Satellite navigation positioning multi-frequency signal anti-noise filtering method constrained by inertial navigation

Abstract

The application discloses a kind of inertial navigation constrained satellite navigation positioning multi-frequency signal anti-noise filtering method, belong to combined navigation technical field, for the problem that abnormal interference leads to multi-frequency signal partial band is interfered, positioning precision drops, the short-time continuous motion information provided by inertial navigation system is used to construct constraint, the consistency residual of satellite navigation solution result and inertial navigation prediction information is detected, and the interference degree of each frequency band is evaluated.On this basis, inertial navigation prediction information is taken as pseudo-observation value and is integrated into multi-frequency combined Kalman filtering model, and the observation noise covariance of each frequency band is adaptively adjusted according to the above evaluation result, so as to suppress the utilization rate of the interfered frequency band, and improve the utilization rate of the uninterfered frequency band.Through the adaptive fusion of inertial navigation motion constraint and multi-frequency signal, the application can realize the smooth suppression and robust output of positioning result when partial band is interfered, and improve the anti-noise performance.

Description

Technical Field

[0001] This invention discloses a noise reduction and filtering method for multi-frequency signals in satellite navigation and positioning constrained by inertial navigation, belonging to the field of integrated navigation technology. Background Technology

[0002] Satellite navigation and positioning technology, with its advantages of high precision, all-weather operation, and all-terrain coverage, has become a core supporting technology in many fields such as aviation, maritime navigation, vehicle navigation, and drone operations. Multi-frequency satellite navigation fusion positioning is currently the mainstream direction of technological development. By integrating multi-band observation data from multiple satellite navigation systems such as GPS, BeiDou, and Galileo, it is possible to effectively increase the number of visible satellites, enhance the observation geometry, significantly improve positioning accuracy and system fault tolerance, and meet the high-precision positioning requirements in complex scenarios.

[0003] However, in practical applications, the carrier platform is often located in a complex electromagnetic environment. Satellite navigation signals are highly susceptible to human interference, electromagnetic noise, and multipath effects during transmission, and the interference often presents as a single frequency band or a partial frequency band being disturbed. Observational data in the interfered frequency band will exhibit significant errors. If these data are directly used in multi-frequency combined positioning calculations, it will lead to a sharp decline in positioning accuracy, abrupt changes in positioning results, and even cause divergence in the navigation system's calculations. This severely affects the stability and reliability of the positioning results, failing to meet the application requirements of aviation, maritime, and autonomous driving fields that have high requirements for navigation continuity and robustness.

[0004] Existing satellite navigation signal anti-interference methods mostly focus on interference suppression in a single system and single frequency band, or achieve signal de-interference through hardware filtering. These methods are ill-suited for multi-frequency fusion positioning scenarios and lack specific discrimination and processing mechanisms for interference in certain frequency bands. While some integrated navigation anti-interference technologies incorporate inertial navigation system information, they only treat inertial navigation as a backup after satellite navigation failure. They fail to fully utilize the short-term, high-continuity, and high-stability motion prediction characteristics of inertial navigation to achieve real-time discrimination and quantitative assessment of the reliability of multi-frequency band observation data. Furthermore, they cannot adaptively weight and fuse observation information based on the degree of interference in each frequency band, resulting in insufficient flexibility and accuracy in anti-interference efforts.

[0005] Therefore, how to rely on the motion constraint characteristics of inertial navigation systems to construct a quantitative assessment mechanism for interference in multiple frequency bands, realize the dynamic identification of the interfered frequency bands and the adaptive adjustment of the observation weights, and still output stable and high-precision positioning results when some frequency bands are disturbed has become a key problem that urgently needs to be solved in the current field of integrated navigation technology. Summary of the Invention

[0006] The purpose of this invention is to provide a noise reduction and filtering method for multi-frequency signals in satellite navigation and positioning under inertial navigation constraints. This method addresses the problems in existing anti-interference methods, such as difficulty in adapting to multi-frequency fusion positioning scenarios, inability to accurately identify and dynamically process disturbances in some frequency bands, and failure to fully utilize inertial navigation motion constraints for adaptive weighted fusion. These problems lead to decreased positioning accuracy, sudden changes in results, and even divergence, resulting in insufficient stability and reliability of the system in complex electromagnetic environments, making it difficult to meet the application requirements of high-demand fields.

[0007] The specific technical solution of this invention is as follows: This invention provides a noise reduction and filtering method for multi-frequency signals in satellite navigation and positioning under inertial navigation constraints, comprising: Step 1: Integrate an inertial measurement unit and a multi-frequency satellite navigation and positioning receiver on the carrier platform, establish a unified carrier coordinate system, perform initial alignment and error parameter calibration on the inertial measurement unit, construct an inertial navigation motion state prediction model based on angular velocity and specific force measurement information, and obtain the inertial navigation predicted position and velocity values ​​of the carrier between adjacent epochs by recursively calculating the inertial measurement data, thereby forming continuous carrier motion constraint information; Step 2: For multiple satellite navigation systems and multiple frequency bands, establish multi-frequency satellite navigation observation models respectively, use the observation data of each frequency band to perform real-time positioning calculations, and obtain the corresponding navigation state estimation results; compare the consistency of the positioning calculation results with the inertial navigation prediction results obtained in Step 1, construct positioning residual or state residual statistics, and complete the construction of the inertial navigation residual constraint vector. Step 3: Construct a multi-frequency combined Kalman filter model with inertial navigation constraints, integrating satellite navigation observation equations and inertial navigation prediction information into the state-space estimation framework. The inertial navigation prediction results are introduced into the filtering model as pseudo-observation information. Based on the inertial navigation residual constraint vector constructed in Step 2, residual analysis is performed to establish a frequency band interference assessment index, enabling a quantitative assessment of the interference level of observation data in each frequency band. According to the frequency band interference assessment index, the observation noise covariance matrix of each frequency band is adaptively adjusted to increase the observation noise variance of the interfered frequency bands and keep the observation noise variance of the higher-quality frequency bands close to the nominal value. This reduces the adverse impact of the interfered frequency band observation information on the state estimation results during the filtering estimation process and improves the utilization efficiency of reliable frequency band observation data. Step 4: During the positioning process, continuously acquire satellite navigation positioning observation data and inertial measurement data, and repeatedly execute steps 2 and 3. Real-time detection and dynamic suppression of interference status of observation data in each frequency band are performed until the positioning task ends, thereby outputting continuous, stable and interference-resistant high-precision multi-frequency positioning and navigation results.

[0008] Further, step 1 includes: Step 1.1: Simultaneously configure an inertial measurement unit (IMU) and a multi-frequency satellite navigation receiver on the carrier platform. The IMU consists of a three-axis gyroscope and a three-axis accelerometer. The three-axis gyroscope is used to acquire the angular velocity information of the carrier in the carrier coordinate system, and the three-axis accelerometer is used to measure the specific force information of the carrier. The satellite navigation and positioning receiver is used to receive navigation signals from multiple signal frequency bands of the satellite navigation system and output the corresponding observation data.

[0009] Establish a carrier coordinate system rigidly connected to the carrier platform. This coordinate system is used to uniformly describe the installation geometry of the inertial measurement unit and the satellite navigation receiver on the carrier, as well as the motion state of the carrier. The origin of the carrier coordinate system can be set at the center of the inertial measurement unit or at the reference point of the carrier platform, and the directions of each coordinate axis are defined according to the structural characteristics of the carrier.

[0010] Before the system starts working, the inertial measurement unit is initialized and initially aligned to obtain the initial attitude, velocity, and position parameters of the inertial navigation system. At the same time, the inertial devices are calibrated to establish an error model for the inertial devices, including gyroscope and accelerometer zero bias, thereby providing the necessary initial conditions for the recursive calculation of the subsequent inertial navigation state.

[0011] Step 1.2: Using the angular velocity and specific force data output by the inertial measurement unit, establish a recursive model of the carrier's motion state between adjacent epochs to continuously predict the carrier's attitude, velocity, and position.

[0012] Assuming in the epoch The angular velocity output by the inertial measurement unit at that moment is The ratio is The time interval between adjacent epochs is Then the carrier speed update relationship can be expressed as: , in, For the calendar The velocity vector of the carrier at any given moment; This is the attitude transformation matrix between the vehicle coordinate system and the navigation coordinate system; This is the vector of gravitational acceleration.

[0013] After completing the velocity update, the recursive relationship of the carrier position can be further obtained: , in, For the calendar The position vector of the carrier in the navigation coordinate system at any given time.

[0014] Through the above recursive calculations, the inertial navigation prediction results of the carrier's position and velocity can be obtained at each observation epoch. The position prediction vector is expressed as follows: , Furthermore, step 2 includes: Step 2.1: Establish a satellite navigation and positioning observation model using multi-frequency observation data output from a satellite navigation receiver. Let the first... The satellite in the pseudorange observations in the frequency band Then its observation equation can be expressed as , in, For the receiver to the first satellites in frequency band pseudorange observations on; The geometric distance between the receiver and the satellite; The speed of light; For receiver clock bias; For satellite clock bias; For tropospheric delay; For ionospheric delay; This includes observation noise and unmodeled errors.

[0015] Among them, geometric distance It can be represented as , In the formula: These are the receiver's position coordinates; For the first The position coordinates of each satellite in the navigation coordinate system.

[0016] When the system simultaneously receives observation signals from multiple frequency bands of a satellite navigation system, the observation equations for each frequency band can be combined to construct a multi-frequency joint positioning model. Linearizing all visible satellite observation equations yields the following matrix form: , in, For observation vectors; Design a matrix for observation; The vector of parameters to be estimated includes receiver position and receiver clock error; This is the observed noise vector.

[0017] By estimating the parameters of the above observation equations, the epoch can be obtained. The satellite navigation positioning result at time t is represented by the position estimation vector as follows: , Step 2.2: Using the difference between the inertial navigation predicted position obtained in Step 1 and the satellite navigation positioning result obtained in Step 2.1, construct the inertial navigation constraint residual, which is used to describe the degree of consistency between the two independent positioning information.

[0018] Establish epoch The vehicle position predicted by the inertial navigation system at any given time is The location obtained by satellite navigation positioning is Then the inertial navigation constraint residual vector can be expressed as , Furthermore, step 3 includes: Step 3.1: After performing positioning calculations using the observation data corresponding to each frequency band, compare the results with the inertial navigation predicted position obtained in Step 1 to detect the degree of anomaly in the observation data of each frequency band.

[0019] Let the first Each frequency band in the epoch The positioning result obtained by solving the corresponding observation data at each time is In step 1, the inertial navigation system predicts the carrier's position as follows: Then the inertial navigation constraint residual vector corresponding to this frequency band can be expressed as: , in, For the first Each frequency band in the epoch The inertial navigation constraint residual vector at time step; This is the position vector calculated for satellite navigation and positioning in this frequency band; This is the position vector predicted by the inertial navigation system.

[0020] Construct frequency band interference assessment indicators: , Step 3.2: After obtaining the interference assessment indexes for each frequency band, the statistical characteristics of the observation data of different frequency bands are adaptively adjusted to reduce the adverse effects of the observation information of the interfered frequency bands on the positioning solution results.

[0021] By constructing an observation noise conditioning model, Dynamic correction of frequency band observation noise covariance: , in, The nominal variance of the observed noise; For the first The adaptive observation noise variance of each frequency band in the current epoch; is the adjustment coefficient, and m is the number of frequency bands participating in the combined positioning.

[0022] As can be seen from the above formula, when a certain frequency band is interfered with, its interference assessment index is... As the frequency band increases, the variance of the observation noise also increases, thereby reducing the impact of observation information in this frequency band on positioning solutions; when the observation quality is good, The variance of the observed noise is relatively small, close to the nominal value, which allows the observation data in this frequency band to be fully used in positioning calculations.

[0023] In the process of multi-frequency observation fusion, the observation noise variance of each frequency band can be constructed into an observation noise covariance matrix: , Through the aforementioned adaptive noise adjustment mechanism, the contribution of observation data in different frequency bands can be dynamically adjusted during subsequent filtering and solving processes.

[0024] Furthermore, step 4 includes: Step 4.1: After completing the adaptive adjustment of the observation noise covariance of each frequency band, the satellite navigation observation information and the inertial navigation prediction information are integrated into the combined state estimation framework for joint solution.

[0025] Let the system state vector be , in, The carrier position vector, The velocity vector of the carrier. This refers to the receiver clock bias.

[0026] Based on the motion prediction information provided by the inertial navigation system, the state prediction equation can be expressed as follows: , in, This is the predicted state value; Let be the state transition matrix.

[0027] The corresponding covariance prediction is , in, To predict the covariance matrix; Let be the system process noise covariance matrix.

[0028] Through the above prediction process, a priori state estimate of the current epoch can be obtained, providing a foundation for subsequent fusion of satellite navigation observation information.

[0029] Step 4.2: In the integrated navigation filtering process, the satellite navigation observation equation can be expressed as: , Based on the frequency band interference assessment results obtained in step 3, The variance of frequency band observation noise can be expressed as , Where m is the number of frequency bands involved in the combined positioning.

[0030] This allows us to construct the observation noise covariance matrix for the current epoch: , When a certain frequency band is affected by interference, its interference assessment index Increase, corresponding to the variance of observation noise As the frequency band increases, the impact of the observation information on the state estimation results is reduced during the filtering calculation process; when the observation quality returns to normal, the variance of its observation noise approaches the nominal value, so that the effective observation information can fully participate in the positioning solution.

[0031] By using the adaptive observation noise covariance modeling described above, the contribution of multi-frequency observation data can be dynamically adjusted during the filtering process.

[0032] Step 4.3 After obtaining the state prediction results and the weighted observation model, the state is updated using the Kalman filter method.

[0033] First, calculate the Kalman gain: , The system state is then updated using the observation residuals: , Simultaneously update the state covariance matrix: , Through the above weighted filtering update process, the influence of observation data in the interfered frequency band can be reduced in the state estimation, while making full use of the information in the uninterrupted frequency band, thereby obtaining more stable and reliable positioning results.

[0034] The beneficial effects of this invention are as follows: A constraint consistency detection mechanism is constructed based on short-time, highly continuous motion information from inertial navigation systems (INS), enabling accurate identification of interference across multiple frequency bands without requiring additional hardware. Interference assessment indices are constructed through INS constraint residual analysis, allowing for quantitative evaluation of the interference levels in different frequency bands and providing a scientifically reliable basis for anti-interference positioning. Adaptive weighted fusion of INS and multi-frequency tightly combined Kalman filtering effectively reduces the weight of interfered frequency bands in state estimation, significantly improving the accuracy, stability, and continuity of satellite navigation and positioning in complex electromagnetic environments. Attached Figure Description

[0035] Figure 1 This is a flowchart of the inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction filtering method in this invention.

[0036] Figure 2 This is a comparison diagram of the X-direction positioning error between the anti-interference PPP and the ordinary PPP in this invention.

[0037] Figure 3 This is a comparison diagram of the Y-direction positioning error between the anti-interference PPP and the ordinary PPP in this invention.

[0038] Figure 4 This is a comparison diagram of the Z-direction positioning error between the anti-interference PPP and the ordinary PPP in this invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0040] This embodiment provides a noise reduction filtering method for multi-frequency signals in satellite navigation and positioning under inertial navigation constraints, including: Step 1: Integrate an inertial measurement unit and a multi-frequency satellite navigation and positioning receiver on the carrier platform, establish a unified carrier coordinate system, perform initial alignment and error parameter calibration on the inertial measurement unit, construct an inertial navigation motion state prediction model based on angular velocity and specific force measurement information, and obtain the inertial navigation predicted position and velocity values ​​of the carrier between adjacent epochs by recursively calculating the inertial measurement data, thereby forming continuous carrier motion constraint information; Step 2: For multiple satellite navigation systems and multiple frequency bands, establish multi-frequency satellite navigation observation models respectively, use the observation data of each frequency band to perform real-time positioning calculations, and obtain the corresponding navigation state estimation results; compare the consistency of the positioning calculation results with the inertial navigation prediction results obtained in Step 1, construct positioning residual or state residual statistics, and complete the construction of the inertial navigation residual constraint vector. Step 3: Construct a multi-frequency combined Kalman filter model with inertial navigation constraints, integrating satellite navigation observation equations and inertial navigation prediction information into the state-space estimation framework. The inertial navigation prediction results are introduced into the filtering model as pseudo-observation information. Based on the inertial navigation residual constraint vector constructed in Step 2, residual analysis is performed to establish a frequency band interference assessment index, enabling a quantitative assessment of the interference level of observation data in each frequency band. According to the frequency band interference assessment index, the observation noise covariance matrix of each frequency band is adaptively adjusted to increase the observation noise variance of the interfered frequency bands and keep the observation noise variance of the higher-quality frequency bands close to the nominal value. This reduces the adverse impact of the interfered frequency band observation information on the state estimation results during the filtering estimation process and improves the utilization efficiency of reliable frequency band observation data. Step 4: During the positioning process, continuously acquire satellite navigation positioning observation data and inertial measurement data, and repeatedly execute steps 2 and 3. Real-time detection and dynamic suppression of interference status of observation data in each frequency band are performed until the positioning task ends, thereby outputting continuous, stable and interference-resistant high-precision multi-frequency positioning and navigation results.

[0041] In one embodiment, step 1 includes: Step 1.1: Simultaneously configure an inertial measurement unit (IMU) and a multi-frequency satellite navigation receiver on the carrier platform. The IMU consists of a three-axis gyroscope and a three-axis accelerometer. The three-axis gyroscope is used to acquire the angular velocity information of the carrier in the carrier coordinate system, and the three-axis accelerometer is used to measure the specific force information of the carrier. The satellite navigation and positioning receiver is used to receive navigation signals from multiple signal frequency bands of the satellite navigation system and output the corresponding observation data.

[0042] Establish a carrier coordinate system rigidly connected to the carrier platform. This coordinate system is used to uniformly describe the installation geometry of the inertial measurement unit and the satellite navigation receiver on the carrier, as well as the motion state of the carrier. The origin of the carrier coordinate system can be set at the center of the inertial measurement unit or at the reference point of the carrier platform, and the directions of each coordinate axis are defined according to the structural characteristics of the carrier.

[0043] Before the system starts working, the inertial measurement unit is initialized and initially aligned to obtain the initial attitude, velocity, and position parameters of the inertial navigation system. At the same time, the inertial devices are calibrated to establish an error model for the inertial devices, including gyroscope and accelerometer zero bias, thereby providing the necessary initial conditions for the recursive calculation of the subsequent inertial navigation state.

[0044] Step 1.2: Using the angular velocity and specific force data output by the inertial measurement unit, establish a recursive model of the carrier's motion state between adjacent epochs to continuously predict the carrier's attitude, velocity, and position.

[0045] Assuming in the epoch The angular velocity output by the inertial measurement unit at that moment is The ratio is The time interval between adjacent epochs is Then the carrier speed update relationship can be expressed as: , in, For the calendar The velocity vector of the carrier at any given moment; for The carrier velocity vector at each epoch; This is the attitude transformation matrix between the vehicle coordinate system and the navigation coordinate system; This is the vector of gravitational acceleration; The time interval between adjacent epochs.

[0046] After completing the velocity update, the recursive relationship of the carrier position can be further obtained: , in, For the calendar The position vector of the carrier in the navigation coordinate system at any given time.

[0047] Through the above recursive calculations, the inertial navigation prediction results of the carrier's position and velocity can be obtained at each observation epoch. The position prediction vector is expressed as follows: , In one embodiment, step 2 includes: Step 2.1: Establish a satellite navigation and positioning observation model using multi-frequency observation data output from a satellite navigation receiver. Let the first... The satellite in the pseudorange observations in the frequency band Then its observation equation can be expressed as , in, For the receiver to the first satellites in frequency band pseudorange observations on; The geometric distance between the receiver and the satellite; The speed of light; For receiver clock bias; For satellite clock bias; For tropospheric delay; For ionospheric delay; This includes observation noise and unmodeled errors.

[0048] Among them, geometric distance It can be represented as , In the formula: These are the receiver's position coordinates; For the first The position coordinates of each satellite in the navigation coordinate system.

[0049] When the system simultaneously receives observation signals from multiple frequency bands of a satellite navigation system, the observation equations for each frequency band can be combined to construct a multi-frequency joint positioning model. Linearizing all visible satellite observation equations yields the following matrix form: , in, For observation vectors; Design a matrix for observation; The vector of parameters to be estimated includes receiver position and receiver clock error; This is the observed noise vector.

[0050] By estimating the parameters of the above observation equations, the epoch can be obtained. The satellite navigation positioning result at time t is represented by the position estimation vector as follows: , Step 2.2: Using the difference between the inertial navigation predicted position obtained in Step 1 and the satellite navigation positioning result obtained in Step 2.1, construct the inertial navigation constraint residual, which is used to describe the degree of consistency between the two independent positioning information.

[0051] Establish epoch The vehicle position predicted by the inertial navigation system at any given time is The location obtained by satellite navigation positioning is Then the inertial navigation constraint residual vector can be expressed as , In one embodiment, step 3 includes: Step 3.1: After performing positioning calculations using the observation data corresponding to each frequency band, compare the results with the inertial navigation predicted position obtained in Step 1 to detect the degree of anomaly in the observation data of each frequency band.

[0052] Let the first Each frequency band in the epoch The positioning result obtained by solving the corresponding observation data at each time is In step 1, the inertial navigation system predicts the carrier's position as follows: Then the inertial navigation constraint residual vector corresponding to this frequency band can be expressed as: , in, For the first Each frequency band in the epoch The inertial navigation constraint residual vector at time step; This is the position vector calculated for satellite navigation and positioning in this frequency band; This is the position vector predicted by the inertial navigation system.

[0053] Construct frequency band interference assessment indicators: , Step 3.2: After obtaining the interference assessment indexes for each frequency band, the statistical characteristics of the observation data of different frequency bands are adaptively adjusted to reduce the adverse effects of the observation information of the interfered frequency bands on the positioning solution results.

[0054] By constructing an observation noise conditioning model, Dynamic correction of frequency band observation noise covariance: , in, The nominal variance of the observed noise; For the first The adaptive observation noise variance of each frequency band in the current epoch; is the adjustment coefficient, and m is the number of frequency bands participating in the combined positioning.

[0055] As can be seen from the above formula, when a certain frequency band is interfered with, its interference assessment index is... As the frequency band increases, the variance of the observation noise also increases, thereby reducing the impact of observation information in this frequency band on positioning solutions; when the observation quality is good, The variance of the observed noise is relatively small, close to the nominal value, which allows the observation data in this frequency band to be fully used in positioning calculations.

[0056] In the process of multi-frequency observation fusion, the observation noise variance of each frequency band can be constructed into an observation noise covariance matrix: , Through the aforementioned adaptive noise adjustment mechanism, the contribution of observation data in different frequency bands can be dynamically adjusted during subsequent filtering and solving processes.

[0057] In one embodiment, step 4 includes: Step 4.1: After completing the adaptive adjustment of the observation noise covariance of each frequency band, the satellite navigation observation information and the inertial navigation prediction information are integrated into the combined state estimation framework for joint solution.

[0058] Let the system state vector be , in, The carrier position vector, The velocity vector of the carrier. This refers to the receiver clock bias.

[0059] Based on the motion prediction information provided by the inertial navigation system, the state prediction equation can be expressed as follows: , in, This is the predicted state value; Let be the state transition matrix.

[0060] The corresponding covariance prediction is , in, To predict the covariance matrix; Let be the system process noise covariance matrix.

[0061] Through the above prediction process, a priori state estimate of the current epoch can be obtained, providing a foundation for subsequent fusion of satellite navigation observation information.

[0062] Step 4.2: In the integrated navigation filtering process, the satellite navigation observation equation is expressed as follows: , Based on the frequency band interference assessment results obtained in step 3, The variance of the frequency band observation noise is expressed as , Where m is the number of frequency bands involved in the combined positioning.

[0063] This allows us to construct the observation noise covariance matrix for the current epoch: , When a certain frequency band is affected by interference, its interference assessment index Increase, corresponding to the variance of observation noise As the frequency band increases, the impact of the observation information on the state estimation results is reduced during the filtering calculation process; when the observation quality returns to normal, the variance of its observation noise approaches the nominal value, so that the effective observation information can fully participate in the positioning solution.

[0064] By using the adaptive observation noise covariance modeling described above, the contribution of multi-frequency observation data can be dynamically adjusted during the filtering process.

[0065] Step 4.3 After obtaining the state prediction results and the weighted observation model, the state is updated using the Kalman filter method.

[0066] First, calculate the Kalman gain: , The system state is then updated using the observation residuals: , Simultaneously update the state covariance matrix: , Through the above weighted filtering update process, the influence of observation data in the interfered frequency band can be reduced in the state estimation, while making full use of the information in the uninterrupted frequency band, thereby obtaining more stable and reliable positioning results.

[0067] Performance testing To clearly and completely illustrate the technical effects of the present invention and verify the effectiveness of the inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction filtering method proposed in this invention, this embodiment designs a comparative test experiment. The aim is to quantitatively evaluate the improvement effect of the method of the present invention in terms of positioning accuracy and robustness in complex electromagnetic environments compared with conventional methods that do not contain the core innovation points of the present invention.

[0068] The test employed a tightly coupled navigation development board integrating a high-precision multi-frequency GNSS receiver (supporting GPS L1 / L2 / L5, BDS B1I / B2I / B3I, etc.) and a tactical-grade MEMS inertial measurement unit. Both comparison algorithms ran on the same hardware platform to ensure consistent input data.

[0069] The method of this invention (labeled "Anti-interference PPP") fully implements all the steps described in claims 1-5 of this invention. The comparative method (labeled "Ordinary PPP") serves as a benchmark for performance evaluation. This method does not contain the core innovation of this invention, namely, it does not perform frequency band interference evaluation based on inertial navigation constraint residuals, nor does it dynamically adjust the observation noise covariance. Specifically, it adopts a conventional loosely combined framework of precise single-point positioning and inertial navigation, where the noise covariance matrix R_k of multi-frequency observations uses a fixed empirical nominal value σ_0^2, which does not adaptively change with the consistency differences between each frequency band and the inertial navigation prediction. This comparative method represents the common technical state in the field before the application of this invention.

[0070] Raw multi-frequency GNSS observation data and synchronized IMU data were collected under actual dynamic scenarios. To simulate typical scenarios of interference in certain frequency bands, during data processing, a mixture of Gaussian white noise and sudden impulse noise of a specific power was artificially superimposed on all satellite observations of 1-2 randomly selected frequency bands (such as the GPS L1 band) within a specific time period. Other frequency bands (such as GPS L5, BDS B2I) remained uninterrupted. Reference benchmark: The trajectory generated by high-precision carrier phase differential post-processing was used as the true reference value for evaluation.

[0071] The testing process strictly follows Figure 1 The flowchart is shown, and the parallel processing of the two algorithms is compared: Data Input and Preprocessing: The same GNSS observation data stream and IMU raw data stream are synchronously input into two processing threads, "Anti-interference PPP" and "Normal PPP," respectively. Unified time synchronization, cycle slip detection, and gross error removal are performed.

[0072] Processing flow of the method of this invention: a. Perform inertial navigation mechanical orchestration to obtain short-time position / velocity predictions.

[0073] b. Perform single-point positioning calculations on the observations for each frequency band to obtain independent position solutions for each frequency band.

[0074] c. Calculate the position residuals between the solutions for each frequency band and the inertial navigation system predictions, and then calculate the interference assessment indexes for each frequency band.

[0075] d. Dynamically adjust the observation noise variance corresponding to each frequency band in the Kalman filter to form an adaptive observation noise covariance matrix.

[0076] e. Perform compactly combined Kalman filtering to output the final localization result.

[0077] Comparison method processing flow: a. Use the same inertial navigation prediction information.

[0078] b. Steps 2.c and 2.d are not performed during Kalman filter fusion.

[0079] c. Perform compactly combined Kalman filtering and output the localization result.

[0080] Results evaluation: The position sequences output by the two methods are compared with the high-precision reference true values, and the error sequences in the X, Y, and Z directions in the geocentric coordinate system are calculated respectively.

[0081] The positioning errors of "anti-interference PPP" and "ordinary PPP" were compared, and the results are as follows: Figure 2 , Figure 3 , Figure 4 As shown in the figure, the shaded areas indicate the time periods during which human interference was applied.

[0082] From the temporal distribution of single-direction positioning errors (Figures 2-4), both the error curves of "ordinary PPP" and "anti-interference PPP" exhibit dynamic fluctuations over time. Their error change trends are consistent with the spatiotemporal characteristics of satellite signal propagation. However, the error fluctuation amplitude of "anti-interference PPP" is significantly smaller than that of "ordinary PPP." Its error peaks are controlled within ±2 m, ±3 m, and ±2 m in the X, Y, and Z directions, respectively. In contrast, "ordinary PPP" experienced error jumps exceeding ±2 m during some observation periods (e.g., 16:00-20:00), even reaching an extreme error value close to -3 m in the Y direction. Furthermore, throughout the entire observation period, the error distribution of "anti-interference PPP" remains more concentrated near 0, exhibiting lower dispersion and avoiding the large error jumps caused by signal interference seen in "ordinary PPP." This demonstrates the stabilizing effect of the anti-interference algorithm on temporal positioning error.

[0083] Quantitative statistical analysis shows that the root mean square (RMS) positioning errors of the "ordinary PPP" algorithm in the X, Y, and Z directions are 0.542 m, 0.589 m, and 0.533 m, respectively. After three-dimensional spatial error synthesis calculation, its three-dimensional positioning RMS reaches 0.962 m. However, the PPP algorithm with the anti-interference mechanism reduces the positioning error RMS in the X, Y, and Z directions to 0.400 m, 0.468 m, and 0.377 m, respectively, with the three-dimensional positioning RMS simultaneously optimized to 0.722 m. Error optimization calculations show that the Z direction has the largest optimization magnitude, reducing the error by approximately 29.3% compared to the "ordinary PPP" algorithm; the X direction error is reduced by 26.2%, and the Y direction error by 20.5%, resulting in an overall improvement of 24.9% in three-dimensional positioning accuracy. The significant reduction in errors in each direction and the improvement in three-dimensional positioning accuracy quantitatively verify the effectiveness of the "anti-interference PPP" algorithm in error suppression. Furthermore, the differences in optimization magnitude in different directions reflect the targeted differences in the algorithm's ability to suppress interference from satellite signals in different frequency bands. Experimental data show that the inertial navigation constrained noise filtering method provided by this invention, by introducing inertial navigation prediction as a constraint to evaluate the reliability of each frequency band and dynamically adjusting the observation weights accordingly, can effectively solve the technical problem of sharp decline in positioning accuracy and divergence of results in the "ordinary PPP" method when some frequency bands are disturbed. This invention improves the positioning accuracy, continuity and anti-interference robustness of multi-frequency satellite navigation and inertial combination systems in complex electromagnetic environments.

[0084] During the solution iteration process, a comprehensive evaluation is carried out on the state estimation results of continuous multi-epochs. Combining the carrier motion characteristics and the preset positioning accuracy standard, the state estimation results are judged from three dimensions: the fluctuation range of the state estimation value, the cumulative level of the observation residual, and the convergence trend of the estimation error. When all evaluation indicators in each dimension meet the preset threshold conditions, the positioning solution is judged to have entered a stable state, and the three-dimensional anti-interference high-precision positioning results of the carrier platform are output.

[0085] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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 or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for noise reduction and filtering of multi-frequency signals for satellite navigation and positioning under inertial navigation constraints, characterized in that, include: Step 1: Integrate the inertial measurement unit and multi-frequency satellite navigation and positioning receiver on the carrier platform, establish a unified carrier coordinate system, perform initial alignment and error parameter calibration of the inertial measurement unit, construct an inertial navigation motion state prediction model based on angular velocity and specific force measurement information, and obtain the inertial navigation predicted position and velocity values ​​of the carrier between adjacent epochs by recursively calculating the inertial measurement data, thereby forming continuous carrier motion constraint information; Step 2: For satellite navigation systems and frequency bands, establish multi-frequency satellite navigation observation models respectively, use the observation data of each frequency band to perform real-time positioning calculations, and obtain navigation state estimation results; compare the consistency of the positioning calculation results of each frequency band with the inertial navigation prediction results obtained in Step 1, construct positioning residual or state residual statistics, complete the construction of inertial navigation residual constraint vectors, and establish frequency band interference assessment indicators to achieve quantitative assessment of the degree of interference of observation data in each frequency band; Step 3: Construct a multi-frequency combined Kalman filter model with inertial navigation constraints, incorporating satellite navigation observation equations and inertial navigation prediction information into the state-space estimation framework. The inertial navigation prediction results are used as pseudo-observation information and introduced into the filter model. Based on the frequency band interference evaluation index, the observation noise covariance matrix of each frequency band is adaptively adjusted. Step 3 also includes: After obtaining the interference assessment indicators for each frequency band, the statistical characteristics of the observation data from different frequency bands are adaptively adjusted to reduce the adverse impact of the interference frequency band observation information on the positioning solution results. This is achieved by constructing an observation noise adjustment model. Dynamic correction of frequency band observation noise covariance: ； in, To observe the nominal variance of the noise, For the first Each frequency band Adaptive observation noise variance of epochs For adjustment coefficients, The number of frequency bands participating in the combined positioning. For frequency band interference assessment indicators; Step 4: During the positioning process, continuously acquire satellite navigation positioning observation data and inertial measurement data, and repeatedly execute steps 2 and 3. Real-time detection and dynamic suppression of interference status of observation data in each frequency band are performed until the positioning task ends, and high-precision multi-frequency positioning and navigation results are output.

2. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 1, characterized in that, Step 1 also includes: Using the angular velocity and specific force data output by the inertial measurement unit, a recursive model of the carrier's motion state between adjacent epochs is established to continuously predict the carrier's attitude, velocity, and position. Assuming in the epoch The angular velocity output by the inertial measurement unit at that moment is The ratio is The time interval between adjacent epochs is The carrier coordinate system is The carrier speed update relationship is expressed as ； in, For the calendar The velocity vector of the carrier at time t. for The carrier velocity vector at each epoch. This is the attitude transformation matrix between the vehicle coordinate system and the navigation coordinate system. The vector of gravitational acceleration. The time interval between adjacent epochs. After completing the velocity update, the recursive relationship of the carrier position is obtained, and the formula is: ; in, For the calendar The position vector of the carrier in the navigation coordinate system at any given time. For the calendar The position vector of the vehicle in the navigation coordinate system at each time point is calculated recursively to obtain the inertial navigation prediction results of the vehicle's position and velocity at each observation epoch. The position prediction vector is expressed as: ； in, For location prediction vectors, For directional prediction components.

3. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 2, characterized in that, Before establishing a recursive model of the carrier's motion state between adjacent epochs using the angular velocity and specific force data output by the inertial measurement unit (IMU), the following steps are included: An IMU and a multi-frequency satellite navigation receiver are simultaneously configured on the carrier platform. The IMU consists of a three-axis gyroscope and a three-axis accelerometer. The three-axis gyroscope is used to acquire the angular velocity information of the carrier in the carrier coordinate system, and the three-axis accelerometer is used to measure the specific force information of the carrier. The satellite navigation and positioning receiver is used to receive navigation signals from the satellite navigation system's signal frequency band and output the corresponding observation data. A carrier coordinate system is established on the carrier platform and rigidly connected to the carrier. The coordinate system is used to uniformly describe the installation geometric relationship between the inertial measurement unit and the satellite navigation receiver on the carrier and the motion state of the carrier. The origin of the carrier coordinate system is set at the center of the inertial measurement unit or at the reference point of the carrier platform, and the direction of each coordinate axis is defined according to the structural characteristics of the carrier. Initialization and initial alignment operations are performed on the inertial measurement unit to obtain the initial attitude, velocity, and position parameters of the inertial navigation system. Error calibration is performed on the inertial devices, and an error model of the inertial devices, including gyroscope zero bias and accelerometer zero bias, is established to provide initial conditions for the recursive calculation of the inertial navigation state.

4. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 1, characterized in that, Step 2 also includes: A satellite navigation and positioning observation model is established using multi-frequency observation data output from a satellite navigation receiver. Let the first frequency be... The satellite in the pseudorange observations in the frequency band The observation equation is expressed as ; in, For the receiver to the first satellites in frequency band pseudorange observations on The geometric distance between the receiver and the satellite. The speed of light; For receiver clock bias, For satellite clock bias, For tropospheric delay, For ionospheric delay, This includes observation noise and unmodeled errors. By estimating the parameters of the observation equation, the epoch is obtained. The satellite navigation positioning result at time t is represented by the position vector as follows: ; in for The observation position vector of an epoch. These are the components in each direction.

5. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 1, characterized in that, Step 2 also includes Let the first Each frequency band in the epoch The positioning result obtained by solving the corresponding observation data at each time is In step 1, the inertial navigation system predicts the carrier's position as follows: Then the inertial navigation constraint residual vector corresponding to this frequency band is expressed as: ； in, For the first Each frequency band in the epoch The inertial guidance constraint residual vector at time t. This is the position vector obtained from satellite navigation and positioning in this frequency band. The position vector predicted by the inertial navigation system; Construct frequency band interference assessment indicators: ； in, For the first Each frequency band in the epoch The inertial navigation constraint residual vector at time t.

6. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 5, characterized in that, In the process of multi-frequency observation fusion, the observation noise variance of each frequency band is constructed into an observation noise covariance matrix: ； in, To observe the noise covariance matrix, The first The observation noise variance of the frequency band is dynamically adjusted through an adaptive noise adjustment mechanism to achieve the contribution of observation data in different frequency bands.

7. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 1, characterized in that, Step 3 also includes: After adaptive adjustment of the observation noise covariance for each frequency band, satellite navigation observation information and inertial navigation prediction information are integrated into the combined state estimation framework for joint solution. Let the system state vector be... ; in, The carrier position vector, The velocity vector of the carrier. For receiver clock bias, Based on the motion prediction information provided by the inertial navigation system, the state prediction equation is expressed as follows: ； in, This is the predicted state value. Here is the state transition matrix. This is the state value of the previous epoch. The corresponding covariance prediction is ； in, To predict the covariance matrix, Here is the state transition matrix. Let be the covariance matrix of the previous epoch. The system process noise covariance matrix is... The prediction process yields a priori estimates of the current epoch, providing a foundation for fusing satellite navigation observation information.

8. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 1, characterized in that, Step 3 also includes: In the integrated navigation filtering process, the satellite navigation observation equation is expressed as... ； in, For the observation vector, Design a matrix for observation. Let be the parameter vector to be estimated, containing receiver position and receiver clock error. For the observed noise vector; Based on the frequency band interference assessment results The variance of the frequency band observation noise is Its observation noise covariance matrix is By using adaptive observation noise covariance modeling, the contribution of multi-frequency observation data is dynamically adjusted during the filtering process. After obtaining the state prediction results and weighted observation model, the state is updated using the Kalman filtering method. First, calculate the Kalman gain: ； in, For Kalman gain, To predict the covariance matrix, Design a matrix for observation. Let be the covariance matrix of the previous epoch. To observe the noise covariance matrix, The system state is then updated using the observation residuals: ； in, To update the state value, This is the predicted state value. For Kalman gain, These are satellite observations. Design a matrix for observation. Simultaneously update the state covariance matrix: ； in, To update the covariance matrix, It is the identity matrix. For Kalman gain, Design a matrix for observation. To predict the covariance matrix.

9. The inertial navigation-constrained satellite navigation and positioning multi-frequency signal noise reduction and filtering method according to claim 1, characterized in that, Step 4 also includes: During the solution iteration process, a comprehensive evaluation is carried out on the state estimation results of continuous multi-epochs. Combining the carrier motion characteristics and the preset positioning accuracy standard, the state estimation results are judged from three dimensions: the fluctuation range of the state estimation value, the cumulative level of the observation residual, and the convergence trend of the estimation error. When all evaluation indicators in each dimension meet the preset threshold conditions, the positioning solution is judged to have entered a stable state, and the three-dimensional anti-interference high-precision positioning results of the carrier platform are output.

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