoch minus a fixed delay, the value of which is determined by the sampling period of the job control. Near this output time, the mobile terminal extracts correction estimates from several adjacent epochs in the historical state sequence and performs smoothing synthesis using an exponential kernel weight. The weights monotonically decrease with time distance, ensuring that estimates closer to the output time have a larger weight. After smoothing, the terminal uses the broadcast ephemeris log to calculate the broadcast satellite state at the output time, then superimposes the smoothing correction to obtain the terminal's precise satellite trajectory and clock error product, and outputs the uncertainty descriptor along with it.

[0096] The fixed-delay smoothing output uses a discrete exponential kernel form, and the smoothing output is given by a weighted sum of the corrected estimation sequences:

[0097] ;

[0098] Where: smooth output : The smoothed correction vector corresponding to the fixed time delay output time, including the orbital three-axis correction components, clock error correction components, and necessary deviation correction components; correction estimation sequence : The correction estimate vector output by the correction state filter at a historical epoch; epoch index : Represents the historical offset relative to the current epoch, with values ​​ranging from the set of integers. Sample size : The number of historical samples contained in the smoothing window, a positive integer; the attenuation coefficient. The decay intensity parameter of the exponential kernel is a positive real number. The larger the value, the faster the weight decays with the historical offset.

[0099] Furthermore, the output time with a fixed time delay can be directly indexed from the historical state sequence. If the output time falls between two epochs, the components of the cubic Hermite interpolation pair can be interpolated on the time axis. The first derivative required for interpolation can be given by the drift term inside the corrected state filter or the difference between adjacent samples, ensuring the feasibility of the interpolation process.

[0100] After the smooth output is completed, the mobile terminal overlays and encapsulates it with the broadcast satellite status to form a terminal precision satellite trajectory and clock error product, and writes the status tag source information into the output header field, so that step three can identify that the output comes from a version-consistent available, version transition, or late backfill path.

[0101] Specifically, the output time is determined by a fixed time delay, and the corrected estimate sequence is smoothed and synthesized using exponential kernel weights to form a smooth output. The results are then superimposed and packaged with the broadcast ephemeris calculation results to form a terminal precision satellite trajectory and clock error product, which also carries an uncertainty description quantity.

[0102] In use, the output point is shifted from the current epoch to a fixed-delay epoch and then smoothed by kernel synthesis, so that the information replenishment caused by delayed backfilling is presented in a smooth form, reducing transient input changes on the control side. The output encapsulation carries path source semantics and uncertainty descriptions, enabling step three to directly perform job index mapping and degradation recovery determination based on the same semantic system.

[0103] Step 3: Transform the continuous equivalent corrections and uncertainty descriptions output from Step 2 into operational criteria, operational statuses, and action instructions that can be directly used for agricultural operation control, while maintaining the conservatism and traceability of the uncertainty descriptions under the condition that multiple sources of corrections coexist and their correlations are unknown.

[0104] For work sites where both on-board broadcast correction paths and network differential correction paths coexist, the precise satellite trajectories and clock error products from different sources are first unified into the same data semantics. Then, the correction inputs for each satellite are screened for compatibility. This avoids sending obviously incompatible inputs directly into the fusion calculation, which would cause status jitter on the work side, and forms a verifiable screening evidence chain.

[0105] Cellular links in agricultural operation areas may fluctuate due to terrain, inter-row obstruction, and equipment antenna sway. The correction records for the same satellite from the network differential correction path and the on-board broadcast correction path may be misaligned on the timeline. Simultaneously, the cross-version bridging path in step two may generate bridging correction vectors and soft-inject them using measurement injection coefficients during version transitions. If the operation side does not distinguish between the actual measurement update output and the bridging soft-injection output, the transition period output and the normal period output may be mixed, causing semantic confusion at the fusion entry point. Therefore, it is necessary to first perform homogenization labeling and compatibility screening to ensure that subsequent conservative fusion is performed among comparable objects.

[0106] For each satellite, the mobile terminal retrieves one precise satellite trajectory and clock error product record from different sources, and reads the source identifier, corresponding status label, and corresponding measurement injection coefficient from the record header field. And whether the record is formed by the bridging correction vector; the terminal uses the same epoch output time as the alignment reference, and aligns the smooth outputs from different sources according to the reference. If the alignment time falls between two epochs, the interpolation process in step two is used to perform time alignment on each component to ensure that the compatibility comparison occurs at the same time semantics.

[0107] After alignment, the terminal prioritizes source status labels: when a source status label indicates a true interruption, that source will not be included in the fusion process at the current epoch; when a source status label indicates a version transition and its measurement injection coefficient is within the soft injection range, that source will only be considered as a candidate input for compatibility comparison but not as the preferred fusion input; when a source status label indicates a version that is consistent and available, late, or out of order and is within the backfill window, that source will be included in the preferred candidate set. Subsequently, the terminal performs compatibility screening within the preferred candidate set. The screening criteria are whether the terminal's precise satellite trajectory difference and clock difference from different sources on the same satellite exhibit interpretable continuous changes. The evidence is determined by whether the difference sequences of adjacent epochs are continuous and the order of magnitude of the difference sequences and the uncertainty descriptors from step two.

[0108] Compatibility screening uses the difference between precise satellite trajectories and clock differences from terminals of different sources at the same satellite and output time as the discrimination metric. This discrimination metric forms a difference sequence over several epochs. If the difference sequence exhibits sign reversal or amplitude abrupt change without version transition / late backfill status label support, the source at that satellite and epoch is downgraded to a candidate or eliminated. The difference sequence buffer length is consistent with a fixed time-delay window to ensure semantic alignment.

[0109] To ensure that compatibility filtering is feasible and verifiable, the mobile terminal employs a two-stage filtering chain: first, field-level filtering excludes records with missing fields, misaligned timestamps, or status tags indicating actual interruptions; then, sequence-level filtering excludes records where the differential sequence exhibits a reverse mutation within one epoch and lacks status tag support. During sequence-level filtering, the terminal maintains a differential sequence cache for the most recent few epochs. This cache is built at the satellite level and uses the same satellite identifier index as the circular buffer in step one to avoid index drift.

[0110] Meanwhile, field-level filtering can replace source identifiers with transmission link identifiers, and sequence-level filtering can replace differential sequence continuity with differential sequence monotonicity tests. As long as the filtering input is still based on status labels, measurement injection coefficients, and bridging participation identifiers, and the output is still a set of candidate sources that can enter fusion, the terms and objects can remain unchanged.

[0111] In use, first, the source identifier, status label, measurement injection coefficient, and bridging participation identifier are used to complete the unification and time alignment. Then, a set of candidate sources that can enter the fusion is output according to two filtering chains: field-level and sequence-level. The fusion entry object is unified in terms of time semantics and source semantics, and subsequent fusion calculations face comparable and smooth outputs. This avoids mixing in misaligned records during fusion. Status labels and measurement injection coefficients serve as a filtering evidence chain, ensuring that version transitions and actual interruptions present different input qualifications on the job side, reducing the job side's misuse of transition period outputs.

[0112] Based on the candidate source set, the smoothed outputs from multiple sources of the same satellite are conservatively fused, and the uncertainty descriptor is also fused simultaneously to avoid underestimating the uncertainty descriptor when the source correlation is unknown. Unlike the position result layer switching, the fusion is always completed at the correction layer. The output is still the equivalent correction that can be superimposed on the broadcast ephemeris, and it carries the equivalent uncertainty descriptor for direct use in the construction of subsequent operation criteria.

[0113] Correction information from different sources may share parts of the upstream processing link or the observation network, and there may be unobservable correlations between their error terms. If the correlations are unknown, the uncertainty description may be compressed to an unreasonable level, which may lead to an optimistic assessment of risk by the operational criteria.

[0114] To ensure that the downgrade and recovery triggers in step three do not depend on the premise of known correlation, a conservative fusion is performed using the covariance convergence concept, and the weight calculation is made public as a terminal-executable univariate search process to avoid conceptual description.

[0115] The mobile terminal selects two candidate source records for each satellite as inputs for fusion. The inputs include the source one smoothed output vector and the source one uncertainty description matrix, as well as the source two smoothed output vector and the source two uncertainty description matrix. If there are more than two candidate source sets, the terminal fuses them pairwise according to the compatibility screening score to form an iterative fusion chain, ensuring that each step still satisfies the conservative semantics of covariance intersection.

[0116] During the fusion process, the mobile terminal first fuses the uncertainty description matrices to form an equivalent uncertainty description matrix. Then, it uses the equivalent uncertainty description matrix to perform information domain synthesis on the smoothed output vector, ultimately obtaining the equivalent correction vector. The covariance convergence conservative fusion method uses weighting coefficients to control the proportion of information from the two sources, first obtaining the equivalent uncertainty description matrix. :

[0117] ;

[0118] Where: Equivalent uncertainty description matrix : A symmetric positive definite matrix used to describe the equivalent corrected uncertainty after conservative fusion, whose value range is the set of symmetric positive definite matrices; Source-one uncertainty description matrix Source 1 uncertainty description matrix, whose value range is the set of symmetric positive definite matrices; Source 2 uncertainty description matrix. The uncertainty description matrix carried by the source two record takes values ​​within the set of symmetric positive definite matrices;

[0119] Conservative fusion weighting coefficient : A scalar coefficient controlling the proportion of information from the two sources, with a value range of [value range missing]. Its function is to adjust the dependence of the fusion result on the two sources under the premise of conservatism;

[0120] After obtaining the information, the mobile terminal synthesizes the equivalent correction vector using the information domain. :

[0121] ;

[0122] Where: equivalent correction vector The correction vector output after conservative fusion includes orbital three-axis correction components, clock error correction components, and bias correction components incorporated into the fusion; Source 1 correction vector. The correction vector of Source 1 is formed by extracting the correction components from the smoothed output of Source 1, and its value range is constrained by the satellite orbit scale and clock error scale.

[0123] Source 2 correction vector The correction vector recorded in Source 2 is formed by extracting the correction components from the smoothed output of Source 2, and its value range is constrained by the satellite orbit scale and clock error scale; the equivalent uncertainty description matrix. The matrix obtained from the previous formula serves to map the synthesized result of the information domain back to the correction vector domain in this formula.

[0124] Source-one uncertainty description matrix Same as above, its function is to provide source one information domain weights; source two uncertainty description matrix. Same as above, its function is to provide source two information domain weights; conservative fusion weight coefficients. Same as above, its function is to adjust the proportion of information from the two sources.

[0125] The specific form of the weighted objective function:

[0126] ;

[0127] objective function Used to select conservative fusion weight coefficients A scalar function, taking values ​​from the set of real numbers, serves to measure the volumetric scale of the equivalent uncertainty description matrix; conservative fusion weighting coefficients. The range of values ​​is Equivalent uncertainty description matrix : A symmetric positive definite matrix calculated using the conservative fusion formula of covariance intersection; The function is a logarithmic determinant, and its stability is improved by first calculating the logarithm of the determinant and then taking the exponent.

[0128] The conservative fusion weight coefficients are solved using a one-dimensional search process: the mobile terminal selects a sequence of candidate weights within an interval, calculates the logarithm of the determinant of the equivalent uncertainty description matrix for each candidate weight, and selects the candidate weight that minimizes this logarithm, thus choosing a fusion result with more concentrated information under conservative constraints. This solution process can employ the golden section method or a grid search; the terminal only needs to perform univariate function evaluation and interval shrinkage. As an equivalent implementation, the objective function for weights can be replaced by the logarithm of the determinant with a trace function. As long as the weight solution remains constrained and the fusion form maintains the covariance intersection structure, the conservative semantics can remain consistent.

[0129] When using this method, a covariance convergence conservative fusion is employed within the candidate source set to first obtain the equivalent uncertainty description matrix from the fusion. Then, an equivalent correction vector is synthesized in the information domain. And solve using a one-dimensional search process. Under the condition of unknown source correlation, the equivalent uncertainty description matrix maintains conservative semantics, providing input basis that is not easily underestimated for the construction of subsequent operation criteria; fusion occurs in the correction layer rather than the result layer, and the operation side always receives continuous input of the equivalent correction vector, reducing the semantic break on the operation side caused by the switching of the result layer.

[0130] The output equivalent correction vector and equivalent uncertainty description matrix are further mapped into verifiable criteria for agricultural operations. This allows operational control to depend not on fixed interruption duration thresholds, but on a decision chain based on whether the upper bound of the prediction meets the operational threshold. The key is to disclose the mapping relationship and the construction method of the upper bound scale, so that the criteria can be reproduced by those skilled in the art.

[0131] The closed-loop management system for agricultural operations truly focuses on the control risks associated with lateral offset, heading offset, trajectory spacing deviation, upper limit distance, and disturbance tolerance endurance. These quantities are not directly equivalent to the uncertainty description of a single satellite's correction. If the magnitude of the correction uncertainty description is directly used as the trigger for downgrades, situations arise where changes in satellite geometry alter operational risks while the correction uncertainty description remains unchanged, leading to a disconnect between the criterion and operational risk. Therefore, it is necessary to map the correction uncertainty description to the operational indicator space and construct a comparable upper bound for prediction.

[0132] The mobile terminal first determines the operational index vector, which includes at least three components: lateral offset, heading offset, and trajectory spacing deviation. These components are then linked to the components of the equivalent correction vector through a linearization relationship in the observation equation. This linearization relationship is given by a sensitivity mapping matrix, where each column corresponds to the effect of a small perturbation of one correction component on each component of the operational index vector.

[0133] The sensitivity mapping matrix can be obtained through analytical differentiation or numerical differentiation: the terminal applies a perturbation step size to each component and recalculates the job index vector. The perturbation step size is controlled by a perturbation step size coefficient, which takes values ​​in the range of positive real numbers and scales with the dimensions of the components to ensure that the numerical differentiation is not dominated by dimensions. After obtaining the sensitivity mapping matrix, the terminal maps the equivalent uncertainty description matrix to the job index uncertainty description matrix, and then constructs a prediction upper bound scale from this matrix and compares it with the job threshold.

[0134] The mapping of the uncertainty description matrix of the work performance index adopts the form of matrix congruence transformation:

[0135] ;

[0136] Where: Uncertainty description matrix of work performance indicators : A symmetric positive semi-definite matrix used to describe the semantics of uncertainty in the task indicator vector, taking the values ​​of a set of symmetric positive semi-definite matrices; sensitivity mapping matrix : A linearized mapping matrix connecting the equivalent correction vector and the task indicator vector, taking the values ​​of the set of real matrices; sensitivity mapping matrix For task indicator vectors For equivalent correction vector Jacobian matrix:

[0137] ;

[0138] Job indicator vector It must contain at least one or more components of lateral deviation, heading deviation indication, and track spacing deviation; equivalent correction vector. The correction layer output from step three is a unified input.

[0139] Equivalent uncertainty description matrix : A symmetric positive definite matrix, whose value range is the set of symmetric positive definite matrices, which is used as input in this formula to provide the semantics of the correction layer uncertainty.

[0140] After obtaining the uncertainty description matrix of the operational index, the terminal constructs a prediction upper bound scale as a single scalar criterion. The prediction upper bound scale uses the maximum eigenvalue operator pair for value selection:

[0141] ;

[0142] Where: the upper bound scale of the prediction : A nonnegative scalar used to characterize the envelope scale of the uncertainty of the performance index, with values ​​ranging from 1 to 2. It compresses the matrix criterion into a single-value criterion that can be directly compared with the job threshold; the maximum eigenvalue operator : Maximum eigenvalue extraction operator for symmetric matrices, input is a symmetric positive semi-definite matrix, output is a non-negative real number; Uncertainty description matrix for work performance indicators Same as above, used as input to the maximum eigenvalue operator;

[0143] After the upper bound scale of the prediction is constructed, the mobile terminal uses the job threshold coefficient as the comparison object. The job threshold coefficient is formed by the job type configuration: corresponding thresholds are formed for sowing, fertilization and spraying operations, and the dimensions are consistent with the components of the job index vector.

[0144] Input sources for work indicators: The work line (e.g., a straight work line or a curved work line) is set by the operator or imported from the site work task file; the trajectory spacing parameter is obtained from the machine width / row spacing configuration; the vehicle's current speed and heading can be provided by the wheel speed sensor and heading sensor (or inertial measurement unit); if no external sensors are configured, the speed and heading output from the positioning calculation are used as substitutes, and the source type is marked in the work record.

[0145] The terminal further calculates the expected sustainable operating time by discretizing and extrapolating the changes in vehicle kinematics and observed geometry within the future prediction window, progressively updating the sensitivity mapping matrix, and recalculating the upper bound of the prediction scale. The discrete moment when the job threshold coefficient is first exceeded can be found. This first exceedance moment can be solved using a linear search or a binary search method. The terminal only needs to implement a closed loop of time stepping, criterion calculation, and threshold comparison.

[0146] As an example: When a sprayer travels along the long side of a plot, the terminal simultaneously receives the outputs of the satellite-broadcast correction path and the network differential correction path. Subsequently, network link jitter occurs, and status labels are delayed or out of order in adjacent epochs. The terminal first filters the set of candidate sources that can be fused, and then outputs the equivalent correction vector and the equivalent uncertainty description matrix. Next, calculate the uncertainty description matrix of the operational index and the upper bound scale of the prediction. The terminal screen continuously updates the operation status information and provides text prompts for the sustainable operation time in the prediction window, allowing the driver to determine whether to continue spraying along the current line or prepare to adjust the operation method at the end of the field.

[0147] Methods for obtaining the sensitivity mapping matrix: Analytical differentiation path: Based on the pseudorange observation equation, partial derivatives are calculated for the satellite position / clock error correction, forming a linear relationship between correction error and ranging error; then, the ranging error is mapped to the terminal position error using the geometric matrix obtained from the positioning solution; finally, the position error is projected onto the work line coordinate system to obtain operational indicators such as lateral offset and heading offset. Numerical differentiation path: A perturbation step size is applied to each component of the equivalent correction vector, and the operational indicator vector is calculated repeatedly. The difference between the two is divided by the perturbation step size to obtain the corresponding column of the sensitivity mapping matrix. The perturbation step size is bound to the component dimensions (e.g., position components use position perturbation step size, clock error components use clock error perturbation step size), and it is required that a complete operational indicator calculation can still be completed after perturbation.

[0148] When using it, the sensitivity mapping matrix maps the equivalent uncertainty description matrix to the job performance uncertainty description matrix. Then, the upper bound scale of the prediction is obtained by using the maximum eigenvalue operator and compared with the operation threshold coefficient, thereby forming an executable computation chain for the expected sustainable operation time.

[0149] The minimum prediction model for the expected sustainable operation time: the vehicle movement within the future prediction window is discretized by using a constant speed along the operation line or a constant speed and constant heading model; when the satellite geometry and sensitivity mapping matrix is ​​updated over time, it can be obtained by extrapolating the satellite ephemeris of the current epoch and using the growth rule of the correction uncertainty description matrix.

[0150] The operational criteria are derived from the description of the uncertainty in the correction layer. The dimensional relationships between the criteria and lateral offset, heading offset, and trajectory spacing deviation are explicitly disclosed, facilitating reproduction and parameter tuning. The upper bound of the prediction scale is compressed from the matrix criteria into a single-value criterion, which can be directly used by the operator for threshold comparison and time step solution, avoiding the direct exposure of complex matrix criteria to the control side. The operational threshold coefficient and recovery threshold coefficient are given by the operational type configuration file. The recovery threshold coefficient is strictly smaller than the operational threshold coefficient to form hysteresis. This configuration file can be factory preset or loaded by the operator selecting the operational mode.

[0151] Based on the predicted upper bound scale and the estimated sustainable operation time, an adaptive degradation and smooth recovery action chain is formed. The triggering reasons, triggering times, and corresponding input semantics of the action chain are written into the operation record for subsequent verification and delivery. Emphasis is placed on the executableness of the action chain, the traceability of the trigger chain, and the hysteresis of the recovery chain to avoid frequent back-and-forth switching during the operation, which would cause difficulties in understanding for the operator.

[0152] Agricultural operation control involves human-machine collaboration. Operators need to see clear state changes and clear triggering reasons. If the system switches back and forth around a threshold, it will be difficult for the operator to determine when to take over and when to resume operation. Furthermore, the controller may repeatedly receive different levels of trajectory input in a short period of time, causing steering wheel vibration. Therefore, it is necessary to introduce hysteresis logic to give degradation triggers and recovery triggers different criterion boundaries, and to record the triggering reasons and input semantics together for verification.

[0153] Mobile terminals describe job levels using a job state machine, which includes at least four states: job hold, degrade preparation, degrade execution, and recovery preparation. State transitions are determined by an upper bound of the prediction scale. Driven by both expected sustainable operation time and semantic status labels: When the operation threshold coefficient is about to be exceeded within the prediction window, the state machine enters a degraded preparation state, and the terminal outputs a deceleration command or an increase overlap command to the controller, while also prompting the operator on the interface; when the operation threshold coefficient has been exceeded or the expected sustainable operation time has reached zero, the state machine enters a degraded execution state, and the terminal outputs a low-level navigation trajectory to the controller or prompts for manual takeover, while also injecting the status label and measurement coefficients at that moment. The system checks whether a bridging correction vector is involved and writes a summary of the equivalent uncertainty description matrix into the job record. If, within several subsequent epochs, the system returns to within the recovery threshold coefficient and the status label returns to a version that is consistent with the available version, late, or out of order but within the backfill window, the state machine enters the recovery preparation state. The terminal uses a fixed-delay smooth output as the trajectory input base and gradually removes the degradation action, eventually returning to the job hold state. Different configuration values ​​are used for the recovery threshold coefficient and the job threshold coefficient to create a hysteresis boundary between degradation and recovery, avoiding repeated switching near the threshold.

[0154] The mobile terminal decomposes the action chain into two parallel chains: control-side action output and human-machine interface (HMI) alarm output. Control-side action output includes: switching the control target from the operational trajectory to a lower-level navigation trajectory, limiting the maximum rate of change of steering angle, triggering deceleration gears, and triggering overlapping control strategies for spray valves. HMI alarm output includes: displaying the current operational level, displaying the estimated continuous operational time, and displaying the reason for the downgrade. The operational record encapsulation uses a structured field writing method, with fields including at least: timestamp, satellite identifier set summary, status tag statistical summary, whether it is in version transition, whether late backfilling has occurred, summary of the equivalent correction vector, summary of the equivalent uncertainty description matrix, and prediction upper bound scale. Trigger action type. As an equivalent implementation, the control-side action output can be replaced by a deceleration command to an angle-limiting command, and the human-machine interface alarm output can be replaced by a text prompt to an audio-visual prompt, as long as the state machine transition remains... With the expected sustainable operation time and status label semantics as the driving force, and the operation record fields still containing trigger reasons and input semantics, the executability and traceability of the action chain can be maintained.

[0155] As an example: When a rice transplanter enters a soft muddy area near a paddy field ridge, changes in the vehicle's attitude worsen antenna obstruction, causing delayed recovery of the network differential correction path. The terminal screen displays the operation status changing from operation hold to degraded preparation state, prompting the operator to reduce speed. As the transplanter continues along the edge of the field, the upper bound of the prediction scale continues to rise. The terminal switches the operation status to degraded execution state, the controller changes the steering control target to a low-level navigation trajectory and limits the steering wheel change speed. The operator can see the degraded reason field on the interface and choose to continue moving slowly. Subsequently, the transplanter returns to an unobstructed area, the status label returns to version consistent and available, the upper bound of the prediction scale drops to within the recovery threshold coefficient, the terminal enters recovery preparation state and gradually removes the angle limiting strategy, the interface prompts that the operation status has returned to operation hold, and the operation log saves the trigger chain of this degrade and recovery for easy review after the shift.

[0156] When used, it is used to predict the upper bound scale. The expected sustained operation time and status label semantics drive the hysteresis transition of the job state machine, and output control-side actions and human-machine interface alarms in parallel. Simultaneously, structured fields are written into the job record to solidify the triggering reasons and input semantics. Degradation and recovery are controlled by hysteresis boundaries, and state transitions are continuous. Operators can see state changes and reason fields consistent with the trigger chain on the interface. The job record solidifies the triggering actions and input semantics, enabling subsequent verification of whether the degradation reason stems from version transition, delayed backfilling, or a genuine interruption, providing a basis for delivery and maintenance.

[0157] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0158] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0159] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0160] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0161] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for high-precision satellite trajectory processing of mobile terminals based on Kalman filtering algorithm, characterized in that: include, Receive broadcast ephemeris and high-precision correction information, and write the broadcast ephemeris version identifier, the message timestamp of the high-precision correction information, the associated version identifier and the field integrity flag into the correction record database and cache it according to satellite, forming a satellite-by-satellite correction candidate set and status label; A correction state filter is established for each satellite based on the status label. Kalman filtering is used for prediction and updating. During version transition, a bridging correction vector is generated by the difference between the precise satellite status anchor point and the broadcast ephemeris. When the satellite is late or out of order, the correction is backfilled and propagated forward. The output is a fixed-delay smooth equivalent correction vector and an equivalent uncertainty description matrix. The terminal's precise satellite trajectory and clock error products are generated using the equivalent correction vector and equivalent uncertainty description matrix, and mapped to the operation index vector and prediction upper bound. The prediction upper bound is compared with the operation threshold coefficient and recovery threshold coefficient to drive the operation state machine to output the operation level and downgrade or recovery instructions. For each satellite at each epoch, correction records are selected from the satellite-by-satellite correction candidate set and status labels are generated. Among them, version consistency means that the associated version identifier is consistent with the broadcast ephemeris version identifier and the fields are complete. Version transition means that the broadcast ephemeris version identifier has been updated and the correction record corresponds to the old version. Late or out-of-order means that the message timestamp is behind the current epoch and is within the backfill window. True interruption means that there are no available correction records for several consecutive epochs.

2. The high-precision satellite trajectory processing method for mobile terminals according to claim 1, characterized in that: The correction record library establishes a circular buffer based on satellite number and a time index based on message timestamp. When receiving high-precision correction information, it inserts it into the corresponding position according to the time index and writes the broadcast ephemeris version identifier, associated version identifier, field integrity flag, delay duration, and correction category into the corresponding correction record. Correction records that exceed the cache window are eliminated according to time.

3. The high-precision satellite trajectory processing method for mobile terminals according to claim 2, characterized in that: Version transition determination is based on version difference, which is determined by the minimum difference between the broadcast ephemeris version identifier and the associated version identifier. When the associated version identifier is missing, the corresponding correction record is marked as missing version identifier and its priority in the satellite-by-satellite correction candidate set is reduced.

4. The high-precision satellite trajectory processing method for mobile terminals according to claim 3, characterized in that: The state variables of the correction state filter include orbital triaxial correction, clock error correction and its drift term. When the version is consistent and available, the correction record is used as the measurement input to perform the update. When there is a real interruption, only the prediction is performed and the equivalent uncertainty description matrix is ​​expanded. The update process introduces measurement injection coefficients based on the state label to adjust the measurement update intensity.

5. The high-precision satellite trajectory processing method for mobile terminals according to claim 4, characterized in that: The precise satellite state anchor point is determined by the precise satellite trajectory and clock error product of the previous epoch terminal. The bridging correction vector is formed by the difference between the precise satellite state anchor point and the satellite position and clock error obtained from the broadcast ephemeris. The position difference is then projected into radial, tangential, and normal unit vectors to generate a three-dimensional orbital bridging correction.

6. The high-precision satellite trajectory processing method for mobile terminals according to claim 5, characterized in that: When a correction is late or out of order, the historical state of the correction status filter is saved in the cache window of the correction record library. After receiving a late correction record, the historical epoch is located according to the message timestamp to perform backfilling and updating, and the recorded status label is propagated forward to the current epoch.

7. The high-precision satellite trajectory processing method for mobile terminals according to claim 6, characterized in that: When the terminal receives multi-source corrections, it first performs compatibility screening based on the differential sequence of the terminal's precise satellite trajectory and clock error products. Then, at the correction layer, it uses the covariance intersection method to obtain the fusion result of the equivalent correction vector and equivalent uncertainty description matrix that have passed the screening. The intersection weight is determined by one-dimensional search and the fusion matrix is ​​positive definite.

8. The high-precision satellite trajectory processing method for mobile terminals according to claim 7, characterized in that: The operation index vector is calculated based on the terminal's precise satellite trajectory and clock difference product in the operation line coordinate system. The upper bound of the prediction is determined by the operation uncertainty obtained by the equivalent uncertainty description matrix through sensitivity mapping. The maximum eigenvalue of the operation uncertainty is obtained by power iteration as the upper bound of the prediction. The sensitivity mapping is obtained by perturbing each component of the equivalent correction vector according to a preset perturbation step size and recalculating the operation index vector.

9. The high-precision satellite trajectory processing method for mobile terminals according to claim 8, characterized in that: The job state machine is set to four states: hold, degrade preparation, degrade execution, and recovery preparation. The state transition is triggered by the comparison result between the prediction upper bound and the job threshold coefficient and the recovery threshold coefficient, and the transition is required to be executed after several consecutive epochs meet the same triggering condition. The job state machine outputs the job level, the estimated duration of the job, and the instructions corresponding to the current state, including downgrade instructions and recovery instructions, and writes them to the job log.

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