Operating vehicle multi-source fusion high-precision positioning method based on Beidou inertial cooperation

Abstract

The invention discloses a Beidou inertial cooperative operating vehicle multi-source fusion high-precision positioning method, and relates to the technical field of vehicle-mounted navigation positioning, and the method comprises the steps: S1, completing GNSS / IMU / wheel speed collection, PPS alignment, external parameter calibration and quality control at an end side, and carrying out the uplink at unified event time; s2, constructing a short window factor graph and an IMM, carrying out adaptive switching between RTK / PPP / DR, and outputting HPL by adopting logarithm domain covariance update and RAIM; s3, an out-of-order is rearranged according to event time, and probability association and double-time-axis smoothing are implemented; s4, performing deduplication shaping on the cloud edge stream, introducing an HPL perception fence and performing multi-channel convergence; s5, driving mirror image updating by scene reweighting, soft minimum and tail risk; centimeter / decimeter-level positioning, tunnel exit convergence, fence low false alarm and end-to-end time delay P95 < = 1s can be realized under complex shielding, and playback and statistics are kept consistent.

Description

Technical Field

[0001] This invention relates to the field of vehicle navigation and positioning technology, specifically to a high-precision positioning method for operating vehicles using BeiDou inertial coordination and multi-source fusion. Background Technology

[0002] The daily operation and maintenance of highways are showing a trend towards grouping, all-weather, and cross-scenario operations: long-distance mainline inspections, continuous tunnel maintenance, interconnected interchanges and elevated highways, low-speed and intensive dispatching at toll stations and service areas, and emergency rescue operations in severe weather or at night are carried out in parallel. Current vehicle positioning systems mostly rely on BeiDou / multi-constellation RTK or PPP single-stack solutions, combined with conventional extended Kalman filtering for trajectory estimation and background trajectory playback; simple dead reckoning compensation is commonly used in highly obscured areas such as tunnels and urban canyons. On the platform side, mainstream systems use JT / T 808 access and rule engines for electronic fence determination and alarm distribution, with fences often using geometric inclusion or fixed threshold speed / direction strategies for binary determination. The above system can achieve good positioning in open scenarios, but under complex conditions such as occlusion, multiple paths, weak networks, and multiple vehicles running in parallel, it exposes problems such as cross-modal misalignment caused by clock asynchrony and inconsistent external parameters, the fixed noise model's inability to adapt to sudden environmental changes, trajectory breakage caused by late and duplicate packets, inconsistency between playback and statistical caliber, and false alarms / no alarms caused by the lack of complete quantization in fences. It is difficult to meet the comprehensive requirements of centimeter to decimeter level accuracy, end-to-end low latency, and auditability.

[0003] The core technical problem this invention aims to solve is: how to construct a continuous processing chain that integrates BeiDou / inertial multi-source fusion with safety linkage, under conditions of high obstruction and strong reflection such as highway operating vehicles being in high-obstruction and high-reflection environments such as tunnels, interchanges, urban canyons, toll / service areas, and rainy / foggy nights, and where cellular links experience jitter, duplication, and delayed reporting, so that the three links of positioning, trajectory, and fence alarm can maintain temporal consistency and computable risk under unified event time, unified external parameters, and integrity constraints.

[0004] The problem arises from several factors. First, the receiver's local clock and IMU timescale are not from the same source, and the rapid coupling of dynamic lever arms and attitude changes leads to cross-modal observation misalignment. Multipath and occlusion cause time-varying measurement quality, which traditional single-model and fixed-noise filtering cannot adapt to. The introduction of GNSS at tunnel entrances and exits causes abrupt convergence changes, and common methods lack a systematic approach to re-acquisition and ambiguity reconstruction after exiting the tunnel. Second, weak networks cause out-of-order and repetitive acquisition frames. If the platform directly writes the data according to the reception time, it will disrupt kinematic continuity and induce trajectory crosstalk. At the same time, existing electronic fences mostly use geometric inclusion for binary judgment, failing to convert positioning uncertainty into protection limits for decision-making. They lack integrity constraints centered on HPL / HAL, resulting in frequent boundary grazing misjudgments and delayed identification of loitering behavior. Furthermore, mode switching lacks probabilistic scheduling (between RTK / PPP / DR), the gating strategy does not combine time weight and covariance propagation, and off-order repair lacks dual time axis consistency constraints, resulting in unequal playback and inconsistent statistical calibers; alarm aggregation is based on OR logic superposition, which cannot suppress occasional anomalies in a single channel, and the P95 latency of the end-to-end processing link cannot be adaptively allocated according to the scenario.

[0005] This problem is particularly prominent in critical operations such as maintenance convoy lane changes and berthing, handling of emergencies, and construction windows in abnormal weather, resulting in: misjudgment of work vehicle entry and exit, delays in the passage of emergency vehicles, broken track evidence chains, and inconsistencies between command and dispatch playback and on-site facts, ultimately weakening the ability of digital coordination and safety management. 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 positioning method for operational vehicles using BeiDou inertial coordination and multi-source fusion. S1 completes GNSS / IMU / wheel speed acquisition, PPS alignment, extrinsic parameter calibration, and quality control at the end-user side, uplinking with a unified event time. S2 constructs a short-window factor map and IMM, adaptively switching between RTK / PPP / DR, employing logarithmic domain covariance updates and RAIM output HPL. S3 reorders events by time, implementing probabilistic correlation and dual-time axis smoothing. S4 performs deduplication and shaping in cloud-edge-stream processing, introducing HPL-sensory fencing and multi-channel convergence. S5 drives mirror updates with scene reweighting, soft minimum, and tail risk. This method achieves centimeter / decimeter-level positioning, tunnel exit convergence, and low false alarms for fencing even under complex occlusion conditions, with an end-to-end latency P95≤1s, thus solving 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] The BeiDou-inertial cooperative multi-source fusion high-precision positioning method for operating vehicles observes BeiDou, inertial navigation, and wheel speed, uses an event time mapping operator to unify the time scale, performs external participation dynamic lever arm correction, constructs a quality score-weight mapping, carries idempotent keys uplink according to logarithmic congestion scheduling, and outputs standardized data frames.

[0011] Based on the standardized data frame, factor graph short window optimization is performed, and IMM is used to switch between RTK / PPP-AR, PPP, and DR to update the noise covariance with log Euclidean algorithm, and output the state covariance and HPL.

[0012] The fusion product frames are rearranged according to the event time, and the probability gating association is performed based on the state covariance and the HPL. Dual time axis smoothing is then performed to output the vehicle trajectory, trajectory quality score and event confidence.

[0013] The input is shaped and deduplicated using the idempotent key, and a four-segment time-delay convex optimization budget is performed; based on the signed distance, direction difference, dwell time and combined with the HPL modeling fence intrusion probability, the alarm probability is obtained by suppressive aggregation.

[0014] Representative reweighted matching scenario moments are used to form an acceptance score by aggregating multiple indicators with entropy regularization soft minimum; the tail excess of the difference between the HPL and the alarm limit is used to define the integrity risk, and the weights of the mirror descent mode and platform parameters are updated.

[0015] Furthermore, the event time mapping operator continuously estimates based on the discrete model of local phase and fractional frequency offset, combined with pulse second calibration and superimposed cable delay constant, estimates the frequency offset change rate, unifies the receiver and inertial navigation local time into event time, updates the frequency at a frequency not less than one hertz, and re-estimates the mapping result as the window rolls, and uses it as the sole time stamp for subsequent quality weighting, idempotent scheduling and factor graph indexing.

[0016] Furthermore, the extrinsic parameters are used for dynamic lever correction in the navigation coordinate system. The attitude is given by inertial calculation, and instantaneous displacement compensation is constructed by coupling the vehicle body angular velocity and the lever vector. The time residual term and the installation extrinsic parameters are incorporated into the correction model and continuously updated to output an observation sequence with a unified spatial reference. The vehicle body position in the navigation coordinates serves as the entry point for subsequent fusion.

[0017] Furthermore, the quality score-weight mapping takes the carrier-to-noise ratio, multipath index and residual magnitude as input, generates weights through a continuously differentiable soft gating function and writes them into the standardized data frame, and performs logarithmic congestion scheduling according to queue occupancy and carries the idempotent key and time slice number. The weights are consistent with the unified spatial reference system in the event time domain and are used for adaptive calling by the factor graph and the mode.

[0018] Furthermore, the factor graph short window optimization simultaneously includes weighted satellite position factors, inertial pre-integration factors, wheel speed factors, and road geometry set constraints. It also employs a robust kernel with bounded influence to perform Gauss-Newton or Levenberg-Marquardt iterations on the window of the event time index and output the state and covariance. The geometry set consists of the road centerline and a strip buffer. The short window covers a fixed number of frames and is solved in a unified time domain.

[0019] Furthermore, the mode adaptation adopts a three-model interactive multi-model framework to perform evidence fusion among carrier fixed index, visible satellite count, corrected data availability and the integrity quantification;

[0020] The constraint weights and observation noise are adjusted according to the posterior mode probability, and soft switching is performed between modes. The mode set includes RTK or PPP integer cycles, PPP and DR. The mode transition probability is non-zero and row-normalized, and is used as the modulation term of the log-Euclidean update intensity and subsequent gating input.

[0021] Furthermore, the noise covariance is updated exponentially in the logarithmic Euclidean domain, the forgetting factor is modulated by the mode probability and the satellite weight, and a positive definite lower bound is set as a lower limit constraint. The updated observation covariance and process covariance are back-injected into the factor graph and the correlation gating, and are synchronously recorded for historical tracing. The update is performed in each short window period and maintains the matrix symmetric positive definite property.

[0022] Furthermore, the horizontal protection limit is obtained by projecting the state covariance onto a horizontal plane and introducing an integrity coefficient. The horizontal protection limit and the state covariance are stored together and used as inputs to the gating radius in step three and the fence threshold in step four. The protection limit is also passed downstream over time and associated with the alarm limit for consistency verification. The sampling and short window update rhythm are consistent with the alarm limit.

[0023] Furthermore, the probabilistic gating association combines the Mahalanobis distance of the geometric residual with the event time lag into a gating distance. The time weight is adaptively adjusted by the horizontal protection limit, and candidate allocation and probabilistic normalization matching are performed using a trajectory pool. Unmatched frames enter the delay buffer of the new trajectory and are subsequently re-associated. The maximum dwell time of the delay buffer is constrained by the four-segment time delay convex optimization budget and maintains order consistency constraints among overlapping candidates.

[0024] Furthermore, the dual-time-axis smoothing applies bounded curvature regularization to the event time axis and slowness constraint to the reception time axis. The sliding window length is one to three seconds. The trajectory quality score and event confidence are constructed using the horizontal protection limit, normalized gating distance, and curvature, and the weight and gating threshold of the next round are written back. The trajectory quality score and event confidence are written into the fusion product frame for fence determination consumption.

[0025] Furthermore, the access shaping is performed with queue occupancy as input for logarithmic time fine-tuning, and the idempotent key is formed by device identifier and time slice hash; the four-segment delay convex optimization budget allocates budgets for access, stream processing, fence determination and alarm distribution and satisfies the end-to-end delay upper limit constraint and is periodically re-estimated, and the sum of the budget vectors is equal to the upper limit and is adjusted with queue depth and risk level as adjustment signals.

[0026] Furthermore, the fence intrusion probability is composed of signed distance, direction difference, and dwell time and is scaled by the horizontal protection limit, and the alarm probability is generated by suppressive convergence and channel weights.

[0027] The acceptance score adopts entropy regularized soft minimum and updates the mode weights and platform parameters with mirror descent to form a closed loop. The representative reweighting performs moment matching on the working condition distribution at the sample level and uses integrity risk as the target input.

[0028] (III) Beneficial Effects

[0029] This invention provides a high-precision multi-source fusion positioning method for operating vehicles using BeiDou inertial coordination, which has the following advantages:

[0030] Dynamic lever compensation is achieved by combining attitude rotation matrix and lever vector. At the same time, quality control and satellite weights are constructed using carrier-to-noise ratio, cycle slip, and multipath markers. Standardized data frames with unified coordinates and fields are generated, which significantly reduces cross-modal misalignment and provides a stable and traceable input caliber for subsequent fusion.

[0031] The system adaptively switches between differential fixed, precise single-point, and dead reckoning modes using mode probabilities, and maintains positive definiteness and fast adaptation by updating logarithmic Euclidean covariance. It also outputs position, covariance, and horizontal protection limit, providing a consistent and reliable quantitative entry point for subsequent association and fencing.

[0032] Multi-target association is performed using gated distances that include time terms, under the joint constraints of state covariance and time weights. Playback and event semantics are unified by dual-time axis consistency smoothing, ultimately forming a trajectory set carrying horizontal protection limits and trajectory quality scores. This ensures the stable maintenance of trajectory continuity and identifier consistency under conditions of multiple vehicles running in parallel, late arrivals, and duplicate messages.

[0033] Online, resources are dynamically allocated across access, stream processing, fencing, and notification segments based on latency budget. Within the fencing engine, signed distance is used to unify the determination of circles, polygons, corridors, and along-line strips. Horizontal protection limits, directional differences, and dwell time are mapped to fencing intrusion probabilities. Then, soft aggregation is performed with channels such as reverse driving and sudden braking based on alarm probabilities to ensure that the determination criteria are consistent with the upstream uncertainty quantification.

[0034] Different operating conditions and multi-dimensional indicators are unified into an acceptance score. The tail integrity risk of the horizontal protection limit relative to the alarm limit is used to characterize low-frequency high-risk scenarios. Finally, the weights are written back to the geometric constraint weights, noise adaptive strength, time weights and delay budget through mirror update, so that the evaluation system, algorithm parameters and platform resource orchestration form a repeatable closed-loop optimization path and keep it matched with the business operating conditions. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the multi-source fusion high-precision positioning method for operating vehicles according to the present invention. Detailed Implementation

[0036] 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.

[0037] Please see Figure 1 This invention provides a high-precision positioning method for operating vehicles using BeiDou inertial coordination and multi-source fusion, comprising:

[0038] Step 1: Transform the original observations from a mixed state with multiple clocks, multiple coordinates, and varying quality into a standardized state with unified time scale, unified external parameters, quantifiable quality, and reproducible uplink, and output standardized data frames.

[0039] In high-speed and tunnel scenarios, the local clocks of the BeiDou receiver and the inertial navigation unit are not from the same source. Time-domain mismatch and phase drift will cause cross-mode observation alignment errors. At the same time, there is a rigid arm between the antenna phase center and the inertial navigation coordinate origin. The superposition of vehicle attitude changes and small time deviations introduces dynamic arm errors. In addition, satellite visibility, multipath and cycle slip will lead to uneven distribution of observation quality. If the observations are sent to the fusion layer indiscriminately, inconsistent estimations are likely to be triggered. Finally, if the uplink encapsulation fails to maintain idempotency and low congestion under weak network conditions, it is difficult for the platform to perform causal playback and consistency verification.

[0040] Therefore, by integrating four organically coupled technical points—event time alignment, external participation dynamic lever arm correction, soft gating quality weighting, and low-congestion idempotent scheduling—a standardized data frame that can be directly invoked by the fusion layer is formed. First, a unified time mapping operator flattens the time domains of each sensor. Then, external participation dynamic lever arm correction unifies the spatial reference system. Next, a continuously differentiable quality score-weight mapping suppresses gross errors, ensuring the numerical stability of subsequent factor maps. Finally, a logarithmic congestion correction scheduling function arranges uplink times and carries idempotent metadata, ensuring cloud-side replay equivalence.

[0041] By using a unified time mapping operator and dynamic lever compensation, BeiDou observations, inertial navigation observations, and wheel speed observations are compressed into the same time scale and the same spatial reference system, and the aligned navigation coordinate observation sequence is output.

[0042] Due to local crystal oscillator frequency offset and temperature drift, the BeiDou receiver time scale and inertial navigation time scale exhibit slow drift and micro-abrupt changes. If only a single PPS calibration is relied upon and the continuity of the drift is ignored, the event time will still retain nanosecond-level errors, which are amplified into spatial meter-level errors during high-speed turns. At the same time, the spatial offset between the antenna phase center and the inertial navigation origin forms a dynamic lever component under the combined effect of the vehicle angular rate and small time deviations, which needs to be eliminated within the extrinsic parameter framework.

[0043] First, the discrete dynamics of local phase and fractional frequency offset are established, and based on this, an event-time mapping operator is constructed to map the receiver's local time to event time. The following phase-frequency offset evolution model is adopted:

[0044]

[0045] Where: local phase : Describes the phase of the local clock, is a real number, and reflects the cumulative time error; fractional frequency offset : Describes the dimensionless deviation of the local clock from the ideal frequency. Frequency deviation rate : Describes the rate of change of fractional frequency offset, as Sampling step size : Interval between adjacent observations Noise item : Describes phase perturbations of unmodeled jitter, for .

[0046] Based on this, define the event time mapping:

[0047]

[0048] Among them: event time The unified timestamp used for merging is a real number of seconds; local time. : Local timestamp of the receiver or inertial navigation system, in real seconds;

[0049] Mapping Operator : A deterministic operator that maps local time to event time, with time-domain aligned mapping, in the form of the equation above; Cable delay can be obtained by PPS-aligned Kalman-enhanced or least-squares sliding window estimation. Set using known link calibration constants. The recommended update frequency is ≥1Hz.

[0050] Local phase Same as above, used to subtract cumulative phase error; fractional frequency offset Same as above, used to correct frequency scaling; cable delay. The fixed delay introduced by the RF link and processing chain is... .

[0051] By first estimating the fractional frequency offset and its rate of change, and then applying the mapping operator, all observations are recalibrated to event time, eliminating slow scaling and fixed link delays, thus providing a unified timescale for subsequent extra-space participation in quality control.

[0052] In practice, the uniformity of event time significantly reduces cross-modal interpolation errors; explicit compensation for fractional frequency offset and fixed delay improves alignment stability at tunnel entrances and exits; after time domain flattening, compensation for subsequent dynamic lever terms is no longer amplified by nanosecond-level time differences.

[0053] Using a unified time scale and with the navigation coordinate system as the primary reference, rigid external parameter modeling is performed on the arm from the antenna phase center to the inertial navigation origin. Dynamic components caused by angular rate and residual time deviation are then superimposed to construct the corrected vehicle position.

[0054]

[0055] Wherein: Navigation coordinates GNSS position The three-dimensional position of the antenna phase center in the navigation coordinate system, calculated by BeiDou; the vehicle position in the navigation coordinate system. : Position of the inertial navigation origin after external dynamic lever arm compensation; attitude rotation matrix An orthogonal matrix from the vehicle coordinate system to the navigation coordinate system, with elements of: They satisfy orthogonality; Obtained by IMU attitude calculation; Determined through external parameter calibration; Directly by The residual estimate is obtained;

[0056] Volume coordinate angular velocity Angular velocities of the three axes in the vehicle coordinate system, in units of Based on vehicle dynamics, it is usually lever arm vector : A three-dimensional vector pointing from the inertial navigation origin to the antenna phase center, which remains fixed after installation; time deviation residual The remaining minor alignment error after standardizing the time scale. Vector cross product operator : represents the vector cross product of angular velocity and lever arm, which yields a first-order approximation of the displacement induced by instantaneous linear velocity.

[0057] This correction formula aligns the spatial reference system with the navigation coordinates and explicitly compensates for dynamic levers coupled with attitude changes, thus avoiding position drift caused by sharp turns and asymmetrical installations.

[0058] In use, the external participation in the dynamic lever arm compensation significantly reduces the instantaneous position deviation during high-speed direction changes; observations after a unified spatial reference frame can enter the fusion layer with minimal degrees of freedom; the explicit retention of the time residual term provides observable measurements for subsequent mass weights and robust kernel settings.

[0059] A continuous and differentiable quality score-weight mapping is used to suppress gross errors and non-line-of-sight errors, and a logarithmic congestion correction time-domain scheduling function is used to ensure ordered uplink and idempotent replay under weak network conditions. Finally, a data frame with quality weight and idempotent metadata is output.

[0060] In urban canyons and tunnel entrances, satellite geometry and reflection environments change rapidly. If hard thresholds are used to exclude satellites, usability will decrease. If satellites are included without distinction, numerical instability will occur. Therefore, differentiable soft gating functions are needed to ensure that low-quality measurements are included with low weights, thereby maintaining geometric observability.

[0061] Meanwhile, weak networks and cellular congestion can cause sudden queue accumulation. If real-time congestion detection and scheduling correction are not performed, it will lead to timing disorder and false out-of-bounds errors on the platform side. It is necessary to smooth the uplink rhythm and carry idempotent information through a time-domain scheduling function.

[0062] First, a quality score is constructed using the carrier-to-noise ratio, multipath metrics, and residual magnitude. Then, continuous weights are generated using a logistic function for subsequent measurement weighting in the fusion process.

[0063]

[0064] Among them: quality score :satellite At the moment The overall quality score is a real number; carrier-to-noise ratio :satellite Carrier-to-noise ratio, in units , Carrier-to-noise ratio benchmark Smoothing constant Multi-path indicators A dimensionless index constructed from the characteristics of code phase difference. residual amplitude :satellite The absolute value of the current solution residual, in meters. Weighting coefficients The non-negative weights of each feature .

[0065] Then map the quality scores to weights:

[0066]

[0067] Where: weight : Continuous weights used for measurement weighting Steepness coefficient : Control the sensitivity of weights to scoring, for Scoring threshold The score corresponding to the median weight is a real number.

[0068] This continuous mapping avoids the sharp drop in usability caused by hard thresholding, allowing weak quality measures to retain geometric information with low weights; the logarithmic and absolute terms of the score together suppress multipath and residual anomalies; and the differentiability of the weights ensures numerical smoothness of the subsequent factor graph.

[0069] When used, the quality soft gating maintains the measurement geometry and suppresses gross errors in the occlusion boundary region; the differentiability of the weights improves the stability of optimization convergence; the scoring parameters can be transferred across scenarios, facilitating batch deployment.

[0070] In the event time series, the transmission time is fine-tuned based on the real-time queue occupancy to suppress congestion and maintain causal order; simultaneously, an idempotent key is constructed using a fixed time slice number and device identifier to ensure that deduplication and replay are equivalent on the platform side. The scheduling time is defined as:

[0071]

[0072] Among them; scheduling time : No. The actual time when each data packet was sent; event time : The time of the observed event; the baseline delay Base send offset, in seconds. Smoothing coefficient Congestion correction strength, for Queue occupancy at the previous moment : Instantaneous depth of the uplink buffer, in packets or bytes; scale constant Normalization metric, a positive number, used to avoid singularities.

[0073] The idempotent key consists of a device number and a time slice number. The time slice number is obtained by quantizing the event time according to a fixed slice length, ensuring that duplicate reports can be completely deduplicated by the platform. Logarithmic correction is approximately linear when the queue is low-occupancy, but its growth is limited when the queue is high-occupancy, thus avoiding synchronous congestion.

[0074] When in use, the scheduling function significantly reduces congestion jitter in weak network environments and maintains timing consistency; idempotent encapsulation ensures that the platform can perform lossless deduplication and causal replay; sharing event time and unified extrinsic parameters with quality weights ensures consistency between the end and the cloud.

[0075] Step 2: Under the constraints of unified spatiotemporal benchmark and quality weight, construct a continuous link of factor graph short window optimization + mode adaptive IMM + noisy log Euclidean update + integrity HPL evaluation, output state estimation and reliability quantification results, and solidify them into a standardized fusion product that can be consumed in the next step.

[0076] Operating vehicles are in rapidly changing environments such as open fields, canyons, and tunnels, and the observed geometry and noise characteristics are time-varying. If only fixed noise and a single filter are used, it is difficult to balance real-time performance and robustness, and drift and loss of lock are likely to occur at the occlusion boundary.

[0077] Therefore, it is necessary to use a short-window factor plot at event time. Perform batch consistency optimization based on satellite weights. Improve observability by incorporating road geometry constraints; simultaneously, adaptively switch between RTK / PPP-AR, PPP, and DR modes using mode probabilities to avoid mismatch with a single model; then, maintain positive covariance and quickly adapt to noise abrupt changes using log-Euclidean updates; finally, use horizontal protection limits... The metrics ensure accuracy and completeness throughout downstream fencing and security strategies.

[0078] By optimizing the geometric consistency of unified multi-source observations in the same time domain and spatial reference system using factor graph short window optimization, and by using mode adaptive probability scheduling to stably switch under different visibility and dynamic conditions, state estimation can achieve a tension balance between real-time performance and robustness.

[0079] The navigation coordinates output in the previous step indicate the vehicle's position. The dynamic lever arm and time residuals have been eliminated, but the observation quality still fluctuates with the environment; therefore, it is necessary to adjust the satellite weights. Explicitly inject optimization objectives, and use road / lane geometry sets. To achieve observability compensation; considering that the optimal model differs in different scenarios, it is necessary to use pattern probabilities Soft switching is performed between RTK / PPP-AR, PPP, and DR to reduce convergence instability caused by abrupt changes. Multi-factor consistency is first encoded using a factor graph objective function, and then the mode probability is updated using IMM and fed back to the noise and constraint strength of the objective function, forming a short-cycle closed loop of optimization-probability-re-optimization.

[0080] To simultaneously utilize high-quality BeiDou observations, inertial pre-integration, and wheel speed constraints, and to enhance observability through road geometry, in a length of... The objective function is constructed as follows within the short window:

[0081]

[0082] Where: objective function The weighted sum of residuals within the short window is a non-negative real number used for minimization; the short window index set. Coverage length is Event time window, Frame; Visible satellite set :time The set of participating satellite indexes;

[0083] Robust kernel function : Bounded influence function, used to suppress gross errors, specific form is shown in the following formula; for GNSS position factor, residual , where the observation function Output navigation coordinate position components;

[0084] Jacobi Take the derivative of position with respect to state. The IMU pre-integration factor is a concatenation of standard pre-integration residuals (velocity / attitude / position); the wheel speed factor residual is the velocity difference projected onto the direction of travel. The above ensures... It can be directly implemented using Gauss-Newton / Levenberg-Marquardt.

[0085] Satellite weight : Continuous weights from the previous step GNSS residuals :satellite At any moment Measurement residuals, vectors in meters; observation covariance :satellite Measurement noise covariance, real symmetric positive definite matrix; IMU residuals : Pre-integration error vector, with units of velocity / angle; process covariance : Inertial navigation process noise covariance, real symmetric positive definite matrix; wheel speed residual Mileage constraint residuals, in meters per second; wheel speed noise covariance. Wheel speed noise covariance, positive definite matrix; geometric constraint weights Road / lane constraint strength Distance function The shortest distance from the vehicle's location to the geometric set, in meters;

[0086] Assume the road centerline is a curve The band half-width function is The corridor distance is defined as:

[0087]

[0088] in Continuous piecewise cubic splines, constant or random Piecewise constants. If it's a polygonal fence, take... The Euclidean distance to the polygon boundary is positive on the outside and negative on the inside, with the sign determined by the normal (see below). (Detailed definition). This definition can be achieved through 1D line search or nearest-point projection;

[0089] Navigation coordinates vehicle position : The three-dimensional position of the vehicle body in navigation coordinates output in the previous stage, in meters; geometric set : The set of road centerlines / lane boundaries, including spatial curves and strip buffer zones.

[0090] To ensure sufficient disclosure, a robust kernel function of the Geman-McClure form is selected:

[0091]

[0092] Robust kernel value : Residual Scale Bounded response, Residual Scale :refer to scalar results, non-negative real numbers; kernel scale parameters : A positive parameter that controls the intensity of inhibition. .

[0093] When using it, by weighting the satellites With robust core Composite structures retain their geometric contribution without diverging under multipath and weak signal conditions; distance constraints Significantly improves lateral visibility in interchange and ramp scenarios; the short window design satisfies both end-side computing power requirements and ensures rapid reconstruction in rapidly changing environments.

[0094] Under varying visibility and dynamic conditions, the optimal model varies between RTK / PPP-AR, PPP, and DR. Therefore, soft switching based on mode probability is performed and fed back to the noise and constraint strength of the objective function, with the following update:

[0095]

[0096] Where: mode probability :time model Choose the probability. And for all The summation is 1; the observational likelihood is... :Model The likelihood of the current observation is positive and comes from the joint density of the residuals and covariance; using the Gaussian assumption, let the joint residuals be... Joint covariance ,but:

[0097]

[0098] Among them, dimensions The total observation dimension of the participating factors; This is derived from covariance splicing and linearization propagation under this model.

[0099] Transition probability From the model Transfer to model The probability, Normalization; prior pattern probability :time model Probability; Model Set : .

[0100] When used, the pattern probability Continuous evolution avoids estimation oscillations caused by hard switching; when the posterior mode probability When the height is increased, the system automatically increases the geometric constraint weights. It also suppresses the GNSS factor weights, forming a self-stable response to occlusion; the dual constraints of likelihood and transition prevent the model from remaining in a suboptimal state for a long time. For a moment hour, The probability of the mode; as a supplementary explanation: RTK / PPP-AR, PPP, and DR are three localization modes under the multi-model adaptive (IMM) framework, and their respective meanings are as follows (and are given by mode probability). Soft handover):

[0101] RTK / PPP-AR (Carrier Phase Fixed Cycle):

[0102] Meaning: Utilizing a high-precision solution with fixed carrier phase integers. RTK is for relative positioning (differential correction via a reference station / network, commonly using RTCM); PPP-AR is for precise single-point positioning + ambiguity fixing (using precise clock track and hardware offset / SSR or PPP-B2b, independent of local base stations). Typical inputs: Multi-frequency, multi-constellation phase / code observations + (RTK: short-range differential; PPP-AR: wide-area SSR / PPP-B2b) + integrity / quality metrics. Applicable scenarios: When there is open sky, good signal quality, and available correction data, it serves as the highest precision layer.

[0103] PPP (Precision Single Point Positioning, Float Solution):

[0104] Meaning: Single-point positioning based on precise clock track and bias correction, with unfixed carrier ambiguity (floating point). Accuracy and convergence are superior to standard single-point positioning but inferior to RTK / PPP-AR. Typical inputs: Multi-frequency, multi-constellation observations + precise clock track / bias product (or SSR) + quality indicators; no rigid dependence on local base stations. Applicable scenarios: Used as an intermediate layer when correction data is available but difficult to fix in integer cycles, or when complex environments cause AR instability.

[0105] DR (Dead-Reckoning):

[0106] Meaning: When GNSS is unavailable or extremely weak, calculations are performed using an inertial measurement unit (IMU), wheel speed / odometer, vehicle kinematics, and necessary map / lane constraints. Errors accumulate over time / mileage. Typical inputs: IMU pre-integration, wheel speed, ZUPT / ZAR detection, (optional) lane / road geometry factors. Applicable scenarios: tunnels, urban canyons, areas with severe obstruction, or temporary link interruptions; used as a continuity assurance layer. After GNSS is restored, it is incorporated into PPP / RTK convergence.

[0107] Key points of adaptive handover (briefly):

[0108] Model set: , by pattern probability Continuous updates, not hard switching. Triggering criteria: observed likelihood (innovation size / consistency), visible star count and C / N0, differential / SSR availability, fixed integer ratio (FixRatio), integrity index (such as HPL / RAIM), and short-term hysteresis and probability threshold, which comprehensively determine whether to switch from DR→PPP→RTK / PPP-AR or reverse the step.

[0109] Output method: Each mode is set according to... It participates in the integration and constraint weight adjustment to achieve a smooth transition and robustness.

[0110] Without compromising the positive covariance definiteness, the system rapidly adapts to observation noise and process noise, while maintaining a horizontal protection limit. The error ellipsoid is mapped to a safety threshold, thereby passing accuracy and integrity to downstream fence linkage.

[0111] Occlusion and multipath propagation lead to non-stationary noise statistics. Updating the covariance using a traditional weighted average can easily cause numerical instability or violate positive definiteness; therefore, updates need to be performed on a positive definite matrix manifold. Log-Euclidean updates are employed, and an innovative vector-driven adaptive strength is used. Regarding integrity, the horizontal projection of the state covariance needs to be coupled with the integrity coefficient to obtain… Supply and alarm limits Compare and trigger measurement removal and mode downgrade.

[0112] For each satellite channel and sensing factor, define an exponentially weighted update of the noise covariance in the logarithmic domain:

[0113]

[0114] Wherein: observation covariance :satellite At any moment The noise covariance is a real symmetric positive definite matrix; adaptive intensity. The forgetting factor is determined by the pattern probability and weight. Matrix logarithm With matrix index : Matrix functions defined by eigenvalue decomposition, preserving symmetry and positive definiteness; innovative vectors :satellite Measurement innovation, vector, unit: meter; stability term : To prevent low-rank positive numbers, identity matrix Same-dimensional identity matrix; historical covariance : Noise covariance of the previous time step, positive definite matrix.

[0115] In practice, the logarithmic Euclidean update maintains positive definiteness while suppressing anomalous innovations, thus avoiding numerical collapse in linear domain updates; adaptive strength From pattern probability With satellite weight Co-modulation enables rapid amplification of covariance under occlusion conditions and rapid convergence under open conditions; this update is directly fed back to the objective function and likelihood. This leads to a two-level closed loop of estimation-noise-estimation.

[0116] To project the estimated uncertainty onto the horizontal plane and couple it with the integrity factor, the horizontal protection limit is calculated:

[0117]

[0118] Where: Horizontal protection limit :time Horizontal protection limit; integrity factor Based on integrity risk level amplification factor, ; Maximum eigenvalue : Matrix maximum eigenvalue operation; indicates taking the maximum eigenvalue of the matrix within the parentheses;

[0119] Horizontal projection matrix : 3D covariance Projected onto the horizontal plane Matrix; State covariance : Uncertainty of the state after short window optimization, a real symmetric positive definite matrix.

[0120] When in use, the horizontal protection limit A conservative measurement of the most unfavorable horizontal direction using the form of the maximum eigenvalue can be directly compared with the alarm limit. Compare triggered measurement elimination with pattern downgrading; when the posterior pattern probability Increased state covariance When expanded, the horizontal protection limit It then rises and automatically degrades in the fence linkage, forming an end-to-end coupling from estimation to safety; this mechanism avoids over-optimism caused by acting solely on mean square error-like indicators.

[0121] Step 3: Under the constraints of unified time and space and integrity, the fusion product frames of multiple vehicles, multiple sources and multiple time delays are orderly compiled into a fleet trajectory that is time-consistent, reliably associated, replay isomorphic and trustworthy, so as to eliminate the impact of out-of-order, reduce false associations and provide a computable trustworthy entry point for electronic fence and safety linkage.

[0122] In scenarios such as highway entrances and exits, tunnel complexes, and multi-level interchanges, the arrival time of the fused product frames often differs from the event time, and intermittent gaps caused by network issues and occlusions between different vehicles may occur. If the time sequence is not reconstructed first, followed by correlation gating based on state covariance and integrity, and finally converged using a unified dual-timeline playback and quality scoring, the trajectory breakpoint rate and false correlation rate will significantly increase in congested road sections, leading to false triggering and non-alerts of electronic fences.

[0123] Based on event time The out-of-order measurements are re-arranged using the main timescale and the state covariance is used for consistency. With horizontal protection limit The probabilistic gating of co-modulation enables cross-frame correlation, thereby maintaining trajectory continuity and robust correlation under weak network and occlusion conditions.

[0124] The fusion output frames from the previous stage have been unified to event times at the edge. However, uplink congestion and retransmissions can cause non-monotonic receiving timing. If the trajectory is written directly in the receiving order, it will disrupt kinematic continuity and amplify the random fluctuations in short-window estimation. Therefore, it is necessary to introduce a monotonicity constraint on event times and apply a weighted penalty to all frame pairs that violate monotonicity. On this basis, each newly arrived observation is then matched with the current active trajectory pool using a gating system. The gating radius is determined by both state covariance and integrity, maintaining geometric consistency while introducing quantitative constraints on security and availability into the correlation process.

[0125] To restore the monotonicity of the event time series without discarding off-order observations, a trajectory is defined. The off-order loss function imposes a continuously differentiable logarithmic penalty on all adjacent frame pairs that violate monotonicity:

[0126]

[0127] Among them: off-order loss Trajectory The off-order penalty, a non-negative real number; a set of frame pairs. All satisfied Later in the order of receipt However, adjacent pairs of events do not satisfy the monotonicity requirement; event time : The main timescale unified by the mapping operator in step one, in seconds; slope coefficient : A positive parameter that controls the penalty kurtosis. . Adaptable , The average queue depth is set to the window level to suppress excessive penalties during congestion periods.

[0128] The loss increases exponentially with time reversal, thus guiding the rearrangement algorithm to minimize the cost while maintaining the original receiving order as much as possible; due to the use of a smooth logarithmic-exponential form, the subsequent joint optimization with short window smoothing has good numerical properties.

[0129] When used, it effectively suppresses motion spikes caused by time reversal when weak network jitter and retransmission coexist; when a sudden late packet occurs in the same vehicle, it can restore monotonicity with minimal adjustment cost; the output time-consistent sequence provides a stable prediction basis for subsequent gating.

[0130] After time consistency is achieved, new frames need to be assigned to the active trajectory. To suppress false associations and avoid over-conservatism, a gated distance containing geometric residuals and time lag terms is constructed, with a horizontal protection limit. Adaptive modulation time penalty weights:

[0131]

[0132] Among them: gate distance Candidate observations With trajectory The combined distance is dimensionless; geometric residuals The difference between candidate observations and trajectory prediction observations, with units consistent with the observation space; joint covariance. A positive definite matrix consisting of the measurement Jacobian matrix, the state covariance, and the observation covariance; time lag. Time weight: The time difference between candidate observed events and trajectory prediction, in seconds; Non-negative weights modulated by the horizontal protection limit. ,in , State covariance Trajectory The state covariance comes from the short-window output of step two; the observation covariance... The observed covariance of the current participating channel is derived from the log-Euclidean adaptive method in step two; the Jacobian matrix is ​​measured. The linearization of the state by the observation model. .

[0133] This distance is used for gating and normalization, and then applied for probabilistic correlation with a horizontal protection limit. Time weighting during magnification As the system increases its tolerance, it becomes more inclined to match time proximity to suppress erroneous overlap, thus explicitly bringing integrity factors into the association process.

[0134] When in use, it effectively reduces the risk of adjacent vehicles exchanging routes in mixed-traffic and merging sections; in the initial stage of obstruction restoration, it... The modulated time term suppresses cross-vehicle adsorption; the covariance and integrity from step two are directly applied to the correlation radius, forming an integrated closed loop of estimation and correlation.

[0135] After achieving time consistency and reliable correlation, the trajectory is reconstructed using dual-timeline consistency smoothing and a trajectory quality score is generated. Simultaneously, quality and integrity are compressed into an event confidence score, serving as a direct input for fence and safety linkage. In convoy mode, the platform needs to reconstruct the actual movement on the event timeline and achieve traceable playback on the receiving timeline. Smoothing only on a single timeline can easily lead to the paradox of seemingly smooth playback but inconsistent event sequences.

[0136] To this end, it is necessary to introduce joint consistency constraints on event time and reception time to make the trajectory isomorphic under the two time axes. Subsequently, it is also necessary to integrate the geometric stability of the trajectory in the current window, the gating distance statistics and the horizontal protection limit into a single quality score, and further propagate it into event-level confidence, so that the fence engine can directly call the threshold.

[0137] To avoid playback jitter and constrain anomalous foldback, a bounded curvature regularization term is applied to the event timeline, while coupling with the slowness constraint of the reception timeline, constructing a window-level consistency cost:

[0138]

[0139] Wherein: Consistency cost Trajectory The cost of the dual time axis is a non-negative real number; velocity component. Trajectory At any moment The velocity vector from the state Extraction, unit is Weight matrix : Positive semidefinite weighted matrix of velocity differences, element range Microregular Avoid sharp, non-differentiable positive numbers. ; Reception time The timestamp of the frame received by the platform, in seconds; event time. : Uniform master timescale from step one, in seconds; coupling coefficient The trade-off factor for consistency between the two time axes. Window collection : The set of indices in the current resmoothing window, covering event times of 1–3 seconds.

[0140] The first term employs a bounded curvature regularization of the Charbonnier form to preserve differentiability and suppress spike accelerations; the second term penalizes the bias of the reception / event with the absolute value of the time difference, making the playback statistically isomorphic to the real motion.

[0141] When in use, it significantly reduces the rewinding feeling in playback caused by off-order repair; in sharp bends and lane change scenarios, it limits excessive curvature without sacrificing realistic dynamics; dual time axis coupling ensures that the temporal semantics of operation and maintenance playback and compliance traceability are consistent.

[0142] To compress geometric stability, correlation reliability, and integrity into a single index, and to construct a trajectory quality score and propagate it as an event confidence score, the following differentiable mapping is adopted:

[0143]

[0144] Among them: trajectory quality score Trajectory At any moment mass fraction, Sigmoid function Defined as Differentiable mappings; coefficients Non-negative weights Horizontal protection limit The completeness quantification of the output from step two, in meters;

[0145] Normalized gated distance The average gate distance normalized to the threshold. ; A sliding window average gate distance regularization method is used to avoid instantaneous spikes affecting scoring stability. Curvature index. : A dimensionless curvature measure based on velocity and heading variations. .

[0146] When the horizontal protection limit When the gating distance and curvature decrease (increase confidence), the score rises; the score is then bound to the decision threshold of the event type to generate event confidence and enter the fence and security linkage.

[0147] In use, during the interchange merging phase, the scoring is sensitive to both geometric and temporal consistency, thus enabling early detection of potential false associations; at tunnel entrances and exits, the horizontal protection limit... The dominant term ensures that the quality rises steadily rather than abruptly during the rapid convergence phase; the differentiability of the score allows it to serve as a priori for the next round of short window weights, achieving cross-step self-consistency.

[0148] Step 4: Under unified time and space constraints and integrity constraints, complete the continuous processing chain of access shaping - latency budgeting - fence determination - alarm linkage, and output an auditable fence / security event flow with low latency and low false alarms.

[0149] The uplink data from the fleet faces pressure to achieve idempotent deduplication and out-of-order correction at edge sites and in the cloud. Without data reshaping and latency budget allocation, fence determination can be affected by sudden congestion and out-of-order events, leading to false boundary violations or missed alerts. Furthermore, if the fence threshold does not consider horizontal protection limits... Dynamic amplification can easily lead to accidental triggering in scenarios such as tunnel entrances and interchange complexes.

[0150] At the time of the event Under a unified timescale, idempotent shaping and out-of-order suppression are performed on inbound data, and adaptive budgeting is performed on the latency of the four segments of access-stream processing-fence determination-alarm distribution, so that the end-to-end P95 is controlled. Specifically, the 95th percentile (P95) of the end-to-end latency of the entire processing link is stably kept within a predetermined threshold.

[0151] Due to weak network jitter and duplicate reporting, the platform needs to remove duplicate packets and perform bounded delay shaping on late packets without losing frames. At the same time, it needs to adaptively allocate delay budgets based on the queue occupancy of each segment, so as to prioritize the real-time performance of the fence determination segment during congestion.

[0152] By introducing access time shaping at the edge access point, the actual entry time of each data packet is fine-tuned based on the event time to detect congestion and duplication, thereby suppressing out-of-order delivery and ensuring idempotent alignment.

[0153]

[0154] Where: access shaping time : No. The integer timestamp used for each data packet entering the database is used for downstream end-to-end sorting; event time The output of step one is a unified timestamp, in seconds; congestion weight. Logarithmic shaping strength , real number;

[0155] Inbound queue usage Access buffer depth, in packets or bytes, non-negative real number; normalized scale. Positive constants are used to scale queue depth. Repeat penalty coefficient The amount of time suppression applied to duplicate messages. Indicator functions A binary function that takes the value 1 if the predicate is true and 0 otherwise; a set of idempotent keys. The set of idempotent keys of data packets accepted within the current time window, used for duplicate identification.

[0156] For full disclosure, idempotent key Irreversible hashing using time slices and device identifiers:

[0157]

[0158] Where: idempotent key : Identifier An irreversible hash value of a packet, 128 bits or more wide; hash operator : Deterministic, irreversible mapping with a range of fixed-length binary strings; Using SHA-256, the first 128 bits of the output are used as the key; time slice length The device identifier constitutes the input; device identifier Unique vehicle / terminal identifier, string; time segment length Event duration quantification slice length, ; Integer operator Round down to the nearest integer, mapping the time to a fixed episode number.

[0159] In practice, logarithmic suppression-based integer shaping exhibits near-zero latency in low queues and smooth growth in high queues, avoiding synchronous congestion; idempotent keys suppress duplicate packets upon arrival at the access layer, limiting out-of-order jitter. The magnitude; uniform plastic surgery time Throughout the entire process, ensure isomorphism with the dual-time-axis consistency constraint in step three.

[0160] To adaptively allocate the budget for each segment within the total delay limit, an immediate solution for the following convex objective is proposed:

[0161]

[0162] Where: Optimal budget vector Optimal allocation of four time delay segments; current budget vector : Consists of four components , , , Composition, non-negative; nominal budget Reference vector given during design, in seconds; weight matrix : Positive semidefinite weight matrix, element range Adjust the deviation penalty for each segment; total delay limit. End-to-end delay constraint, in seconds, typical value. ;

[0163] Queue usage : Real-time queue depth for each segment, a non-negative real number; adjustment coefficient Queue sensitivity Numerical stability term : To prevent small positive numbers from being divided by zero ; All-one vector : Constrain the sum of the budgets for each segment.

[0164] When in use, if congestion worsens in a certain segment, its corresponding budget... Automatically reduce speed to increase processing rate, while fenced sections High-risk windows will be affected by the weight matrix. Weighted and prioritized; and the pattern probability in step two. Quality score in step three During coordinated operation, the total processing link can be dynamically reduced during dead reckoning DR-dominated or low-quality phases to maintain P95 latency from crossing the threshold.

[0165] At horizontal protection limit Under the integrity constraints, spatial relationships, movement direction and dwell time are coupled into the fence intrusion probability, and softly converged with channels such as reverse driving, sudden braking and speeding, and uniformly mapped into alarm probability and action level.

[0166] Determining a fence solely based on geometric inclusion relationships ignores positioning uncertainties and is prone to false triggering at occlusion boundaries. Furthermore, simple or logically superimposed multi-channel security events can amplify false alarms. Therefore, a comprehensive fence probability model is needed, with probability convergence to suppress occasional anomalies in single channels.

[0167] Mapping fence relationships with uncertainty inflation to intrusion probabilities in navigation coordinates:

[0168]

[0169] Among them: fence intrusion probability :time The probability of intrusion, Sigmoid mapping Defined as Differentiable functions; weighting coefficients : Non-negative real numbers used to adjust the three contributions. ;

[0170] Signed distance : The signed nearest distance from a point to the fence boundary, negative inside and positive outside; Circle / Polygon: ,in Indicates within the region, Indicates outside the region, For boundaries. Corridor / line strip: see above. The sign is determined by the lateral displacement direction and the normal sign. This diameter is related to... Normalization compatibility, ensuring It can be calculated.

[0171] Horizontal protection limit Step 2: Completeness quantification; Stability term Small positive numbers prevent division by zero. ;Direction difference The angle between the vehicle's heading and the fence's normal (or traffic direction), and its range. ; stay time : Cumulative time the vehicle spent within the fenced area or adjacent zone, in seconds; reference time : Retention normalization constant, a positive number.

[0172] When using, when the horizontal protection limit When the distance term is increased, the intrusion probability is amplified and the intrusion probability decreases, which is equivalent to expanding the fence according to uncertainty; the direction consistency term suppresses false triggering of edge-grabbing; the loitering term amplifies the processing of slow intrusion and long-term loitering, and the coupling of the three significantly reduces false alarms at the boundary.

[0173] The probability of fence intrusion is aggregated with the event probabilities of backtracking, sudden braking, and speeding through various channels to form an alarm probability, which is then mapped and bound to the action level.

[0174]

[0175] Among them: alarm probability The total alarm probability after multi-channel aggregation. Channel set A finite set of channels including fence intrusion, wrong-way driving, sudden braking, speeding, and prolonged idling; channel weights. : Trust weights for each channel Trajectory quality score With pattern probability Adaptive generation; Generated by soft maximum normalization: , can be , The channel probability is obtained by linear combination with the channel stability statistics. :aisle At any moment The probability of the event, .

[0176] In practice, the product-type inhibition structure is naturally insensitive to sporadic single-channel anomalies, only showing a significant increase when multiple pieces of evidence are consistent; combined with and The adaptive weighting can reduce the impact of low-reliability channels in scenarios where DR is dominant and quality is degraded; it can also reduce the alarm probability. With alarm limit By binding it to action thresholds, an interpretable mapping and tiered handling of probability-action levels can be achieved.

[0177] Step 5: In multiple scenarios, representative reweighting is used to ensure that the sample structure is consistent with the target working condition, thereby aggregating the dispersed index entropy regularization into a comparable single acceptance score, and using integrity risk constraints and mirror update strategies to drive the iterative convergence of algorithm parameters and platform thresholds in reverse with the acceptance results.

[0178] The actual operating conditions of vehicles exhibit non-stationary and long-tailed distributions across dimensions such as open fields, canyons, tunnels, toll stations, and rainy / foggy / nighttime conditions. Directly using uniform sampling to statistically analyze performance would overestimate common operating conditions and underestimate challenging scenarios. Furthermore, a single indicator cannot describe the coordinated constraints of accuracy, continuity, integrity, latency, and fence reliability; a unified aggregation using entropy-regularized soft minimum operators oriented towards the weakest link is necessary. Moreover, pass / fail assessment should not solely rely on average performance but should also examine the horizontal protection limit. Relative alarm limit Tail risks; ultimately, the experimental criteria must be written back to the algorithm and platform to adjust the geometric constraint weights. Noise adaptive intensity Gating time weights With delay budget Collaborative parameter adjustment forms a closed-loop engineering process of measurement, judgment, and modification.

[0179] By reweighting data samples across different operating conditions, we ensure that the data samples are consistent with the target deployment distribution. Then, we use the entropy regularized soft minimum operator to aggregate multi-dimensional indicators into a single acceptance score, ensuring that the weakest link is fully reflected in a statistical sense.

[0180] The event stream generated in step four is stable and usable in the order of reception, but the scenario proportion may not be consistent with the target road network. Therefore, representative reweighting is first performed at the sample level, and then performance loss metrics such as accuracy R95, tunnel drift rate, tunnel exit convergence time, end-to-end latency, fence false / missed alarms, and direction determination accuracy are normalized into the same dimension. Finally, a soft minimum operator is used to aggregate the metrics to obtain an acceptance score that is more sensitive to the weakest link. In this way, the metrics are no longer isolated from each other, but are adjusted for weakest link priority through a unified risk tendency parameter.

[0181] To align the sample distribution with the target working condition distribution, an exponential skew weight is introduced, mapping the scene feature vector of each sample to a weight and applying moment matching constraints:

[0182]

[0183] Where: Sample weight :sample Non-negative weights Used for weighting all subsequent statistics; exponential skewness coefficient vector : A parameter vector that adjusts the importance of each scene dimension; a real number vector; scene feature vector. :sample Scene encoding, such as road type, occlusion level, weather / day / night, vehicle speed segmentation, etc., element range Or a real number that has been dimensionlessly standardized;

[0184] Normalized denominator : Ensure that the sum of the weights equals 1 for each term; target moment vector : The proportion of the target deployment scenario or the expected feature moment, and the range of elements. .

[0185] The aforementioned exponential skew constitutes a strictly realizable representative alignment: by solving the exponential skew coefficient vector. The weighted scenario moments are made equal to the target moments, thus statistically ensuring that they are identical to the operating conditions encountered after the road is started. Weights This information is then used to calculate all subsequent indicators and risks, ensuring that the verification process fully reflects the long-tail operating conditions.

[0186] In practice, rare conditions such as long tunnels and severe weather are amplified in the deployment ratio; common conditions are not excessively diluted; and the vector of exponentially tilted coefficients is used. The re-estimation shows that the experimental set can sustainably approach the new operational target road network and has migration capabilities.

[0187] The weighted multidimensional indicators are mapped to a single acceptance score, using an entropy-regularized soft minimum operator that is sensitive to the weakest link:

[0188]

[0189] Among them: acceptance score The smaller the value, the better the overall performance; it is a non-negative real number; temperature parameter. : A positive number that controls the degree of minimization. , Approaching strict minimum; weighting coefficient The non-negative weights of each indicator And satisfy the condition that the summation is 1; performance loss metric The original metrics (such as R95, drift rate, convergence time, latency, and fence miss / false alarm) are thresholded and dimensionlessly normalized to obtain dimensionless quantities. .

[0190] The operator is in It approximates the worst-case scenario in smaller scenarios, while retaining continuous sensitivity to other indicators, preventing unstable jumps due to minor fluctuations in a single indicator. Indicator weights Trajectory quality score With pattern probability The time integral generation makes continuity and tunnel exit convergence more important during the DR-dominated period.

[0191] When using, through and The adjustable mechanism allows managers to seamlessly transition between the weakest priority and overall equilibrium; scores Maintaining differentiability and interpretability during operating condition switching facilitates subsequent analysis of parameter sensitivity; the soft minimum structure unifies the indicators of different physical quantity dimensions onto a sortable scale.

[0192] With horizontal protection limit relatively The tail excess is used as the core metric to construct integrity risk, and it is combined with the acceptance score into a single objective function. Through mirror descent, small steps are iterated on pattern weights, fence thresholds, geometric constraint weights, and time delay budgets to form a convergent engineering closed loop.

[0193] Based solely on acceptance scores As a criterion, low-probability but high-risk integrity mismatches are ignored; therefore, tail risk in the form of conditional risk value is introduced to transform the upper quantile of the positive out-of-limit distribution into a scalar measure; subsequently, unconstrained-constrained unified optimization is performed on the probabilistic simplex and positive parameter space in combination with the exponential update of mirror descent, so that the parameter update naturally remains within the feasible region.

[0194] With positive part function The excess envelope is encapsulated, and the tail risk is defined using quantile integrals:

[0195]

[0196] Among them: integrity risk : Tail expectation at the horizontal level Confidence level Real numbers between 0 and 1 ;

[0197] quantile operator Random variables in quantiles The right inverse function at a given quantile level returns the corresponding scalar, essentially mapping a random variable (or its distribution / sample) to a value at a given quantile level; it is a generalized inverse distribution function. (Level protection limit) : Integrity quantification from step two; alarm limits : Alarm thresholds set for fences and security policies, in meters; Positive part For the input, take the portion not less than 0, ensuring that risk is contributed only when the limit is exceeded. This applies to the excess amount across the sample set. Perform a weighted empirical distribution (weights) ), using weighted order statistical approximation And then Perform the trapezoidal integral.

[0198] This risk aggregates the degree of exceeding limits in the tail interval of all time series samples into a comparable quantity, which is more revealing of low-frequency, high-risk integrity gaps than the mean or median; through representative weighting Weighted, integrity risk The sensitivity to long-tail conditions has been further enhanced.

[0199] During use, integrity risks exist during the weak signal recovery phase at the tunnel exit. Follow The tail compression significantly reduces the convergence, which can truly reflect the convergence. In urban canyons with multiple paths, the risk does not overreact to transient jitter, avoiding excessive rectification. As a supporting constraint for the acceptance score S, it can prevent the risk of average excellence but extreme value poor from spilling over.

[0200] Integrate acceptance scores and integrity risks into a unified objective. Perform exponential updates of mirror descent within the probability and positive parameter feasible region:

[0201]

[0202] Where: the updated weight vector : A concatenated vector containing channel weights, pattern weights, and indicator weights, located on the probability simplex; the current weight vector. : Vectors of the same dimension, with non-negative elements and a sum of 1; Hadamard multiplication Element-wise multiplication of vectors; learning rate Positive step size, Objective function : A scalar objective composed of acceptance scores and integrity risk weights; gradient : The gradient of the target with respect to the weights, with real numbers as elements; a one-dimensional vector. Used for normalization to ensure that the result remains in the probabilistic simplex.

[0203] In the implementation, the current weight vector Mapping to specific parameters: Channel weights are mapped to the weights of fences and abnormal channels; pattern weights are mapped to the pattern transition matrix and weights in step two; and index weights are mapped to the soft minimum operator. The geometric constraint weights are updated using an exponential mapping with non-negative parameters. Noise adaptive intensity Gating time weights The time delay budget is biased to keep it within the feasible region.

[0204] In practice, multi-parameter collaborative updates can achieve fast convergence in small steps without violating physical constraints; this is achieved through integration with time delay budgeting. The linkage allows for priority to be allocated to the budget of fences and alarm segments during congestion, thus enabling targeted mitigation of the root causes of non-compliance in the next round of testing; the exponential mirror descent naturally inhibits overcorrection and avoids oscillations.

[0205] 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.

[0206] Those skilled in the art will 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.

[0207] 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.

[0208] 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.

[0209] 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 high-precision positioning method for operational vehicles using BeiDou inertial coordination and multi-source fusion, characterized by: include, For BeiDou, inertial navigation, and wheel speed observations, the event time mapping operator is used to unify the time scale, external participation dynamic lever arm correction is performed, a quality score-weight mapping is constructed, and the data is carried uplink with idempotent keys according to logarithmic congestion scheduling to output standardized data frames. Based on the standardized data frame, factor graph short window optimization is performed, and IMM is used to switch between RTK / PPP-AR, PPP, and DR to update the noise covariance with log Euclidean algorithm, and output the state covariance and HPL. The fusion product frames are rearranged according to the event time, and the probability gating association is performed based on the state covariance and the HPL. Dual time axis smoothing is then performed to output the vehicle trajectory, trajectory quality score and event confidence. The input is shaped and deduplicated using the idempotent key, and a four-segment time-delay convex optimization budget is performed; based on the signed distance, direction difference, dwell time and combined with the HPL modeling fence intrusion probability, the alarm probability is obtained by suppressive aggregation. Representative reweighted matching scenario moments are used to aggregate multiple indicators with entropy regularization soft minimum to form an acceptance score; Integrity risk is defined by the tail-end exceedance of the difference between HPL and alarm limit, and the weight of the mirror descent update mode and platform parameters are used.

2. The multi-source fusion high-precision positioning method for operating vehicles according to claim 1, characterized in that: The event time mapping operator continuously estimates based on a discrete model of local phase and fractional frequency offset, combined with pulse-second calibration and superimposed cable delay constant, to estimate the frequency offset change rate, unify the receiver and inertial navigation local time into event time, update frequency not less than one hertz, the mapping result is re-estimated as the window rolls, and serves as the unique time stamp for subsequent quality weighting, idempotent scheduling and factor graph indexing.

3. The multi-source fusion high-precision positioning method for operating vehicles according to claim 2, characterized in that: The externally involved dynamic lever correction is performed in the navigation coordinate system, the attitude is given by inertial calculation, and instantaneous displacement compensation is constructed by coupling the vehicle body angular velocity and the lever vector; The time residual term and installation extrinsic parameters are incorporated into the correction model and continuously updated to output an observation sequence with a unified spatial reference. The navigation coordinates of the vehicle body position serve as the entry point for subsequent fusion.

4. The multi-source fusion high-precision positioning method for operating vehicles according to claim 3, characterized in that: The quality score-weight mapping takes the carrier-to-noise ratio, multipath index and residual magnitude as input, generates weights through a continuously differentiable soft gating function and writes them into the standardized data frame, and performs logarithmic congestion scheduling according to queue occupancy and carries the idempotent key and time slice number. The weights are consistent with the unified spatial reference system in the event time domain and are used for adaptive calling by the factor graph and the mode.

5. The multi-source fusion high-precision positioning method for operating vehicles according to claim 1, characterized in that: The factor graph short window optimization contains weighted satellite position factors, inertial pre-integration factors, wheel speed factors and road geometry set constraints, and uses a bounded influence robust kernel to perform Gauss-Newton or Levenberg-Marquardt iterations on the event time indexed window and output state and covariance, the geometry set consists of road centerline and strip buffer, short window covers fixed frame number and solves in unified time domain.

6. The method of claim 1 or 4, wherein: The mode adaptation uses a three-model interacting multiple model framework to perform evidence fusion between carrier fixed indicators, number of visible satellites, availability of correction data and the integrity quantification; The mode probability posterior adjusts the constraint weight and observation noise and performs soft switching between modes, the mode set includes RTK or PPP integer cycle, PPP and DR, the mode transition probability is non-zero and row normalized, and serves as a modulation term of log-Euclidean update strength and subsequent gating input.

7. The method of claim 6, wherein: The noise covariance is exponentially weighted updated in log-Euclidean domain, the forgetting factor is jointly modulated by the mode probability and the satellite weight, and a positive definite lower bound is set as a lower bound constraint, the updated observation covariance and process covariance are fed back to the factor graph and associated gating, and are recorded for historical tracing, the update is performed in each short window period and maintains matrix symmetric positive definite property.

8. The method of claim 7, wherein: The horizontal protection limit is obtained by projecting the state covariance to the horizontal plane and introducing an integrity coefficient, the horizontal protection limit and the state covariance are stored together, and provide input to the gating radius of step three and the fence threshold of step four, and are passed downstream over time series, and are associated with the alarm limit for consistency checking, and their sampling and short window update rhythm are consistent.

9. The method of claim 8, wherein: The probabilistic gating association combines the Mahalanobis distance of geometric residuals and event time lag into a gating distance, the time weight is adaptively adjusted by the horizontal protection limit, and the trajectory pool is used for candidate allocation and probabilistic normalized matching, unmatched frames enter the delay buffer of new trajectories and accept subsequent re-association, the maximum residence time of the delay buffer is constrained by the four-stage time delay convex optimization budget, and maintains sequential consistency constraint between overlapping candidates.

10. The method of claim 1 or 8, wherein: The double time axis smoothing applies bounded curvature regularization on the event time axis and slowness constraint on the reception time axis, the sliding window length is 1 to 3 seconds, and the horizontal protection limit, normalized gating distance and curvature constitute trajectory quality score and event confidence and are written back to the next round of weight and gating threshold, the trajectory quality score and event confidence are written into the fusion product frame for fence judgment consumption.

11. The method of claim 1, wherein: the access shaping takes the queue occupancy as input to perform logarithmic time fine-tuning, and takes the device identifier and time slice hash to form the idempotent key; the four-stage latency convex optimization budgets the access, stream processing, fence decision, and alert distribution, satisfies the end-to-end latency upper bound constraint, and re-estimates periodically, the sum of the budget vectors equals the upper bound, and takes the queue depth and risk level as the adjustment signal.

12. The method of claim 1, 9, or 10, wherein: the fence intrusion probability is composed of the signed distance, direction difference, and dwell time, and is scaled by the horizontal protection limit, the alert probability is generated by inhibitory convergence and each channel weight; the acceptance score adopts entropy-regularized soft minimum, and updates the model weight and platform parameter by mirror descent to form a closed loop, the representative re-weighting performs moment matching on the working condition distribution at the sample level, and the integrity risk is jointly taken as the target input.

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