A kalman filtering multi-path measurement time difference fusion method and device

Abstract

The application discloses a Kalman filtering multi-path measurement time difference fusion method, comprising the following steps: acquiring historical data of multi-path measurement time difference and obtaining a series of historical mean values; monitoring multi-path measurement time difference input, determining as interruption when determining observation value missing or invalid for any one path based on the historical mean values, performing interruption compensation, and dynamically adjusting process noise covariance according to interruption duration; dynamically allocating weights based on historical data; fusing multi-path time difference data through Kalman filtering and outputting smoothed time difference measurement results. Through interruption compensation strategy (virtual observation, weight adjustment) and sliding window smoothing, even if single-path or multi-path input is interrupted, continuous fusion measurement time difference can still be output; the dynamic weight allocation mechanism fully utilizes the statistical correlation of multi-path time difference, and dynamically adjusts the weight according to real-time reliability; the process noise covariance Q is dynamically updated to adapt to the time-varying noise environment, and adaptive noise processing is realized.

Description

Technical Field

[0001] This invention relates to the field of Kalman filtering technology, and in particular to a method and apparatus for fusing multiple metering time differences using Kalman filtering. Background Technology

[0002] In satellite time synchronization monitoring, simultaneously collecting and fusing multiple time difference measurement data of the same type is crucial for improving the accuracy of time difference monitoring. Current technologies typically use simple weighted averaging or median filtering to fuse multiple time difference measurement data, but these methods suffer from the following core problems:

[0003] The method is highly sensitive to interruptions. When the single or multiple metering time difference inputs are interrupted, the traditional method cannot maintain continuous output. The fixed weight allocation strategy cannot be adaptively adjusted when the input is interrupted, which leads to outliers (such as the instantaneous noise of the remaining channels) having an amplified impact on the fusion result. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a Kalman filter multi-channel metering time difference fusion method and device. The method can adaptively handle metering time difference interruptions and utilize redundant information to improve fusion robustness, thereby ensuring continuous, stable and high-precision single time difference metering data output in various scenarios.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] In a first aspect, this application discloses a Kalman filter-based multi-channel measurement time difference fusion method, comprising: acquiring historical data of multi-channel measurement time differences and obtaining a series of historical averages; monitoring the multi-channel measurement time difference inputs, determining an interruption based on the historical averages when any channel has missing or invalid observations, generating virtual observations for the interrupted channel and reducing its fusion weight, and dynamically adjusting the process noise covariance according to the interruption duration; calculating and assigning a first dynamic weight based on the historical data in the case of an interruption, otherwise assigning a second dynamic weight; fusing the multi-channel time difference data through Kalman filtering and outputting a smoothed time difference measurement result.

[0007] Furthermore, the historical data includes the mean time difference, historical interruption frequency, historical observation mean, and historical observation noise standard deviation; where μ i Let σ be the historical observation mean of the i-th path. i Z represents the historical observation noise standard deviation of the i-th channel; Z is continuously obtained as the real-time observation value of the measurement time difference of N channels. 1,k Z 2,k ... Z N,k If |Z i,k -μ i |≤3σ iIf the result is 0, it indicates that the real-time observation of the i-th path at the current time k is a valid observation that has not been interrupted; otherwise, it is an interruption.

[0008] Furthermore, the step of generating virtual observations for the interrupted path and reducing their fusion weights includes: using the smoothed value from the previous time step. As a virtual observation, the weights of the previous time step are reduced by 50% and used as virtual weights.

[0009] Furthermore, the dynamic adjustment of the process noise covariance based on the interruption duration includes: if there are 3 consecutive interruptions, increasing the process noise covariance Q by Q. drift ; where Q drift This represents the process noise covariance drift coefficient.

[0010] Furthermore, when the interrupted circuit resumes outputting a valid measurement time difference, it is considered an interruption recovery, and the process noise covariance Q is reduced by Q. drift Q = QQ drift .

[0011] Furthermore, the step of calculating and allocating a first dynamic weight based on the historical data in the event of an interruption, and otherwise allocating a second dynamic weight, includes: when an interruption occurs, the observation result is valid. i =0; otherwise, the observation is valid. i =1; In case of interruption, assign the first dynamic weight:

[0012] ω i，k-1 The weight is the same as the weight from the previous time step; if no error is detected or the system recovers after an interruption, a second dynamic weight is assigned.

[0013] Where, α i τ is the reliability coefficient. k-1 This is the estimated value of the fusion state at the previous moment.

[0014] Furthermore, the weights are normalized to normalize the sum of the weights of the effective time difference input paths to 1:

[0015] In the formula, ω c，k The time difference weight is used to measure the time difference at time k for the c-th path.

[0016] Furthermore, the Kalman filter fusion of multiple time difference data includes:

[0017] In the prediction phase, based on the state estimate τ from the previous time step... k-1 covariance P at the previous moment k-1 Predict the current state; during the update phase, dynamically adjust the fused observation value Z based on the effective observations. k and observation covariance Rk Corrected state estimation τ k Covariance P k .

[0018] Furthermore, the smoothed time difference measurement result includes: state filtering, in order to suppress high-frequency noise, the Kalman filter result is subjected to sliding window filtering to obtain the state smooth value.

[0019] Secondly, this application also discloses a Kalman filter multi-channel metering time difference fusion device, comprising: a storage device storing a computer program that implements the Kalman filter multi-channel metering time difference fusion method according to any one of claims 1-9; and a processor that performs read and write operations on the storage device to execute the computer program stored therein.

[0020] The beneficial effects of the present invention include at least the following:

[0021] By employing interruption compensation strategies (virtual observation, weight adjustment) and sliding window smoothing, continuous fused measurement time difference can still be output even if single or multiple inputs are interrupted, thus maintaining a continuous and stable time difference output when single or multiple measurement time difference inputs are interrupted.

[0022] The dynamic weight allocation mechanism makes full use of the statistical correlation of multiple time differences. The weight of the interrupted path is dynamically adjusted according to the real-time reliability, which significantly improves the error compared with the traditional averaging method. Its effect has been verified by simulation method, thereby ensuring the efficient use of redundant information.

[0023] The process noise covariance Q is dynamically updated to adapt to the time-varying noise environment and achieve adaptive noise processing. Attached Figure Description

[0024] Figure 1 This is a schematic flowchart of a multi-channel metering time difference fusion method based on some embodiments of this application using Kalman filtering;

[0025] Figure 2 This is a schematic diagram illustrating the interruption determination and relay compensation process according to some embodiments of this application;

[0026] Figure 3 This is a schematic diagram of the Kalman filtering process according to some embodiments of this application. Detailed Implementation

[0027] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] See Figures 1-3 This invention provides a method and apparatus for fusion of multi-channel metering time difference using Kalman filtering.

[0029] A Kalman filter-based multi-channel metering time difference fusion method according to an embodiment of this application includes:

[0030] Acquire historical data on multi-channel metering time differences and obtain a series of historical averages;

[0031] The system monitors multiple metering time difference inputs and determines an interruption when any input is missing or invalid based on the historical average. For example, a validity judgment benchmark can be constructed based on the historical average; when a real-time observation is missing or deviates from the historical average by more than a preset range, it is determined to be an interruption. Virtual observations are generated for the interrupted inputs, and their fusion weights are reduced. The process noise covariance is dynamically adjusted according to the interruption duration. This ensures that the system maintains a continuous data stream even if single or multiple inputs are interrupted. Correspondingly, increasing the noise covariance during prolonged interruption reflects increased model uncertainty, while decreasing the noise covariance during interruption recovery enables adaptive tracking of the noise environment.

[0032] Based on the historical data, a first dynamic weight is calculated and assigned in the event of an interruption. For example, the weight can be reduced by combining the historical reliability coefficient. Otherwise, a second dynamic weight is assigned. For example, the weight is determined by combining the historical reliability coefficient, real-time observation bias, and observation noise variance. Finally, normalization is performed so that the sum of the effective path weights is always 1, ensuring efficient use of redundant information.

[0033] Multiple time difference data are fused using Kalman filtering, and a smoothed time difference measurement result is output to ensure output continuity and robust fusion.

[0034] refer to Figure 1 Understanding that obtaining the initial state estimate τ0 is necessary when executing the method, this embodiment uses N metered time differences collected from multiple time difference metering devices, Z. 1，t Z 2，t …, Z N,t Then, the average time difference of the N paths over the first 30 cycles is used as the initial value τ0 for state estimation:

[0035]

[0036] Using the initial state estimate τ0, the smoothed state estimate value is calculated.

[0037] Similarly, the historical observation average is obtained by averaging the time differences of various measurement methods over the previous 30 periods:

[0038] A series of historical observation mean values ​​μ1, μ2, ..., μ were obtained. N Then, the standard deviation of historical observation noise is obtained by calculating the standard deviation of the measurement time difference for each path over the previous 30 cycles:

[0039] The corresponding historical observation noise standard deviations σ1, σ2, ..., σ are obtained. N .

[0040] The interruption frequency of the previous 30 cycles was used to calibrate the historical interruption frequency and obtain a series of reliability coefficients α1, α2, ..., α3. N The lower the interrupt frequency α i The larger the value, the higher the percentage of uninterrupted time difference in historical statistics; for example, if the i-path experiences 6 interruptions in the first 30 cycles, α... i It is 0.8.

[0041] Based on the various initial values ​​obtained from the above steps, the following embodiments are carried out.

[0042] For example, each time difference metering device (i.e., each channel) independently detects whether an interruption has occurred. The interruption determination process includes: continuously acquiring real-time observations Z of multiple metering time differences. 1,k Z 2,k ... Z N ,k. In subsequent examples, the weight ω i Initially α i Covariance P0 = 1.0 ns 2 Process noise covariance Q = 10 -4 ns 2 Process noise covariance drift Q drift =10 -8 ns 2 .

[0043] For details, please refer to [link / reference]. Figure 2 To understand, taking the i-th path as an example, if Z i,k If it exists, the data link is normal and the observation has been received (indicating no hardware interruption); furthermore, if |Z| is satisfied simultaneously... i,k -μ i |≤3σ i If the result is true, it indicates that the real-time observation of the i-th path at the current time k is a valid observation, and there is no interruption at either the software or hardware level; otherwise, it is considered an interruption.

[0044] Next, we will explain in detail the two cases: the observation is considered a valid observation, and the observation value is considered an interruption.

[0045] The observation is a valid observation, i.e., it satisfies |Z i,k -μ i |≤3σ iIn this case, the observation results are valid. i =1, number of consecutive interruptions in observation lost i =0; otherwise, the observation is valid. i =0, the number of consecutive observation interruptions is represented as ++lost i Of course, in different pathways, valid observation results are recorded as valid0, valid1, ..., valid N The initial values ​​are all 1, and the number of consecutive observation terminals is recorded as lost0, lost1, ..., lost N And initially all of them are 0. In the diagram, the valid condition is determined. i == 0 indicates that the channel was valid at the previous moment. If the channel was invalid at the previous moment, the noise covariance of the channel needs to be updated to become valid.

[0046] Continuing with the example of the i-th path, when an interrupt occurs, there are two possible scenarios: interruption persists or interruption resumes. See below for further details. Figure 2 understand.

[0047] Interrupt compensation is performed while the interruption persists, using the smoothed value from the previous moment. As virtual observations, the weights of the previous time step are reduced by 50% and used as virtual weights. If there is a continuous interruption for 3 cycles, the process noise covariance Q is increased by Q. drift This reflects the increased uncertainty in the model, as shown in the following formula:

[0048]

[0049] Q = Q + Q dr i ft (lost i =3)

[0050] In the formula, For the virtual observation value at time k on path i, Let ω be the virtual weight at time k in the i-th path when it is not normalized. i,k-1 Let be the normalized weights at time k-1 on path i.

[0051] Therefore, when an interruption is detected in a certain path, the system will use the state smoothing value of the previous moment as the virtual observation value of that path to fill it in, and immediately reduce the fusion weight of that path (e.g., reduce it by 50%), thereby effectively preventing the impact of missing data or outliers on the multi-channel fusion output; if the interruption continues, the system will further dynamically increase the process noise covariance corresponding to that path, characterizing the increase in model uncertainty, making the filter more dependent on the predicted value and other valid path data.

[0052] When the interrupted circuit resumes outputting a valid metering time difference, it is considered an interruption recovery, and the process noise covariance Q is reduced by Q. drift :

[0053] Q = QQ drift .

[0054] In some embodiments, the aforementioned weights are dynamically adjusted; specifically, the weight ω at time k. i,k The following will be explained separately for cases where an interruption is detected, and cases where no interruption is detected or cases where the interruption is recovered.

[0055] In case of interruption:

[0056]

[0057] If not detected or resumed after interruption:

[0058]

[0059] Therefore, compared to existing technologies where multi-path time difference data exhibits noise correlation during normal operation, such as synchronization fluctuations caused by environmental multipath effects, but this characteristic is not effectively utilized to suppress errors, this embodiment addresses this issue by employing a dynamic weight allocation mechanism. When calculating the weight of each path, it not only considers its historical reliability coefficient (calibrated by the interruption frequency) but also incorporates in real-time the deviation between the current observation value and the system fusion state estimate, as well as the observation noise variance of that path. This allows the weights to dynamically reflect the real-time quality and reliability of each path's data. Specifically, when some paths are interrupted, the system automatically reduces their weights and more rationally allocates weights to the remaining valid paths.

[0060] Then, the weights are normalized to normalize the sum of the weights of the effective metering time difference input paths to 1:

[0061] In the formula, ω c,k Measure the time difference weight for the c-th path at time k.

[0062] Specifically, the weight ω i,k The time difference weight is measured at time k on the i-th path.

[0063] Furthermore, adaptive Kalman filtering is performed based on the above embodiments, referring to... Figure 3 As shown, the specific steps include the following:

[0064] S1, Prediction Phase:

[0065] Based on the state estimate τ from the previous moment k-1 covariance P at the previous moment k-1 Predict the current state:

[0066] τ k|k-1 =τ k-1 +Δτ drift

[0067] P k|k-1 =P k-1 +Q

[0068] In the formula, Δτ drift This is the low-frequency drift term for measuring time difference. If the system is a linear dynamic system, the drift is usually determined by the state transition equation. Here, it is assumed to be 0, τ. k|k-1 For state estimation and prediction, P k|k-1 For covariance prediction.

[0069] S2, Update Phase:

[0070] The fused observation value Z is dynamically adjusted based on the effective observations. k and observation covariance R k Corrected state estimation τ k Covariance P k :

[0071]

[0072] Where, τ k|k For state estimation updates, P k|k For covariance updates, K k For Kalman gain, P k|k-1 τ k|k-1 For covariance prediction.

[0073] S3, State Filtering:

[0074] To suppress high-frequency noise, a sliding window filter is applied to the Kalman filter results to obtain smoothed state values:

[0075]

[0076] In the formula, τ k-2|k-2 For the state estimation at time k-2, τ k-1|k-1 For the state estimate at time k-1, τ k|k This is the state estimate at time k (the current time).

[0077] In this way, the sliding window smoothing process applied to the final Kalman filter output ensures the continuity of the output signal and overcomes the fatal flaw of traditional methods where interruption leads to failure.

[0078] Therefore, this application embodiment utilizes the statistical correlation of multiple time difference measurement data to dynamically allocate fusion weights. The weights of interrupted paths are dynamically adjusted (reduced weights) and process noise covariance based on the missing duration. Combined with prediction smoothing and online noise estimation, this ensures continuous and stable fusion output of multiple time difference measurement data in interrupted scenarios.

[0079] A Kalman filter-based multi-channel metering time difference fusion device according to an embodiment of this application includes a memory and a processor, which can be implemented based on any computer device. The memory stores a computer program that implements the Kalman filter-based multi-channel metering time difference fusion method described in the above embodiment; the processor performs read and write operations on the memory to execute the stored computer program, thereby implementing the above method.

[0080] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A Kalman filter-based multi-channel metering time difference fusion method, characterized in that, include: Historical data on multi-channel metering time differences are acquired, and a series of historical averages are obtained; the historical data includes the average time difference, historical interruption frequency, historical observation average, and historical observation noise standard deviation; wherein, Let be the historical observation mean of the i-th path. Let be the standard deviation of the historical observation noise of the i-th path; Multiple metering time difference inputs are monitored to continuously obtain N real-time metering time difference observations. , ... If any path is determined to be missing or invalid based on the historical average, it is considered an interruption. Virtual observations are generated for the interrupted path, and its fusion weight is reduced: the smoothed value from the previous time step is used. As virtual observations, the weights of the previous time step are reduced by 50% and used as virtual weights. The process noise covariance is dynamically adjusted according to the duration of the interruption: if there are 3 consecutive interruptions, the process noise covariance is adjusted accordingly. Increase ;in, This refers to the process noise covariance drift coefficient; Based on the historical data, a first dynamic weight is calculated and assigned in the event of an interruption; otherwise, a second dynamic weight is assigned. When an interruption occurs, the observed results... Otherwise, the observation results In the event of an interruption, assign the first dynamic weight: hour, ;in, , The weights are from the previous time step, where the subscript i indicates the i-th path and the superscript virtual indicates a virtual value. The virtual weights at time k on the i-th path; In the event that no detection is detected or the system recovers after an interruption, a second dynamic weight is assigned: hour, ;in, For reliability coefficient, This is the estimated fusion state value from the previous moment. This represents the real-time observation value of the time difference for the i-th metering channel; The Kalman filter is used to fuse multiple time difference data and output a smoothed time difference measurement result.

2. The Kalman filter multi-channel metering time difference fusion method according to claim 1, characterized in that: If satisfied If the result is positive, it indicates that the real-time observation of the i-th path at the current time k is a valid observation that has not been interrupted; otherwise, it is an interruption.

3. The Kalman filter multi-channel metering time difference fusion method according to claim 1, characterized in that: When the interrupted circuit resumes outputting a valid measurement time difference, it is considered an interruption recovery, and the process noise covariance is then... reduce : 。 4. The Kalman filter multi-channel metering time difference fusion method according to claim 1, characterized in that, The weights are normalized to ensure that the sum of the weights of the effective time difference input paths is normalized to 1: In the formula, The time difference weight is used to measure the time difference at time k for the c-th path.

5. The Kalman filter multi-channel metering time difference fusion method according to claim 1, characterized in that, The Kalman filter fusion of multiple time difference data includes: In the prediction phase, based on the state estimate from the previous time step... covariance with the previous moment Predict the current state; During the update phase, the fused observations are dynamically adjusted based on the effective observations. and observation covariance Corrected state estimation Covariance .

6. The Kalman filter multi-channel metering time difference fusion method according to claim 5, characterized in that, The smoothed time difference measurement results include: State filtering involves applying a sliding window filter to the Kalman filter result to suppress high-frequency noise, resulting in a smoothed state value.

7. A Kalman filter-based multi-channel metering time difference fusion device, characterized in that, include: The storage device stores a computer program that implements the Kalman filter multi-channel metering time difference fusion method according to any one of claims 1-6; A processor that performs read and write operations on the memory to execute computer programs stored therein.

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