Fractional order Kalman filtering method and system based on GIS bus colored noise distribution
By employing the fractional-order Kalman filtering method, the estimation accuracy problem of electric field signals in GIS busbars under colored noise environments was solved, achieving high-precision electric field distribution estimation and fault early warning, adapting to complex noise environments, and improving the safety and stability of power systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-27
- Publication Date
- 2026-03-27
AI Technical Summary
Existing filtering methods have low estimation accuracy in the presence of colored noise in the electric field signal of GIS bus, and are difficult to adapt to time-varying noise, resulting in increased state estimation bias and filter divergence.
A fractional-order Kalman filter method based on the colored noise distribution of GIS bus is adopted. By establishing a continuous-time linear fractional-order system, the characteristics of colored noise are analyzed. The Tustin generating function method is used for discretization. The augmented state vector and augmented system equations are constructed by the augmented vector method. A fractional-order Kalman filter is designed for dynamic gain adjustment to eliminate colored noise interference.
It significantly improves the accuracy and robustness of electric field distribution estimation, can adapt to time-varying noise environments, suppresses colored noise interference, provides high-quality data support, and supports the safe operation and fault early warning of power systems.
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Figure CN121749949A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of signal processing and filtering, in particular to a fractional order Kalman filtering method and system based on GIS bus colored noise distribution. BACKGROUND
[0002] The gas insulated switchgear (GIS) bus is a key component in the power system, and its operating state directly affects the safety and stability of the power grid. In the process of GIS bus electric field monitoring, the electric field signals collected by the sensor are easily disturbed by various complex noises. These noises include not only the thermal noise of the sensor itself, but also the noise generated by environmental electromagnetic interference, equipment mechanical vibration, partial discharge and switch operation. Such noise has time correlation, showing colored noise characteristics, and its statistical characteristics are non-uniformly distributed in the frequency domain, which is significantly different from the independent characteristics of traditional white noise.
[0003] Currently, in the field of signal filtering and state estimation, Kalman filtering and its improved algorithms are widely used. However, the traditional Kalman filtering method is based on the assumption that the noise is white noise, that is, the noise is independent between different times. In the actual GIS bus monitoring environment, the noise often has memory effect and time correlation, belonging to the category of colored noise. At this time, if the traditional filtering method is continued to be used, it is easy to cause the state estimation deviation to increase, the convergence speed to slow down, and even the filter to diverge in the scene with strong noise.
[0004] In addition, the existing filtering methods are mostly based on integer order system models, which are difficult to accurately describe the fractional order characteristics existing in the dynamic change process of GIS bus electric field, such as non-locality and memory effect, thereby causing model mismatch and further affecting the estimation accuracy. Especially under complex operating conditions such as high voltage and strong electromagnetic interference, the traditional method lacks the ability of adaptive adjustment to the statistical characteristics of noise, and it is difficult to adapt to the time-varying noise environment.
[0005] Therefore, in view of the colored noise distribution problem existing in the GIS bus electric field signal, it is necessary to propose a method to improve the accuracy of electric field distribution estimation and the robustness of the system, so as to meet the actual needs of high-precision monitoring and fault warning of the power system. SUMMARY
[0006] The technical problem to be solved by the present application is how to improve the estimation accuracy of the GIS bus electric field signal in the strong colored noise environment by using the existing filtering technology.
[0007] The present application solves the above technical problems by the following technical means: a fractional order Kalman filtering method based on GIS bus colored noise distribution, comprising: S1. Establish the state equation and output equation of the continuous-time linear fractional-order system, and perform colored noise characteristic analysis on the process noise and measurement noise; S2. The continuous-time fractional-order system is discretized using the Tustin generating function method. S3. Construct the augmented state vector and augmented system equations using the augmented vector method; S4. Design a fractional-order Kalman filter to dynamically adjust the gain of noise autocorrelation. S5. The fractional-order Kalman filter described above is used to filter the real-time acquired GIS bus electric field data to eliminate colored noise interference.
[0008] This invention establishes the state and output equations of a continuous-time linear fractional-order system, specifically analyzing the colored characteristics of process and measurement noise, thus overcoming the limitations of the traditional "white noise" assumption. Combined with the Tustin generating function method for discretization, it accurately approximates the dynamics of the fractional-order operator, reducing model errors and providing a more realistic system foundation for subsequent filtering. The augmented vector method is used to construct augmented state and system equations, incorporating the statistical characteristics of colored noise into the estimation framework. This enables synchronous tracking of the correlation between system state and noise, avoiding direct interference from noise with the state estimation results and significantly enhancing estimation stability. The designed fractional-order Kalman filter can dynamically adjust its gain to match the time-varying correlation of colored noise in real time. Compared to traditional fixed-gain methods, it exhibits stronger robustness to non-stationary and correlated noise, significantly improving filtering accuracy and convergence speed. When applied to real-time filtering of GIS bus electric fields, it effectively suppresses colored noise caused by electromagnetic coupling, improves the data signal-to-noise ratio, and provides high-quality data support for equipment condition assessment, insulation defect identification, and fault early warning, contributing to the safe operation of power systems.
[0009] Furthermore, the continuous-time linear fractional system is specifically as follows: A continuous-time linear fractional-order system is established, and its state-space model is as follows:
[0010] in, Here is the state transition matrix. To control the input matrix, For the observation matrix, For differential operators, For continuous time variables, For fractional order, It is the system state vector. It is a control input. It's process noise. It measures noise.
[0011] Furthermore, the colored noise characteristic analysis of process noise and measurement noise specifically involves: The statistical properties are described by a given covariance relation, and their calculation formula is as follows:
[0012] in, E [ ] represents the cross-covariance matrix of process noise and measurement noise. As a noise source, To measure the noise source, For discrete-time variables, For a specific moment in discrete time, For discrete impulse functions, Let be the cross-covariance matrix of the process noise source and the measurement noise source.
[0013] Further, step S3 includes: Define augmented state vector and augmented noise vector :
[0014] in, The transition matrix of the augmented system; The covariance matrix of the augmented noise is ,and ; in, This represents actual process noise. Let be the covariance matrix of the process noise sources. To measure the covariance matrix of the noise source; Augmented state equation:
[0015] in, A counter for traversing historical information during the calculation process, starting from 1 or 0 and continuing until... , for The state vector of the augmented system at time t. In order to be in The control input vector at time t, for The augmented noise vector at time step 1. To augment the state transition matrix of the system, To augment the control input matrix of the system, The noise input matrix of the augmented system; The corresponding augmented output equation becomes: ,in, , It is an identity matrix.
[0016] Further, step S4 includes: S4.1 State Prediction
[0017] in, In order to be in The optimal state estimate of the augmented state vector at time t; Using the deadline All information at any given moment, for Predict the augmented state at any given time; S4.2 Covariance Prediction The calculation formula is:
[0018] in, for Error covariance matrix of state estimation at time step. Let be the noise input matrix of the augmented system at time 1. The noise input matrix of the augmented system at time 0; S4.3 Kalman Gain Calculation according to The optimal Kalman gain is calculated, and the filter dynamically adjusts this gain based on the autocorrelation of the noise. S4.4, State Update
[0019] Using the observations at the current time Correct the state prediction to obtain the optimal state estimate for the current time step. ; S4.5, Covariance Update .
[0020] This invention also provides a fractional-order Kalman filter system based on the colored noise distribution of GIS buses, comprising: The system modeling module is used to establish the state equations and output equations of a continuous-time linear fractional-order system, and to perform colored noise characteristic analysis on process noise and measurement noise. The discretization module is used to discretize the continuous-time fractional-order system using the Tustin generating function method. The augmented system construction module is used to construct augmented state vectors and augmented system equations using the augmented vector method. The dynamic gain adjustment module is used to design the dynamic gain adjustment of the fractional-order Kalman filter to the noise autocorrelation. The real-time filtering module is used to filter the real-time acquired GIS bus electric field data using the fractional-order Kalman filter to eliminate colored noise interference.
[0021] Furthermore, the continuous-time linear fractional system is specifically as follows: A continuous-time linear fractional-order system is established, and its state-space model is as follows:
[0022] in, Here is the state transition matrix. To control the input matrix, For the observation matrix, For differential operators, For continuous time variables, For fractional order, It is the system state vector. It is a control input. It's process noise. It measures noise.
[0023] Furthermore, the colored noise characteristic analysis of process noise and measurement noise specifically involves: The statistical properties are described by a given covariance relation, and their calculation formula is as follows:
[0024] in, E [ ] represents the cross-covariance matrix of process noise and measurement noise. As a noise source, To measure the noise source, For discrete-time variables, For a specific moment in discrete time, For discrete impulse functions, Let be the cross-covariance matrix of the process noise source and the measurement noise source.
[0025] Furthermore, the augmentation system construction module includes: Define augmented state vector and augmented noise vector :
[0026] in, The transition matrix of the augmented system; The covariance matrix of the augmented noise is ,and ; in, This represents actual process noise. Let be the covariance matrix of the process noise sources. To measure the covariance matrix of the noise source; Augmented state equation:
[0027] in, A counter for traversing historical information during the calculation process, starting from 1 or 0 and continuing until... , for The state vector of the augmented system at time t. In order to be in The control input vector at time t, for The augmented noise vector at time step 1. To augment the state transition matrix of the system, To augment the control input matrix of the system, The noise input matrix of the augmented system; The corresponding augmented output equation becomes: ,in, , It is an identity matrix.
[0028] Furthermore, the dynamic gain adjustment module includes: State prediction
[0029] in, In order to be in The optimal state estimate of the augmented state vector at time t; Using the deadline All information at any given moment, for Predict the augmented state at any given time; Covariance prediction The calculation formula is:
[0030] in, for Error covariance matrix of state estimation at time step. Let be the noise input matrix of the augmented system at time 1. The noise input matrix of the augmented system at time 0; Kalman gain calculation according to The optimal Kalman gain is calculated, and the filter dynamically adjusts this gain based on the autocorrelation of the noise. Status update
[0031] Using the observations at the current time Correct the state prediction to obtain the optimal state estimate for the current time step. ; Covariance Update .
[0032] The advantages of this invention are: (1) Improved model accuracy: The use of fractional-order system models can more accurately describe the dynamic characteristics of actual physical systems and reduce model mismatch errors.
[0033] (2) Enhanced noise processing capability: By modeling colored noise and constructing augmented systems, the limitations of traditional methods in processing related noise are effectively solved.
[0034] (3) Strong adaptive capability: The system has the function of adaptive parameter adjustment, which can adapt to time-varying noise environment and dynamic changes of the system.
[0035] (4) Good engineering practicality: The algorithm has moderate computational complexity, meets the requirements of real-time processing, and is easy to implement and promote in engineering.
[0036] (5) Stability assurance: Through rigorous stability analysis and numerical calculation methods, the stability of the filtering process under various working conditions is ensured. Attached Figure Description
[0037] Figure 1 This is a flowchart of the fractional-order Kalman filtering method based on the colored noise distribution of GIS bus in Embodiment 1 of the present invention; Figure 2 This is a global signal comparison diagram of Embodiment 1 of the present invention; Figure 3 These are partial detail comparison images of Embodiment 1 of the present invention; Figure 4 This is an error comparison chart of Embodiment 1 of the present invention; Figure 5 This is a comparison chart of performance indicators for Embodiment 1 of the present invention. Detailed Implementation
[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, 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.
[0039] Example 1 like Figure 1This is a flowchart of a fractional-order Kalman filter method based on the colored noise distribution of GIS buses. The fractional-order Kalman filter method based on the colored noise distribution of GIS buses includes: S1. Establish the state equation and output equation of the continuous-time linear fractional-order system, and perform colored noise characteristic analysis on the process noise and measurement noise.
[0040] Specifically, S1.1, modeling of fractional-order systems. A continuous-time linear fractional-order system is established, and its state-space model is as follows:
[0041] in, The state transition matrix describes the evolution of the system state over time. The control input matrix describes the effect of the control input on the state. The observation matrix describes the effect of the control input on the state. For differential operators, For continuous time variables, For fractional order, It is the system state vector. It is a control input. It's process noise. It measures noise.
[0042] S1.2, Colored Noise Modeling In real-world systems, the noise w(k) and v(k) (discrete sampled values) are not white noise, but rather time-dependent fractional-order colored noise, and there is a correlation between them. Their statistical properties are described by a given covariance relationship: This indicates a process noise source. With measurement noise source The same time is related, among which, E [ ] represents the cross-covariance matrix of process noise and measurement noise. As a noise source, To measure the noise source, For discrete-time variables, For a specific moment in discrete time, For discrete impulse functions, Let be the cross-covariance matrix of the process noise source and the measurement noise source.
[0043] S2. The continuous-time fractional-order system is discretized using the Tustin generating function method.
[0044] Specifically, this step transforms the continuous system into a discrete form suitable for computation, employing a fractional-order Kalman filter algorithm based on the Tustin generating function method to transform the continuous-time fractional-order differential operator. The transfer function is converted into a discrete-time transfer function, thus obtaining the discrete-time state equation of the system.
[0045] S3. Construct augmented state vectors and augmented system equations using the augmented vector method.
[0046] Building an augmentation system To transform the colored noise problem into a standard white noise filtering problem, an augmented state vector is defined. and augmented noise vector :
[0047] in, This is the transition matrix of the augmented system.
[0048] The covariance matrix of the augmented noise is ,and .
[0049] in, This represents actual process noise. Let be the covariance matrix of the process noise sources. To measure the covariance matrix of the noise source.
[0050] Augmented state equation:
[0051] in, A counter for traversing historical information during the calculation process, starting from 1 or 0 and continuing until... , for The state vector of the augmented system at time t. In order to be in The control input vector at time t, for The augmented noise vector at time step 1. To augment the system's state transition matrix, describing the system state from... Time's up The evolutionary pattern of time, The control input matrix of the augmented system represents the control input. Impact on the state The noise input matrix of the augmented system represents the noise. The impact on the state.
[0052] The corresponding augmented output equation becomes: ,in, , It is an identity matrix.
[0053] S4. Design a fractional-order Kalman filter to dynamically adjust the gain for noise autocorrelation.
[0054] Based on the augmented system described above, a fractional-order Kalman filter is designed. The filter recursively performs the following steps: S4.1 State Prediction
[0055] in, In order to be in The optimal state estimate of the augmented state vector at time t.
[0056] S4.2 Covariance Prediction The calculation formula is:
[0057] S4.3 Kalman Gain Calculation according to The optimal Kalman gain is calculated, and the filter dynamically adjusts this gain based on the autocorrelation of the noise, thereby optimizing the filtering effect.
[0058] S4.4, State Update
[0059] Using the observations at the current time Correct the state prediction to obtain the optimal state estimate for the current time step. .
[0060] S4.5, Covariance Update .
[0061] Update the error covariance matrix of the estimated state for recursive calculation in the next period.
[0062] S5. The fractional-order Kalman filter described above is used to filter the real-time acquired GIS bus electric field data to eliminate colored noise interference.
[0063] Specifically, the designed fractional-order Kalman filter is applied to the real-time acquired electric field data stream.
[0064] Data input: Real-time acquisition of electric field observation data .
[0065] Online filtering: The filter performs the five core steps in step S4 above in each sampling period.
[0066] Output: Output the optimal state estimate The middle corresponds to the original system state. The part that is filtered, noise-free, and more accurate electric field distribution estimate.
[0067] Experimental Test 1. Experimental Environment Preparation Stage 1.1 Experimental Environment Configuration Experimental verification was conducted using a numerical computing platform.
[0068] Set a fixed seed in the random number generator to ensure that the experimental results are reproducible.
[0069] Define a time vector with a duration of 2 seconds and a sampling frequency of 1000Hz, generating a total of 1000 data points.
[0070] 1.2 Parameter Preset Establish a discrete time series: 0 to 2 seconds, with uniform sampling.
[0071] Set the sampling frequency to 1000Hz.
[0072] Initialize the parameters and data structures of each filtering algorithm.
[0073] 2. Test Signal Construction Stage 2.1 Construction of Real Electric Field Signal Generate a composite electric field signal containing multiple physical features: 50Hz power frequency fundamental component: amplitude 1.2.
[0074] 150Hz third harmonic component: amplitude 0.8.
[0075] 250Hz fifth harmonic component: amplitude 0.5.
[0076] Transient pulse component: Gaussian pulses with amplitudes of 0.3 and 0.4 are added at 0.5 seconds and 1.2 seconds, respectively.
[0077] Gradually varying background field: 2Hz low-frequency modulated signal, amplitude 0.2.
[0078] 2.2 Colored Noise Structure Simulate complex noise environments in actual engineering projects: Low-frequency correlated noise: generated using a third-order autoregressive model to characterize environmental electromagnetic interference.
[0079] High-frequency correlated noise: generated using another set of third-order autoregressive models to simulate equipment operating noise.
[0080] Pulse noise: 20 pulse interferences are injected at random locations to simulate random electromagnetic shocks.
[0081] The three types of noise are superimposed according to preset weights to form a comprehensive colored noise.
[0082] 2.3 Construction of Observation Signals The real electric field signal is directly superimposed with colored noise.
[0083] Ensure the signal-to-noise ratio is at an extremely low level to simulate a harsh monitoring environment.
[0084] 3. Filtering Algorithm Implementation Phase 3.1 Implementation of Traditional Filtering Methods Mean filtering: Smoothing is performed using an 11-point sliding window.
[0085] Traditional Kalman filtering: simulated implementation based on a third-order low-pass filter.
[0086] Gaussian filtering: Weighted smoothing is performed using a custom Gaussian kernel function.
[0087] 3.2 Implementation of Fractional Kalman Filter Initialize the state vector and historical data storage structure.
[0088] Design an adaptive gain adjustment mechanism.
[0089] Implement a fractional-order memory effect module.
[0090] Construct a complete recursive computation framework.
[0091] 4. Performance Evaluation and Analysis Phase 4.1 Qualitative Visual Analysis Generate four independent comparison graphs: Global signal comparison chart: Shows the filtering effect of each method over the entire time range.
[0092] Comparison of local details: Zooming in on a specific time period highlights the ability to preserve details.
[0093] Error Comparison Chart: Plot the curve of estimation error changing over time.
[0094] Performance metrics comparison chart: The RMSE values of each method are displayed in the form of a bar chart.
[0095] 4.2 Quantitative Performance Evaluation Calculate the root mean square error index.
[0096] The methods are ranked by performance based on their error values.
[0097] Calculate the relative percentage improvement.
[0098] 4.3 Results Recording and Output Output detailed performance comparison results.
[0099] Record key performance indicators and observations.
[0100] Save the generated comparison graphs for analysis.
[0101] 5. Comparative Analysis of Filtering Methods 5.1 Global Signal Comparison Analysis like Figure 2 As shown, the fractional-order Kalman filter based on the colored noise distribution of GIS bus provided by this invention differs significantly from various traditional filtering methods in terms of global signal processing performance. The real electric field signal contains a 50Hz power frequency component, harmonic components, transient pulse components, and slowly varying background field components. The observed signal is heavily contaminated by colored noise, resulting in an extremely low signal-to-noise ratio.
[0102] Traditional mean filtering (orange dashed line) exhibits severe signal distortion and insufficient ability to capture transient pulse details, leading to loss of signal features. Traditional Kalman filtering (green dotted line), while possessing some noise reduction capability, has limited effectiveness in suppressing colored noise, leaving noticeable residual noise. Gaussian filtering (red dashed line) exhibits significant phase lag, resulting in a slow response to rapidly changing signals.
[0103] In contrast, the fractional-order Kalman filter (solid blue line) based on the colored noise distribution of GIS bus in this invention effectively suppresses various noise interferences while maintaining signal integrity. Especially in the 0.1-0.4 second time interval, this method captures transient pulses most accurately, and the signal waveform closely matches the real signal, demonstrating its superior performance in complex noise environments.
[0104] 5.2 Analysis of the ability to retain local details Figure 3 The effects of various filtering methods on the details of local time periods are shown. In the magnified view of 400-600 sample points (0.8-1.2 seconds), the limitations of traditional filtering methods become more apparent.
[0105] Mean filtering completely smooths out the rapid changes in a signal, leading to severe waveform distortion. While traditional Kalman filtering can track the basic trend of a signal, it exhibits significant estimation bias and response lag in the details. Gaussian filtering has the most pronounced delay effect, failing to respond promptly to rapid changes in the signal.
[0106] The method of this invention exhibits superior performance in local detail processing; the filtered signal almost completely overlaps with the real signal, accurately reproducing the subtle changes in the signal. This excellent detail preservation capability is of great value for fault diagnosis and condition assessment of power equipment.
[0107] 5.3 Analysis of Estimation Error Characteristics Figure 4 The results show how the estimation error of each method changes over time. The error curve of the traditional method fluctuates greatly and shows a significant spike at the moment of signal change, indicating that it is not adaptable to non-stationary signals.
[0108] Mean filtering has the largest error amplitude and exhibits systematic bias; traditional Kalman filtering shows drastic error fluctuations; Gaussian filtering has relatively stable errors, but the amplitude is still relatively high. In contrast, the method of this invention has the smallest error curve amplitude and the most stable fluctuations, maintaining a stable low error level throughout the entire time range.
[0109] This stable low-error characteristic demonstrates that the method of the present invention has excellent adaptive capability, and can dynamically adjust the filtering parameters according to the changes in noise statistical characteristics, ensuring that accurate estimation results can be obtained under different operating conditions.
[0110] 5.4 Comprehensive Performance Evaluation Figure 5 The methods were quantitatively evaluated using the root mean square error (RMSE) metric. Data shows that the method of this invention has the lowest RMSE value, improving upon traditional Kalman filtering by 30-40% and over 50% compared to mean filtering.
[0111] This performance improvement is of great significance in practical engineering applications: in GIS busbar electric field monitoring, the improved estimation accuracy directly translates into improved condition assessment accuracy, providing more reliable technical support for equipment fault early warning and operation and maintenance decisions. The technical advantages of this invention are particularly pronounced in applications requiring extremely high precision, such as high-voltage power equipment monitoring and precision electromagnetic measurement.
[0112] 6. Conclusion The comparative analysis across the four dimensions presented above fully demonstrates the significant advantages of the fractional-order Kalman filtering method described in this invention in processing electric field signals containing colored noise. This method not only effectively addresses the limitations of traditional filtering methods in handling correlated noise, but also achieves an optimal balance between noise suppression and detail preservation through fractional-order system modeling and adaptive parameter adjustment, providing a reliable technical solution for accurate measurements in complex electromagnetic environments.
[0113] Example 2 Based on Embodiment 1, Embodiment 2 also provides a fractional-order Kalman filter system based on the colored noise distribution of GIS bus, including: The system modeling module is used to establish the state equations and output equations of a continuous-time linear fractional-order system, and to perform colored noise characteristic analysis on process noise and measurement noise.
[0114] Specifically, a continuous-time linear fractional system is as follows: A continuous-time linear fractional-order system is established, and its state-space model is as follows:
[0115] in, Here is the state transition matrix. To control the input matrix, For the observation matrix, For differential operators, For continuous time variables, For fractional order, It is the system state vector. It is a control input. It's process noise. It measures noise.
[0116] The colored noise characteristics analysis of process noise and measurement noise is as follows: Statistical properties are described by a given covariance relation:
[0117] in, E [ ] represents the cross-covariance matrix of process noise and measurement noise. As a noise source, To measure the noise source, For discrete-time variables, For a specific moment in discrete time, For discrete impulse functions, Let be the cross-covariance matrix of the process noise source and the measurement noise source.
[0118] The discretization module is used to discretize the continuous-time fractional-order system using the Tustin generating function method.
[0119] The augmented system construction module is used to construct augmented state vectors and augmented system equations using the augmented vector method.
[0120] Specifically, the augmentation system building modules include: Define augmented state vector and augmented noise vector :
[0121] in, This is the transition matrix of the augmented system.
[0122] The covariance matrix of the augmented noise is ,and .
[0123] in, This represents actual process noise. Let be the covariance matrix of the process noise sources. To measure the covariance matrix of the noise source.
[0124] Augmented state equation:
[0125] in, A counter for traversing historical information during the calculation process, starting from 1 or 0 and continuing until... , for The state vector of the augmented system at time t. In order to be in The control input vector at time t, for The augmented noise vector at time step 1. To augment the state transition matrix of the system, To augment the control input matrix of the system, The noise input matrix of the augmented system.
[0126] The corresponding augmented output equation becomes: ,in, , It is an identity matrix.
[0127] The dynamic gain adjustment module is used to design the dynamic gain adjustment of the fractional-order Kalman filter to the noise autocorrelation.
[0128] The dynamic gain adjustment module includes: State prediction
[0129] in, In order to be in The optimal state estimate of the augmented state vector at time t.
[0130] Using the deadline All information at any given moment, for Predict the augmented state at any given time.
[0131] Covariance prediction The calculation formula is:
[0132] in, for Error covariance matrix of state estimation at time step. Let be the noise input matrix of the augmented system at time 1. The noise input matrix of the augmented system at time 0.
[0133] Kalman gain calculation according to The optimal Kalman gain is calculated, and the filter dynamically adjusts this gain based on the autocorrelation of the noise.
[0134] Status update
[0135] Using the observations at the current time Correct the state prediction to obtain the optimal state estimate for the current time step. .
[0136] Covariance Update .
[0137] The real-time filtering module is used to filter the real-time acquired GIS bus electric field data using the fractional-order Kalman filter to eliminate colored noise interference.
[0138] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A fractional-order Kalman filtering method based on the colored noise distribution of GIS busbars, characterized in that, include: S1. Establish the state equation and output equation of the continuous-time linear fractional-order system, and perform colored noise characteristic analysis on the process noise and measurement noise; S2. The continuous-time fractional-order system is discretized using the Tustin generating function method. S3. Construct the augmented state vector and augmented system equations using the augmented vector method; S4. Design a fractional-order Kalman filter to dynamically adjust the gain of noise autocorrelation. S5. The fractional-order Kalman filter described above is used to filter the real-time acquired GIS bus electric field data to eliminate colored noise interference.
2. The fractional-order Kalman filtering method based on the colored noise distribution of GIS bus according to claim 1, characterized in that, The continuous-time linear fractional system is specifically as follows: A continuous-time linear fractional-order system is established, and its state-space model is as follows: in, Here is the state transition matrix. To control the input matrix, For the observation matrix, For differential operators, For continuous time variables, For fractional order, It is the system state vector. It is a control input. It's process noise. It measures noise.
3. The fractional-order Kalman filtering method based on the colored noise distribution of GIS bus according to claim 1, characterized in that, The specific steps for performing colored noise characteristic analysis on process noise and measurement noise are as follows: The statistical properties are described by a given covariance relation, and their calculation formula is as follows: in, E [ ] represents the cross-covariance matrix of process noise and measurement noise. As a noise source, To measure the noise source, For discrete-time variables, For a specific moment in discrete time, For discrete impulse functions, Let be the cross-covariance matrix of the process noise source and the measurement noise source.
4. The fractional-order Kalman filtering method based on the colored noise distribution of GIS bus according to claim 1, characterized in that, Step S3 includes: Define augmented state vector and augmented noise vector : in, The transition matrix of the augmented system; The covariance matrix of the augmented noise is ,and ; in, This represents actual process noise. Let be the covariance matrix of the process noise sources. To measure the covariance matrix of the noise source; Augmented state equation: in, A counter for traversing historical information during the calculation process, starting from 1 or 0 and continuing until... , for The state vector of the augmented system at time t. In order to be in The control input vector at time t, for The augmented noise vector at time step 1. To augment the state transition matrix of the system, To augment the control input matrix of the system, The noise input matrix of the augmented system; The corresponding augmented output equation becomes: ,in, , It is an identity matrix.
5. The fractional-order Kalman filtering method based on the colored noise distribution of GIS bus according to claim 1, characterized in that, Step S4 includes: S4.1 State Prediction in, In order to be in The optimal state estimate of the augmented state vector at time t; Using the deadline All information at any given moment, for Predict the augmented state at any given time; S4.2 Covariance Prediction The calculation formula is: in, for Error covariance matrix of state estimation at time step. Let be the noise input matrix of the augmented system at time 1. The noise input matrix of the augmented system at time 0; S4.3 Kalman Gain Calculation according to The optimal Kalman gain is calculated, and the filter dynamically adjusts this gain based on the autocorrelation of the noise. S4.4, State Update Using the observations at the current time Correct the state prediction to obtain the optimal state estimate for the current time step. ; S4.5, Covariance Update 。 6. A fractional-order Kalman filter system based on the colored noise distribution of GIS busbars, characterized in that, include: The system modeling module is used to establish the state equations and output equations of a continuous-time linear fractional-order system, and to perform colored noise characteristic analysis on process noise and measurement noise. The discretization module is used to discretize the continuous-time fractional-order system using the Tustin generating function method. The augmented system construction module is used to construct augmented state vectors and augmented system equations using the augmented vector method. The dynamic gain adjustment module is used to design the dynamic gain adjustment of the fractional-order Kalman filter to the noise autocorrelation. The real-time filtering module is used to filter the real-time acquired GIS bus electric field data using the fractional-order Kalman filter to eliminate colored noise interference.
7. The fractional-order Kalman filter system based on the colored noise distribution of GIS bus according to claim 6, characterized in that, The continuous-time linear fractional system is specifically as follows: A continuous-time linear fractional-order system is established, and its state-space model is as follows: in, Here is the state transition matrix. To control the input matrix, For the observation matrix, For differential operators, For continuous time variables, For fractional order, It is the system state vector. It is a control input. It's process noise. It measures noise.
8. The fractional-order Kalman filter system based on the colored noise distribution of GIS bus according to claim 6, characterized in that, The specific steps for performing colored noise characteristic analysis on process noise and measurement noise are as follows: The statistical properties are described by a given covariance relation, and their calculation formula is as follows: in, E [ ] represents the cross-covariance matrix of process noise and measurement noise. As a noise source, To measure the noise source, For discrete-time variables, For a specific moment in discrete time, For discrete impulse functions, Let be the cross-covariance matrix of the process noise source and the measurement noise source.
9. The fractional-order Kalman filter system based on the colored noise distribution of GIS bus according to claim 6, characterized in that, The augmentation system construction module includes: Define augmented state vector and augmented noise vector : in, The transition matrix of the augmented system; The covariance matrix of the augmented noise is ,and ; in, This represents actual process noise. Let be the covariance matrix of the process noise sources. To measure the covariance matrix of the noise source; Augmented state equation: in, A counter for traversing historical information during the calculation process, starting from 1 or 0 and continuing until... , for The state vector of the augmented system at time t. In order to be in The control input vector at time t, for The augmented noise vector at time step 1. To augment the state transition matrix of the system, To augment the control input matrix of the system, The noise input matrix of the augmented system; The corresponding augmented output equation becomes: ,in, , It is an identity matrix.
10. The fractional-order Kalman filter system based on the colored noise distribution of GIS bus according to claim 6, characterized in that, The dynamic gain adjustment module includes: State prediction in, In order to be in The optimal state estimate of the augmented state vector at time t; Using the deadline All information at any given moment, for Predict the augmented state at any given time; Covariance prediction The calculation formula is: in, for Error covariance matrix of state estimation at time step. Let be the noise input matrix of the augmented system at time 1. The noise input matrix of the augmented system at time 0; Kalman gain calculation according to The optimal Kalman gain is calculated, and the filter dynamically adjusts this gain based on the autocorrelation of the noise. Status update Using the observations at the current time Correct the state prediction to obtain the optimal state estimate for the current time step. ; Covariance Update 。