A low-orbit enhanced GNSS high-precision positioning method based on an interactive multi-model robust filter

Abstract

The application relates to the technical field of satellite navigation, and discloses a low-orbit enhanced GNSS high-precision positioning method based on an interactive multi-model robust filter, which is fused with LEO satellite observation data. The characteristics of low orbit height and fast spatial geometric configuration change of the LEO satellite are used to quickly update the spatial constraint of an observation equation, significantly shorten the PPP convergence time, and improve the positioning precision. An IMM framework is introduced to realize adaptive fusion of multiple motion models. Meanwhile, an equivalent covariance matrix is designed to suppress non-Gaussian noise and abnormal gross errors. In a dynamic scene, the PPP convergence time can be further shortened and the positioning precision can be improved, and the method is suitable for dynamic precise positioning in a complex urban environment.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation technology, and in particular to a low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering. Background Technology

[0002] Global Navigation Satellite System (GNSS) provides precise positioning, navigation, and timing services globally, 24 / 7, and is widely used in surveying and exploration, natural disaster monitoring, and intelligent transportation. Precise Point Positioning (PPP), requiring only single receiver observation data and combining precise ephemeris, precise clock bias, and various error correction models, can achieve positioning accuracy from centimeters to decimeters, and has become a key technology in the field of high-precision GNSS positioning.

[0003] GNSS satellites generally operate in medium to high orbits, experiencing minimal spatial geometric changes over short periods. This results in slow updates to the spatial constraints of the observation equations, leading to prolonged convergence times for PPP filtering. In recent years, some scholars have proposed using Low Earth Orbit (LEO) satellites to enhance GNSS positioning performance. LEO satellites, with their low orbital altitude and rapid spatial geometric changes, can shorten PPP convergence times. Furthermore, in complex urban environments, receiver motion states are highly variable, and a single pre-defined motion model is insufficient to fully describe the actual motion state, easily leading to significant state prediction errors. Simultaneously, observation data may be affected by non-Gaussian noise or outliers, reducing the system's positioning accuracy. The Interacting Multiple Model (IMM) framework can adaptively fuse multiple motion models to adapt to changes in receiver motion states in complex urban environments. Robust filtering techniques suppress non-Gaussian noise and outliers by designing equivalent covariance.

[0004] Therefore, developing an interactive multiple model robust filtering (IMMRF) method suitable for low-orbit enhanced GNSS PPP is essential for improving the precision positioning performance in complex urban environments. Summary of the Invention

[0005] The purpose of this invention is to provide a low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering, which solves the problems in the prior art such as long convergence time of GNSS PPP filtering, difficulty of single motion model adapting to changes in receiver motion state in complex urban environments, and reduced positioning accuracy due to interference from non-Gaussian noise and abnormal gross errors in observation data.

[0006] To achieve the above objectives, this invention provides a low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering, comprising the following steps:

[0007] Construct a precise single-point positioning observation model for a low-orbit enhanced GNSS system;

[0008] Construct the equivalent covariance matrix of measurement noise;

[0009] Construct multi-model state transition equations;

[0010] Model interaction and filter updates are based on an interactive multi-model framework;

[0011] Update the model probabilities of each motion model;

[0012] The filtering results from each model are fused and the optimal state estimate is output.

[0013] The "Construction of a Precise Single-Point Positioning Observation Model for a Low-Earth Orbit Enhanced GNSS System" includes the following steps:

[0014] An ionospheric-free combination model was used to linearly combine the dual-frequency observations of the low-orbit enhanced GNSS system to eliminate the first-order ionospheric delay.

[0015] Define the state vector to be estimated, including receiver position, receiver clock error, zenith tropospheric delay, and phase ambiguity of the ionosphere-free combination;

[0016] Based on the above ionosphere-free combination model and state vector, a precise single-point positioning observation equation for the low-orbit enhanced GNSS system is established.

[0017] The "Construction of Equivalent Covariance Matrix for Measurement Noise" includes the following steps:

[0018] The measurement noise covariance matrix is ​​constructed using a random function model of elevation angle;

[0019] Calculate the standardized posterior residual vector and determine the variance inflation factor based on a preset constant;

[0020] Multiplying the diagonal elements of the measurement noise covariance matrix by the variance expansion factor yields the equivalent measurement noise covariance matrix.

[0021] The "Construction of multi-model state transition equations" includes the following steps:

[0022] The receiver motion state is described using a constant velocity model, a constant acceleration model, and a constant steering model.

[0023] Define the state transition matrices for constant speed, constant acceleration, and constant steering models based on the sampling time interval;

[0024] The process noise covariance matrices for constant speed, constant acceleration, and constant steering models are defined based on constant variance.

[0025] The section on "Model Interaction and Filter Update Based on an Interactive Multi-Model Framework" includes the following steps:

[0026] Based on the model probabilities of each model at the previous time step, the optimal estimated state and the estimation error covariance are interactively fused.

[0027] The state and covariance after interaction and fusion are used as the inputs of each model at the current time.

[0028] Each model is updated independently using robust filtering, and non-Gaussian noise and outliers are suppressed by using the equivalent covariance matrix of measurement noise.

[0029] The "updating the model probabilities of each motion model" section includes the following steps:

[0030] Calculate the prior residual vector and prior residual covariance matrix for each model;

[0031] The model probabilities are updated based on the degree of matching between each model and the observed data.

[0032] The step of "integrating the filtering results of each model and outputting the optimal state estimate" includes the following steps:

[0033] Based on the updated probabilities of each model, the state estimates and error covariance of each model are weighted and fused.

[0034] Output the optimal estimated state and the estimation error covariance at the current moment.

[0035] This invention presents a high-precision GNSS positioning method for low-Earth orbit (LEO) augmented by robust interactive multi-model (IPM) filtering, which integrates LEO satellite observation data. Leveraging the low orbital altitude and rapid changes in spatial geometry of LEO satellites, the spatial constraints of the observation equations can be quickly updated, significantly shortening the PPP convergence time and improving positioning accuracy. An IMM framework is introduced to achieve adaptive fusion of multiple motion models. Simultaneously, an equivalent covariance matrix is ​​designed to suppress non-Gaussian noise and outliers. In dynamic scenarios, the PPP convergence time can be further shortened and positioning accuracy improved, making it suitable for dynamic precision positioning in complex urban environments. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0037] Figure 1 This is a flowchart of a low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering provided by the present invention.

[0038] Figure 2 This is a spatial distribution map of the GPS constellation in the embodiment.

[0039] Figure 3 This is a spatial distribution diagram of the LEO constellation in the embodiment.

[0040] Figure 4 This is a graph showing the change in the number of visible satellites for the receiver under the three system combinations in the embodiment.

[0041] Figure 5 This is a diagram of the receiver's motion trajectory in a dynamic scene as shown in the embodiment.

[0042] Figure 6 This is a graph showing the probability changes of CA, CV, and CT models in a dynamic scene using the IMMRF algorithm of the present invention in this embodiment. Detailed Implementation

[0043] The embodiments of the present invention are described in detail below. Examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, but should not be construed as limiting the present invention.

[0044] Please see Figures 1 to 6 This invention provides a high-precision positioning method for low-orbit enhanced GNSS based on interactive multi-model robust filtering, comprising the following steps:

[0045] S1 constructs a precise single-point positioning observation model for a low-orbit enhanced GNSS system;

[0046] S11 uses an ionospheric-free combination model to linearly combine the dual-frequency observations of the low-orbit enhanced GNSS system to eliminate the first-order ionospheric delay.

[0047] S12 defines the state vector to be estimated, including the receiver position, receiver clock error, zenith tropospheric delay, and phase ambiguity of the ionospheric combination;

[0048] Based on the above-mentioned ionosphere-free combination model and state vector, S13 establishes the precise single-point positioning observation equation for the low-orbit enhanced GNSS system.

[0049] Specifically, the PPP observation equations for the LEO-enhanced GNSS system are defined. The PPP observation model adopts an ionospheric-free combination model, which eliminates the first-order ionospheric delay by linearly combining the dual-frequency observations of the LEO-enhanced GNSS system. The ionospheric-free combination model is expressed as:

[0050]

[0051] In the formula, This represents LEO satellite pseudomoment observations without ionospheric assemblies. This represents LEO satellite carrier phase observations without ionospheric assemblies. This represents GNSS satellite pseudomoment observations without ionospheric assemblies. This represents GNSS satellite carrier phase observations without ionospheric assemblies. and This represents the carrier frequency of two carrier signals. express The pseudo-moment observations corresponding to the frequency, express The carrier phase observation value corresponding to the frequency, express The pseudo-moment observations corresponding to the frequency, express The carrier phase observation value corresponding to the frequency, Indicates the geometric distance between the receiver and the satellite. This represents the speed of light in a vacuum. Indicates receiver clock bias. Indicates LEO satellite clock bias. Indicates the clock bias of GNSS satellites. Indicates tropospheric delay, This represents the receiver-side pseudo-moment hardware delay for ionosphere-free combinations. This indicates the pseudo-moment hardware delay at the LEO satellite end without ionospheric assemblies. This represents the pseudo-moment hardware delay at the GNSS satellite end without ionospheric assemblies. This indicates the receiver-side carrier phase hardware delay without ionospheric assemblies. This indicates the hardware delay of the carrier phase at the LEO satellite end without ionospheric assemblies. This indicates the hardware delay of the carrier phase at the GNSS satellite end without ionospheric assemblies. Indicates the phase ambiguity of the ionosphere-free combination. This represents the pseudo-moment measurement noise of the ionosphere-free assembly. This represents carrier phase measurement noise without ionospheric assemblies. This represents the remaining unmodeled errors. In the ionosphere-free combined model, the state vector to be estimated is:

[0052]

[0053] In the formula, Indicates the location of the receiver. Indicates the receiver speed. This indicates the receiver's acceleration. Indicates receiver clock bias. Indicates the wet delay of the zenith troposphere. Indicates the phase ambiguity of the ionosphere-free combination. This represents the number of visible satellites. Therefore, the observation equations for the ionospheric-free combination model can be expressed as:

[0054]

[0055] In the formula, express The observation vector at time t, express The observation matrix at time, express The state vector at time t, express The measurement noise vector at time step.

[0056] S2 constructs the equivalent covariance matrix of measurement noise;

[0057] S21 uses an elevation angle random function model to construct the measurement noise covariance matrix;

[0058] S22 calculates the standardized posterior residual vector and determines the variance magnification factor based on a preset constant;

[0059] S23 multiplies the diagonal elements of the measurement noise covariance matrix by the variance expansion factor to obtain the equivalent measurement noise covariance matrix.

[0060] Specifically, the equivalent covariance matrix of the measurement noise is defined. The PPP stochastic model is represented by an elevation angle stochastic function model, expressed as:

[0061]

[0062]

[0063] In the formula, The standard deviation of the pseudo-moment measurement error is represented by... The standard deviation of the carrier phase measurement error is represented by... and Indicates the carrier phase error factor. Indicates the satellite's elevation angle. This represents the error ratio between the carrier phase and the pseudo-moment. It can be defined according to the PPP stochastic model. The measurement noise covariance matrix at time t is expressed as:

[0064]

[0065] In the formula, express The measurement noise covariance matrix at time step. The standard deviation of the pseudo-moment measurement error is represented by... This represents the standard deviation of the carrier phase measurement error. The equivalent covariance matrix is ​​obtained using the Institute of Geodesy and Geophysics (IGG) III function. In the IGG III function, Time-equivalent covariance matrix The The diagonal elements can be represented as:

[0066]

[0067] In the formula, express Time-measured noise equivalent covariance matrix The diagonal elements, express Time-measured noise covariance matrix The diagonal elements, express The first moment One variance inflation factor. Let express The posterior residual vector at time t. express The posterior residual covariance matrix at time t. express The posterior residual standard deviation vector at time t. express The standardized posterior residual vector at time t is expressed as:

[0068]

[0069]

[0070]

[0071]

[0072] In the formula, express Post-hoc residual covariance matrix The diagonal elements, express posterior residual standard deviation vector at time step The One element, express Time-posterior residual vector The One element, express Time-standardized posterior residual vector The The element. Then, the... The variance inflation factor can be expressed as:

[0073]

[0074] In the formula, This represents two constants.

[0075] S3 constructs multi-model state transition equations;

[0076] S31 uses a constant velocity model, a constant acceleration model, and a constant steering model to describe the receiver's motion state;

[0077] S32 defines the state transition matrices for constant speed, constant acceleration, and constant steering models based on the sampling time interval;

[0078] S33 defines the process noise covariance matrix for constant speed, constant acceleration, and constant steering models based on constant variance.

[0079] Specifically, we define the PPP state equations. The PPP dynamic model describes the motion process of the dynamic system through state vectors, and the state equations can be expressed as:

[0080]

[0081] In the formula, express The state vector at time t, express The state vector at time t, express The state transition matrix at time t, express The process noise vector at time step. The PPP dynamic model employs a constant velocity (CV) model, a constant acceleration (CA) model, and a constant turn (CT) model. The state transition matrices of these models are as follows:

[0082]

[0083]

[0084]

[0085] In the formula, This represents the state transition matrix of the CV model. This represents the state transition matrix of the CA model. This represents the state transition matrix of the CT model. Indicates the sampling time interval. Represents the identity matrix. Represents the zero matrix. The state transition matrix of the CT model. In the matrix and for:

[0086]

[0087]

[0088] In the formula, Indicates the steering angular velocity. This represents the sampling time interval. Define the process noise covariance matrix. for:

[0089]

[0090] In the formula, This represents the constant variance of receiver acceleration, receiver clock error, and noise from the zenith tropospheric wet delay process. Indicates the sampling time interval. and Represents the zero matrix. This indicates the number of visible satellites.

[0091] S4 is based on an interactive multi-model framework for model interaction and filter updates;

[0092] S41 integrates the optimal estimated state and the estimation error covariance based on the model probabilities of each model at the previous time step.

[0093] S42 uses the fused state and covariance as the input to each model at the current time.

[0094] Each model in S43 is independently updated with robust filtering, and non-Gaussian noise and outliers are suppressed by using the equivalent covariance matrix of measurement noise.

[0095] Specifically, the weighted least squares algorithm is used to solve the observation equations of PPP. The state at any given moment. The state optimization problem at each time step is reduced to:

[0096]

[0097] In the formula, express The state vector at time t, express The observation vector at time t, express The observation matrix at time, Represents the weight matrix. , express The measurement noise covariance matrix at time t. Solving the above optimization problem, we obtain:

[0098]

[0099]

[0100] In the formula, express The state vector at time t, express The error covariance matrix at time t.

[0101] Consider three prior models: the CV model, the CA model, and the CT model. Let the matrix... This represents the transition probability matrix of the prior model. .matrix The element Indicates from the model Transfer to model The prior probability of . Furthermore, let express The time-major filter for the "model" The confidence (probability) of "is the true model" is then the prior fusion correlation coefficient. Represented as:

[0102]

[0103] Assuming in Time, Model The output state is ,Model The output error covariance matrix is: ,So Time model Input status and input error covariance matrix can be The model is in The optimal estimated state and the covariance of the estimation error at time t are fused together and expressed as:

[0104]

[0105]

[0106] exist At any given moment, for the model The optimal state is estimated using robust filtering. Let... express Time model The prior state, express Time model The prior error covariance matrix, express Time model Kalman gain, for Time model The posterior state, for Time model The posterior error covariance matrix is ​​then...

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] In the formula, express Time model The state transition matrix, express Time model The process noise covariance matrix, Indicates the adaptive factor. , express Time model The equivalent covariance matrix of measurement noise.

[0113] S5 updates the model probabilities of each motion model;

[0114] S51 calculates the prior residual vector and prior residual covariance matrix for each model;

[0115] S52 updates the model probabilities based on the degree of matching between each model and the observed data.

[0116] Specifically, let express Time model The prior residual (news) vector, express Time model The prior residual covariance matrix. Then, Time model The prior residual vector and the prior residual covariance matrix are expressed as follows:

[0117]

[0118]

[0119] Calculate the likelihood probability (matching degree) using the Gaussian probability density function. Its expression is:

[0120]

[0121] In the formula, Represents the dimension of the observed quantity. express Time model The prior residual (news) vector, express Time model The prior residual covariance matrix. Therefore, the model... probability for:

[0122]

[0123] S6 integrates the filtering results of each model and outputs the optimal state estimate.

[0124] S61 performs weighted fusion of the state estimates and error covariance of each model based on the updated probabilities of each model;

[0125] S62 outputs the optimal estimated state and the estimation error covariance at the current moment;

[0126] Specifically, by weighting and fusing the state estimates and error covariance of each model, we can obtain... The output of the IMMRF algorithm at time 10 is the estimated state. and output estimated covariance matrix for:

[0127]

[0128]

[0129] Example:

[0130] This example simulates the constellations of GPS, BDS, and LEO using the Satellite Tool Kit (STK) software platform. The GPS constellation spatial distribution map is shown below. Figure 2 As shown in the diagram, the spatial distribution of the LEO constellation is as follows: Figure 3 As shown. Figure 4 The number of satellites observable by receivers located at 55.12°S and 78.29°E for single GPS, GPS+BDS, and GPS+BDS+LEO systems is given. It can be seen that adding LEO satellites increases the number of satellites visible to the receiver. Simultaneously, dual-frequency pseudorange and carrier phase observation data from GPS, BDS, and LEO systems to the ground receiver are simulated using a PPP observation model. PPP positioning calculations are performed using the Constant Acceleration Robust Filtering (CARF), Interactive Multi-Model Extended Filtering (IMMEF), and the Interactive Multi-Model Robust Filtering (IMMRF) algorithm of this invention under three system combinations: single GPS, GPS+BDS, and GPS+BDS+LEO. Positioning performance is measured by two indicators: convergence time and root mean square error (RMS). The positioning result is considered convergent when the ENU three-dimensional orientation positioning error is less than 0.1m and the duration reaches 1 minute. The expression for RMS is:

[0131]

[0132] In the formula, express The actual location of the time receiver. express The estimated position of the time receiver. This represents the total number of time intervals involved in the positioning calculation.

[0133] Simulation example:

[0134] This simulation aims to study the PPP positioning performance in dynamic scenarios. Figure 5The receiver's motion trajectory is given, in which the receiver accelerates uniformly from 0 to 4 minutes, performs a turning maneuver from 4 to 21 minutes, switches to uniform motion from 21 to 28 minutes, and performs another turning maneuver from 28 to 45 minutes. Figure 6 The IMMRF algorithm of this invention is presented in... Figure 5 Probability changes of CV, CA, and CT models in dynamic scenes. Figure 6 As can be seen, the CA model has the highest probability during the receiver's uniform acceleration phase, while the CT model has the highest overall probability during the turning maneuver phase; the CV model has the highest probability during the uniform motion phase. This indicates that the IMMRF algorithm can adaptively switch motion models according to the receiver's motion state. Table 1 shows the PPP positioning performance of the CARF, IMMEF, and IMMRF algorithms under different system combinations. Table 1 shows that introducing LEO satellites can significantly shorten the PPP convergence time and improve positioning accuracy. Compared with the CARF and IMMEF algorithms, the IMMRF algorithm proposed in this invention has a shorter convergence time and higher positioning accuracy. This is due to the adaptive fusion of multiple motion models under the IMM framework and the effective suppression of non-Gaussian noise and outliers by the designed equivalent covariance. In conclusion, the IMMRF algorithm proposed in this invention has good positioning performance in low-Earth orbit augmented GNSS systems.

[0135] Table 1 Dynamic PPP Location Performance

[0136]

[0137] Theoretical analysis and simulation results demonstrate that, compared to single GPS systems and GPS+BDS systems, the system incorporating LEO satellites significantly shortens the PPP convergence time and improves positioning accuracy. Compared to existing single-model robust filtering algorithms, the interactive multi-model robust filtering algorithm can adaptively fuse multiple motion models, further shortening the PPP convergence time and improving positioning accuracy. Compared to existing interactive multi-model extended filtering algorithms, the interactive multi-model robust filtering algorithm effectively suppresses non-Gaussian noise and outliers by utilizing equivalent covariance, further shortening the PPP convergence time and improving positioning accuracy. In conclusion, the IMMRF algorithm proposed in this invention exhibits excellent positioning performance in LEO-enhanced GNSS systems and is suitable for dynamic precision positioning in complex urban environments.

[0138] Beneficial effects:

[0139] (1) Compared with the PPP positioning method of GNSS system, the method of this application integrates LEO satellite observation data. By taking advantage of the characteristics of LEO satellites, such as low orbital altitude and rapid changes in spatial geometry, the spatial constraints of the observation equations can be updated quickly, significantly shortening the PPP convergence time and improving the positioning accuracy.

[0140] (2) Compared with existing extended filter-based solutions, the method in this application introduces the IMM framework to achieve adaptive fusion of multiple motion models. Simultaneously, an equivalent covariance matrix is ​​designed to suppress non-Gaussian noise and outliers. In dynamic scenarios, this can further shorten the PPP convergence time and improve positioning accuracy, making it suitable for dynamic precision positioning in complex urban environments.

[0141] The above-disclosed embodiments are merely one or more preferred embodiments of this application and should not be construed as limiting the scope of this application. Those skilled in the art can understand that all or part of the processes for implementing the above embodiments and equivalent changes made in accordance with the claims of this application still fall within the scope of this application.

Claims

1. A high-precision positioning method for low-orbit enhanced GNSS based on interactive multi-model robust filtering, characterized in that, Includes the following steps: Construct a precise single-point positioning observation model for a low-orbit enhanced GNSS system; Construct the equivalent covariance matrix of measurement noise; Construct multi-model state transition equations; Model interaction and filter updates are based on an interactive multi-model framework; Update the model probabilities of each motion model; The filtering results from each model are fused and the optimal state estimate is output.

2. The low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering as described in claim 1, characterized in that, The "Construction of a Precise Single-Point Positioning Observation Model for a Low-Earth Orbit Enhanced GNSS System" includes the following steps: An ionospheric-free combination model was used to linearly combine the dual-frequency observations of the low-orbit enhanced GNSS system to eliminate the first-order ionospheric delay. Define the state vector to be estimated, including receiver position, receiver clock error, zenith tropospheric delay, and phase ambiguity of the ionosphere-free combination; Based on the above ionosphere-free combination model and state vector, a precise single-point positioning observation equation for the low-orbit enhanced GNSS system is established.

3. The low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering as described in claim 1, characterized in that, The steps in "Constructing the Equivalent Covariance Matrix of Measurement Noise" include: The measurement noise covariance matrix is ​​constructed using a random function model of elevation angle; Calculate the standardized posterior residual vector and determine the variance inflation factor based on a preset constant; Multiplying the diagonal elements of the measurement noise covariance matrix by the variance expansion factor yields the equivalent measurement noise covariance matrix.

4. The low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering as described in claim 1, characterized in that, The "Construction of Multi-Model State Transition Equations" includes the following steps: The receiver motion state is described using a constant velocity model, a constant acceleration model, and a constant steering model. Define the state transition matrices for constant speed, constant acceleration, and constant steering models respectively based on the sampling time interval; The process noise covariance matrices for constant speed, constant acceleration, and constant steering models are defined based on constant variance.

5. The low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering as described in claim 1, characterized in that, The "Model Interaction and Filter Update Based on Interactive Multi-Model Framework" includes the following steps: Based on the model probabilities of each model at the previous time step, the optimal estimated state and the estimation error covariance are interactively fused. The state and covariance after interaction and fusion are used as the inputs of each model at the current time. Each model is updated independently using robust filtering, and non-Gaussian noise and outliers are suppressed by using the equivalent covariance matrix of measurement noise.

6. The low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering as described in claim 1, characterized in that, The "Update Model Probabilities for Each Motion Model" section includes the following steps: Calculate the prior residual vector and prior residual covariance matrix for each model; The model probabilities are updated based on the degree of matching between each model and the observed data.

7. The low-orbit enhanced GNSS high-precision positioning method based on interactive multi-model robust filtering as described in claim 1, characterized in that, The process of "integrating the filtering results of various models and outputting the optimal state estimate" includes the following steps: Based on the updated probabilities of each model, the state estimates and error covariance of each model are weighted and fused. Output the optimal estimated state and the estimation error covariance at the current moment.

Images