Multi-information fusion positioning method for high-speed trains based on Beidou satellite

Abstract

The present invention discloses a high-speed train multi-information fusion positioning method based on Beidou satellites, which relates to the field of satellite navigation and positioning technology. The method comprises the following steps: designing a high-speed train multi-information fusion positioning scheme; establishing a nonlinear train state model based on the train kinematic equation based on the train multi-information fusion positioning scheme; constructing a train measurement model with the train position, speed, acceleration, heading angle and pitch angle as state vectors; based on the tracking target set by the train state model and the train measurement model, estimating the train state by fusing the IMM-UKF / PF model of the unscented Kalman filter UKF and the particle filter PF, and citing the ACW and short-term error feedback mechanism in the state fusion. The method can improve positioning accuracy and robustness, and can also enhance the dynamic response capability in complex scenarios.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation and positioning technology, and in particular to a Beidou satellite-based high-speed train multi-information fusion positioning method. Background Art

[0002] Traditional train positioning technology primarily relies on infrastructure such as track circuits and ground transponders, as well as onboard equipment such as axle speed sensors and inertial navigation units. However, these hardware devices suffer from cumulative positioning errors in practical applications, particularly in complex operating environments, which can affect positioning reliability. Therefore, by deeply integrating the Beidou satellite navigation system with existing train positioning technology, high-precision positioning of train position information can be achieved, which is of significant significance for ensuring rail transit operational safety and improving transportation efficiency.

[0003] Existing research focuses on improving train positioning accuracy through improved filtering algorithms, supplemented by methods such as multi-model fusion optimization and multi-sensor fusion frameworks. However, the operating environment of high-speed trains is complex and changeable, including the smooth dynamics of straight-line high-speed travel, the nonlinear characteristics of curves, and the possibility of satellite lock loss. Traditional single filtering algorithms lack adaptability when positioning in some complex scenarios. Summary of the Invention

[0004] The technical problem to be solved by the present invention is how to provide a Beidou satellite-based high-speed train multi-information fusion positioning method that can improve positioning accuracy and robustness and enhance dynamic response capabilities in complex scenarios.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a high-speed train multi-information fusion positioning method based on Beidou satellites, comprising the following steps:

[0006] Design a multi-information fusion positioning solution for high-speed trains;

[0007] Based on the train multi-information fusion positioning solution, a nonlinear train state model based on the train kinematic equation is established;

[0008] Establish a nonlinear train state model based on the train kinematic equations;

[0009] The train measurement model is constructed using the train position, speed, acceleration, heading angle and pitch angle as state vectors;

[0010] Based on the tracking target set by the train state model and the train measurement model, the train state is estimated by fusing the IMM-UKF / PF model, which is a combination of the unscented Kalman filter (UKF) and the particle filter (PF), and referencing the ACW and short-term error feedback mechanism in the state fusion.

[0011] The beneficial effect of adopting the above technical solution is that the method described in this application significantly improves the nonlinear dynamic adaptability and multi-sensor fusion performance of the IMM-UKF / PF algorithm in high-speed train positioning by introducing adaptive confidence weights and a short-term error feedback mechanism. In the case of satellite loss of lock, the short-term error feedback mechanism uses reliable Beidou satellite data before loss of lock to calculate the error trend and feed it back to the state estimate. Combined with the robust weight distribution of ACW, it effectively slows down the drift of the inertial measurement unit, significantly reduces position error, improves positioning accuracy, and comprehensively enhances algorithm performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0013] Figure 1 This is a main flow chart of the method according to an embodiment of the present invention;

[0014] Figure 2 is a flow chart of multi-sensor information fusion in the method according to an embodiment of the present invention;

[0015] Figure 3 This is a flow chart of the IMM-UKF / PF algorithm in the method according to an embodiment of the present invention;

[0016] Figure 4 This is a diagram showing the high-speed train trajectory estimation result of the present invention;

[0017] Figure 5 This is a diagram showing the estimated speed of a high-speed train according to the present invention;

[0018] Figure 6 This is a curve diagram of the model probability results in the IMM-UKF / PF algorithm of the present invention. DETAILED DESCRIPTION

[0019] The following is a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0020] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0021] Overall, such as Figure 1As shown, the embodiment of the present invention discloses a high-speed train multi-information fusion positioning method based on Beidou satellite, comprising the following steps:

[0022] Design a multi-information fusion positioning solution for high-speed trains;

[0023] Based on the train multi-information fusion positioning solution, a nonlinear train state model based on the train kinematic equation is established;

[0024] The train measurement model is constructed using the train position, speed, acceleration, heading angle and pitch angle as state vectors;

[0025] Based on the tracking target set by the train state model and the train measurement model, the train state is estimated by fusing the IMM-UKF / PF model, which is a combination of the unscented Kalman filter (UKF) and the particle filter (PF), and referencing the ACW and short-term error feedback mechanism in the state fusion.

[0026] The following is a detailed description of the above steps based on the specific content:

[0027] 1) High-speed train multi-information fusion positioning specifically includes:

[0028] The BeiDou Navigation System verifies satellite signal quality in real time through Receiver Autonomous Integrity Monitoring (RAIM) technology, and builds a tightly coupled combined positioning model in conjunction with the Inertial Navigation System (INS). It utilizes a carrier phase smoothed pseudorange algorithm to suppress multipath effects and ionospheric delay errors. In complex environments along the track (such as tunnels and mountainous areas), satellite lock may be lost, and the receiver cannot provide direct position and velocity information. If the system relies entirely on BeiDou satellites, positioning will be interrupted, resulting in navigation failure. For scenarios requiring continuous positioning, such as high-speed trains, lock loss may pose a safety hazard. Therefore, a multi-source data fusion strategy is adopted, combining BDS with axle speed sensors, INS, and other sensors.

[0029] Inertial navigation systems integrate and process the angular velocity and acceleration information output by inertial sensors to autonomously calculate the train's real-time position, heading, and attitude parameters in three-dimensional space, without relying on external signal sources. Train axle speed sensors, with a known initial position, use pulse sensors to measure the number of pulses generated by wheel rotation. This pulse count, combined with wheel dimensions, calculates distance traveled and continuously accumulates this information for positioning. However, their accuracy is susceptible to pulse count deviations caused by wheel spin / slip, parameter misalignment caused by long-term wheel wear, and cumulative errors. Figure 2 This is the flow chart of multi-sensor information fusion;

[0030] 2) Establish a train state model. Considering the characteristics of multi-source heterogeneous data such as Beidou satellite navigation, wheel speed sensors, and inertial navigation, a nonlinear state space model based on the train kinematic equations needs to be established. Specifically, the model includes:

[0031] The state transition equation is used to describe the train state from Time has come The change of time is designed based on kinematic principles and takes process noise into consideration.

[0032] (1)

[0033] in, is a nonlinear state transfer function; is the process noise, which represents the uncertainty of the model; is the state vector, are the positions of the train in the x, y and z directions respectively, is the speed of the train along the heading angle, is the acceleration of the train, The heading angle of the train determines the direction of travel and is directly related to the track geometry. It remains unchanged during straight-line motion and changes with the angular velocity during turning motion. is the pitch angle of the train, that is, the bank angle.

[0034] The train state model is:

[0035] (2)

[0036] in, The time step matches the sensor sampling frequency to ensure that the algorithm responds quickly to real-time data; is the angular velocity of the train when turning; is the rate of change of the pitch angle, which indicates the change in the slope of the track on which the train is running; is the process noise, corresponding to each state component respectively.

[0037] 3) Establish a train measurement model, using the train's position, velocity, acceleration, heading angle, and pitch angle as state vectors to achieve precise positioning of the train. Specifically, this includes:

[0038] The observation equation describes the sensor measurements With the state vector The relationship between them is usually of the form:

[0039] (3)

[0040] in, is the measurement noise, which is zero-mean Gaussian white noise with covariance of ,Right now ; For the measurement function, map the state to the observation space:

[0041] (4)

[0042] (5)

[0043] (6)

[0044] in, is the absolute position of the train on the track; and Medium acceleration component[ ] is the scalar acceleration Projection in three-dimensional space, and Affected by the heading angle and pitch angle, the horizontal component is adjust, Only affected by the pitch angle, reflecting the acceleration in the vertical direction, The angular velocity represents the rate of change of the heading angle; the wheel speedometer measures the speed of the train along the track.

[0045] 4) Design IMM-UKF / PF interactive fusion positioning algorithm, such as Figure 3 As shown, specifically including:

[0046] like Figure 2 As shown in the figure, the IMM-UKF / PF algorithm designed in this paper achieves efficient state estimation for nonlinear dynamic systems by integrating the unscented Kalman filter (UKF) and the particle filter (PF). The models interact to generate mixed states and covariances. The UKF processes Gaussian noise through sigma points, while the PF captures nonlinear characteristics using particle sampling. After the filter is updated, the model probability is updated based on the likelihood. The state fusion innovatively incorporates ACW and short-term error feedback mechanisms, better adapting to the nonlinear dynamics and multi-sensor fusion requirements of high-speed train positioning.

[0047] 4-1) Model interaction, using the model probability and estimation results of the previous moment (k-1), generate the initial state and covariance for each filter at the current moment (k) as the starting point for filter update:

[0048] Mixing probability:

[0049] (7)

[0050] in, The model at the previous moment probability; is the conditional probability, indicating that arrive The mixture weights of the model Represents the target model at the current moment, For UKF, For PF, model represents the model at the previous moment, For UKF, For PF; is the element of the Markov transition probability matrix.

[0051] Mixed state: For UKF, the mixed state is calculated by linear weighted average of the estimated states of UKF and PF at the previous moment, so the mixed state Defined as:

[0052] (8)

[0053] For PF, the generation of mixed state is more complicated because the state of PF is represented by a set of particles rather than a single mean. Therefore, a sampling-based method is adopted: first, the sampled particles are estimated from the UKF (obeying the normal distribution), then merged with the original particles of PF, and finally a new set of particles is generated by weighted sampling with the mixed probability, and then the mean is calculated as the mixed state. Mathematically, the mixed state is the mean of the new particle set:

[0054] (9)

[0055] in, is the number of particles.

[0056] For each model Calculate the mixed covariance and compensate for the differences between models through weighted covariance to avoid state jumps during switching:

[0057] (10)

[0058] in, The model at the previous moment The posterior covariance of The model at the previous moment The posterior state estimate of ; For the model Estimation of the mixed state.

[0059] 4-2): Filter update, dynamic fusion operation of two filters, update state estimation and covariance, and generate likelihood values ​​at the same time to provide a basis for probability update:

[0060] UKF update: Generate Sigma points through formula (1) to capture the nonlinear characteristics of the state distribution, and use formula (4) to propagate , we get the predicted observation mean and covariance:

[0061] (11)

[0062] (12)

[0063] in, is the state vector dimension, the value is 7, , a total of 15 sigma points.

[0064] Calculate Kalman gain , and finally calculate the system status update:

[0065] (13)

[0066] (14)

[0067] PF Update: Get Hybrid Particle Sets from Model Interaction Layer , each particle has an initial weight, corresponding to the kinematic model (Equation (2)) applied to each particle and adding process noise to generate a new particle set:

[0068] (15)

[0069] in, .

[0070] The measurement update calculates the observation prediction for each particle through equation (4) , weights are updated and normalized to concentrate particles in the high probability area of ​​the state space:

[0071] (16)

[0072] (17)

[0073] in, It reflects the degree of match between each particle and the actual observation. Particles with small errors receive higher weights, while particles with large errors have weights close to zero.

[0074] Final estimate is the particle weighted average, covariance Reflecting uncertainty in estimates:

[0075] (18)

[0076] (19).

[0077] 4-3) Model probability update, calculate the model likelihood of UKF and PF respectively, UKF likelihood Based on the Gaussian distribution of predicted observations, the PF likelihood Based on the particle weighted likelihood sum:

[0078] (20)

[0079] (twenty one)

[0080] Likelihood can reflect the degree of match between the trajectory estimated by the filter and the actual sensor observation. The higher the value, the more consistent the model is with the data, and the probability The higher.

[0081] According to the likelihood value and mixing probability of the filter, the model probability at the current moment is updated to achieve switching:

[0082] (twenty two)

[0083] 4-4): Adaptive confidence weight, by analyzing the estimated error distribution of UKF and PF in the recent time window, evaluates the reliability of each filter and dynamically adjusts its weight in state fusion accordingly:

[0084] Observation error norm:

[0085] (twenty three)

[0086] in, is the time step , For the current moment, is the sliding window length; Representation filter (UKF or PF) at the moment The error size, which measures the gap between the observation predicted by the filter and the actual observation; Indicates time The actual observation vector of Representation filter At the moment state estimation; represents the observed value predicted by the state estimate through the measurement model.

[0087] Median Error: Use the median to evaluate filter reliability; filters with smaller errors are more reliable. The median is more robust than the mean and is suitable for non-Gaussian noise (such as sudden interference when the satellite loses lock).

[0088] (twenty four)

[0089] in, For filter At the moment The median error, Median operation takes the middle value of the error set.

[0090] Confidence weight: The error difference is converted into a weight. The filter with smaller error contributes more, ensuring a more accurate fusion result.

[0091] (25)

[0092] in, For filter The confidence weight factor of (unitless, range 0~1); is a scaling factor that controls the sensitivity of the error to the weight.

[0093] 4-5): Short-term error feedback, by analyzing the prediction error of the filter in the last W steps, calculating the average deviation And feed back to the current estimate, according to the correction amount Correcting short-term error accumulation:

[0094] (26)

[0095] (27)

[0096] (28)

[0097] Among them, W is a constant, which represents the sliding window length and short-term historical information; To correct the ratio, control the feedback amplitude and avoid excessive adjustments.

[0098] 4-6): Apply short-term error feedback to UKF and PF estimates to form a corrected state , combined with the model probability and adaptive confidence weights , after normalization, we get the new weight , and then get the fusion state and fusion covariance .

[0099] (29)

[0100] (30)

[0101] (31).

[0102] This invention innovatively introduces adaptive confidence weights and a short-term error feedback mechanism, significantly improving the nonlinear dynamic adaptability and multi-sensor fusion performance of the IMM-UKF / PF algorithm for high-speed train positioning. In satellite lock-loss scenarios, the short-term error feedback mechanism utilizes reliable BeiDou satellite data from before the loss of lock to calculate error trends and feed them back into the state estimate. Combined with the robust weight distribution of ACW, this effectively mitigates inertial measurement unit drift, significantly reduces position error, improves positioning accuracy, and comprehensively enhances algorithm performance.

[0103] The initial position of the high-speed train is set to [0, 0], and the initial speed is 75 m / s. The experiment simulates the train's trajectory. From 0 to 30 seconds, it travels in a straight line, and after 30 seconds, it turns: from 30 to 60 seconds, it enters the transition curve section, and from 60 to 100 seconds, it enters the circular curve section. The motion characteristics of the high-speed train on straight tracks and curves are simulated, and MATLAB software is used for simulation. The running results are shown as follows: Figure 4-Figure 5 shown. Figure 5 Reference [8] is a simplified robust UKF algorithm, and reference [9] is a UKF-PF algorithm. Figure 6 This is a curve diagram of the model probability results in the IMM-UKF / PF algorithm of the present invention.

[0104] By integrating multi-source data from the Beidou Navigation System, the Inertial Navigation System, and axle speed sensors through a multi-sensor information fusion system, train distance and speed parameters can be calculated in real time. This breaks through the limitations of traditional track circuits, migrates core control functions to the onboard platform, and achieves autonomous train positioning and control. This not only reduces the deployment density and maintenance costs of trackside signaling equipment, but also significantly improves operational adaptability and reliability in complex scenarios by enhancing system redundancy and data collaboration capabilities.

[0105] In high-speed train positioning, the multi-source information obtained is input into the UKF / PF fusion module through the IMM framework. UKF and PF each have their own advantages and limitations. This invention innovatively constructs a collaborative filtering architecture of UKF and PF through the IMM framework, fully leveraging their complementarity. UKF processes Gaussian noise, while PF captures nonlinear and non-Gaussian features, enabling model switching to adapt to different dynamics. During the state fusion stage, ACW and short-term error feedback mechanisms are introduced. Fusion weights are optimized based on the matching degree between filter estimates and observations and the short-term error, better coping with satellite loss of lock in train positioning. Ultimately, high-precision position and velocity information is output, providing stronger robustness support for high-speed train positioning.

[0106] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A high-speed train multi-information fusion positioning method based on Beidou satellite, characterized in that The steps include: Design a multi-information fusion positioning solution for high-speed trains; Based on the train multi-information fusion positioning solution, a nonlinear train state model based on the train kinematic equation is established; The train measurement model is constructed using the train position, speed, acceleration, heading angle and pitch angle as state vectors; Based on the tracking target set by the train state model and the train measurement model, the train state is estimated by fusing the IMM-UKF / PF model, which combines the unscented Kalman filter (UKF) and the particle filter (PF). The ACW and short-term error feedback mechanism are used in the state fusion. By analyzing the estimation error distribution of UKF and PF in the recent time window, the reliability of each filter is evaluated and its weight in state fusion is dynamically adjusted accordingly: Observation error norm: （23） in, is the time step , For the current moment, is the sliding window length; Representation filter At the moment The error size is used to measure the gap between the observation predicted by the filter and the actual observation; Indicates time The actual observation vector of Representation filter At the moment state estimation; represents the observed value predicted by the state estimate through the measurement model; Median Error: （24） in, For filter At the moment The median error, Median operation, taking the middle value of the error set; Confidence Weight: （25） in, For filter The confidence weight factor of is the scaling factor that controls the sensitivity of the error to the weight Short-term error feedback: By analyzing the prediction error of the filter in the last W steps, the average deviation is calculated And feed back to the current estimate, according to the correction amount Correcting short-term error accumulation: （26） （27） （28） Among them, W is a constant, which represents the sliding window length and short-term historical information; To correct the ratio, control the feedback amplitude; Apply short-term error feedback to UKF and PF estimates to form the corrected state , combined with the model probability and adaptive confidence weights , after normalization, we get the new weight , and then get the fusion state and fusion covariance : （29） （30） （31）。 2. The BeiDou satellite-based high-speed train multi-information fusion positioning method according to claim 1, characterized in that: The method for designing a high-speed train multi-information fusion positioning solution includes the following steps: The BeiDou navigation system verifies satellite signal quality in real time through RAIM (Receiver Autonomous Integrity Monitoring). It builds a tightly coupled positioning model with the inertial navigation system (INS). It uses a carrier phase smoothed pseudorange algorithm to suppress multipath effects and ionospheric delay errors. To address satellite lock loss in complex environments along the track, a multi-source data fusion strategy is employed, including the BDS, train axle speed sensors, and INS. The inertial navigation system (INS) integrates and processes the angular velocity and acceleration information output by the inertial sensor to infer the train's real-time position, heading, and attitude parameters in three-dimensional space. The train axle speed sensor uses a pulse sensor to measure the number of pulses generated by the wheel rotation based on a known initial position, calculates the traveled distance based on the wheel size, and continuously accumulates the pulses to achieve positioning.

3. The BeiDou satellite-based high-speed train multi-information fusion positioning method according to claim 1, characterized in that: The train state model is constructed by the following method: The state transition equation is used to describe the train state from Time has come The change of time is designed based on the kinematic principle and takes into account the process noise: （1） in, is a nonlinear state transfer function; is the process noise, which represents the uncertainty of the model; is the state vector, are the positions of the train in the x, y and z directions respectively, is the speed of the train along the heading angle, is the acceleration of the train, The heading angle of the train determines the direction of travel and is directly related to the track geometry. It remains unchanged during straight-line motion and changes with the angular velocity during turning motion. is the train pitch angle; The train state model is: （2） in, is the time step, which matches the sensor sampling frequency; is the angular velocity of the train when turning; is the rate of change of the pitch angle, which indicates the change in the slope of the track on which the train is running; is the process noise, corresponding to each state component respectively.

4. The BeiDou satellite-based high-speed train multi-information fusion positioning method according to claim 1, characterized in that: The method for establishing the train measurement model comprises the following steps: The observation equation describes the sensor measurement value With the state vector The relationship between them can be expressed as: （3） in, is the measurement noise, and the covariance is ,Right now ; For the measurement function, map the state to the observation space: （4） （5） （6） in, is the absolute position of the train on the track; Medium acceleration component[ ] is the scalar acceleration Projection in three-dimensional space, and Affected by the heading angle and pitch angle, the horizontal component is adjust, Affected by the pitch angle, it reflects the acceleration in the vertical direction. The angular velocity represents the rate of change of the heading angle; the wheel speedometer measures the speed of the train along the track.

5. The BeiDou satellite-based high-speed train multi-information fusion positioning method according to claim 1, characterized in that: The method for estimating the train state comprises the following steps: The unscented Kalman filter (UKF) and the particle filter (PF) are dynamically fused through the IMM framework. The models interact to generate mixed states and covariances. The unscented Kalman filter (UKF) processes Gaussian noise through Sigma points, and the particle filter (PF) uses particle sampling to capture nonlinear characteristics. After the filter is updated, the model probability is updated based on the likelihood value, and ACW and short-term error feedback mechanisms are introduced in state fusion to better adapt to the nonlinear dynamics and multi-sensor fusion requirements of high-speed train positioning.

6. The BeiDou satellite-based high-speed train multi-information fusion positioning method according to claim 5, characterized in that: The model interaction includes the following steps: Using the model probability and estimation results of the previous moment k−1, the initial state and covariance of each filter at the current moment k are generated as the starting point of the filter update. The mixing probability is: （7） in, The model at the previous moment probability; is the conditional probability, indicating that arrive The mixture weights of the model Represents the target model at the current moment, is the unscented Kalman filter UKF, For particle filter PF, model represents the model at the previous moment, is the unscented Kalman filter UKF, It is particle filter PF; is the element of Markov transition probability matrix; Mixed state: For the unscented Kalman filter UKF, the mixed state is calculated by linearly weighted averaging the estimated states of UKF and PF at the previous moment. Defined as: （8） For particle filter PF, the mixed state is the mean of the new particle set: （9） in, is the number of particles; For each model Calculate the mixed covariance and compensate for the differences between models through weighted covariance to avoid state jumps during switching: （10） in, The model at the previous moment The posterior covariance of The model at the previous moment The posterior state estimate of ; For the model Estimation of the mixed state.

7. The BeiDou satellite-based high-speed train multi-information fusion positioning method according to claim 6, characterized in that: Filter update, dynamic fusion runs two filters, updates state estimates and covariances, and generates likelihood values ​​at the same time: UKF update: Generate Sigma points through the state transfer equation to capture the nonlinear characteristics of the state distribution and use the measurement function to propagate , we get the predicted observation mean and covariance: （11） （12） in, is the state vector dimension, ; Calculate Kalman gain , and finally calculate the system status update: （13） （14） PF Update: Get Hybrid Particle Sets from Model Interaction Layer , each particle has an initial weight, and the train state model is used for each particle to generate a new set of particles: （15） in, ; Measurement updates calculate the observation prediction for each particle using the observation equation , weights are updated and normalized to concentrate particles in the high probability area of ​​the state space: （16） （17） in, It reflects the degree of match between each particle and the actual observation. Particles with small errors receive higher weights, while particles with large errors have weights approaching zero. Final estimate is the particle weighted average, covariance Reflecting uncertainty in estimates: （18） （19）。 8. The BeiDou satellite-based high-speed train multi-information fusion positioning method according to claim 7, characterized in that: Calculate the model likelihood of UKF and PF respectively, UKF likelihood Based on the Gaussian distribution of predicted observations, the PF likelihood Based on the particle weighted likelihood sum: （20） （21） Likelihood is used to reflect the degree of match between the trajectory estimated by the filter and the actual sensor observation. The higher the value, the more consistent the model is with the data, and the probability The higher; According to the likelihood value and mixing probability of the filter, the model probability at the current moment is updated to achieve switching: （22）。

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