Aircraft fuel quantity measurement self-adaptive filtering method, system and equipment based on multi-dimensional statistic dynamic adaptation and medium
By using an adaptive filtering method that dynamically adapts to multi-dimensional statistics, the accuracy problem of fuel quantity signals under complex operating conditions is solved, and efficient suppression of mixed noise is achieved, thereby improving the accuracy and signal-to-noise ratio of fuel quantity measurement.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-31
- Publication Date
- 2026-03-17
AI Technical Summary
Existing fuel quantity signal filtering methods are insufficient to meet measurement accuracy requirements under complex operating conditions and cannot effectively suppress mixed interference from fuel sloshing, random noise, and impulse noise.
An adaptive filtering method with dynamic adaptation of multi-dimensional statistics is adopted, including signal acquisition and preprocessing, multi-level filtering and data fusion. The filtering parameters are dynamically adjusted through coarse filtering, pulse detection and fine filtering stages. Combined with the mean, variance and kurtosis characteristics of the fuel quantity signal, the method can effectively suppress mixed noise.
It improves the accuracy of fuel quantity measurement, effectively suppresses low-frequency shaking, Gaussian noise and impulse noise under complex operating conditions, improves the signal-to-noise ratio and reduces filtering error.
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Figure CN121682016A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of airborne electronic measurement, and particularly relates to a kind of aircraft fuel oil measurement self-adapting filtering method, system, equipment and medium based on multi-dimension statistics dynamic adaptation. BACKGROUND
[0002] Aircraft fuel oil measurement is the core link of flight safety and range management, and its accuracy directly affects flight decision (such as endurance time estimation, fuel distribution strategy). Fuel oil signals are usually collected by capacitive, ultrasonic or pressure sensors, and converted into digital quantities after signal conditioning.
[0003] In actual working conditions, the oil signal is easily disturbed by the following factors, including: fuel sloshing noise: aircraft maneuvering (such as climbing, turning) causes the fuel to fluctuate violently in the tank, causing low-frequency periodic fluctuation noise; sensor random noise: Gaussian white noise caused by electronic component thermal noise, electromagnetic interference, etc.; impulse noise: occasional peak interference caused by transient contact failure of the sensor, transient line breakage, etc.; non-stationary characteristics: oil volume continuously decreases during fuel consumption, and presents time-varying characteristics after superimposing sloshing noise.
[0004] Existing fuel oil filtering methods mainly include: mean filtering: high-frequency noise is suppressed by sliding average, but the suppression effect on low-frequency sloshing noise is poor, and the oil volume may be lagged due to excessively large window; Kalman filtering: depends on fuel consumption model (such as engine fuel consumption rate) to predict oil volume, but model error (such as actual fuel consumption rate deviating from the nominal value) will cause filtering drift; median filtering: has certain suppression ability to impulse noise, but cannot distinguish between normal sloshing noise and abnormal impulse, and effective signals may be mistakenly filtered out.
[0005] Patent documents CN112306789A and CN109884567A both focus on a single noise type (such as only suppressing high-frequency noise or impulse noise), and do not comprehensively consider the mixed interference of fuel sloshing (low-frequency fluctuation), random noise (Gaussian), and impulse noise (occasional peak), which cannot meet the measurement accuracy requirements under complex working conditions. SUMMARY
[0006] The purpose of the present application is to provide a kind of aircraft fuel oil measurement self-adapting filtering method, system, equipment and medium based on multi-dimension statistics dynamic adaptation, to solve the problem that the existing fuel oil signal filtering method is difficult to meet the measurement accuracy requirements under complex working conditions.
[0007] The present application is realized by the following technical solutions: The aircraft fuel oil measurement self-adapting filtering method based on multi-dimension statistics dynamic adaptation includes the following steps: S01, signal acquisition and pretreatment; the fuel quantity digital signal output by the sensor is divided into continuous time blocks according to a fixed time window; S02, calculation of multi-dimensional statistics; including the mean, variance, and kurtosis of the current time block; S03, multi-stage filtering processing; including a coarse filtering stage, a pulse detection stage, and a fine filtering stage; in the coarse filtering stage, an initial window is set according to the historical maximum variance, and a sliding weighted average filter is used to output a coarse filtering signal; in the pulse detection stage, whether the current point is a pulse noise point is judged according to the residual error between the current time block and the coarse filtering signal; in the fine filtering stage, for non-pulse noise points, the fine filtering window and the weight are dynamically adjusted in combination with the variance and the kurtosis of the current time block; S04, data fusion and conversion; the original value of the data pulse point is retained, and the fine filtering result of the non-pulse point is combined to obtain a complete filtered signal.
[0008] In some embodiments of the present application, normalization processing is performed on each time block in step S01.
[0009] In some embodiments of the present application, the historical maximum variance in step S03 is the maximum value of the variances of the previous three time blocks.
[0010] In some embodiments of the present application, the step of outputting a coarse filtering signal by using a sliding weighted average filter includes: window division; for the nth point in the time block, the neighborhood window is [n-Wc+1, n+Wc-1]; weight calculation; the weight is represented as ; wherein k=1, 2, …, N, and Wc is the window size; weighted average filtering; for the nth point, the output coarse filtering signal value is the sum of the products of the sampling points in the neighborhood and the corresponding weights.
[0011] In some embodiments of the present application, in step S03, when the residual error between the calculated current time block and the coarse filtering signal is greater than the pulse threshold, the current point is marked as a pulse noise point.
[0012] In some embodiments of the present application, in the fine filtering stage, for non-pulse noise points, the step of dynamically adjusting the fine filtering window and the weight in combination with the variance and the kurtosis of the current time block includes: window adjustment; when the variance is greater than the variance threshold, the window is reduced to 1 / 2 of the initial window, otherwise the window is expanded to the initial window; weight calculation; adaptive weighted average is used, and is represented as Where α is the exponential decay coefficient, β is the smoothing coefficient, γ is the kurtosis compensation coefficient, K0 is the mean kurtosis of normal oil volume fluctuations, Kmax is the preset maximum kurtosis, k represents the position of the neighborhood point currently participating in the weight calculation, and n represents the position of the target point currently being filtered. Weighted average filtering: A finely filtered signal is obtained by weighting and averaging the sampling points in its neighborhood.
[0013] In some embodiments of the present invention, in step S04, the actual fuel quantity is obtained by combining the fuel tank calibration parameters with the filtered signal conversion.
[0014] On the other hand, the present invention also provides an adaptive filtering system for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics, used to execute the aforementioned adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics; comprising: The signal preprocessing module is used for signal segmentation, normalization, and loading of calibration parameters; The multi-dimensional statistics calculation module is used to calculate the mean, variance, and kurtosis in real time. The multi-level filtering execution module includes a coarse filtering unit, a pulse detection unit, and a fine filtering unit. The coarse filtering unit is used for moving weighted averaging, the pulse detection unit is used for residual threshold judgment, and the fine filtering unit is used for adaptive weight calculation. The parameter adaptive adjustment module is used to dynamically adjust the window size and weight coefficients based on variance and kurtosis; The output module is used to convert the filtered signal into the actual fuel quantity by combining the fuel tank calibration parameters.
[0015] On the other hand, the present invention also provides an electronic device, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to execute the adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics by executing the executable instructions.
[0016] On the other hand, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the aforementioned adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics.
[0017] Compared with the prior art, the present invention has the following advantages and beneficial effects: This invention achieves efficient suppression of mixed noise (low-frequency sloshing, Gaussian noise, and impulse noise) by real-time monitoring of the multi-dimensional statistical characteristics (mean, variance, and peak value) of the fuel quantity signal, combined with a multi-level structure of "coarse filtering-pulse detection-fine filtering" and dynamically adjusting the filtering parameters, thereby improving the accuracy of fuel measurement under complex operating conditions.
[0018] By using coarse filtering for rapid noise reduction, pulse detection for precise location of anomalies, and fine filtering for dynamic parameter adjustment, multi-level collaborative filtering can be achieved, balancing efficiency and accuracy.
[0019] Without needing prior knowledge of fuel sloshing frequency or noise models, the system automatically optimizes windows and weights through real-time calculated statistics, enabling online adaptive adjustments to adapt to varying operating conditions during different flight phases (such as cruise, climb, and descent). Attached Figure Description
[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0021] Figure 1 This is a flowchart of the adaptive filtering method according to an embodiment of the present invention.
[0022] Figure 2 This is a logic diagram for real-time calculation of multi-dimensional statistics in an embodiment of the present invention.
[0023] Figure 3 This is the frame of the adaptive filtering system in an embodiment of the present invention. Detailed Implementation
[0024] To make the objectives, technical solutions, and advantages of this application clearer, specific embodiments of this application will be described in further detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely for explaining this application and not for limiting it. It should also be noted that, for ease of description, only the parts relevant to this application are shown in the drawings, not all of them. Before discussing exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe operations (or steps) as sequential processes, many of these operations can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations can be rearranged. The process can be terminated when its operation is completed, but may also have additional steps not included in the drawings. The process can correspond to a method, function, procedure, subroutine, subprogram, etc.
[0025] This invention addresses the mixed interference characteristics of "low-frequency fluctuation + Gaussian noise + impulse noise" in fuel quantity signals. It employs a staged processing method, which uses coarse filtering to suppress high-frequency noise, pulse detection to locate abnormal peaks, and fine filtering combined with multi-dimensional statistics to dynamically adjust the window and weights, thereby achieving high-precision measurement of fuel quantity under complex operating conditions.
[0026] In some embodiments of the present invention, the adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics includes the following steps: S01, Signal Acquisition and Preprocessing The digital signal of fuel quantity output from the sensor (e.g., sampling frequency fs ranging from 10Hz to 100Hz) is divided into continuous time blocks according to a fixed time window Tw, and represented as follows: x =[ x 1 , x 2 ,…, x N The formula is: N = fs·Tw, where Tw can be 0.5s to 2s, corresponding to 5 to 20 sampling points; and each time block is normalized to eliminate the influence of sensor zero bias, thus obtaining the preprocessed signal. x ( n ), n=1,2,…,N.
[0027] S02, Real-time calculation of multidimensional statistics Calculate the current time block x ( n Multidimensional statistics, including: mean ; the average estimate used to characterize the current oil quantity; x(k) is the current time block. x ( n The kth sampling point; variance Used to characterize the severity of oil volume fluctuations (the variance of low-frequency sloshing noise will be relatively large). Kurtosis; used to measure the degree of signal spikes (the kurtosis of impulse noise is significantly higher than that of normal fluctuations).
[0028] S03, Multi-stage filtering processing 1) Coarse filtering stage Based on historical maximum variance Set the initial window ;in, Typically, the maximum variance of the first three time blocks is taken; k is an empirical coefficient, ranging from 3 to 5; A weighted average filter is used to output a coarsely filtered signal yf(n) to suppress high-frequency noise (such as sensor thermal noise); the sliding weighted average filter is a linearly decreasing series with weights that are high at the center and low on both sides, with the center weight accounting for 70%~80%; including: a. Window division For the nth point within the time block, its neighborhood window is [n-Wc+1, n+Wc-1].
[0029] b. Weight calculation, expressed as: Where k = 1, 2, ..., N, and Wc is the initial window size.
[0030] c. Weighted average filtering For the nth point, its coarse filter value is the sum of the products of the sampling points in the neighborhood and their corresponding weights; expressed as: ; where x(k) is the value of the kth sampling point in the current domain.
[0031] 2) Pulse detection stage Calculate the residual e(n) = x(n) - yf(n) between the current time block and the coarsely filtered signal. If |e(n)| > Tp, then mark n as an impulse noise point, ensuring that normal fluctuation points with a probability less than 0.3% are not misjudged; where Tp is the impulse threshold, taken as 3σ. max .
[0032] 3) Fine filtering stage For non-impulse noise points, combine the variance σ of the current time block. 2 Dynamically adjust the fine filter window Wf and weights in conjunction with kurtosis K. ;include: a. Window adjustment If σ 2 >σ th (σ) th If the threshold is set to Wf=Wc / 2, it indicates the presence of significant low-frequency jitter. The window should be narrowed to track the jitter changes; otherwise, the window should be expanded to Wf=Wc to smooth out the remaining noise.
[0033] b. Weight Calculation Adaptive weighted average is used, with weights It consists of two parts: ; in: α is the exponential decay coefficient, used to control for neighborhood influence, for example, it is set to 0.6; β is a smoothing coefficient used to control the decay rate; for example, it can be set to 0.1. γ is the kurtosis compensation coefficient; K0 is the mean kurtosis of normal oil volume fluctuations, for example, 1.0; Kmax is the preset maximum kurtosis, for example, 4.0; k represents the position of the neighboring point currently participating in the weight calculation; n represents the current location of the target point being filtered; When the kurtosis K is close to K0 (the kurtosis with normal fluctuations), γ≈1, and the weights are mainly exponentially decaying to smooth out noise; when K is significantly greater than K0 (close to impulse noise), γ≈0 to avoid oversmoothing near the peaks.
[0034] c. Weighted average filtering The finely filtered signal yc(n) is obtained by weighted averaging of its neighborhood sampling points, and is expressed as: ; Where x(k) is the original signal, and if k is a pulse point, yc(n) takes the original value x(k).
[0035] S04, Data Fusion and Transformation The original values of the data pulse points are retained and combined with the fine-filtered result yc(n) of the non-pulse points to finally obtain the complete filtered signal. .
[0036] The actual fuel quantity is converted from the fuel tank calibration parameters (such as sensor position and corresponding fuel quantity curve).
[0037] In some embodiments, an adaptive filtering system for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics includes: The signal preprocessing module is used for signal segmentation, normalization, and loading of calibration parameters; The multi-dimensional statistics calculation module is used to calculate the mean, variance, and kurtosis in real time. The multi-level filtering execution module includes a coarse filtering unit, a pulse detection unit, and a fine filtering unit. The coarse filtering unit is used for moving weighted averaging, the pulse detection unit is used for residual threshold judgment, and the fine filtering unit is used for adaptive weight calculation. The parameter adaptive adjustment module is used to dynamically adjust the window size and weight coefficients based on variance and kurtosis; The output module is used to convert the filtered signal into the actual fuel quantity by combining the fuel tank calibration parameters.
[0038] This invention simultaneously utilizes mean (oil level), variance (fluctuation intensity), and kurtosis (pulse characteristics) to characterize signal properties, specifically suppressing low-frequency fluctuations, Gaussian noise, and impulse noise. Compared with single statistical quantity filtering (such as using only variance), it improves anti-interference capability and achieves multi-dimensional noise suppression.
[0039] By using coarse filtering for rapid noise reduction, pulse detection for precise location of anomalies, and fine filtering for dynamic parameter adjustment, multi-level collaborative filtering can be achieved, balancing efficiency and accuracy.
[0040] Without needing prior knowledge of fuel sloshing frequency or noise models, the system automatically optimizes windows and weights through real-time calculated statistics, enabling online adaptive adjustments to adapt to varying operating conditions during different flight phases (such as cruise, climb, and descent).
[0041] Under typical fuel sloshing (variance σ) 2 Under mixed interference of sensor noise (Gaussian noise standard deviation σ=0.1) and occasional pulses (peak value 3σ), the signal-to-noise ratio is improved by 8~12dB compared with the traditional mean filter, and the error is reduced by more than 60% compared with the Kalman filter (model error 5%).
[0042] The adaptive filtering method and system for measuring aircraft fuel quantity of the present invention will be described in detail below with reference to specific embodiments.
[0043] Taking a certain type of civil aircraft fuel quantity measurement system as an example, the sensor type is capacitive, the sampling frequency is f_s=20Hz, the fuel tank capacity is 10000L, and the adaptive filtering process for aircraft fuel quantity measurement is as follows: S01, Signal Acquisition and Preprocessing The fuel quantity signal was collected during the cruise phase (without maneuvering) and climb phase (with fuel sloshing), with a sampling interval of T=0.05s.
[0044] Normalization is performed on each time block (Tw=1s, i.e., 20 sampling points) to eliminate sensor zero bias (e.g., initial zero position error of 0.5L).
[0045] S02, Real-time calculation of multidimensional statistics Taking a certain time block during the climb phase as an example: The mean of the original signal x(n) is μ = 4200L (reflecting the current oil level); Variance σ 2 =0.8 (significantly higher than σ during the cruise phase) 2 =0.3, indicating the presence of shaking); Kurtosis K=2.5 (higher than the normal fluctuation K0=1.2, but not reaching the pulse threshold Tp=3σ) max =3×0.8≈2.7, therefore there is no impulse noise).
[0046] S03, Multi-stage filtering processing Coarse filtering stage: historical maximum variance = 1.0 (maximum variance of the first three time blocks), initial window \(W_c = 5\times1.0\approx5\), and \(y_f(n)\) is obtained after weighted averaging.
[0047] Pulse detection stage: The maximum absolute value of the residual \(e(n)=x(n)-y_f(n)\) is \(2.2L < T_p = 2.7L\), and there is no pulse noise point marked.
[0048] Fine filtering stage: The current variance \(\sigma\) 2 = 0.8 > \(\sigma\) th = 0.5 (\(\sigma\) th is the stationary threshold, taking the historical mean \(0.3 + 2\times\) standard deviation \(0.1 = 0.5\)), so the window is reduced to \(W_f = 5 / 2 = 2\); the kurtosis \(K = 2.5\) is close to \(K_0 = 1.2\), \(\gamma = 0.8\), and the weights mainly decay exponentially (smooth jitter noise).
[0049] S04, Data fusion and conversion The filtered signal \(y_c(n)\) is merged with the original value without pulse points and converted into the actual fuel quantity through the fuel tank calibration parameters (fuel quantity - capacitance curve corresponding to the sensor position). Finally, the fluctuation amplitude of the output result is reduced by 70% compared with the original signal, and the lag is reduced by 0.1 s compared with the traditional mean filtering (window fixed at 10).
[0050] On the other hand, the present invention also provides an electronic device, including: [[ID=2,2]]A processor; and, A memory for storing executable instructions of the processor; Wherein, the processor is configured to execute the adaptive filtering method for aircraft fuel quantity measurement based on multi-dimensional statistics dynamic adaptation by executing the executable instructions.
[0051] On the other hand, the present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the adaptive filtering method for aircraft fuel quantity measurement based on multi-dimensional statistics dynamic adaptation is implemented.
[0052] As described above, it is only a preferred embodiment of the present invention, and does not impose any form of limitation on the present invention. Any simple modification or equivalent change made to the above embodiments based on the technical essence of the present invention falls within the protection scope of the present invention.
Claims
1. An adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics, characterized in that, Includes the following steps: S01, Signal Acquisition and Preprocessing: Divide the digital signal of fuel quantity output by the sensor into continuous time blocks according to a fixed time window; S02. Calculate multidimensional statistics, including the mean, variance, and kurtosis of the current time block. S03, Multi-stage filtering processing; It includes a coarse filtering stage, a pulse detection stage, and a fine filtering stage; In the coarse filtering stage, an initial window is set based on the historical maximum variance, and a sliding weighted average filter is used to output the coarse filtered signal. During the pulse detection phase, the residual between the current time block and the coarse filtered signal is used to determine whether the current point is a pulse noise point. During the fine filtering stage, for non-impulse noise points, the fine filtering window and weights are dynamically adjusted based on the variance and kurtosis of the current time block. S04, Data Fusion and Transformation; The original values of the data pulse points are retained and combined with the fine filtering results of the non-pulse points to obtain the complete filtered signal.
2. The adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics as described in claim 1, characterized in that, In step S01, each time block is normalized.
3. The adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics as described in claim 1, characterized in that, In step S03, the historical maximum variance is the maximum variance of the first three time blocks.
4. The adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics as described in claim 1, characterized in that, The steps for outputting a coarse-filtered signal using a moving weighted average filter include: Window partitioning; for the nth point within a time block, its neighborhood window is [n - Wc+1, n + Wc-1]; Weight calculation; weight is represented as Where k = 1, 2, ..., N, and Wc is the window size; Weighted average filtering; for the nth point, the output coarse-filtered signal value is the sum of the products of the sampling points in the neighborhood and their corresponding weights.
5. The adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics according to claim 1, characterized in that, In step S03, when the residual between the calculated current time block and the coarse filtered signal is greater than the pulse threshold, the current point is marked as a pulse noise point.
6. The adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics according to claim 1, characterized in that, In the fine-filtering stage, for non-impulse noise points, the steps of dynamically adjusting the fine-filtering window and weights based on the variance and kurtosis of the current time block include: Window adjustment: If the variance is greater than the variance threshold, the window is reduced to half the size of the initial window; otherwise, the window is expanded to the size of the initial window. Weight calculation; an adaptive weighted average is used, expressed as Where α is the exponential decay coefficient, β is the smoothing coefficient, γ is the kurtosis compensation coefficient, K0 is the mean kurtosis of normal oil volume fluctuations, Kmax is the preset maximum kurtosis, k represents the position of the neighborhood point currently participating in the weight calculation, and n represents the position of the target point currently being filtered. Weighted average filtering: A finely filtered signal is obtained by weighting and averaging the sampling points in its neighborhood.
7. The adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics according to claim 1, characterized in that, In step S04, the actual fuel quantity is obtained by combining the fuel tank calibration parameters with the filtered signal conversion.
8. An adaptive filtering system for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics, characterized in that, An adaptive filtering method for measuring aircraft fuel quantity based on dynamic adaptation of multi-dimensional statistics, as described in any one of claims 1-7; comprising: The signal preprocessing module is used for signal segmentation, normalization, and loading of calibration parameters; The multi-dimensional statistics calculation module is used to calculate the mean, variance, and kurtosis in real time. The multi-level filtering execution module includes a coarse filtering unit, a pulse detection unit, and a fine filtering unit. The coarse filtering unit is used for moving weighted averaging, the pulse detection unit is used for residual threshold judgment, and the fine filtering unit is used for adaptive weight calculation. The parameter adaptive adjustment module is used to dynamically adjust the window size and weight coefficients based on variance and kurtosis; The output module is used to convert the filtered signal into the actual fuel quantity by combining the fuel tank calibration parameters.
9. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the adaptive filtering method for aircraft fuel quantity measurement based on dynamic adaptation of multi-dimensional statistics as described in any one of claims 1-7 by executing the executable instructions.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the adaptive filtering method for measuring aircraft fuel quantity based on dynamic adaptation of multi-dimensional statistics as described in any one of claims 1-7.
Citation Information
Patent Citations
Phase angle calibration device of ultra-low frequency response analyzer
CN109884567A
Power supply fault monitoring system and method
CN112306789A