Single-antenna gnss-based carrier high-precision heading calculation method and device

Abstract

A single-antenna GNSS-based carrier high-precision heading solution method and device, combined with carrier phase epoch difference and average Doppler observation value to construct a joint displacement solution model, introduce correlation entropy to suppress abnormal observation and non-Gaussian noise, and obtain a robust displacement solution; the robust displacement solution of continuous multiple epochs is converted to the current epoch station coordinate system, and a local two-dimensional discrete trajectory is constructed; a cubic B-spline is used to fit the local trajectory, and the first derivative of the cubic B-spline trajectory function is used to calculate the instantaneous velocity of the current epoch in the north direction and the east direction, and the direction of the instantaneous velocity vector is taken as the heading angle output, instead of the heading angle calculation based on the single-epoch displacement vector direction, to correct the geometric deviation between the carrier displacement secant direction and the true heading tangent direction. The present application can improve the precision and robustness of the heading solution in complex environment and various motion states, and fully exert the advantages of single-antenna scheme in low cost, miniaturization and easy deployment.

Description

Technical Field

[0001] This invention belongs to the field of precise positioning technology of Global Navigation Satellite System (GNSS), specifically relating to a high-precision heading calculation technology for a carrier based on single-antenna GNSS. Background Technology

[0002] In emerging applications such as autonomous driving, drone and mobile robot navigation, high-precision motion state estimation of the vehicle is fundamental to achieving environmental perception, path planning and precise control. The heading angle, as a key attitude parameter characterizing the vehicle's motion direction, directly impacts the vehicle's safety and navigation performance through its real-time estimation, continuity, and accuracy. With the rapid development of GNSS positioning technology, low-cost GNSS receivers are widely used in various smart terminals. Real-time, high-precision attitude calculation of vehicles based on GNSS has significant engineering application value and promotional implications in complex scenarios and under various motion states.

[0003] Methods for calculating a vehicle's heading angle using GNSS can be mainly divided into two categories: one is attitude measurement based on multiple antennas, and the other is position or velocity vector orientation based on a single antenna. Multi-antenna attitude measurement methods are independent of the vehicle's motion state, offering advantages such as drift-free operation and high accuracy, but their high hardware cost makes them difficult to widely adopt in consumer-grade terminals. In contrast, single-antenna methods calculate the vehicle's pitch and heading angles using displacement or velocity vectors, resulting in a simpler hardware structure and greater adaptability. Among these, velocity vector-based heading calculations typically rely on Doppler frequency shift observations to calculate the vehicle's instantaneous velocity. However, Doppler observations have significant noise, which can easily lead to decreased velocity measurement performance in low-speed motion or complex environments, thus causing heading angle jitter. The Time-Differenced Carrier Phase (TDCP) method utilizes the carrier phase changes between adjacent epochs to construct an observation model. Over short time intervals, it can effectively eliminate common errors such as satellite clock bias, receiver clock bias, and some atmospheric delay, thereby obtaining high-precision relative displacement information. Therefore, TDCP technology is considered one of the effective means for achieving high-precision velocity and heading measurement with a single antenna. However, in complex environments such as urban canyons and shaded areas, carrier phase observations are prone to signal interruptions, cycle slips, and gross errors, making it difficult to effectively guarantee the continuity and robustness of displacement calculations. Furthermore, most existing TDCP heading calculation methods directly calculate the heading angle using single-epoch displacement vectors, i.e., using the position increment direction between adjacent epochs as the current carrier heading. The inventors' team discovered that this type of method essentially approximates the actual motion tangent direction using the trajectory secant direction. Under conditions of linear motion of the carrier, this approximation has good applicability; however, in complex maneuvering scenarios such as carrier turning and low dynamics, significant geometric deviations easily occur between the displacement vector direction and the true heading direction, resulting in lag errors and systematic deviations in the heading angle, as shown in Figure 2: N (north direction) and E (east direction) constitute the horizontal plane of the station-centered northeast-sky coordinate system, providing a reference benchmark for the heading angle calculation; t0, t1, t2, and t3 represent consecutive epoch times, corresponding to the carrier's positions at different epochs; the smooth curve represents the true trajectory of the carrier's continuous motion within the horizontal plane; the heading tangent direction is the carrier's true heading at the current position (e.g., at t1); the displacement secant direction is the result of the traditional single-epoch method using the displacement vector direction between adjacent epochs as the heading angle, essentially the direction of the line connecting two points on the trajectory, rather than the instantaneous tangent direction at the current epoch. Figure 2 It is known that when the vehicle is in a maneuvering state such as turning, there is a significant geometric deviation between the displacement secant direction and the true heading tangent direction (i.e., the angle Δφ2 between the two direction lines at t3 in the figure). This deviation is particularly significant when the trajectory curvature is large, leading to a systematic heading lag error in traditional methods. Existing methods have not revealed the cause of this deviation, nor have they proposed effective correction methods.

[0004] To address the instability in displacement calculations caused by anomalies in GNSS observations under complex environments, existing research typically employs methods such as observation quality control and robust estimation to improve the reliability of the results. However, anomalies in complex environments often exhibit characteristics such as continuous occurrence, multi-source superposition, and non-Gaussian distribution. Relying solely on observation quality control is insufficient to completely identify all anomalies, and conventional robust estimation methods tend to experience a significant performance degradation when the proportion of anomalies is high, thus limiting the continuity and robustness of displacement calculations. Furthermore, existing single-antenna heading calculation methods primarily utilize local displacement information between adjacent epochs, failing to fully exploit the spatiotemporal correlations contained in continuous motion trajectories across multiple epochs. Therefore, it is difficult to accurately characterize the instantaneous motion direction of the vehicle under complex motion conditions while suppressing local observation anomalies.

[0005] Therefore, there is an urgent need to research a high-precision heading calculation method for single-antenna GNSS systems in complex environments and with various motion states. This method should improve the robustness of displacement calculation while fully utilizing multi-epoch continuous motion information to enhance the accuracy, continuity, and real-time performance of heading calculation. This approach has significant research value and application implications for leveraging the advantages of single-antenna schemes in terms of low cost, miniaturization, and ease of deployment, thereby improving the practicality and environmental adaptability of GNSS heading calculation technology. Summary of the Invention

[0006] This invention aims to overcome the problems of low accuracy, poor robustness, and limited engineering applicability of existing single-antenna GNSS heading calculation techniques in complex environments and under various motion conditions. In complex environments such as urban canyons and forest cover, carrier phase observations are prone to signal interruptions, cycle slips, and gross errors. Traditional heading calculation methods based on single-epoch displacement vectors are easily affected by observational anomalies and deterioration of satellite geometry, leading to decreased heading calculation accuracy and insufficient robustness. Furthermore, these methods typically approximate the true heading tangent direction of the vehicle by using the displacement secant direction between adjacent epochs. This can easily generate significant geometric deviations in complex maneuvering scenarios such as vehicle turns and low-dynamic operations, resulting in increased heading angle calculation errors, significant lag, and even continuous heading calculation failures. To address this, this invention proposes a high-precision heading calculation method and system for a carrier based on single-antenna GNSS. By introducing a relevant entropy robust estimation mechanism, the continuity and robustness of displacement calculation under complex environments are improved. Furthermore, by combining multi-epoch trajectory construction and B-spline continuous fitting, the geometric deviation between the displacement secant direction and the actual heading tangent direction under complex maneuvering scenarios such as carrier turning and low dynamics is corrected, thereby achieving high-precision and highly robust heading calculation.

[0007] The above-mentioned technical problems of the present invention are mainly solved by the following technical solutions: A high-precision heading calculation method for a carrier based on single-antenna GNSS includes the following steps: Acquire multi-frequency, multi-system observation data from the GNSS receiver, preprocess carrier phase and Doppler observations, and complete cycle slip detection and gross error detection. A joint displacement solution model is constructed based on the carrier phase epoch difference and the average Doppler observation to obtain the displacement solution for the current epoch. For the joint displacement calculation model, a correlation entropy robust estimation is introduced to suppress anomalous observations and non-Gaussian noise, thereby improving the robustness of displacement calculation under complex environments. A multi-epoch displacement sequence is constructed using robust displacement solutions from multiple consecutive epochs, and the multi-epoch displacement sequence is uniformly transformed to the station center coordinate system of the current epoch. A local two-dimensional discrete trajectory is constructed based on the multi-epoch displacement sequence, and a cubic B-spline is used to fit the local trajectory. The instantaneous velocities in the north and east directions at the current epoch are calculated based on the first derivative of the cubic B-spline trajectory function, and then converted to obtain the heading angle. The vector direction of the instantaneous velocity is used as the heading angle of the current epoch to replace the heading angle calculation based on the displacement vector direction of a single epoch. This corrects the geometric deviation between the displacement secant direction of the download body and the actual heading tangent direction in complex maneuvering scenarios, and outputs the carrier heading information.

[0008] Furthermore, the cycle slip detection includes joint detection of cycle slips using the lock identification information LLI of carrier phase observations and Geometry-Free combined observations. The gross error detection includes judging the quality of observations based on satellite elevation angle and signal-to-noise ratio, and removing observations with low elevation angle or low signal-to-noise ratio to reduce the impact of abnormal observations such as cycle slips, multipath effects, and non-line-of-sight propagation on displacement calculation.

[0009] Moreover, the joint displacement calculation model includes an observation equation based on the differential observations between carrier phase epochs and an observation equation based on the average Doppler observations. The average Doppler observations are used to improve the performance degradation of displacement calculation under complex environments where carrier phase observations are missing or satellite geometry deteriorates.

[0010] Moreover, the robust correlation entropy estimation is a robust estimation method based on the maximum correlation entropy criterion. By assigning adaptive weights to the observations corresponding to the residuals, it suppresses anomalous observations and non-Gaussian noise, thereby improving the accuracy and robustness of displacement calculation in complex environments.

[0011] Moreover, the multi-epoch displacement sequence is constructed by accumulating the displacement solutions of multiple epochs within a continuous time window, and uniformly transformed to the station center northeast-sky coordinate system corresponding to the current epoch to form a local two-dimensional discrete trajectory.

[0012] Moreover, cubic B-spline trajectory fitting uses no fewer than four effective displacement epochs within a continuous time window as input, and reconstructs a continuous curve from the local two-dimensional discrete trajectory using a cubic B-spline function.

[0013] Furthermore, the instantaneous velocity at the current epoch is obtained by solving the first derivative of the cubic B-spline trajectory function at the current moment, and the heading angle at the current epoch is calculated based on the instantaneous velocity to replace the heading angle calculation based on the displacement vector direction of a single epoch. This allows for the correction of the geometric deviation between the displacement secant direction of the downloaded body and the actual heading tangent direction in complex maneuvering scenarios.

[0014] Furthermore, when the displacement amplitude of the current epoch is lower than the preset motion threshold, the carrier is determined to be in a low dynamic or static state and the heading angle calculation is paused; when the number of effective displacement epochs within the time window meets the preset minimum window length, the three-dimensional B-spline trajectory fitting and heading angle calculation process is executed.

[0015] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the carrier high-precision heading calculation method based on single-antenna GNSS as described above.

[0016] On the other hand, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the carrier high-precision heading calculation method based on single-antenna GNSS as described above.

[0017] This invention constructs a robust displacement calculation model based on the combined carrier phase epoch difference and average Doppler observations through the above technical solution, improving the continuity and robustness of displacement calculation in complex environments. Simultaneously, by fitting multi-epoch displacement trajectories with cubic B-splines, the tangent direction of the trajectory is used instead of the traditional single-epoch displacement secant direction for heading angle calculation, thereby effectively reducing geometric deviations in complex maneuvering scenarios such as vehicle turning and low-dynamic conditions, and improving the accuracy and robustness of single-antenna GNSS heading calculation.

[0018] Compared with the prior art, the present invention has the following significant advantages: (1) The continuity and robustness of TDCP displacement calculation under complex environment are significantly enhanced.

[0019] This invention utilizes carrier phase epoch difference and average Doppler observations in the TDCP displacement calculation stage, combined with cycle slip detection, gross error detection, and related entropy robust estimation, to effectively suppress abnormal observations and non-Gaussian noise. This can improve the continuity and robustness of displacement calculation in complex environments, thereby improving problems such as decreased heading angle calculation accuracy and insufficient robustness caused by displacement calculation anomalies.

[0020] (2) The accuracy and robustness of heading angle calculation under complex maneuvering scenarios are significantly improved.

[0021] This invention continuously fits multi-epoch displacement sequences using cubic B-splines, and uses the trajectory tangent direction to replace the traditional single-epoch displacement secant direction for heading angle calculation. This effectively compensates for the geometric deviation between the displacement secant direction and the actual heading tangent direction, thereby significantly improving the accuracy and robustness of heading angle calculation in complex maneuvering scenarios.

[0022] The present invention is simple and convenient to implement, highly practical, and solves the problems of low practicality and inconvenience in actual application of related technologies. It can improve user experience and has significant market value. Attached Figure Description

[0023] Figure 1 This is a schematic diagram illustrating the principle of an embodiment of the present invention.

[0024] Figure 2 is a schematic diagram of the geometric relationship between the direction of the displacement secant and the direction of the trajectory tangent during curvilinear motion.

[0025] Figure 3 is a time series diagram of the heading angle calculation error of the present invention and the prior art.

[0026] Figure 4 is a schematic diagram of the overall process of an embodiment of the present invention. Detailed Implementation

[0027] The following will further explain the concept, specific structure and technical effects of the present invention in conjunction with the accompanying drawings and embodiments, so as to fully understand the purpose, features and effects of the present invention.

[0028] Example 1: This embodiment provides a high-precision heading calculation method for a carrier based on single-antenna GNSS. First, a joint displacement calculation model is constructed based on the Time-Differenced Carrier Phase (TDCP) and the average Doppler observations. Correlation entropy robust estimation is introduced to suppress abnormal observation errors and non-Gaussian noise in complex environments, thereby improving the continuity and robustness of the displacement calculation. Subsequently, a local motion trajectory is constructed using displacement information from multiple consecutive epochs, and cubic B-splines are used to continuously fit and reconstruct the local trajectory. The instantaneous velocity at the current epoch is calculated using the first derivative of the trajectory function, and the heading angle is further converted to obtain the heading angle. This reduces the geometric deviation between the displacement secant direction and the true heading tangent direction in traditional single-epoch heading calculation, achieving high-precision and high-robustness single-antenna GNSS heading calculation in complex environments and under various motion conditions.

[0029] See Figure 1In one possible implementation, this embodiment provides a carrier high-precision heading calculation method based on single-antenna GNSS, comprising the following steps: (1) Acquire multi-frequency and multi-system observation data output by GNSS receiver, preprocess carrier phase and Doppler observation values, and complete cycle slip detection and gross error detection; The cycle slip detection includes joint detection of cycle slips using the Loss of Lock Indicator (LLI) information of carrier phase observations and Geometry-Free combined observations. The gross error detection includes judging the quality of observations based on satellite elevation angle and signal-to-noise ratio, and removing observations with low elevation angle or low signal-to-noise ratio to reduce the impact of abnormal observations such as cycle slips, multipath effects, and non-line-of-sight propagation on displacement calculation.

[0030] (2) Based on the carrier phase epoch difference and the average Doppler observation, a joint displacement solution model is constructed to obtain the displacement solution of the current epoch; The joint displacement calculation model includes an observation equation based on the differential observations between carrier phase epochs and an observation equation based on the average Doppler observations. The average Doppler observations are used to improve the performance degradation of displacement calculation under complex environments where carrier phase observations are missing or satellite geometry deteriorates.

[0031] (3) For the joint displacement calculation model, a correlation entropy robust estimation is introduced to suppress abnormal observations and non-Gaussian noise, thereby improving the robustness of displacement calculation under complex environments; The robust correlation entropy estimation is a robust estimation method based on the maximum correlation entropy criterion. By assigning adaptive weights to the observations corresponding to the residuals, it suppresses anomalous observations and non-Gaussian noise, thereby improving the accuracy and robustness of displacement calculation in complex environments.

[0032] (4) Construct a multi-epoch displacement sequence using the robust displacement solution of multiple consecutive epochs, and uniformly transform the displacement sequence to the current epoch station center coordinate system; The multi-epoch displacement sequence is constructed by accumulating the displacement solutions of multiple epochs within a continuous time window, and uniformly transformed to the station center northeast-sky coordinate system corresponding to the current epoch to form a local two-dimensional discrete trajectory.

[0033] (5) Construct a local two-dimensional discrete trajectory based on the multi-epoch displacement sequence, and fit the local trajectory using cubic B-splines; (6) Calculate the instantaneous velocities in the north and east directions at the current epoch based on the first derivative of the cubic B-spline trajectory function, and further convert them to obtain the heading angle, and output the carrier heading information; This improves the accuracy and robustness of GNSS heading calculations in complex environments and under various motion conditions.

[0034] The cubic B-spline trajectory fitting uses no less than four effective displacement epochs within a continuous time window as input, and reconstructs a continuous curve from the local two-dimensional discrete trajectory using a cubic B-spline function.

[0035] The instantaneous velocity at the current epoch is obtained by solving the first derivative of the cubic B-spline trajectory function at the current moment, and the heading angle at the current epoch is calculated based on the instantaneous velocity, thereby correcting the geometric deviation between the displacement secant direction and the actual heading tangent direction of the downloaded body in complex maneuvering scenarios.

[0036] When the displacement amplitude of the current epoch is lower than the preset motion threshold, the carrier is determined to be in a low dynamic or static state and the heading angle calculation is paused; when the number of effective displacement epochs within the time window meets the preset minimum window length, the cubic B-spline trajectory fitting and heading angle calculation process is executed.

[0037] The aforementioned method first constructs a robust displacement calculation model by combining carrier phase epoch difference and average Doppler observations. It then incorporates cycle slip detection, gross error detection, and related entropy robust estimation to effectively suppress the impact of anomalous observations and non-Gaussian noise on displacement calculation, achieving continuous and robust displacement calculation in complex environments. Subsequently, the displacements from multiple epochs within the time window are uniformly transformed to the current epoch's station-centric coordinate system, constructing a local two-dimensional discrete trajectory. Finally, cubic B-splines are used to continuously fit the local trajectory, and the instantaneous velocity at the current epoch is calculated based on the first derivative of the trajectory function. This reduces the geometric deviation between the displacement secant direction and the true heading tangent direction in complex maneuvering scenarios, achieving high-precision heading angle calculation. This method effectively improves the accuracy and robustness of heading calculation in complex environments and under various motion conditions, fully leveraging the advantages of single-antenna schemes in terms of low cost, miniaturization, and easy deployment. It enhances the practicality and environmental adaptability of GNSS heading calculation technology, making it particularly suitable for emerging applications such as autonomous driving, UAV, and mobile robot navigation.

[0038] Example 2 See Figure 4 The embodiment provides a method for high-precision heading calculation of a carrier based on single-antenna GNSS, which specifically includes the following steps: S1. GNSS observation data preprocessing and quality control This step acquires multi-frequency, multi-system observation data output from the GNSS receiver, preprocesses the carrier phase and Doppler observations, and completes cycle slip detection and gross error detection. Specifically, it includes the following sub-steps: S11. Acquire multi-frequency, multi-system carrier phase observations, Doppler observations, and navigation message information output by the GNSS receiver, and filter the raw observation data based on satellite elevation angle, signal-to-noise ratio, and observation integrity.

[0039] S12. Joint cycle slip detection is performed using the Loss of Lock Indicator (LLI) information of carrier phase observations and Geometry-Free (GF) combined observations. The quality of the observations is judged by combining the satellite elevation angle and signal-to-noise ratio, and satellite data with cycle slips or abnormal observations are removed to improve the continuity and robustness of subsequent displacement calculations.

[0040] S13. Perform quality checks on the preprocessed observations to obtain a set of valid observation data for displacement calculation.

[0041] S2. Displacement calculation based on the joint difference between carrier phase epochs and mean Doppler observations This step constructs a joint displacement solution model based on the carrier phase epoch difference and the average Doppler observations to obtain the displacement solution for the current epoch: After completing the preprocessing of the observation data, observation equations are constructed based on the carrier phase epoch difference observations and the average Doppler observations, respectively, forming a joint displacement solution model, as shown in Equation (1). Furthermore, to reduce the impact of anomalous observations and non-Gaussian noise on the displacement solution, this embodiment introduces a robust correlation entropy estimation, the correlation entropy function of which is shown in Equation (5). During the joint solution, the observation noise variance is determined using a signal-to-noise ratio stochastic model. Based on the joint displacement observation model and the robust correlation entropy estimation method, the displacement parameters of the current epoch are solved, and a robust displacement solution is output.

[0042] The specific implementation includes the following sub-steps: S21. Based on the carrier phase epoch difference and the average Doppler observations, observation equations are constructed respectively to form a joint displacement solution model, the calculation formula of which is: (1) in, Indicates the carrier wavelength; and These represent the carrier phase epoch difference observations and the average Doppler observations, respectively. Indicates the time interval between epochs; Indicates the satellites between epochs The change in distance from the receiver; Represents the speed of light; and These represent the change in clock bias of carrier phase observations and the clock speed of average Doppler observations, respectively. and These represent the noise of the corresponding observations, and their variances are determined using a signal-to-noise ratio stochastic model.

[0043] Construct the original observation weight matrix based on the variance of each observation. : (2) in, Indicates the first The variance of each observation. The number of observations, () represents a diagonal matrix.

[0044] The joint displacement calculation model includes three displacement parameters, one carrier phase clock error change parameter, and one average Doppler clock velocity parameter. A linearized observation equation is established based on the joint displacement calculation model, where the design matrix consists of the first-order partial derivatives of the parameters to be estimated in the observation equation. Parameter estimation is performed using the weighted least squares method with the original observation weight matrix. (3) And calculate the observation residuals: (4) in, This represents the weighted least squares estimate of the parameter vector to be estimated. Represents the design matrix, with superscripts. and These represent the transpose and inverse of the matrix, respectively. Represents the observation vector. This represents the observation residual; the observation residual serves as the input for subsequent robust estimation.

[0045] S22. To reduce the impact of anomalous observations and non-Gaussian noise on the joint displacement solution results, the correlation entropy robust estimation method is introduced into the joint displacement solution model constructed in step S21. The correlation entropy weights corresponding to each observation are calculated based on the observation residuals, and their correlation entropy functions are... Represented as: (5) And construct the relevant entropy weight matrix : (6) in, Indicates the first The residuals corresponding to each observation value The kernel width parameter represents the relevant entropy kernel, and exp() is the natural exponential function. The number of observations is denoted by . The larger the residual, the smaller its corresponding weight, thereby suppressing anomalous observations and non-Gaussian noise.

[0046] The original observation weight matrix is ​​corrected using the aforementioned correlation entropy weight matrix to obtain the updated observation weight matrix. : (7) The parameters of the joint displacement solution model are re-estimated using an iterative reweighted least squares method until the parameter changes between two adjacent iterations meet a preset convergence condition. For example, the iteration is terminated when the L2 norm of the displacement parameter change between two adjacent iterations is less than 0.001m, or when the number of iterations reaches 10.

[0047] S23. Based on the updated observation weight matrix, perform parameter estimation for the joint displacement solution model and output the robust displacement solution for the current epoch. This information is then used as input for subsequent trajectory reconstruction and heading angle calculation.

[0048] S3. Construction of Multi-Epoch Shift Sequences This step introduces a relevant entropy robust estimation to suppress anomalous observations and non-Gaussian noise in the joint displacement calculation model, thereby improving the robustness of displacement calculation under complex environments. After obtaining the robust displacement solution for the current epoch, the displacement results of multiple epochs within a continuous time window are accumulated to construct a multi-epoch local displacement sequence. Subsequently, the displacement sequence is uniformly transformed to the station-centric northeast-sky coordinate system corresponding to the current epoch, and a local two-dimensional discrete trajectory point set is constructed with the current epoch as the origin.

[0049] To ensure the validity of the heading calculation, only valid trajectory points with displacement amplitudes greater than a preset threshold are retained. For example, at a sampling rate of 1Hz, a static motion judgment threshold of 0.1 m is used, and the number of valid displacement epochs within the time window is no less than 4, which is sufficient to complete the subsequent heading angle calculation.

[0050] The specific implementation includes the following sub-steps: S31. In the current epoch As the end point of the time window, select the current epoch and the consecutive epochs preceding it. Each epoch forms a local time window. Window length It can be preset to an empirical value. In one embodiment, A value of 5 means the time window contains 5 consecutive epochs, corresponding to robust displacement increments between 4 adjacent epochs. (Based on the current epoch...) Using the corresponding receiver position as the origin, establish a station-centric northeast-sky (ENU) coordinate system, and uniformly transform the robust displacement solutions of each adjacent epoch within the time window obtained in step S2 to the ENU coordinate system, resulting in: (8) in, Indicates the first From the first epoch to the 1st century The representation of robust displacement increments in the ENU coordinate system for each epoch. , , These represent the components of the displacement increment in the east, north, and sky directions, respectively; the coordinate axes of the ENU coordinate system are in the east, north, and sky directions, respectively.

[0051] S32. In the current epoch Corresponding local coordinates Using the origin as the starting point, the position coordinates of each historical epoch relative to the current epoch are reconstructed by recursively calculating the ENU displacement increments of adjacent epochs within the time window. : (9) in, (10) Indicates the first The local position of each epoch in the ENU coordinate system with the receiver position of the current epoch as the origin. These represent the coordinate components of the location in the east, north, and sky directions, respectively. The east and north components of each local location are extracted to construct a set of local two-dimensional discrete trajectory points. : (11) S33. Horizontal displacement amplitude based on robust displacement increments from adjacent epochs. (12) Motion state determination is performed, retaining only valid displacement epochs that satisfy the condition that the horizontal displacement amplitude is greater than a preset threshold, in order to avoid amplifying the heading angle calculation error due to excessively small displacement when the carrier is stationary or moving at low speed. In one embodiment, for a 1Hz sampling rate, the threshold can be set to 0.1 m; for other sampling rates, it can be proportionally converted according to the sampling interval and the corresponding average velocity threshold.

[0052] If the number of valid displacement epochs that meet the conditions within the window is less than 4, then the trajectory information within the current window is considered insufficient, and trajectory fitting and heading angle calculation will not be performed. The calculation will be re-performed after the conditions are met in subsequent epochs.

[0053] S4. Local trajectory fitting based on cubic B-splines This step utilizes robust displacement solutions from multiple consecutive epochs to construct a multi-epoch displacement sequence, and then uniformly transforms the displacement sequence to the current epoch's station center coordinate system; After obtaining the local two-dimensional discrete trajectory points, the B-spline function is used to perform continuous curve fitting on the local trajectory. Its mathematical expression is shown in equation (13).

[0054] B-spline fitting can reconstruct discrete displacement points into continuous, smooth local trajectories, thus better describing the true motion state of the vehicle within a short time window. Compared with the single-epoch method, this method has better trajectory representation capabilities and is particularly suitable for heading angle compensation in complex maneuvering scenarios such as vehicle turning and low dynamics.

[0055] The specific implementation includes the following sub-steps: S41. Based on the local two-dimensional discrete trajectory points obtained in step S3, construct a node sequence using the timestamps corresponding to the trajectory points. Determine cubic B-spline control points based on the local two-dimensional discrete trajectory points and the node sequence, and construct a continuous trajectory using a cubic B-spline function. The trajectory function is expressed as follows: (13) in, This represents the two-dimensional continuous trajectory obtained through fitting. Indicates the first indivual B-spline basis functions; Indicates the first One control point, The length of the window; The degree of the B-spline is 3 in this embodiment, which can ensure the local continuity and first-order continuous differentiability of the trajectory while taking into account the trajectory fitting accuracy and computational efficiency. The node parameters represent the physical meaning of the trajectory time. When the GNSS data has a fixed sampling rate, the node parameters use a uniform node sequence; when the sampling interval changes, the node parameters construct a non-uniform node sequence based on the actual timestamps corresponding to each trajectory point.

[0056] S42. Reconstruct the local motion trajectory of the carrier using the fitted continuous trajectory. Unlike existing methods that calculate the heading angle based on the displacement secant direction of adjacent epochs, this invention first constructs a continuous trajectory using a multi-epoch robust displacement sequence, then calculates the first derivative of the continuous trajectory with respect to the time variable, analytically obtaining the velocity vector corresponding to the trajectory at any epoch. The direction of this velocity vector is the actual motion tangent direction of the carrier, thereby correcting the geometric deviation between the trajectory secant direction and the actual motion tangent direction, and improving the accuracy, continuity, and real-time performance of heading angle calculation under complex motion conditions.

[0057] S5. Heading Angle Calculation This step constructs a local two-dimensional discrete trajectory based on the multi-epoch displacement sequence, and fits the local trajectory using cubic B-splines: The first derivative of the fitted B-spline trajectory at the current moment is obtained to get the instantaneous velocity component in the tangent direction of the trajectory. Then, the heading angle of the current epoch is calculated based on the eastward and northward velocity components, and its expression is shown in Equation (15). Since the trajectory direction is inversely related to the actual direction of vehicle movement, the obtained heading angle needs to be rotated 180° to obtain the true heading angle of the current epoch when outputting the heading result.

[0058] The specific implementation includes the following sub-steps: S51. The continuous trajectory function obtained in step S41 Regarding time variables Find the first derivative and evaluate it at the time parameter corresponding to the current epoch. Calculate the instantaneous velocity components in the east and north directions at the current epoch. The expression is: (14) in, This represents the instantaneous velocity vector corresponding to the current epoch; and Representing the instantaneous velocity components in the east and north directions respectively, by respectively... and Seeking information about time The first derivative is obtained; This represents the two-dimensional continuous trajectory function of the carrier in the east-north plane obtained by fitting in step S41. , and The trajectories are eastward and northward respectively, with respect to time. Continuous functions; This indicates that the continuous trajectory function is related to the time variable. The first derivative is the instantaneous velocity vector of the carrier in the horizontal plane. It should be noted that since the heading angle only involves the direction in the horizontal plane, formula (14) only extracts the two horizontal components of east and north, and the sky component does not participate in the heading angle calculation.

[0059] S52. Calculate the heading angle based on the instantaneous velocity components of the current epoch. The expression is as follows: (15) in, This represents the heading angle at the current epoch. The quadrant in which the heading angle lies is automatically determined based on the signs of the instantaneous velocity components in the east and north directions, and the calculation results are mapped to the interval. For example, if the vehicle is moving forward, the heading angle is output directly; if the vehicle is reversing, the heading angle is rotated 180°.

[0060] S53. Output the heading angle result for the current epoch.

[0061] S6. Real-time updates and continuous output of heading results This step calculates the instantaneous velocities in the north and east directions at the current epoch based on the first derivative of the cubic B-spline trajectory function, and further converts them to obtain the heading angle, outputting the carrier heading information; thereby improving the accuracy and robustness of GNSS heading calculation in complex environments and under various motion conditions.

[0062] The specific implementation includes the following sub-steps: S61. After calculating the current heading angle at each epoch, output the heading angle of the current epoch as the current heading of the carrier.

[0063] S62. When new epoch observation data is received, the local two-dimensional discrete trajectory points and corresponding node sequences are updated using a sliding time window. The earliest epoch in the window is removed, and the current epoch is added to the time window to form a new time window.

[0064] S63. Based on the effective displacement sequence within the updated time window, redetermine the cubic B-spline control points, construct a continuous trajectory, and repeat the cubic B-spline trajectory fitting, instantaneous velocity calculation, and heading angle calculation according to steps S4 and S5 to achieve continuous real-time updating of the carrier's heading.

[0065] To verify the effectiveness of the proposed high-precision heading calculation method and system based on single-antenna GNSS, a vehicle-mounted dynamic experiment was conducted in a city. The experimental equipment used a Huace Navigation M620 low-cost GNSS receiver module, supporting dual-frequency observations from GPS, BDS, and Galileo systems, with a sampling rate of 1 Hz, continuously acquiring dynamic observation data for approximately 45 minutes. The reference ground truth was obtained using the POMS-GI7683 high-precision integrated navigation system, post-processed using Inertial Explore 8.90 software for integrated navigation calculation. The inertial navigation heading angle was used as the reference ground truth, and the antenna phase center position was used as the position reference ground truth. The experimental route covered various typical urban road scenarios, including open roads, tall buildings, tree shade, intersections, and U-turns, to fully verify the applicability of the invention in complex environments. The heading angle is calculated using the following three methods: (1) the heading angle is calculated using the instantaneous velocity of a single epoch calculated by Doppler observations; (2) the heading angle is calculated using the single epoch displacement calculated by combining carrier phase and Doppler observations (TDCP-LD); (3) the heading angle is calculated using the method of fitting the TDCP-LD multi-epoch displacement trajectory with cubic B-spline proposed in this invention.

[0066] The experimental results are shown in Figure 3, and the error statistics are shown in Table 1. The results demonstrate that the method proposed in this invention has the highest accuracy in calculating the heading angle. Throughout the test, the root mean square (RMS) error of the heading angle using the method of this invention was 0.784°, and the error in the 95% confidence interval was 1.58°, significantly better than the traditional single-epoch method. Specifically, compared to the single-epoch displacement method, the heading angle accuracy of this invention is improved by approximately 34.16% in the 95% confidence interval; compared to the Doppler instantaneous velocity method, the heading angle accuracy is improved by approximately 33.05%.

[0067] Table 1. Statistics of heading angle calculation errors for the three methods (°)

[0068] In summary, the high-precision heading calculation method and system for carriers based on single-antenna GNSS proposed in this invention improves the continuity and reliability of single-epoch displacement calculation by using a joint displacement calculation model and related entropy robust estimation. Furthermore, by fitting multi-epoch displacement sequences with cubic B-spline trajectories and using the trajectory tangent direction instead of the displacement secant direction to calculate the heading angle, the geometric deviation of the heading angle generated during carrier turning is effectively reduced. This significantly improves the accuracy and robustness of heading angle calculation in complex urban environments, and can meet the engineering application requirements of high-precision heading calculation for low-cost GNSS equipment. This verifies that the invention has good technical effects and engineering application value.

[0069] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0070] The following describes the carrier high-precision heading calculation electronic device based on single-antenna GNSS provided by the present invention. The carrier high-precision heading calculation electronic device based on single-antenna GNSS described below can be referred to in correspondence with the carrier high-precision heading calculation method based on single-antenna GNSS described above.

[0071] The electronic device may include a processor, a communications interface, a memory, and a communication bus. The processor, communications interface, and memory communicate with each other via the communication bus. The processor can call logical instructions from the memory to execute a high-precision heading calculation method for a carrier based on single-antenna GNSS, mainly including the software processing portion described above.

[0072] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0073] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the software processing part of the carrier high-precision heading calculation method based on single-antenna GNSS provided by the above methods.

[0074] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the software processing portion of the carrier high-precision heading calculation method based on single-antenna GNSS provided by the above methods.

[0075] The device embodiments described above are merely illustrative. 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 modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0076] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-precision heading calculation method for a carrier based on single-antenna GNSS, characterized in that: Includes the following steps, Acquire multi-frequency, multi-system observation data from the GNSS receiver, preprocess carrier phase and Doppler observations, and complete cycle slip detection and gross error detection. A joint displacement solution model is constructed based on the carrier phase epoch difference and the average Doppler observation to obtain the displacement solution for the current epoch. For the joint displacement calculation model, a correlation entropy robust estimation is introduced to suppress anomalous observations and non-Gaussian noise, thereby improving the robustness of displacement calculation under complex environments. A multi-epoch displacement sequence is constructed using robust displacement solutions from multiple consecutive epochs, and the multi-epoch displacement sequence is uniformly transformed to the station center coordinate system of the current epoch. A local two-dimensional discrete trajectory is constructed based on the multi-epoch displacement sequence, and a cubic B-spline is used to fit the local trajectory. The instantaneous velocities in the north and east directions at the current epoch are calculated based on the first derivative of the cubic B-spline trajectory function, and then converted to obtain the heading angle. The vector direction of the instantaneous velocity is used as the heading angle of the current epoch to replace the heading angle calculation based on the displacement vector direction of a single epoch. This corrects the geometric deviation between the displacement secant direction of the download body and the actual heading tangent direction in complex maneuvering scenarios, and outputs the carrier heading information.

2. The carrier high-precision heading calculation method based on single-antenna GNSS according to claim 1, characterized in that: The cycle slip detection includes joint detection of cycle slips using the lock identification information LLI of carrier phase observations and Geometry-Free combined observations. The gross error detection includes judging the quality of observations based on satellite elevation angle and signal-to-noise ratio, and removing observations with low elevation angle or low signal-to-noise ratio to reduce the impact of abnormal observations such as cycle slips, multipath effects, and non-line-of-sight propagation on displacement calculation.

3. The method for high-precision heading calculation of a carrier based on single-antenna GNSS as described in claim 1, characterized in that: The joint displacement calculation model includes an observation equation based on the differential observations between carrier phase epochs and an observation equation based on the average Doppler observations. The average Doppler observations are used to improve the performance degradation of displacement calculation under complex environments where carrier phase observations are missing or satellite geometry deteriorates.

4. The method for high-precision heading calculation of a carrier based on single-antenna GNSS as described in claim 1, characterized in that: The robust correlation entropy estimation is a robust estimation method based on the maximum correlation entropy criterion. By assigning adaptive weights to the observations corresponding to the residuals, it suppresses anomalous observations and non-Gaussian noise, thereby improving the accuracy and robustness of displacement calculation in complex environments.

5. The carrier high-precision heading calculation method based on single-antenna GNSS as described in claim 1, characterized in that: The multi-epoch displacement sequence is constructed by accumulating the displacement solutions of multiple epochs within a continuous time window, and uniformly transformed to the station center northeast-sky coordinate system corresponding to the current epoch to form a local two-dimensional discrete trajectory.

6. The method for high-precision heading calculation of a carrier based on single-antenna GNSS as described in claim 1, characterized in that: The cubic B-spline trajectory fitting uses at least four effective displacement epochs within a continuous time window as input, and reconstructs a continuous curve from the local two-dimensional discrete trajectory using a cubic B-spline function.

7. The method for high-precision heading calculation of a carrier based on single-antenna GNSS as described in claim 1, characterized in that: The instantaneous velocity at the current epoch is obtained by solving the first derivative of the cubic B-spline trajectory function at the current moment. The heading angle at the current epoch is calculated based on the instantaneous velocity to replace the heading angle calculation based on the displacement vector direction of a single epoch. This allows for the correction of the geometric deviation between the displacement secant direction of the downloaded body and the actual heading tangent direction in complex maneuvering scenarios.

8. The carrier high-precision heading calculation method based on single-antenna GNSS as described in claim 1, characterized in that: When the displacement amplitude of the current epoch is lower than the preset motion threshold, the carrier is determined to be in a low dynamic or static state and the heading angle calculation is paused; when the number of effective displacement epochs within the time window meets the preset minimum window length, the cubic B-spline trajectory fitting and heading angle calculation process is executed.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the carrier high-precision heading calculation method based on single-antenna GNSS as described in any one of claims 1 to 8.

10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements the carrier high-precision heading calculation method based on single-antenna GNSS as described in any one of claims 1 to 8.

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