A Multi-Antenna GNSS and INS Fusion Vehicle Attitude Determination Method and Device Based on Split CIF

Abstract

The application discloses a multi-antenna GNSS and INS fusion vehicle attitude determination method and device based on Split CIF, and the method comprises the following steps: acquiring a gyroscope recursive attitude source, a multi-antenna GNSS attitude source and an accelerometer attitude source; performing first-stage local fusion on the gyroscope recursive attitude source and the accelerometer attitude source through Split CIF to obtain a first vehicle attitude local estimation; performing second-stage local fusion on the gyroscope recursive attitude source and the multi-antenna GNSS attitude source through Split CIF to obtain a second vehicle attitude local estimation; and performing third-stage main fusion on the first vehicle attitude local estimation and the second vehicle attitude local estimation through Split CIF to obtain a vehicle attitude global estimation. The application jointly utilizes the attitude calculated by a gyroscope, the pitch angle and roll angle attitude derived by an accelerometer and the attitude derived by a multi-antenna GNSS, thereby improving the observability and robustness of the attitude; meanwhile, the hierarchical Split CIF design considers the correlation fusion in three stages, thereby improving the attitude precision.

Description

Technical Field

[0001] This invention relates to the field of positioning and navigation technology, and in particular to a method and apparatus for determining vehicle attitude based on the fusion of multi-antenna GNSS and INS using Split CIF. Background Technology

[0002] Accurate and continuous vehicle attitude estimation is crucial for autonomous driving, advanced driver assistance systems (ADAS), and intelligent transportation applications. Heading, pitch, and roll directly impact the navigation accuracy and trajectory planning of autonomous platforms. Inertial navigation systems (INS) estimate attitude through gyroscope integration, offering high short-term accuracy, but their errors accumulate over time. In contrast, multi-antenna global navigation satellite systems (GNSS) provide drift-free three-axis attitude estimation via carrier phase-based baseline vector estimation. However, in urban environments, their continuity and reliability often degrade due to signal blockage and multipath effects. Due to their complementary nature, multi-antenna GNSS / INS combinations have been widely used for robust, high-precision attitude determination. However, because all sensors are mounted on the same platform and interact during estimation, correlations may exist between the resulting multi-source attitude estimates. Ignoring these correlations can lead to measurement anomalies that reduce the robustness of the fusion and cause inconsistencies in the estimates.

[0003] For multi-antenna GNSS attitude determination, correctly resolving carrier phase integer ambiguities is crucial for obtaining high-precision baseline solutions. Existing ambiguity resolution methods can be categorized into three types: measurement domain methods, coordinate domain search methods, and ambiguity domain search methods. Among these, the least squares ambiguity decorrelation adjustment (LAMBDA) method, which considers the correlation between floating-point ambiguities, is theoretically optimal and has been widely adopted. Subsequent research has further accelerated the ambiguity decorrelation process to improve computational efficiency. However, in urban environments, the limited number of visible satellites and degraded observation quality can lead to ill-conditioned normal equations and unreliable floating-point solutions, severely impacting the resolution success rate. To enhance ambiguity resolution, three complementary strategies have been developed. The first is geometric optimization of the antenna array, but this is limited by finite installation space. The second is constraint-based ambiguity resolution: C-LAMBDA utilizes prior baseline length constraints, increasing the single-frequency, single-epoch resolution success rate from 3.5% to 73.7%, while MC-LAMBDA further introduces the relative azimuth relationships between multiple baselines. The third is auxiliary sensors or attitude prior assistance. A single-epoch resolution success rate exceeding 99% was achieved using attitude priors from inertial sensors. Existing research proposed a pitch-constrained ambiguity function method (PCAFM), reducing yaw and pitch search candidates by 67.55% and 97.51%, respectively. An INS-assisted single-frequency GPS / BDS combination was developed, employing a partial ambiguity resolution (PAR) strategy, achieving a fixation rate exceeding 90% and centimeter-level accuracy. A pitch-constrained LAMBDA method was developed for GNSS compasses, demonstrating that pitch information derived from road smoothness or accelerometer output can improve ambiguity resolution in complex urban vehicle-mounted tests. These studies indicate that utilizing auxiliary attitude or inertial information is an effective and valuable approach to enhancing GNSS attitude determination under conditions of decreased satellite visibility. However, improving GNSS ambiguity processing alone cannot guarantee attitude continuity under deteriorating GNSS conditions; multi-sensor fusion remains essential.

[0004] Existing multi-antenna GNSS attitude determination methods mainly focus on GNSS baseline vector modeling and attitude parameter calculation, or utilize INS / MEMS information to assist in ambiguity resolution and bridge the gap in GNSS performance degradation. Current research has proposed a dual-antenna GNSS / MEMS fusion algorithm with fault detection and elimination (FDE), reporting heading, pitch, and roll accuracies of 0.20°, 0.39°, and 0.28° under GNSS-constrained conditions. Recent research has expanded in this direction, introducing adaptive filtering and more sensors, including dual-antenna GNSS / MEMS-MARG fusion using multiple measurement update schemes, and robust single-antenna GNSS / MEMS fusion using hybrid time-difference technology. Under the same GNSS-assisted INS paradigm, introducing dual-antenna GNSS heading observations into low-cost GNSS / INS / MEMS systems improves heading observability and navigation control accuracy in vehicle-like applications. Pairwise combinations of multi-antenna GNSS with accelerometers, and pairs of accelerometers with gyroscopes, have also been extensively studied. Compared to these pairwise or GNSS-assisted combination schemes, how to jointly utilize gyroscope, accelerometer, and multi-antenna GNSS attitude information within a distributed fusion framework that considers correlation still requires further research.

[0005] Simultaneous utilization of gyroscope, accelerometer, and multi-antenna GNSS attitude information is not merely a simple extension of existing pairwise fusion schemes; it represents an important and valuable approach to improving vehicle attitude determination in complex environments. These three information sources offer complementary observability and error characteristics. Gyroscope estimation provides high-rate attitude continuity and short-term accuracy, but its errors accumulate over time. Accelerometer measurements provide a drift-free gravity reference for pitch and roll, but are susceptible to specific force disturbances caused by maneuvers and cannot observe heading. Multi-antenna GNSS baselines provide an absolute geometric attitude reference, especially heading, but their reliability decreases with satellite obstruction, multipath propagation, and ambiguity fixation failures. Therefore, jointly utilizing these three information sources provides complementary constraints and redundancy even when the performance of any one source degrades. Existing research has shown that fusing GNSS, accelerometer, and rotation sensor measurements can improve dynamic motion tracking, and multi-antenna GNSS / accelerometer fusion can utilize real-time GNSS attitude correction to correct accelerometer projection errors. These findings indicate that heterogeneous attitude source fusion is a promising direction for achieving robust vehicle attitude determination.

[0006] However, the benefits of jointly using these heterogeneous information sources come with a fundamental correlation problem that has not been adequately addressed in existing attitude fusion frameworks. In vehicular systems, gyroscopes, accelerometers, and GNSS antenna arrays observe the motion of the same platform and are affected by common environmental disturbances. Therefore, the attitude estimates generated by these information sources are not strictly independent. If traditional fusion treats them as independent measurements, common information may be repeatedly calculated, leading to an underestimation of the fusion covariance and ultimately, overconfidence or inconsistency in the estimates. Therefore, the key challenge lies not only in how to use more attitude information but also in how to use this information without repeatedly calculating related parts. This challenge directly prompts us to adopt a fusion strategy that considers correlation, consistently and boundedly handling unknown correlations while preserving useful independent information.

[0007] Most existing multi-source attitude fusion methods employ a centralized architecture, processing all sensor data in a single filter. This lack of fault isolation capability prevents them from fully leveraging the complementary advantages of heterogeneous sensors. Distributed fusion architectures address these limitations by deploying multiple parallel local filters, each processing a specific subset of measurements, thus providing modularity and fault isolation. However, their inherent redundancy introduces unknown correlations between local estimates—temporal correlations within each filter and spatial correlations between filters due to shared process noise models and prior information. Standard Extended Kalman Filtering (EKF) and Unscented Kalman Filtering (UKF) methods assume conditional independence of information sources, thus ignoring this correlation and producing inconsistent and often overconfident estimates, potentially even diverging. Recent fusion research also emphasizes the need to explicitly address unknown correlations between local estimates to ensure consistency; for example, inverse covariance cross-filtering schemes provide bounded handling of such correlations in asynchronous distributed systems. Covariance cross-filtering (CIF) guarantees consistency under unknown correlations by treating all source information as perfectly correlated, but is therefore overly conservative. To overcome this problem, Split CIF was proposed, which decomposes the local error covariance into correlated components from the shared inference process and independent components from the sensor's own updates; covariance cross-validation is applied only to the former, thus fully preserving the information gain brought by the latter. Since then, Split CIF has been successfully applied to multi-vehicle cooperative localization, multi-robot localization, vehicle time-relative localization, and integrated navigation. However, the application of Split CIF in multi-antenna GNSS / INS attitude determination still requires further research, and existing related studies pay little attention to experimentally based physical correlation analysis, making it difficult to fully reflect the actual error characteristics of different sensor branches. Summary of the Invention

[0008] The purpose of this invention is to overcome the aforementioned defects and problems in the prior art and provide a vehicle attitude determination method and apparatus based on SplitCIF multi-antenna GNSS and INS fusion. By jointly utilizing the attitude calculated by the gyroscope, the pitch and roll angle attitude derived from the accelerometer, and the attitude derived from the multi-antenna GNSS, the observability and robustness of the attitude are improved. At the same time, the proposed layered Split CIF design improves the attitude accuracy by considering correlation in the fusion at three stages.

[0009] To achieve the above objectives, the technical solution of the present invention is:

[0010] In a first aspect, the present invention provides a method for determining vehicle attitude based on the fusion of multi-antenna GNSS and INS using Split CIF, comprising:

[0011] Obtain the one-step predicted vehicle attitude obtained by the gyroscope recursion, and use it as the gyroscope recursive attitude source;

[0012] The heading obtained by gyroscope recursion is used as a priori constraint to help fix the carrier phase integer ambiguity of multi-antenna GNSS, and the attitude of the three-axis vehicle is calculated from the fixed baseline vector, which serves as the attitude source of multi-antenna GNSS.

[0013] Using the position, velocity, and zero-speed detection information exported from GNSS, the specific force measured by the vehicle accelerometer is compensated, and the pitch and roll angles of the vehicle are calculated from the compensated gravity direction, which serves as the accelerometer attitude source.

[0014] The gyroscope recursive attitude source and the accelerometer attitude source are fused in the first stage using a separation covariance cross-filtering algorithm to obtain a first local vehicle attitude estimate; the gyroscope recursive attitude source and the multi-antenna GNSS attitude source are fused in the second stage using a separation covariance cross-filtering algorithm to obtain a second local vehicle attitude estimate.

[0015] The first local vehicle attitude estimate and the second local vehicle attitude estimate are fused in the third stage using a separate covariance cross-filtering algorithm to obtain the global vehicle attitude estimate.

[0016] Preferably, the global estimation of the vehicle attitude is as follows:

[0017] ;

[0018] In the formula, For global estimation of vehicle attitude; For local attitude estimation of the first vehicle; For the first The first local estimate of the vehicle attitude obtained at the epoch; For local attitude estimation of the second vehicle; For the first The local attitude estimate of the second vehicle obtained in the epoch; and These are the covariance components related to the shared propagation process in the local estimation of the first and second vehicle attitudes, respectively. and These are the independent covariance components corresponding to the local estimates of the first and second vehicle attitudes, respectively. The mixing parameters for the third-stage main fusion; Main filter gain; The local attitude estimate of the first vehicle is calculated by its related covariance components according to... Inflated covariance; The local attitude estimate of the second vehicle is obtained by processing its relevant covariance components according to... After expansion, the covariance used in the calculation is the equivalent measurement covariance of the second vehicle attitude local estimation in the third-stage main fusion. This represents the total covariance in the global estimation of vehicle attitude. It is the identity matrix; and These are the independent covariance components and the correlated covariance components in the global estimation of vehicle attitude, respectively.

[0019] Preferably, the local attitude estimation of the first vehicle is as follows:

[0020] ;

[0021] In the formula, For local attitude estimation of the first vehicle; For the first The epoch is a one-step prediction of vehicle attitude obtained by recursion from the gyroscope; This is the gyroscope propagation state transition matrix; The vehicle's posture in the previous epoch; This refers to the noise generated during the propagation of the gyroscope. For the first The epochs are pitch and roll angle observations provided by the accelerometer attitude source; For accelerometer observation matrix; Noise for accelerometer attitude observation; and These are the correlated covariance component and the independent covariance component in the gyroscope propagation attitude prediction covariance, respectively. and These are the correlated covariance component and the independent covariance component in the accelerometer attitude observation covariance, respectively. These are the mixing parameters for the first stage of local fusion; The covariance of the gyroscope propagation attitude prediction covariance after expansion by the relevant components; The covariance of the accelerometer attitude observations is dilated by the correlation components; This is the filter gain; , and These are the total covariance, independent covariance components, and correlated covariance components in the local estimation of the first vehicle's attitude, respectively. It is an identity matrix.

[0022] Preferably, the local estimation of the second vehicle attitude is as follows:

[0023] ;

[0024] In the formula, For local attitude estimation of the second vehicle; For the first The epoch is a one-step prediction of vehicle attitude obtained by recursion from the gyroscope; This is the gyroscope propagation state transition matrix; The vehicle's posture in the previous epoch; This refers to the noise generated during the propagation of the gyroscope. For the first The epoch is based on vehicle attitude observations provided by a multi-antenna GNSS attitude source; This is a multi-antenna GNSS attitude observation matrix; Noise in multi-antenna GNSS attitude observations; and These are the correlated covariance component and the independent covariance component in the gyroscope propagation attitude prediction covariance, respectively. and These are the correlated covariance component and the independent covariance component in the covariance of multi-antenna GNSS attitude observations, respectively. The mixing parameters for the second stage of local fusion; The covariance of the gyroscope propagation attitude prediction covariance after expansion by the relevant components; The covariance of multi-antenna GNSS attitude observations is the covariance after dilation of the correlation components; This is the filter gain; , and These are the total covariance, independent covariance components, and correlated covariance components in the local estimation of the second vehicle's attitude, respectively. It is an identity matrix.

[0025] Preferably, the mixing parameters of the third-stage main fusion Hybrid parameters for the first stage of local fusion Hybrid parameters of the second-stage local fusion It is adaptively determined for each epoch, specifically including:

[0026] Within the open interval (0, 1), the relevant covariance components of the two to-be-fused estimates are respectively... and The expansion is then combined according to the information format to obtain the fusion covariance. ; with the determinant of the fusion covariance As the cost function, it is determined through one-dimensional optimization. Minimum mixing parameters The one-dimensional optimization employs the golden section search to locate the globally optimal hybrid parameters within a preset tolerance. This is then used for the corresponding separation covariance cross-filter update.

[0027] Preferably, the step of using the heading obtained recursively from the gyroscope as a priori constraint to assist in fixing the carrier phase integer ambiguity of the multi-antenna GNSS, and then calculating the three-axis vehicle attitude from the fixed baseline vector, includes:

[0028] The fixed baseline vector satisfies the following relationship:

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] In the formula, Represents the first in the carrier coordinate system One baseline vector; This represents the baseline vector in the navigation coordinate system obtained by GNSS with fixed ambiguity for the current epoch; Represents the rotation matrix from the vehicle coordinate system to the navigation coordinate system;

[0034] The attitude correction is estimated by iterative weighted least squares:

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] ; ; ; ;

[0040] In the formula, For Euler angle corrections, ; For designing the matrix; It is a block-diagonal weight matrix; Represents the residual vector; The covariance of the attitude correction for multi-antenna GNSS; For heading angle; The pitch angle; This refers to the roll angle; For the first Covariance of the baseline in the navigation coordinate system; This indicates that the columns of the matrix are stacked into a single column vector; The residual matrix; For measuring noise vectors; The current iteration value Rotation matrix at;

[0041] Angle updated to:

[0042] ;

[0043] Through iteration, until If the value is below a preset threshold, the attitude of the three-axis vehicle can be estimated. .

[0044] Preferably, the step of compensating for the specific force measured by the onboard accelerometer using the position, velocity, and zero-speed detection information derived from GNSS, and calculating the vehicle's pitch and roll angles from the compensated gravity direction, includes:

[0045] Based on Newton's second law in the Earth-fixed rotating coordinate system, the following equation is constructed:

[0046] ;

[0047] In the formula, This is the rotation matrix from the vehicle coordinate system to the navigation coordinate system; This indicates the specific force measured by the onboard accelerometer in the vehicle's coordinate system; This represents the vehicle's acceleration in the navigation coordinate system; The vehicle's speed in the navigation coordinate system; and These are the Earth's rotation angular rate and the entrainment angular rate vectors, respectively. The gravity vector ;

[0048] The ratio after compensation is:

[0049] ;

[0050] In the formula, ;

[0051] The compensated force component is:

[0052] ;

[0053] ;

[0054] ;

[0055] In the formula, , and The comparison after compensation is as follows , and Axial components; The pitch angle; This refers to the roll angle;

[0056] The vehicle's pitch and roll angles are calculated using the following formula:

[0057] ;

[0058] ;

[0059] In the formula, The calculated vehicle pitch angle; The calculated vehicle roll angle.

[0060] Secondly, the present invention provides a multi-antenna GNSS and INS fusion vehicle attitude determination device based on Split CIF, the device being used to implement the above-described multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF, the device comprising:

[0061] The multi-attitude source acquisition module is used to acquire the one-step predicted vehicle attitude obtained by the gyroscope recursion, as the gyroscope recursive attitude source; using the heading obtained by the gyroscope recursion as a priori constraint, it assists in fixing the carrier phase integer ambiguity of the multi-antenna GNSS, and calculates the three-axis vehicle attitude from the fixed baseline vector, as the multi-antenna GNSS attitude source; using the position, velocity and zero-speed detection information derived from GNSS, it compensates for the specific force measured by the on-board accelerometer, and calculates the vehicle's pitch angle and roll angle from the compensated gravity direction, as the accelerometer attitude source;

[0062] The vehicle attitude local estimation module is used to perform a first-stage local fusion of the gyroscope recursive attitude source and the accelerometer attitude source through a separation covariance cross-filtering algorithm to obtain a first vehicle attitude local estimate; and to perform a second-stage local fusion of the gyroscope recursive attitude source and the multi-antenna GNSS attitude source through a separation covariance cross-filtering algorithm to obtain a second vehicle attitude local estimate.

[0063] The vehicle attitude global estimation module is used to perform a third-stage main fusion of the first vehicle attitude local estimation and the second vehicle attitude local estimation through a separation covariance cross-filtering algorithm to obtain the vehicle attitude global estimation.

[0064] Thirdly, the present invention provides a multi-antenna GNSS and INS fusion vehicle attitude determination device based on Split CIF, including a memory and a processor;

[0065] The memory is used to store computer program code and transmit the computer program code to the processor;

[0066] The processor is configured to execute the multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF as described above, according to instructions in the computer program code.

[0067] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF as described above.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0069] This invention discloses a vehicle attitude determination method and apparatus based on Split CIF using multi-antenna GNSS and INS fusion. It jointly utilizes the attitude calculated by the gyroscope, the pitch and roll angles derived from the accelerometer, and the attitude derived from the multi-antenna GNSS. The gyroscope maintains short-term attitude continuity, the accelerometer provides gravity-based horizontal attitude constraints, and the multi-antenna GNSS provides an absolute geometric attitude reference. Compared to relying on a single sensor branch, the combined use of these three improves attitude observability and robustness. Simultaneously, the position and velocity derived from GNSS are used for dynamic compensation by the accelerometer, while the heading calculated by the gyroscope is used to constrain GNSS ambiguity. Furthermore, the first-stage local fusion and the second-stage local fusion share the same gyroscope calculations and observe the same vehicle, ensuring that both local and main fusions contain relevant information. By considering correlations in the three stages of fusion, attitude accuracy is improved. Attached Figure Description

[0070] Figure 1 This is a flowchart of a multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF according to the present invention.

[0071] Figure 2 This is a schematic diagram of the distributed fusion framework proposed in this invention.

[0072] Figure 3 This is a schematic diagram of the multi-antenna baseline configuration on the vehicle proposed in this invention.

[0073] Figure 4 This is a structural block diagram of a multi-antenna GNSS and INS fusion vehicle attitude determination device based on Split CIF proposed in this invention.

[0074] Figure 5 This is a structural block diagram of a multi-antenna GNSS and INS fusion vehicle attitude determination device based on Split CIF proposed in this invention. Detailed Implementation

[0075] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0076] See Figure 1 This invention provides a multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF, comprising:

[0077] S1. Obtain the one-step predicted vehicle attitude obtained by the gyroscope recursion, and use it as the gyroscope recursive attitude source GYR.

[0078] The heading obtained by gyroscope recursion is used as a priori constraint to help fix the carrier phase integer ambiguity of multi-antenna GNSS, and the attitude of the three-axis vehicle is calculated from the fixed baseline vector, which serves as the attitude source ANT of multi-antenna GNSS.

[0079] Using the position, velocity, and zero-speed detection information exported from GNSS, static / dynamic compensation is performed on the specific force measured by the vehicle-mounted accelerometer, and the pitch and roll angles of the vehicle are calculated from the compensated gravity direction, which serves as the accelerometer attitude source (ACC).

[0080] S2. The gyroscope recursive attitude source GYR and the accelerometer attitude source ACC are fused in the first stage using a separation covariance cross-filtering algorithm to obtain the first vehicle attitude local estimate LF1; the gyroscope recursive attitude source GYR and the multi-antenna GNSS attitude source ANT are fused in the second stage using a separation covariance cross-filtering algorithm to obtain the second vehicle attitude local estimate LF2.

[0081] S3. The first local vehicle attitude estimate LF1 and the second local vehicle attitude estimate LF2 are fused in the third stage using the separation covariance cross-filtering algorithm to obtain the global vehicle attitude estimate.

[0082] like Figure 2 As shown, the vehicle attitude determination method based on Split CIF using multi-antenna GNSS and INS fusion proposed in this invention employs a loosely coupled distributed fusion framework. In the GNSS branch, the carrier phase integer ambiguity is first fixed using the LAMBDA method, and the heading calculated by the gyroscope is used as a search constraint and quality control prior to improve the reliability of single-epoch fixing under urban degradation conditions. Then, the GNSS attitude angle is calculated using the baseline vector obtained by weighted least squares. Before using the GNSS attitude solution as a local fusion measurement, it is first verified to reduce the gross errors caused by occlusion and multipath.

[0083] In the accelerometer branch, vehicle acceleration is calculated using position and velocity derived from GNSS data, along with Earth rotation / entrainment angular rate corrections required for accelerometer-based attitude estimation. GNSS velocity and solution states are also used for dynamic / static state identification. A simplified leveling model is employed under zero-speed conditions, while a dynamic compensation model is used during vehicle motion.

[0084] The distributed fusion framework proposed in this invention is built upon three complementary attitude sources: attitude derived from gyroscopes, pitch and roll attitude derived from accelerometers, and attitude derived from multi-antenna GNSS. The distributed fusion framework jointly utilizes gyroscope-derived attitude, accelerometer-based gravity reference, and multi-antenna GNSS baseline geometry to provide complementary attitude constraints.

[0085] The distributed fusion framework comprises three stages: a first-stage local fusion, a second-stage local fusion, and a third-stage main fusion. The first-stage local fusion fuses the gyroscope recursive attitude source with the accelerometer attitude source; the second-stage local fusion fuses the gyroscope recursive attitude source with the multi-antenna GNSS attitude source; and the third-stage main fusion fuses the outputs of the first and second stages of local fusion to obtain the final vehicle attitude. This distributed fusion framework separates the measurements from the GNSS and accelerometer branches, improving fault isolation capabilities. Since the two local fusions share the same gyroscope recursive attitude and vehicle motion, their errors may be correlated. Therefore, Split CIF is employed in the distributed fusion framework to process correlated components in the local and main fusion stages while preserving useful independent measurement information. In the first-stage local fusion, the second-stage local fusion, and the third-stage main fusion, the covariance to be estimated is decomposed into relevant covariance components related to the shared propagation process or vehicle common-mode disturbances and independent covariance components introduced by the independent measurements of each sensor. The relevant covariance components are conservatively bounded, while the independent covariance components are retained, thereby avoiding the repeated inclusion of shared information introduced by gyroscope recursion information, GNSS auxiliary information, or vehicle common-mode disturbances.

[0086] This invention uses four coordinate systems: the geocentric coordinate system is denoted as... The carrier coordinate system is denoted as... The system, whose origin is located at the center of the IMU and is fixedly connected to the vehicle, The axle is along the transverse direction of the vehicle, and its The axle runs longitudinally along the vehicle. The axis points upwards, and the antenna layout and calibration baseline vector are represented in the carrier coordinate system; the navigation coordinate system is denoted as... The system is defined as the local East-North-Sky coordinate system; the geocentric inertial coordinate system is denoted as... System, and It shares the same origin but does not rotate with the Earth; it is only used for arranging equations in inertial mechanics.

[0087] Furthermore, the multi-antenna GNSS array is the only drift-free absolute attitude reference in the vehicle attitude determination framework proposed in this invention. This invention employs a GPS / BDS dual-system single-epoch configuration, whose multi-constellation redundancy improves the reliability of single-epoch ambiguity resolution in urban environments while maintaining receiver low cost. Carrier phase integer ambiguities are resolved using the LAMBDA method, where the gyroscope-derived heading from the INS mechanics orchestration serves as a priori heading constraint, reducing the search space and improving the single-epoch fixation rate under limited satellite visibility. Once the ambiguity is fixed, the resolved baseline vector gives the three-axis vehicle attitude.

[0088] like Figure 3As shown, the three antennas mounted on the roof form two non-parallel baselines. Taking antenna 1 as a common reference, the baseline carrier coordinate system from antenna 1 to antenna 2 ( The three antennas are aligned with the longitudinal (Y) axis of the vehicle coordinate system, and antenna 3 is offset laterally, so that the three antennas form an antenna plane. The vehicle attitude is determined by the coordinate system of the vehicle carrier ( (system) and navigation coordinate system ( Euler angles (roll angles) Pitch angle and heading angle To describe; heading angle The azimuth angle of the projection of the main baseline onto the horizontal plane, measured clockwise from north; elevation angle. The elevation angle of the main baseline in the horizontal plane; the roll angle. The angle is the tilt angle of the antenna plane, which is positive when the right side is raised.

[0089] set up Represents the first in the carrier coordinate system Baseline vectors ( ), and set This represents the baseline vector in the navigation coordinate system obtained by GNSS calculation with fixed ambiguity for the current epoch. For pre-calibration. The rotation matrix of the two vectors from the vehicle coordinate system to the navigation coordinate system. The relationships are as follows:

[0090] ;

[0091] All Baseline vectors stacked column by column and The fixed baseline vector is obtained. .

[0092] In the case of two non-parallel baselines, the rotation matrix has a closed-form (direct) solution for initializing the attitude. Since the direct method cannot utilize more than two baselines and is sensitive to baseline noise, the initial solution is refined by iterative weighted least squares (WLS), where the baseline covariance constitutes the weight matrix, and all available baselines participate in the solution.

[0093] Apply the above equation to the current iteration value. Linearize at this point, and denote the rotation matrix at this iteration as... Then the residual matrix is:

[0094] ;

[0095] because Before applying WLS, vectorize it first, let:

[0096] ;

[0097] in, This represents stacking the columns of the matrix into a single column vector. The linearized observation equation is written as:

[0098] ;

[0099] in, For the residual vector, For Euler angle corrections, This is the measurement noise vector.

[0100] Design Matrix It has gathered The partial derivatives with respect to the three angles take values ​​at the following points: :

[0101] ;

[0102] The block diagonal weight matrix is ​​the baseline covariance of the navigation coordinate system returned by the GNSS engine. Build:

[0103] ;

[0104] in, The first given for the GNSS engine The covariance of the baseline in the navigation coordinate system. Therefore Its dimension and Consistent, the WLS correction and its covariance are:

[0105] ;

[0106] ;

[0107] In the formula, The covariance of the attitude correction for multi-antenna GNSS;

[0108] Angle updated to:

[0109] ;

[0110] Through the above iterative steps, until... Below a preset threshold. As long as at least two non-parallel baselines are available, all three Euler angles can be observed, and the three-axis vehicle attitude can be estimated. and its covariance , as a multi-antenna GNSS attitude source.

[0111] Furthermore, as a long-term gravity reference, the accelerometer's error does not accumulate over time and is limited only by sensor noise and bias. Since gravity is only observable in the horizontal plane, this information source provides the pitch angle. and roll angle heading angle Taken from a multi-antenna GNSS attitude source.

[0112] set up This represents the specific force measured by the triaxial accelerometer in the carrier coordinate system, and is set as follows: Let represent the platform's acceleration in the navigation coordinate system; based on Newton's second law in the Earth-fixed rotating coordinate system, the following equation is constructed:

[0113] ;

[0114] In the formula, This is the rotation matrix from the vehicle coordinate system to the navigation coordinate system; This indicates the specific force measured by the onboard accelerometer in the vehicle's coordinate system; This represents the vehicle's acceleration in the navigation coordinate system. The speed of the vehicle in the navigation coordinate system. , and The speeds are respectively in the east, north, and sky directions. and Derived from GNSS velocity solutions and their inter-epoch differences; and These are the Earth's rotation angular rate and the entrainment angular rate vectors, respectively. The position derived from GNSS is obtained using standard formulas. It is the gravity vector (ENU, negative for the celestial direction). ;

[0115] The ratio after compensation is:

[0116] ;

[0117] In the formula, It is taken from the posture of the previous epoch;

[0118] The compensated force component is:

[0119] ;

[0120] ;

[0121] ;

[0122] In the formula, , and The ratios after compensation are respectively In the carrier coordinate system , and Components on the axis; The pitch angle; This refers to the roll angle;

[0123] because Relying solely on pitch angle and roll angle For ground vehicles traveling on near-horizontal roads, the pitch and roll angles are calculated using the following closed-form solution:

[0124] ;

[0125] ;

[0126] In the formula, The calculated vehicle pitch angle; The calculated vehicle roll angle; It is the arctangent function. Because... This is the projection of gravity onto the carrier's coordinate system. and Solution and heading angle Irrelevant.

[0127] In this invention, the accelerometer attitude branch employs a static-dynamic switching strategy; when the vehicle is stationary or detected as zero speed, the speed difference between epochs is zero, and non-gravitational acceleration is assumed to be negligible. In this case, the original specific force is directly treated as an observation of the direction of gravity, and the aforementioned closed-form degenerates into direct leveling for pitch and roll angle estimation. During vehicle motion, this static assumption no longer holds because the measured specific force includes vehicle acceleration and the Earth's rotation / entrainment rate term. Therefore, as... Figure 2 As shown, before applying the above closed-form, the position derived using GNSS... and speed To compensate for these dynamic components, the zero-velocity detector (ZVD) based on GNSS Doppler observations switches between static and dynamic branches during operation. To suppress broadband noise from the MEMS accelerometer, the ratio is pre-filtered using a low-order Butterworth filter, with its cutoff frequency set according to Allan variance characteristics. The resulting estimate... Its covariance, after being propagated through the above closed loop according to the standard error propagation law, serves as the accelerometer attitude source.

[0128] Furthermore, in multi-sensor information fusion, the estimates to be fused are often not strictly independent, especially when different sensors assist each other, observe the same platform (using the vehicle body as a platform, with gyroscopes, accelerometers, and multi-antenna GNSS arrays all fixed to and moving with it) or share the same propagation model. This coupling introduces temporal correlation within each filter and spatial correlation between different local filters. The proposed architecture also exhibits this characteristic: two local filters share the same gyroscope calculations, while GNSS is used for dynamic compensation of the accelerometer, and the gyroscope information, in turn, constrains the GNSS ambiguity to remain fixed. Standard Kalman fusion, lacking explicit cross-covariance information, effectively treats these estimates as independent, potentially leading to overly optimistic covariance estimates due to redundant calculations of shared information. Traditional CI goes to the other extreme, treating all estimates as perfectly correlated. While this ensures consistency, it often results in overly conservative covariance estimates because it fails to fully utilize useful independent information. Split CIF provides a compromise between these two extremes: it applies CI only to correlated components while preserving independent components through the standard fusion law.

[0129] Two estimates given the same true state and ,in, Direct observation of the complete state ( ),and Through measurement matrix For complete or partial observations; superscript and Let the correlated components and independent components be represented respectively. Then, the Split CIF will be updated as follows:

[0130] ;

[0131] Mixed parameters This determines how the relevant covariance components of the two estimates are allocated in the Split CIF update: the relevant component of the first estimate is amplified. The correlation component of the second estimate is amplified by a factor of two. The value increases by a factor of 1, while the independent components remain unchanged. Larger values... It will decrease the amplification of the first correlated component and increase the amplification of the second, smaller one. Conversely. Instead of being fixed in advance, it is adaptively determined at each epoch through one-dimensional optimization: for candidate values ​​within a given range The amplified covariance is combined in information form to obtain the fused covariance. and with As a cost function. The optimization problem has been proven to be a convex problem; therefore, the golden section search can efficiently locate the global optimum within a specified tolerance. This criterion is used for updates. It conservatively bounds the relevant parts, avoiding redundant calculations of shared information while preserving truly independent measurement information. Compared to traditional CI, Split CIF is less conservative because the independent covariance components of each estimate are preserved during the fusion process.

[0132] In this invention, both the first-stage local fusion and the second-stage local fusion are one-step predicted vehicle attitudes obtained recursively from gyroscopes. Driven by the same gyroscope calculations, their covariance... It includes a shared related component. The first-stage local fusion recursively adjusts the gyroscope attitude and the pitch / roll angle derived from the accelerometer. Fusion; the second stage of local fusion combines the gyroscope recursive attitude with the multi-antenna GNSS three-axis vehicle attitude. To integrate.

[0133] Specifically, the local attitude estimation of the first vehicle is as follows:

[0134] ;

[0135] In the formula, For local attitude estimation of the first vehicle; For the first The epoch is a one-step prediction of vehicle attitude obtained by recursion from the gyroscope; This is the gyroscope propagation state transition matrix; The vehicle's posture in the previous epoch; This refers to the noise generated during the propagation of the gyroscope. For the first The epochs are pitch and roll angle observations provided by the accelerometer attitude source, which refers to the horizontal attitude observations calculated based on the accelerometer specific force information and combined with the static gravity direction or dynamic compensation model. This is the accelerometer observation matrix, used to map the gyroscope propagation attitude to the pitch and roll components observable by the accelerometer. Noise for accelerometer attitude observation; and These are the correlated covariance component and the independent covariance component in the gyroscope propagation attitude prediction covariance, respectively. The correlated covariance component is used to characterize the common error information introduced by the shared gyroscope propagation process, while the independent covariance component is used to characterize the independent uncertainty that is not shared with other observation sources during the gyroscope propagation process. and These are the correlated covariance component and the independent covariance component in the accelerometer attitude observation covariance, respectively. The independent observation uncertainty caused by the accelerometer's own noise, Used to characterize the uncertainties caused by vehicle motion, dynamic compensation residuals, or vehicle-shared disturbances; These are the mixing parameters for the first stage of local fusion. It is used to allocate and expand the relevant covariance components; The covariance of the gyroscope propagation attitude prediction covariance after expansion by the relevant components; The covariance of the accelerometer attitude observations is dilated by the correlation components; This is the filter gain; , and These are the total covariance, independent covariance components, and correlated covariance components in the local estimation of the first vehicle's attitude, respectively. It is the identity matrix of the corresponding dimension.

[0136] Specifically, the local attitude estimation of the second vehicle is as follows:

[0137] ;

[0138] In the formula, For local attitude estimation of the second vehicle; For the first The epoch is a one-step prediction of vehicle attitude obtained by recursion from the gyroscope; This is the gyroscope propagation state transition matrix; The vehicle's posture in the previous epoch; This refers to the noise generated during the propagation of the gyroscope. For the first The epoch is the vehicle attitude observation provided by the multi-antenna GNSS attitude source, which refers to the vehicle attitude observation obtained based on multi-antenna GNSS carrier phase observation, integer ambiguity fixation and baseline vector solution. This is a multi-antenna GNSS attitude observation matrix, used to map the gyroscope propagation attitude to the multi-antenna GNSS observable attitude components; Noise in multi-antenna GNSS attitude observations; and These are the correlated covariance component and the independent covariance component in the gyroscope propagation attitude prediction covariance, respectively. The correlated covariance component is used to characterize the common error information introduced by the shared gyroscope propagation process, while the independent covariance component is used to characterize the independent uncertainty that is not shared with other observation sources during the gyroscope propagation process. and These are the correlated covariance component and the independent covariance component in the covariance of multi-antenna GNSS attitude observations, respectively. This addresses the independent observation uncertainties caused by the noise inherent in multi-antenna GNSS baseline calculation and attitude observation itself. Used to characterize the related uncertainties caused by gyroscope-assisted ambiguity fixation, common vehicle motion, GNSS multipath or baseline geometric errors; The mixing parameters are for the second stage of local fusion. It is used to allocate and expand the relevant covariance components; The covariance of the gyroscope propagation attitude prediction covariance after expansion by the relevant components; The covariance of multi-antenna GNSS attitude observations is the covariance after dilation of the correlation components; This is the filter gain; , and These are the total covariance, independent covariance components, and correlated covariance components in the local estimation of the second vehicle's attitude, respectively. It is the identity matrix of the corresponding dimension.

[0139] This physical mechanism-based decomposition is one of the reasons why Split CIF can retain measurement information and not degenerate into the worst-case CI bound. This results in a local output. and Independent covariance components and This represents the measurement uncertainty unique to each sensor. Specifically, It is related to broadband accelerometer noise, as characterized by Allan variance, while Obtained from the covariance of the baseline vector fixed by LAMBDA. Related covariance components. and Characterizes residual vehicle-sharing disturbances. This physics-based separation allows Split CIF to retain useful measurement information while only conservatively processing certain parts.

[0140] Specifically, both the first-stage and second-stage local fusion outputs are derived from the inertial state driven by the same gyroscope. Therefore, their estimation errors contain a shared correlation component. The Pearson correlation coefficients between the two local fusion outputs are 0.805, 0.361, and 0.989 in pitch, roll, and yaw, respectively. If the standard Kalman fusion is used directly to update and fuse these two local estimates, the shared information may be repeatedly calculated, and the fusion covariance may be underestimated. Therefore, the third-stage main fusion adopts Split CIF, taking... As a priori estimate As a measurement estimate, the global vehicle attitude estimate is:

[0141] ;

[0142] In the formula, For global estimation of vehicle attitude; For local attitude estimation of the first vehicle; For the first The first local estimate of the vehicle attitude obtained at the epoch; For local attitude estimation of the second vehicle; For the first The local attitude estimate of the second vehicle obtained in the epoch; and These are the covariance components related to the shared propagation process in the local estimation of the first and second vehicle attitudes, respectively. and These are the independent covariance components corresponding to the local estimates of the first and second vehicle attitudes, respectively. The mixing parameters for the third-stage main fusion. ; Main filter gain; The local attitude estimate of the first vehicle is obtained by processing its related covariance components according to... Inflated covariance; The local attitude estimate of the second vehicle is obtained by processing its relevant covariance components according to... After expansion, the covariance used in the calculation is the equivalent measurement covariance of the second vehicle attitude local estimation in the third-stage main fusion. This represents the total covariance in the global estimation of vehicle attitude. It is the identity matrix of the corresponding dimension; and These are the independent covariance components and the correlated covariance components in the global estimation of vehicle attitude, respectively.

[0143] Furthermore, the mixing parameters of the third-stage main fusion Hybrid parameters for the first stage of local fusion Hybrid parameters of the second-stage local fusion It is adaptively determined for each epoch, specifically including:

[0144] Within the open interval (0, 1), the relevant covariance components of the two to-be-fused estimates are respectively... and The expansion is then combined according to the information format to obtain the fusion covariance. ; with the determinant of the fusion covariance As the cost function, it is determined through one-dimensional optimization. Minimum mixing parameters The one-dimensional optimization employs the golden section search to locate the globally optimal hybrid parameters within a preset tolerance. This is then used for the corresponding separation covariance cross-filter update.

[0145] The method proposed in this invention differs from existing Split CIF applications in three aspects: (1) Hierarchical Split CIF. Split CIF is used in the first-stage local fusion, the second-stage local fusion, and the third-stage main fusion to ensure information-preserving fusion at each layer of the hierarchical structure. (2) Physically interpretable covariance decomposition. This decomposition is associated with identifiable error sources, namely shared INS recursive errors and local sensor measurement noise, thereby limiting the conservative CI mechanism to the truly shared part of the covariance, rather than acting on the entire covariance as in standard CI. (3) Data-driven design. The choice of Split CIF over EKF or standard CI is determined by cross-correlation analysis based on experimental results, rather than as a methodological default.

[0146] See Figure 4 The present invention also provides a vehicle attitude determination device based on Split CIF multi-antenna GNSS and INS fusion, the device being used to implement the above-described vehicle attitude determination method based on Split CIF multi-antenna GNSS and INS fusion, the device comprising:

[0147] The multi-attitude source acquisition module is used to acquire the one-step predicted vehicle attitude obtained by the gyroscope recursion, as the gyroscope recursive attitude source; using the heading obtained by the gyroscope recursion as a priori constraint, it assists in fixing the carrier phase integer ambiguity of the multi-antenna GNSS, and calculates the three-axis vehicle attitude from the fixed baseline vector, as the multi-antenna GNSS attitude source; using the position, velocity and zero-speed detection information derived from GNSS, it compensates for the specific force measured by the on-board accelerometer, and calculates the vehicle's pitch angle and roll angle from the compensated gravity direction, as the accelerometer attitude source;

[0148] The vehicle attitude local estimation module is used to perform a first-stage local fusion of the gyroscope recursive attitude source and the accelerometer attitude source through a separation covariance cross-filtering algorithm to obtain a first vehicle attitude local estimate; and to perform a second-stage local fusion of the gyroscope recursive attitude source and the multi-antenna GNSS attitude source through a separation covariance cross-filtering algorithm to obtain a second vehicle attitude local estimate.

[0149] The vehicle attitude global estimation module is used to perform a third-stage main fusion of the first vehicle attitude local estimation and the second vehicle attitude local estimation through a separation covariance cross-filtering algorithm to obtain the vehicle attitude global estimation.

[0150] Specifically, the vehicle attitude local estimation module includes local filter 1 and local filter 2. Accelerometer attitude measurements are fed into local filter 1, where acceleration and attitude measurements are fused with the attitude derived from the gyroscope using the Split CIF method. Multi-antenna GNSS attitude measurements are fed into local filter 2, where GNSS attitude measurements are fused with the attitude derived from the gyroscope using the Split CIF method.

[0151] The global vehicle attitude estimation module includes a main filter, and the estimates from two local filters are fed into the main filter to obtain the final vehicle attitude.

[0152] The vehicle attitude determination method proposed in this invention comprises three filtering stages. In the first stage, the gyroscope-accelerometer branch (LF1) fuses the gyro-recursive attitude source (GYR) and the accelerometer attitude source (ACC). In the second stage, the gyroscope-multi-antenna GNSS branch (LF2) fuses the same gyro-recursive attitude source (GYR) and the multi-antenna GNSS attitude source (ANT). In the third stage, the two local outputs are fused by a federated separated covariance cross-filter (F-SCIF) to bound the unknown correlations between the branches. This invention compares single-source local filtering with the three-stage fusion. All errors are calculated relative to the Inertial Explorer (IE) solution. To avoid conflating fixed installation biases with filtering performance, the same process used for all methods is employed to remove constant biases on each axis, including multi-antenna installation misalignment in LF2. No time-varying drift correction or method-specific post-processing is applied.

[0153] Table 1. Attitude error of single-source local filter fusion with F-SCIF

[0154]

[0155] Table 1 shows that no single local branch can provide a complete and highly accurate three-axis attitude solution. The gyroscope-accelerometer branch (LF1) provides a gravity-anchored horizontal reference for pitch and roll, but cannot observe heading; even for pitch and roll, its RMSE is 1.006° and 1.177°, respectively, because vehicle movement contaminates the accelerometer specific force. The gyroscope-multi-antenna GNSS branch (LF2) can observe all three axes, with RMSEs of 0.337°, 0.522°, and 0.211° for pitch, roll, and heading, respectively; however, its roll accuracy is low due to baseline geometry constraints.

[0156] The three-stage federated split CIF fusion produced smaller errors on all three axes, with RMSEs of 0.192°, 0.447°, and 0.105° for pitch, roll, and yaw, respectively. Compared to LF1, pitch and roll decreased by 80.9% and 62.0%, respectively; compared to LF2, the decreases on all three axes were 43.0%, 14.4%, and 50.2%, respectively. The gains in pitch and roll come from two independently observable and complementary sources of information. Notably, yaw was also improved: since the accelerometer does not provide independent azimuth observations, the decrease from 0.211° to 0.105° should not be interpreted as a fusion of two independent yaw observations, but rather primarily as an effect of estimation theory. From a mechanistic perspective, gravity-anchored, drift-free pitch / roll observations tighten the covariance of the accelerometer branch and increase the weight of the smooth gyroscope recursive attitude source (GYR) heading in conservative fusion through attitude cross-covariance. At the same time, it improves the observability of horizontal gyroscope bias, thereby suppressing epoch-by-epoch noise and slow drift of multi-antenna headings without recalculating the inertial information shared by the two branches.

[0157] These results support the core design choice of this invention: no single source of information is sufficient; the accelerometer branch cannot observe heading and is sensitive to maneuvering; and the multi-antenna GNNS branch has limited roll accuracy due to baseline geometry constraints. Therefore, the accuracy on all three axes depends on two-level fusion that considers correlation, and its gain comes from the consistent use of multi-source information by the distributed fusion framework, rather than any single sensor.

[0158] In this invention, the two stages of local fusion, the first stage and the second stage, are not independent; both are calculated using the same gyroscope mechanics, which introduces a shared low-frequency error component, reaching r=0.989 in the heading. Therefore, the master fusion rule determines whether the final estimate remains accurate. To test this effect, four GNSS / INS attitude fusion architectures were implemented on the same 2000s urban-suburban dataset. They used the same ADIS16460 inertial data stream, multi-antenna and accelerometer observations, and initial alignment, differing only in the combination of information sources and the handling of correlations between filters. For simplicity, SCIF is used in the method label to represent Split CIF. The four attitude fusion architectures compared are summarized in Table 2.

[0159] These four methods cover the practical design space of multi-sensor attitude fusion. Centralized EKF (C-EKF) places each observation into a single state update; it is statistically optimal when all measurements are independent and anomalies-free, but does not provide fault isolation. Federated EKF with Carlson information allocation (F-EKF, β allocation) distributes information sources to two local filters and eliminates redundant computations of shared inertial priors through a β=N weighting rule. Hybrid EKF-SCIF (H-EKF-SCIF) retains the EKF local filters but replaces the main update with a separated covariance cross-filter that handles bounded unknown correlations. The fully federated Split CIF (F-SCIF) proposed in this invention consistently applies the separation of independent / correlated covariances in both the local and main layers. Evaluating these four schemes on the same dataset distinguishes the contribution of correlation-considered fusion from the contribution of the federated structure itself.

[0160] Table 2 Configuration of the four pose fusion architectures

[0161]

[0162] Table 3. Statistical analysis of attitude errors of four fusion methods on urban-suburban trajectories in the 2000s.

[0163]

[0164] Table 3 shows the RMSE and standard deviation (STD) of four fusion methods on each axis of a 2000s urban-suburban trajectory. The centralized C-EKF method had the lowest accuracy, with an average RMSE of 0.635° and pitch and roll offsets exceeding 3°. Due to the lack of fault isolation, transiently contaminated observations (especially accelerometer specific forces during cornering or braking) could propagate directly to the global state. Separating the information source into local branches and eliminating redundant computations of shared priors (F-EKF, β allocation) reduced the average RMSE to 0.293°, an improvement of 53.9%. Further gains were obtained by using separated covariance cross-validation to bound the residual inter-filter correlations: H-EKF-SCIF reached 0.263°, and the proposed F-SCIF reached 0.248°, representing a 60.9% reduction relative to C-EKF and a 15.4% reduction relative to F-EKF. The method proposed in this invention provides the lowest RMSE on three axes: pitch 0.192°, roll 0.447°, and yaw 0.105°.

[0165] The greatest improvement occurs on the yaw axis, where the correlation between filters is strongest. For this axis, r = 0.989 is measured, therefore conventional fusion inherits a shared gyroscope-driven error component. The proposed method explicitly binds this component, reducing the yaw RMSE from 0.240° (C-EKF) to 0.105°, eliminating the slow yaw deviation visible on the C-EKF attitude profile. Roll remains the most challenging axis for all methods, primarily due to baseline geometry constraints leading to weak roll observability. For the three federated methods, STD is almost identical to RMSE (Table 3), indicating that their residual errors are close to zero mean. The larger RMSE-STD gap in C-EKF reflects transients caused by maneuvers that it failed to isolate.

[0166] These results demonstrate that the final accuracy derives from both the federated structure and the main fusion that considers correlations. The federated decomposition provides the main gain by isolating source-specific perturbations in local branches. Separating covariance crossover subsequently adds a smaller but consistent improvement by preventing the repeated computation of shared inertial information. Together, these two mechanisms make F-SCIF the most accurate architecture among the four methods tested.

[0167] Accurate vehicle attitude determination in urban environments is crucial for autonomous driving and intelligent transportation systems. Jointly utilizing heterogeneous onboard attitude information is an important and valuable approach to improving attitude observability and robustness, as different sensors can provide complementary constraints. Gyroscopes provide short-term attitude continuity, accelerometers provide gravity-based pitch / roll constraints, and multi-antenna GNSS provides an absolute geometric attitude reference. However, these information sources are installed on the same vehicle platform and assist each other in the processing link, inevitably introducing correlations between attitude estimates. Ignoring these correlations can lead to the reuse of shared information and inconsistent covariance estimates. To address this issue, this invention proposes a hierarchical Split CIF fusion framework for multi-antenna GNSS / INS vehicle attitude determination in urban environments. This framework jointly utilizes three complementary attitude sources: gyroscope-derived pitch / roll, accelerometer-derived pitch / roll, and multi-antenna GNSS-derived attitude. Gyroscopes maintain short-term attitude continuity, accelerometers provide gravity-based horizontal attitude constraints, and multi-antenna GNSS provides an absolute geometric attitude reference. Compared to relying on a single sensor branch, the combined use of all three improves attitude observability and robustness. Multi-sensor collaboration is becoming an important trend in robust navigation and attitude determination, but it also introduces unavoidable correlations that must be explicitly addressed. In the proposed architecture, GNSS-derived position and velocity are used for dynamic compensation by the accelerometer, while the gyroscope-derived heading is used to constrain GNSS ambiguity. Furthermore, the two local filters share the same gyroscope derivation and observe the same vehicle platform. Therefore, both local filter updates and master filter fusion contain relevant information. The proposed hierarchical SplitCIF design addresses this issue by performing correlation-considered fusion in three stages (not just in the final master filter). Empirical correlation analysis confirms the necessity of this design. The pitch and roll errors of the original source show weak correlation (|r|≤0.19), while the outputs of the two local filters exhibit significant correlation, especially in the heading (r=0.989). Ignoring these correlations, traditional Kalman fusion may repeatedly compute shared information and produce overly optimistic covariance estimates. Split CIF avoids this problem by separating the shared components from the sensor-specific covariance components, consistently and boundedly processing the correlated parts while preserving useful independent measurement information. Vehicle experiments conducted in urban-suburban environments demonstrate that the proposed Split CIF-based fusion achieves a significant improvement in attitude accuracy after explicitly processing these correlations. The RMSEs for pitch, roll, and yaw are 0.192°, 0.447°, and 0.105°, respectively, representing a 60.9% reduction in average attitude RMSE compared to centralized EKF.These results demonstrate that the proposed hierarchical Split CIF framework provides an effective paradigm for utilizing mutually supportive multi-source information and can be further extended to camera, LiDAR, odometry, and vehicle motion constraints to improve the robustness and accuracy of autonomous driving navigation.

[0168] See Figure 5 The present invention also provides a multi-antenna GNSS and INS fusion vehicle attitude determination device based on Split CIF, including a memory and a processor;

[0169] The memory is used to store computer program code and transmit the computer program code to the processor;

[0170] The processor is configured to execute the multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF as described above, according to instructions in the computer program code.

[0171] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF as described above.

[0172] Generally, the computer instructions for implementing the method of the present invention can be carried on any combination of one or more computer-readable storage media. Non-transitory computer-readable storage media can include any computer-readable medium except for the signal itself, which is temporarily propagating.

[0173] Computer-readable storage media can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EKROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0174] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as the "C" language or similar programming languages. In particular, Python, suitable for neural network computation, and platform frameworks such as TensorFlow and PyTorch can be used. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer or to an external computer (e.g., via the Internet using an Internet service provider) through any type of network, including a local area network (LAN) or a wide area network (WAN).

[0175] The aforementioned equipment and non-transitory computer-readable storage media can be found in the detailed description of a multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF and its beneficial effects, which will not be repeated here.

[0176] Although embodiments of the present invention have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for determining vehicle attitude based on the fusion of multi-antenna GNSS and INS using Split CIF, characterized in that, include: Obtain the one-step predicted vehicle attitude obtained by the gyroscope recursion, and use it as the gyroscope recursive attitude source; The heading obtained by gyroscope recursion is used as a priori constraint to help fix the carrier phase integer ambiguity of multi-antenna GNSS, and the attitude of the three-axis vehicle is calculated from the fixed baseline vector, which serves as the attitude source of multi-antenna GNSS. Using the position, velocity, and zero-speed detection information exported from GNSS, the specific force measured by the vehicle accelerometer is compensated, and the pitch and roll angles of the vehicle are calculated from the compensated gravity direction, which serves as the accelerometer attitude source. The gyroscope recursive attitude source and the accelerometer attitude source are fused in the first stage using a separation covariance cross-filtering algorithm to obtain a first local vehicle attitude estimate; the gyroscope recursive attitude source and the multi-antenna GNSS attitude source are fused in the second stage using a separation covariance cross-filtering algorithm to obtain a second local vehicle attitude estimate. The first local vehicle attitude estimate and the second local vehicle attitude estimate are fused in the third stage using a separate covariance cross-filtering algorithm to obtain the global vehicle attitude estimate. The mixing parameters of the third-stage main fusion Hybrid parameters for the first stage of local fusion Hybrid parameters of the second-stage local fusion It is adaptively determined for each epoch, specifically including: Within the open interval (0, 1), the relevant covariance components of the two to-be-fused estimates are respectively... and The expansion is then combined according to the information format to obtain the fusion covariance. ; with the determinant of the fusion covariance As the cost function, it is determined through one-dimensional optimization. Minimum mixing parameters The one-dimensional optimization employs the golden section search to locate the globally optimal hybrid parameters within a preset tolerance. This is then used for the corresponding separation covariance cross-filter update.

2. The method for determining vehicle attitude based on Split CIF multi-antenna GNSS and INS fusion according to claim 1, characterized in that, The global estimation of the vehicle attitude is as follows: ； In the formula, For global estimation of vehicle attitude; For local attitude estimation of the first vehicle; For the first The first local estimate of the vehicle attitude obtained at the epoch; For local attitude estimation of the second vehicle; For the first The local attitude estimate of the second vehicle obtained in the epoch; and These are the covariance components related to the shared propagation process in the local estimation of the first and second vehicle attitudes, respectively. and These are the independent covariance components corresponding to the local estimates of the first and second vehicle attitudes, respectively. The mixing parameters for the third-stage main fusion; Main filter gain; The local attitude estimate of the first vehicle is calculated by its related covariance components according to... Inflated covariance; The local attitude estimate of the second vehicle is obtained by processing its relevant covariance components according to... After expansion, the covariance used in the calculation is the equivalent measurement covariance of the second vehicle attitude local estimation in the third-stage main fusion. This represents the total covariance in the global estimation of vehicle attitude. It is the identity matrix; and These are the independent covariance components and the correlated covariance components in the global estimation of vehicle attitude, respectively.

3. The method for determining vehicle attitude based on Split CIF multi-antenna GNSS and INS fusion according to claim 2, characterized in that, The local attitude estimation of the first vehicle is as follows: ； In the formula, For local attitude estimation of the first vehicle; For the first The epoch is a one-step prediction of vehicle attitude obtained by recursion from the gyroscope; This is the gyroscope propagation state transition matrix; The vehicle's posture in the previous epoch; This refers to the noise generated during the propagation of the gyroscope. For the first The epochs are pitch and roll angle observations provided by the accelerometer attitude source; For accelerometer observation matrix; Noise for accelerometer attitude observation; and These are the correlated covariance component and the independent covariance component in the gyroscope propagation attitude prediction covariance, respectively. and These are the correlated covariance component and the independent covariance component in the accelerometer attitude observation covariance, respectively. These are the mixing parameters for the first stage of local fusion; The covariance of the gyroscope propagation attitude prediction covariance after expansion by the relevant components; The covariance of the accelerometer attitude observations is dilated by the correlation components; This is the filter gain; , and These are the total covariance, independent covariance components, and correlated covariance components in the local estimation of the first vehicle's attitude, respectively. It is an identity matrix.

4. The method for determining vehicle attitude based on Split CIF multi-antenna GNSS and INS fusion according to claim 3, characterized in that, The local attitude estimation of the second vehicle is as follows: ； In the formula, For local attitude estimation of the second vehicle; For the first The epoch is a one-step prediction of vehicle attitude obtained by recursion from the gyroscope; This is the gyroscope propagation state transition matrix; The vehicle's posture in the previous epoch; This refers to the noise generated during the propagation of the gyroscope. For the first The epoch is based on vehicle attitude observations provided by a multi-antenna GNSS attitude source; This is a multi-antenna GNSS attitude observation matrix; Noise in multi-antenna GNSS attitude observations; and These are the correlated covariance component and the independent covariance component in the gyroscope propagation attitude prediction covariance, respectively. and These are the correlated covariance component and the independent covariance component in the covariance of multi-antenna GNSS attitude observations, respectively. These are the mixing parameters for the second stage of local fusion; The covariance of the gyroscope propagation attitude prediction covariance after expansion by the relevant components; The covariance of multi-antenna GNSS attitude observations is the covariance after dilation of the correlation components; This is the filter gain; , and These are the total covariance, independent covariance components, and correlated covariance components in the local estimation of the second vehicle's attitude, respectively. It is an identity matrix.

5. The method for determining vehicle attitude based on Split CIF multi-antenna GNSS and INS fusion according to claim 1, characterized in that, The method of using the heading obtained recursively from the gyroscope as a priori constraint, assisting in fixing the carrier phase integer ambiguity of the multi-antenna GNSS, and calculating the three-axis vehicle attitude from the fixed baseline vector includes: The fixed baseline vector satisfies the following relationship: ； ； ； ； In the formula, Represents the first in the carrier coordinate system One baseline vector; This represents the baseline vector in the navigation coordinate system obtained by GNSS with fixed ambiguity for the current epoch; This represents the rotation matrix from the vehicle coordinate system to the navigation coordinate system; The attitude correction is estimated by iterative weighted least squares: ； ； ； ； ； ； ； ； In the formula, For Euler angle corrections, ; For designing the matrix; It is a block-diagonal weight matrix; Represents the residual vector; The covariance of the attitude correction for multi-antenna GNSS; For heading angle; The pitch angle; This refers to the roll angle; For the first Covariance of the baseline in the navigation coordinate system; This indicates that the columns of the matrix are stacked into a single column vector; The residual matrix; For measuring the noise vector; The current iteration value Rotation matrix at; Angle updated to: ； Through iteration, until If the value is below a preset threshold, the attitude of the three-axis vehicle can be estimated. .

6. The method for determining vehicle attitude based on Split CIF multi-antenna GNSS and INS fusion according to claim 1, characterized in that, The process of using GNSS-derived position, velocity, and zero-speed detection information to compensate for the specific force measured by the onboard accelerometer, and then calculating the vehicle's pitch and roll angles from the compensated gravity direction, includes: Based on Newton's second law in the Earth-fixed rotating coordinate system, the following equation is constructed: ； In the formula, This is the rotation matrix from the vehicle coordinate system to the navigation coordinate system; This indicates the specific force measured by the onboard accelerometer in the vehicle's coordinate system; This represents the vehicle's acceleration in the navigation coordinate system; The vehicle's speed in the navigation coordinate system; and These are the Earth's rotation angular rate and the entrainment angular rate vectors, respectively. The gravity vector ; The ratio after compensation is: ； In the formula, ; The compensated force component is: ； ； ； In the formula, , and The comparison after compensation is as follows , and Axial components; The pitch angle; This refers to the roll angle; The vehicle's pitch and roll angles are calculated using the following formula: ； ； In the formula, The calculated vehicle pitch angle; The calculated vehicle roll angle.

7. A multi-antenna GNSS and INS fusion vehicle attitude determination device based on Split CIF, characterized in that, The apparatus is used to implement the vehicle attitude determination method based on Split CIF multi-antenna GNSS and INS fusion according to any one of claims 1 to 6, the apparatus comprising: The multi-attitude source acquisition module is used to acquire the one-step predicted vehicle attitude obtained by the gyroscope recursion, as the gyroscope recursive attitude source; using the heading obtained by the gyroscope recursion as a priori constraint, it assists in fixing the carrier phase integer ambiguity of the multi-antenna GNSS, and calculates the three-axis vehicle attitude from the fixed baseline vector, as the multi-antenna GNSS attitude source; using the position, velocity and zero-speed detection information derived from GNSS, it compensates for the specific force measured by the on-board accelerometer, and calculates the vehicle's pitch angle and roll angle from the compensated gravity direction, as the accelerometer attitude source; The vehicle attitude local estimation module is used to perform a first-stage local fusion of the gyroscope recursive attitude source and the accelerometer attitude source through a separation covariance cross-filtering algorithm to obtain a first vehicle attitude local estimate; and to perform a second-stage local fusion of the gyroscope recursive attitude source and the multi-antenna GNSS attitude source through a separation covariance cross-filtering algorithm to obtain a second vehicle attitude local estimate. The vehicle attitude global estimation module is used to perform a third-stage main fusion of the first vehicle attitude local estimation and the second vehicle attitude local estimation through a separation covariance cross-filtering algorithm to obtain the vehicle attitude global estimation.

8. A vehicle attitude determination device based on Split CIF multi-antenna GNSS and INS fusion, characterized in that, Including memory and processor; The memory is used to store computer program code and to transmit the computer program code to the processor; The processor is configured to execute the multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF as described in any one of claims 1 to 6, according to instructions in the computer program code.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the multi-antenna GNSS and INS fusion vehicle attitude determination method based on Split CIF as described in any one of claims 1 to 6.

Images