A GNSS adaptive filtering positioning method based on multi-core maximum entropy

Abstract

The present invention proposes a GNSS adaptive filtering positioning method based on multi-core maximum entropy, which is designed for complex urban environments and effectively improves the positioning accuracy and robustness of VT-type GNSS receivers in non-Gaussian noise. In this method, the pseudorange and Doppler observation data of the GNSS receiver are first collected and preliminarily processed, and then the state vector and covariance matrix are initialized, and the measurement noise covariance matrix is ​​whitened. The core is to apply the MKMC-KF algorithm, combine the system dynamic model for state prediction, and perform state correction through the current observation data to achieve accurate posterior state estimation. The MKMC-KF algorithm uses kernel density estimation to adaptively determine the kernel bandwidth, assign different kernel functions to different observations, and adapt to their distribution characteristics. Finally, the filtered state information is used for positioning calculation to obtain the accurate position and velocity estimation of the receiver, which significantly enhances the navigation performance under multipath and NLOS conditions.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation (Global Navigation Satellite System, GNSS), and in particular to a GNSS adaptive filtering positioning method based on multi-core maximum entropy. Background Art

[0002] In complex urban environments, vector tracking (VT) receivers can help improve the continuity and availability of navigation positioning. However, the quality of GNSS raw observations is severely degraded by non-Gaussian noise pollution such as multipath and non-line-of-sight, which seriously affects the navigation positioning accuracy of VT receivers.

[0003] Urban areas usually use RTK technology as a solution for high-precision positioning services, but it is usually difficult to obtain Line of Sight (LOS) signals due to the influence of dense buildings and obstacles. Therefore, multipath and non-line-of-sight (NLOS) signals occupy the main components of the observation quantity. In order to achieve better navigation and positioning performance, it is necessary to suppress the influence of multipath and NLOS errors.

[0004] Commonly used nonlinear filtering methods include Extended Kalman Filter (EKF) based on function approximation, Unscented Kalman Filter (UKF) based on deterministic sampling approximation, and Cubic Kalman Filter (CKF) based on quadrature approximation. When the observation noise and system noise do not meet the Gaussian assumption, in order to ensure the filtering performance, particle filter (PF), Gaussian sum filter (GSM), Sage-Husa filter, KF based on variational Bayesian (VB) method, and robust filtering based on M estimation theory have been proposed. For example, robust Bayesian method, Huber method, Tukey method, and correlated observation robust estimation are all robust filtering methods of M estimation, which can handle outliers in measurement data by constructing cost functions.

[0005] In addition, there are also studies that combine Bayesian filtering theory with the Monte Carlo method to complete parameter estimation under non-Gaussian noise models. However, the amount of calculation of this method is related to the number of particles, and there is a problem of particle degradation. Based on the GSM method, some scholars approximate the non-Gaussian system by the sum of a series of Gaussian distributions. When there are enough Gaussian components and the covariance matrix of each component is small enough, the true distribution of the state posterior probability can be approximated. However, the number of its Gaussian components will increase exponentially with the increase of the complexity of the non-Gaussian model.

[0006] In recent years, some scholars have adaptively estimated the covariance matrix of noise based on the Sage-Husa filter through the maximum a posteriori criterion and the new information vector, which can simultaneously handle measurement noise and system noise anomalies. However, when the measurement noise deviates too much from the preset initial noise, it will affect the convergence speed, resulting in a decrease in filtering accuracy or even divergence. It is worth noting that the IGG (I, II, III) anti-error method based on M estimation has also been widely used in dynamic RTK, which can effectively handle the random model of the differential observation equation.

[0007] The navigation solution of the above existing methods is usually based on the KF framework. The working principle of KF in the GNSS data processing process is shown in the figure, where the update process is based on the minimum mean square error (MMSE) criterion to achieve parameter estimation. and , MMSE is described as follows:

[0008]

[0009] In the formula, Expressing hope; Probability density function (PDF) representing a random variable; represents the error vector. It can be seen that MMSE is the error The global integral of the quadratic form represents the difference between the two random variables in the entire space. This criterion is optimal under the Gaussian assumption, but it is not the optimal estimator under the non-Gaussian distribution of noise. The reason is that non-Gaussian noise interference (such as outliers, gross errors or impact noise, etc.) will make Deviation , and the quadratic form further amplifies this effect, making the impact of non-Gaussian error samples on the cost function far greater than other samples, resulting in a huge gap between random variables.

[0010] Although existing methods can alleviate the impact of non-Gaussian noise to a certain extent, they still have serious defects: (1) the system noise and observation noise still need to be preset, and the initial value requirements are strict; (2) since MMSE only uses the second-order moment of the error for parameter estimation, its process focuses more on integrity, and any outlier data will have a serious impact on the estimation results. Therefore, in deep urban canyon environments full of non-Gaussian noise and gross errors, existing methods lack applicability and effectiveness.

[0011] Existing technologies have not been able to solve the problem of nonlinear robust filtering under the interference of non-Gaussian noise such as multipath and NLOS, which actually limits the performance of GNSS navigation and positioning in deep urban canyon environments. At the same time, in addition to the interference caused by multipath and NLOS signals, the original GNSS observations also contain a large amount of complex non-Gaussian noise in various forms such as impact noise and signal interruption. In the process of achieving high-precision dynamic navigation and positioning in urban environments, how to effectively suppress non-Gaussian noise on the basis of fully mining the measurement data information has become a new problem in the current research on robust filtering methods.

[0012] The accuracy and robustness of VT receivers are highly dependent on the high-precision positioning and speed determination results output by KF. Generally, if the filter can effectively handle model uncertainty and model mismatch problems, it can be considered robust. Since the probability distribution of non-Gaussian noise such as multipath and non-line-of-sight in GNSS often presents non-zero offset and thick tail effects, KF is difficult to obtain the optimal solution in such cases. To eliminate the influence of non-Gaussian noise, traditional methods include two types of schemes: (1) inter-epoch difference or absorbing error terms by augmenting the state vector. However, in the conversion process, it is easy to cause an ill-conditioned matrix and introduce additional time delays in the state update process. (2) Robust filtering schemes, such as huber filtering based on M estimation. However, this method often leads to variance expansion and is difficult to reflect the actual noise distribution, so it is difficult to resist the influence of impulse noise or high-order noise on parameter estimation results.

[0013] Therefore, how to improve the robustness of the positioning and navigation filter of the VT-type GNSS receiver, reduce the sensitivity of the filter to low-quality GNSS raw observation data, and improve the efficiency and adaptability in the aluminum foil process are problems that need to be urgently solved in the existing technology.

[0014] It should be noted that the information disclosed in the above background technology section is only used for understanding the background of the present application, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the invention

[0015] The main purpose of the present invention is to overcome the defects of the above-mentioned background technology and provide a GNSS adaptive filtering positioning method based on multi-core maximum entropy.

[0016] To achieve the above object, the present invention adopts the following technical solutions:

[0017] In a first aspect of the present invention, a GNSS adaptive filtering positioning method based on multi-core maximum entropy comprises the following steps:

[0018] S1. Collect the raw observation data of GNSS receiver, including pseudorange and Doppler observation values;

[0019] S2. Initialize the state vector and its covariance matrix to prepare for the start of the filtering process;

[0020] S3. whitening the measurement noise covariance matrix and converting it into a Gaussian noise model;

[0021] S4. Use the Kalman filter MKMC-KF algorithm based on multi-core maximum entropy to predict and update the state of the receiver epoch by epoch; wherein, in the prediction stage, the possible state of the receiver at the current moment is predicted based on the state estimate at the previous moment, combined with the system dynamic model that describes the motion characteristics of the receiver; in the update stage, the predicted state is corrected by the MKMC-KF algorithm using the observation data at the current moment and the measurement noise covariance matrix to obtain a more accurate posterior state estimate, that is, the filtered state vector and its corresponding covariance matrix; in the MKMC-KF algorithm, the kernel bandwidth of each Doppler observation type is adaptively determined according to the distribution characteristics of the pseudorange and Doppler observation using the kernel density estimation method; wherein the multi-core maximum entropy filter assigns different kernel functions to different Doppler observations and pseudoranges to adapt to their distribution characteristics;

[0022] S5. Use the filtered state vector and covariance matrix to perform the positioning algorithm calculation to obtain the accurate position and velocity estimate of the receiver.

[0023] In a second aspect of the present invention, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the GNSS adaptive filtering positioning method based on multi-core maximum entropy is implemented.

[0024] In a third aspect of the present invention, a computer program product includes a computer program, and when the computer program is executed by a processor, the GNSS adaptive filtering positioning method based on multi-core maximum entropy is implemented.

[0025] The present invention has the following beneficial effects:

[0026] The present invention proposes an innovative GNSS adaptive filtering positioning method based on the principle of multi-core maximum entropy (Maximum Correntropy Criterion, MCC), which is particularly suitable for navigation positioning in complex urban environments, and effectively improves the navigation positioning accuracy and robustness of VT-type GNSS receivers under non-Gaussian noise interference. The method does not rely on external hardware sensors and additional hardware resources, and significantly reduces the harmful effects of low-quality data in the positioning solution process by designing a parameter estimation method based on MCC. The present invention reduces the sensitivity to abnormal data by reconstructing the Kalman filter, and adaptively determines the kernel bandwidth parameters of different data types based on the kernel density estimation KDE method, thereby dynamically adjusting the kernel bandwidth of the MCC to ensure filtering efficiency. In addition, the MKMC-KF algorithm proposed in the present invention adopts the MCC cost function to replace the state update process of the traditional Kalman filter, and enhances the suppression ability of multipath and non-line-of-sight (NLOS) noise by grouping different types of observations and assigning different kernel bandwidth parameters. In both static and dynamic scenarios, the MKMC-KF algorithm shows excellent positioning accuracy and robustness, especially when dealing with noise of different types and periods, and can resist its influence on filtering and loop tracking. The significant difference in kernel bandwidth (KBW) between pseudorange and Doppler observations proves that the multi-core filtering scheme can effectively mine the deep features of measurement data, and through the multi-core bandwidth allocation strategy, it realizes a more robust positioning solution that is insensitive to noise, greatly improving the GNSS navigation positioning performance in complex non-Gaussian noise interference scenarios.

[0027] Other beneficial effects of the embodiments of the present invention will be further described below. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of the KF working principle of an embodiment of the present invention.

[0029] Figure 2 It is a working flow chart of the MKMC-KF algorithm for VT-type GNSS receivers according to an embodiment of the present invention.

[0030] Figure 3 Schematic diagram of the KDE method parameter estimation process according to an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The following is a detailed description of the embodiments of the present invention. It should be emphasized that the following description is only exemplary and is not intended to limit the scope and application of the present invention.

[0032] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0033] The embodiment of the present invention provides a GNSS adaptive filtering positioning method based on multi-core maximum entropy, comprising the following steps:

[0034] S1. Collect the raw observation data of GNSS receiver, including pseudorange and Doppler observation values;

[0035] S2. Initialize the state vector and its covariance matrix to prepare for the start of the filtering process;

[0036] S3. whitening the measurement noise covariance matrix and converting it into a Gaussian noise model;

[0037] S4. Use the Kalman filter MKMC-KF algorithm based on multi-core maximum entropy to predict and update the state of the receiver epoch by epoch; in the prediction stage, the possible state of the receiver at the current moment is predicted based on the state estimate at the previous moment, that is, the prior state estimate, combined with the system dynamic model that describes the motion characteristics of the receiver; in the update stage, the predicted state is corrected through the MKMC-KF algorithm using the observation data at the current moment and the measurement noise covariance matrix to obtain a more accurate posterior state estimate, that is, the filtered state vector and its corresponding covariance matrix;

[0038] In the multi-core maximum entropy based Kalman filter MKMC-KF algorithm, the kernel bandwidth of each Doppler observation type is adaptively determined according to the distribution characteristics of the pseudorange and the Doppler observation using a kernel density estimation method; wherein the multi-core maximum entropy filter assigns different kernel functions to different Doppler observations and pseudoranges to adapt to their distribution characteristics;

[0039] S5. Use the filtered state vector and covariance matrix to perform the positioning algorithm calculation to obtain the accurate position and velocity estimate of the receiver.

[0040] The GNSS adaptive filtering positioning method based on multi-core maximum entropy MCC of the present invention suppresses non-Gaussian noise through a parameter estimation method based on MCC without relying on external hardware sensors and additional hardware resource overhead, and effectively improves the navigation positioning accuracy of VT type GNSS receivers in non-Gaussian noise scenarios. Aiming at the problem of insufficient adaptability and robustness of VT receiver filtering solution, the method of the present invention reduces the harmful effects of low-quality data in the positioning solution process. First, the Kalman filter based on the MCC filtering optimization strategy reduces the sensitivity to abnormal data such as gross errors. Secondly, according to the different distribution characteristics of pseudorange and Doppler observations, an adaptive strategy based on kernel density estimation is designed to dynamically adjust the kernel bandwidth of MCC to ensure filtering efficiency, thereby realizing highly robust, highly reliable and highly accurate navigation services in complex urban environments. The present invention improves the anti-interference ability of the navigation filter by mining and utilizing deeper data features, and gives the vector tracking VT higher accuracy and stability. The method replaces MMSE with MCC in filter design, constructs a new loss function based on MCC, and improves the positioning accuracy of VT type receivers. By relaxing the restrictions of the Gaussian assumption on the existing parameter estimation method, the method proposed in the present invention is a more robust positioning solution method that is insensitive to noise.

[0041] In some embodiments, regarding the whitening of the noise covariance matrix and MKMC-KF, in step S3, based on the maximum entropy principle MCC, the prior cost function of the positioning model is constructed, and the prior state estimation is defined; according to the relationship between the state a posteriori error and the measurement error, a mathematical model between the error term and the covariance matrix is ​​established; the state error covariance matrix and the measurement noise covariance matrix are subjected to Cholesky decomposition to obtain a lower triangular matrix, thereby realizing the whitening of the noise covariance matrix. In step S4, the linear relationship model between the state vector and the observation vector is constructed using the whitened covariance matrix; by introducing a transformation matrix, the original state vector and the observation vector are converted into an equivalent representation of the whitened space; in the whitened space, the noise term in the model is converted into an independent Gaussian noise, providing a basis for the implementation of the Kalman filter algorithm; a cost function based on the maximum entropy principle is used to evaluate the matching degree between the measurement data and the estimated state; in the MKMC-KF algorithm, the cost function is used to predict and update the state vector to achieve the optimal estimation of the receiver state.

[0042] like Figure 1As shown, in some embodiments, in step S4, the KF working process of the Kalman filter MKMC-KF algorithm based on multi-core maximum entropy includes: initializing model prior information: setting the initial state vector X and the initial state covariance matrix P for the Kalman filter algorithm based on the initialization information of position and velocity; prediction process: using the system dynamic model to predict the state vector X of the next time step; according to the predicted state vector X, calculating the covariance matrix P of the predicted state; update process: receiving new GNSS observations, including pseudoranges and Doppler observations; calculating the Kalman gain matrix K for fusing the observed data and the predicted state; using the gain matrix K to estimate and update the state to be estimated X; according to the updated state vector X, updating the covariance matrix P; wherein, the system dynamic model is used to describe the evolution of the receiver state over time, including changes in position and velocity.

[0043] like Figure 2 As shown, in some embodiments, in step S4, the specific implementation process of the Kalman filter MKMC-KF algorithm based on multi-core maximum entropy includes: setting the initial parameters of the filtering algorithm; constructing a measurement vector based on pseudorange and Doppler observations collected by the GNSS receiver; determining the kernel bandwidth for different types of observations through a tracking loop; noise covariance whitening, processing the measurement noise covariance matrix to conform to the Gaussian noise model; using the kernel density estimation method to determine the bandwidth parameters of the kernel function based on the distribution characteristics of the observations; executing the MKMC-KF algorithm to perform epoch-by-epoch state updates on the state vector and covariance matrix; using the feedback control mechanism of the code NCO and VTL, using the state estimate of the position and velocity information of the current epoch for feedback control, adjusting the state vector of the filter to optimize the filter performance; the state estimation output, that is, outputting the filtered state vector and covariance matrix, as input for the positioning calculation.

[0044] In some embodiments, the multi-core processing method of the multi-core maximum entropy filter MKMC-KF is optimized. In step S4, in the multi-core maximum entropy filter MKMC-KF, kernel functions are defined for state and observation data to adapt to their distribution characteristics, and the filtering performance is optimized by adaptively selecting the kernel bandwidth KBW; the probability density function of the sample sequence is estimated using kernel density estimation KDE, where the kernel function bandwidth is determined based on data characteristics and empirical rules to ensure the accuracy and robustness of the filtering algorithm. In a further preferred embodiment, the multi-core processing method of the multi-core maximum entropy filter MKMC-KF specifically includes: defining kernel functions of state vectors and measurement vectors to represent system states and observation data; determining kernel parameters, especially kernel bandwidth KBW, as a key influencing factor of filtering performance; allocating different kernel bandwidths to different observation value types to adapt to their respective distribution characteristics and avoid performance degradation or deviation caused by using a single KBW; applying the kernel density estimation KDE method to weight the sample sequence through the kernel function to estimate the probability density function; using Silverman's rule of thumb or other appropriate methods to determine the bandwidth of the kernel function to ensure the accuracy and robustness of the estimation; in the MKMC-KF algorithm, according to the determined kernel bandwidth, the observation data at different epochs are adaptively updated to optimize the state estimation.

[0045] In some embodiments, in step S4, the state update process of the MKMC-KF algorithm includes:

[0046] The cost function is constructed using the maximum entropy principle (MCC), and the updating direction of the state vector is determined through its optimization condition. A multi-core strategy is adopted to dynamically allocate kernel functions and adaptively adjust kernel bandwidth for different observation data to adapt to the non-Gaussian noise distribution. The kernel density estimation (KDE) method is used to adaptively determine the kernel function parameters according to the distribution characteristics of different types of observation data. The sequential solution technology and intermediate matrix are combined to realize the update of the state vector while maintaining the robustness to non-Gaussian noise. The updated results of the MKMC-KF algorithm are applied to the filtering process to replace the corresponding steps in the traditional Kalman filter to complete the accurate estimation of the receiver state.

[0047] This paper proposes an innovative adaptive filtering method based on the multi-core maximum entropy principle, which effectively improves the navigation positioning accuracy and robustness of GNSS receivers in complex urban environments when facing non-Gaussian noise. This method does not rely on external hardware sensors or additional hardware resources. By designing a parameter estimation method based on the maximum entropy principle (MCC), it effectively suppresses non-Gaussian noise, especially under the influence of multipath and non-line-of-sight (NLOS) signals, reducing the adverse effects of low-quality data on positioning solutions.

[0048] The present invention reduces the sensitivity to abnormal data by reconstructing the Kalman filter, and dynamically adjusts the kernel bandwidth using the kernel density estimation (KDE) method to adapt to the different distribution characteristics of pseudorange and Doppler observations. This method not only improves the filtering efficiency, but also enhances the ability to provide high-reliability and high-precision navigation services in complex environments.

[0049] By introducing MCC to replace the traditional minimum mean square error criterion (MMSE), a new loss function is constructed, and the filtering process is transformed into a loss function solution process, thereby improving the positioning accuracy. The method of the present invention relaxes the Gaussian assumption on noise distribution and provides a positioning solution that is insensitive to noise and more robust.

[0050] In addition, the multi-core MCC filtering strategy (MKMC-VT) designed by the present invention improves the efficiency of solution through a sequential update strategy, and shows excellent positioning accuracy and robustness in both static and dynamic scenarios. The MKMC-KF algorithm uses the MCC cost function to replace the state update process of the traditional Kalman filter, assigns different kernel bandwidth parameters to different types of observations, effectively resists the interference of multipath and NLOS noise, and significantly improves the robustness of positioning solution.

[0051] Finally, the present invention proves that the multi-core filtering scheme can effectively mine the deep features of the measurement data, and through the multi-core bandwidth allocation strategy, it achieves a significant improvement in the GNSS navigation and positioning performance in complex non-Gaussian noise interference scenarios.

[0052] Examples

[0053] A GNSS adaptive filtering positioning method based on multi-core maximum entropy method, here called MKMC-VT, its workflow diagram is as follows Figure 2 The filtering process includes: (1) different GNSS types of observations (pseudorange in this embodiment) and Doppler )’s multi-core bandwidth is determined; (2) the noise whitening process. This process transforms the non-Gaussian model into a Gaussian form and constructs the filtering process cost function, which is the basis for the subsequent filtering calculation of the positioning result; (3) the maximum entropy filtering process (MKMC-KF), which realizes the epoch-by-epoch prediction and update of the state to be estimated.

[0054] Exemplarily, the algorithm steps of the MKMC-VT method are as follows:

[0055] 1. Noise covariance matrix whitening and MKMC-KF

[0056] Firstly, based on the MCC criterion, the cost function of the VT receiver positioning model is derived. is the state vector The prior estimate of , the positioning model of VT can be expressed as:

[0057]

[0058] In the formula, is the state posterior error, and the corresponding covariance matrix is ; is the error term, ; is the measurement noise, and the corresponding covariance matrix is .but , , The following relationship exists:

[0059]

[0060] Perform Cholesky decomposition on the above formula, and let and Respectively and After decomposition, the lower triangular matrix is ​​obtained:

[0061]

[0062] Further, let , , . Then the above formula can be transformed into:

[0063]

[0064] Since in the above formula, , so the noise terms in the model are converted into independent Gaussian noises, which means that the model can handle both the non-Gaussian system process noise and the non-Gaussian measurement noise. The cost function corresponding to the above model is:

[0065]

[0066] 2. Multi-core processing of maximum entropy filter

[0067] Assumptions and They are the estimated state and the number of visible satellites in the model, and the state vector and the measurement vector The corresponding kernel function vectors can be defined as:

[0068]

[0069] In MKMC-KF, the kernel parameter vector and The selection of KBW is an important parameter that affects the filtering performance. If the KBW is too large, the sample concentrated area will be over-smoothed, submerging the distribution characteristics, while if the KBW is too small, the sample sparse area will be under-smoothed, resulting in data overfitting. The kernel function that represents the state vector has a relatively stable KBW and will be used in subsequent processing. Fixed at 0.3.

[0070] but, and Generated from different tracking loops, the PDFs of the two samples are very different. If all elements in are assigned the same KBW without distinguishing the types of observations, MKMC-KF will not achieve optimal performance and may even cause serious estimation bias. In order to preserve sample details as much as possible, a multi-core strategy is adopted to assign different KBWs to different types of samples.

[0071] For a sample sequence with values ​​from the same distribution , and estimate its probability density function through KDE for:

[0072] In the formula, and The kernel function and its corresponding KBW are respectively. The former can smooth the estimated curve and determine the weight of the sample during estimation; the latter represents the width of the kernel function at each sample point and determines the number of samples involved in the estimation. In fact, KDE divides the data space into multiple regions, estimates the PDF of sample points in different regions, and then takes the average to finally obtain the PDF of the overall data space. The process is as follows: Figure 3 As shown in the figure, the sample sequence is [0, 4, 7, 9, 10], and KBW=0.5.

[0073] The KBW of the kernel function in KDE can be determined by the following Silverman's rule of thumb:

[0074]

[0075] Based on the above analysis, in MKMC-KF, and The KBW of the samples can be determined separately using the above formula.

[0076] 3. MKMC-KF actual

[0077] To obtain the optimal solution of formula (5), let , ,but

[0078]

[0079] Considering The dimension is , for the convenience of solving, the above formula can be further expressed as the following sequential solution form:

[0080]

[0081] The parts in the above formula are expanded as follows:

[0082]

[0083] In the formula, express No. row vectors; express No. scalar elements; express No. scalar elements; express Scalar elements on the diagonal. Let , it can be simplified as follows (the derivation process is omitted here):

[0084] Therefore, according to the above derivation, the state update process of MKMC-KF can be summarized as:

[0085]

[0086] Using the result given by formula (13), replace Figure 1 The filtering process of the traditional KF is completed by the MKMC-KF method process.

[0087] In view of the shortcomings of the prior art, the embodiments of the present invention improve the anti-interference ability of the navigation filter by mining and utilizing deeper data features, giving VT higher accuracy and stability. This method replaces MMSE with MCC in filter design, constructs a new loss function based on MCC, and transforms the filtering process of GNSS positioning into a solution process of the loss function, thereby improving the positioning accuracy of VT receivers. By relaxing the restrictions of the Gaussian assumption on existing parameter estimation methods, the method proposed by the present invention is a more robust positioning solution method that is insensitive to noise.

[0088] Specifically, the present invention firstly designs a new multi-core MCC filtering strategy (MKMC-VT) using the MCC criterion; secondly, multi-core design is performed on the newly proposed loss function, and the kernel bandwidth (KBW) parameters of different data types are adaptively determined by the kernel density estimation method (KDE). Finally, a sequential update strategy of the state quantity is derived to improve the solution efficiency of MKMC-VT.

[0089] The nonlinear filtering method based on the multi-core maximum entropy strategy proposed in the embodiment of the present invention improves the navigation and positioning performance of the VT receiver under non-Gaussian noise interference. First, the kernel density estimation method is introduced to perform multi-core processing on the measurement data of the tracking loop in the VT receiver. Secondly, the parameter estimation process of the navigation filter is optimized by using the MCC principle, thereby improving the positioning accuracy and robustness of the vector tracking receiver. At the same time, through high-precision position and velocity estimation, the accuracy of the code NCO control quantity in the tracking loop is improved, and the stability of the tracking loop is significantly improved.

[0090] In summary, for VT-type GNSS receivers, the present invention proposes a MKMC-KF algorithm based on MCC. This method adopts the construction of MCC cost function to replace the KF state update process. On the basis of grouping different types of observations, different kernel bandwidth parameters are allocated to different types of measurement data according to KDE. In an environment interfered by multipath and NLOS noise, the navigation filter of VTL is enhanced. Compared with traditional methods, MKMC-KF has the following advantages: MKMC-KF can significantly improve the positioning accuracy in static scenarios; MKMC-KF can resist the influence of different types and periods of noise on filtering and loop tracking in dynamic scenarios, and improve the positioning solution robustness of VT-type receivers. In addition, there is a significant difference between KBW pseudorange and pseudorange rate, indicating that the multi-core filtering scheme designed by the present invention can effectively mine the deep features of the measurement data, and effectively proves the effectiveness of the multi-core bandwidth allocation strategy. Therefore, the proposed MKMC-KF method can effectively improve the GNSS navigation positioning performance in complex non-Gaussian noise interference scenarios.

[0091] An embodiment of the present invention further provides a storage medium for storing a computer program, which at least performs the above method when executed.

[0092] An embodiment of the present invention further provides a control device, comprising a processor and a storage medium for storing a computer program; wherein the processor is configured to execute at least the method described above when executing the computer program.

[0093] An embodiment of the present invention further provides a processor, wherein the processor executes a computer program and at least executes the method described above.

[0094] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. Among them, the non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic random access memory (FRAM), a ferromagnetic random access memory (Flash Memory), a magnetic surface memory, an optical disc, or a compact disc read-only memory (CD-ROM); the magnetic surface memory can be a disk memory or a tape memory. The storage medium described in the embodiments of the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0095] In the several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as: multiple units or components can be combined, or can be integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the components shown or discussed can be through some interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.

[0096] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units; some or all of the units may be selected according to actual needs to achieve the purpose of the scheme of this embodiment.

[0097] In addition, all functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately used as a unit, or two or more units may be integrated into one unit; the above-mentioned integrated units may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0098] A person skilled in the art can understand that: all or part of the steps of implementing the above method embodiment can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above method embodiment; and the aforementioned storage medium includes: mobile storage devices, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), disks or optical disks, etc. Various media that can store program codes.

[0099] Alternatively, if the above-mentioned integrated unit of the present invention is implemented in the form of a software function module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present invention can be essentially or partly reflected in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as mobile storage devices, ROM, RAM, magnetic disks or optical disks.

[0100] The methods disclosed in the several method embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0101] The features disclosed in several product embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0102] The features disclosed in several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments or device embodiments.

[0103] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art of the present invention, several equivalent substitutions or obvious variations can be made without departing from the concept of the present invention, and the performance or use is the same, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A GNSS adaptive filtering positioning method based on multi-core maximum entropy, characterized in that: The following steps are involved: S1. Collect the raw observation data of GNSS receiver, including pseudorange and Doppler observation values; S2. Initialize the state vector and its covariance matrix to prepare for the start of the filtering process; S3. whitening the measurement noise covariance matrix and converting it into a Gaussian noise model; S4. Use the Kalman filter MKMC-KF algorithm based on multi-core maximum entropy to predict and update the state of the receiver epoch by epoch; wherein, in the prediction stage, the possible state of the receiver at the current moment is predicted based on the state estimate at the previous moment, combined with the system dynamic model that describes the motion characteristics of the receiver; in the update stage, the predicted state is corrected by the MKMC-KF algorithm using the observation data at the current moment and the measurement noise covariance matrix to obtain a more accurate posterior state estimate, that is, the filtered state vector and its corresponding covariance matrix; wherein the kernel bandwidth of each Doppler observation type in the MKMC-KF algorithm is adaptively determined according to the distribution characteristics of the pseudorange and Doppler observation using the kernel density estimation method; wherein the multi-core maximum entropy filter assigns different kernel functions to different Doppler observations and pseudoranges to adapt to their distribution characteristics; S5. Use the filtered state vector and covariance matrix to perform the positioning algorithm calculation to obtain the accurate position and velocity estimate of the GNSS receiver.

2. The GNSS adaptive filtering positioning method based on multi-core maximum entropy according to claim 1, characterized in that: In step S3, based on the maximum entropy principle MCC, the prior cost function of the positioning model is constructed, and the prior state estimation is defined; according to the relationship between the state a posteriori error and the measurement error, a mathematical model between the error term and the covariance matrix is ​​established; Perform Cholesky decomposition on the state error covariance matrix and the measurement noise covariance matrix to obtain the lower triangular matrix, and realize the whitening of the noise covariance matrix; In step S4, a linear relationship model between the state vector and the observation vector is constructed using the whitened covariance matrix; By introducing the transformation matrix, the original state vector and observation vector are converted into equivalent representations in the whitened space; in the whitened space, the noise term in the model is converted into independent Gaussian noise; A cost function based on the maximum entropy principle is used to evaluate the matching degree between the measured data and the estimated state; in the MKMC-KF algorithm, the cost function is used to predict and update the state vector to achieve the optimal estimation of the receiver state.

3. The GNSS adaptive filtering positioning method based on multi-core maximum entropy according to claim 1, characterized in that: In step S4, the KF working process of the multi-core maximum entropy Kalman filter MKMC-KF algorithm includes: Initialize model prior information: Based on the initialization information of position and velocity, set the initial state vector X and the initial state covariance matrix P for the Kalman filter algorithm; Prediction process: Use the system dynamic model to predict the state vector X of the next time step; Based on the predicted state vector X, calculate the covariance matrix P of the predicted state; Update process: Receive new GNSS observations, including pseudorange and Doppler observations; calculate the Kalman gain matrix K, which is used to fuse the observation data and the predicted state; use the gain matrix K to estimate and update the state to be estimated X; update the covariance matrix P according to the updated state vector X; Among them, the system dynamic model is used to describe the evolution of the receiver state over time, including changes in position and velocity.

4. The GNSS adaptive filtering positioning method based on multi-core maximum entropy according to claim 1, characterized in that: In step S4, the specific implementation process of the multi-core maximum entropy Kalman filter MKMC-KF algorithm includes: Set the initial parameters of the filtering algorithm; Construct a measurement vector based on pseudorange and Doppler observations collected by the GNSS receiver; By tracking the loop, the kernel bandwidth is determined for different types of observations; Noise covariance whitening, processing the measurement noise covariance matrix to conform to the Gaussian noise model; Using the kernel density estimation method, the bandwidth parameter of the kernel function is determined according to the distribution characteristics of the observed values; Execute the MKMC-KF algorithm to update the state vector and covariance matrix epoch by epoch; Through the feedback control mechanism of the code NCO and VTL, the state estimation of the position and velocity information of the current epoch is used for feedback control to adjust the state vector of the filter to optimize the filter performance; The output filtered state vector and covariance matrix, i.e., state estimate, serve as input for positioning calculation.

5. The GNSS adaptive filtering positioning method based on multi-core maximum entropy according to any one of claims 1 to 4, characterized in that: In the multi-core maximum entropy filter MKMC-KF, kernel functions are defined for state and observation data to adapt to their distribution characteristics, and the filtering performance is optimized by adaptively selecting the kernel bandwidth KBW; the probability density function of the sample sequence is estimated using kernel density estimation KDE, where the kernel function bandwidth is determined based on data characteristics and empirical rules to ensure the accuracy and robustness of the filtering algorithm.

6. The GNSS adaptive filtering positioning method based on multi-core maximum entropy according to claim 5, characterized in that: The multi-core processing method of the multi-core maximum entropy filter MKMC-KF specifically includes: Define the kernel function of the state vector and the measurement vector to represent the system state and observation data; Determine the kernel bandwidth KBW as a key factor affecting filter performance; Assign different kernel bandwidths to different observation types to adapt to their respective distribution characteristics and avoid performance degradation or deviation caused by using a single KBW; The kernel density estimation (KDE) method is applied to weight the sample sequence through the kernel function to estimate the probability density function. Determine the bandwidth of the kernel function to ensure the accuracy and robustness of the estimation; In the MKMC-KF algorithm, the observation data at different epochs are adaptively updated according to the determined kernel bandwidth to optimize the state estimation.

7. The GNSS adaptive filtering positioning method based on multi-core maximum entropy according to any one of claims 1 to 4, characterized in that: In step S4, the state update process of the MKMC-KF algorithm includes: Based on the maximum entropy principle, MCC constructs the cost function and determines the update direction of the state vector through its optimization condition; A multi-core strategy is adopted to dynamically allocate kernel functions for different observation data and adaptively adjust kernel bandwidth to adapt to non-Gaussian noise distribution; Through the kernel density estimation (KDE) method, the kernel function parameters are adaptively determined according to the distribution characteristics of different types of observation data; Combining sequential solution techniques and intermediate matrices, the state vector is updated while maintaining robustness to non-Gaussian noise; The updated results of the MKMC-KF algorithm are applied to the filtering process to replace the corresponding steps in the traditional Kalman filter to complete the accurate estimation of the receiver state.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the GNSS adaptive filtering positioning method based on multi-core maximum entropy is implemented as described in any one of claims 1 to 7.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the GNSS adaptive filtering positioning method based on multi-core maximum entropy is implemented as described in any one of claims 1 to 7.

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