Optimized Kalman filtering method for improving thermocouple temperature measurement accuracy

Abstract

The invention relates to an optimized Kalman filtering method for improving thermocouple temperature measurement accuracy. The method comprises the following steps: S1, establishing a temperature state equation and an observation equation of a temperature measurement object; s2, determining a thermal model parameter value and an optimized Kalman filtering parameter value; s3, collecting temperature measurement data of the thermocouple; s4, performing real-time standard Kalman filtering and real-time mean filtering on the temperature measurement data; and S5, at each temperature measurement moment, performing information fusion on the real-time standard Kalman filtering result and the real-time mean filtering result, performing small-amplitude convergence on the real-time standard Kalman filtering result to the real-time mean filtering result to obtain an optimized Kalman filtering posterior estimated value of the temperature measurement data, and calculating the optimal Kalman filtering posterior estimated value of the temperature measurement data according to the optimal Kalman filtering posterior estimated value. Deviation caused by error accumulation is eliminated on the premise of keeping the smoothness of a temperature measurement data curve. The method has the beneficial effects that when the values of the thermal model parameters and the Kalman filtering parameters are not accurate, the temperature measurement deviation of the thermocouple is small, and the temperature measurement precision and accuracy are high.

Description

[Technical field]

[0001] The present invention relates to the field of satellite aerospace technology, and in particular to an optimized Kalman filtering method for improving the temperature measurement accuracy of a thermocouple. [Background technology]

[0002] The temperature measurement accuracy of a temperature measuring element includes indicators at two levels: precision and accuracy. The temperature measurement accuracy represents its ability to resolve weak temperature signals, and the accuracy represents the deviation of its measurement results from the true value.

[0003] Thermocouples, platinum resistance, and thermistors are three common types of temperature measurement components. In comparison, thermocouples have the advantages of no self-heating, rapid temperature response, no need for power supply, low cost, good component consistency, wide temperature measurement range, and small temperature drift. However, due to its weak output signal, it is easily affected by environmental electromagnetic interference to generate high-intensity noise, so its application in the field of precise temperature measurement and control of spacecraft is greatly limited.

[0004] Signal post-processing through filtering can improve the temperature measurement accuracy of thermocouples to a certain extent. Common filtering methods include mean filtering, limiting filtering, median filtering, etc. However, the temperature measurement noise of thermocouples is as high as tens of mK or even more than 100 mK. The above filtering methods cannot effectively suppress the temperature measurement noise and reduce the temperature measurement noise to the mK level, and cannot improve the temperature measurement accuracy.

[0005] The Kalman filter method can correct the measurement results according to the thermal model of the temperature measurement object, and has a good noise suppression effect. However, the actual application effect of this method is very dependent on the accuracy of the thermal model and the reasonable value of the Kalman filter parameters. In actual engineering, the thermal model parameters and Kalman filter parameters of the temperature measurement object are often difficult to be highly accurate. There are model deviations or inaccurate parameters during application. Inaccurate parameter values ​​can easily lead to poor noise suppression effects or deviations of the filtering results from the true value, resulting in reduced temperature measurement accuracy or precision. In addition, there is great difficulty in selecting its parameters, and there is often a problem that it is difficult to ensure both accuracy and precision at the same time.

[0006] Kalman filtering is an algorithm that uses the linear system state equation to optimally estimate the system state through the system input and output observation data; since the observation data includes the influence of noise and interference in the system, the optimal estimate can also be regarded as a filtering process.

[0007] The present invention aims at the technical problems that the temperature measurement precision or accuracy of the prior art is low and it is often difficult to ensure both precision and accuracy at the same time, and makes technical improvements to the thermocouple temperature measurement Kalman filter method. [Summary of the invention]

[0008] The purpose of the present invention is to provide a Kalman filtering method with small deviation in thermocouple temperature measurement and high temperature measurement accuracy when the values ​​of thermal model parameters and Kalman filtering parameters are inaccurate.

[0009] To achieve the above object, the technical solution adopted by the present invention is an optimized Kalman filtering method for improving the accuracy of thermocouple temperature measurement, which comprises the following steps:

[0010] S1. Establish the temperature state equation and observation equation of the temperature measurement object;

[0011] S2, determining the thermal model parameter values ​​and optimizing the Kalman filter parameter values;

[0012] S3, collecting temperature measurement data of thermocouples;

[0013] S4, performing real-time standard Kalman filtering and real-time mean filtering on the temperature measurement data;

[0014] S5. At each temperature measurement moment, the real-time standard Kalman filter and real-time mean filter results are fused, and the real-time standard Kalman filter results are slightly converged to the real-time mean filter results to obtain the optimized Kalman filter posterior estimate of the temperature measurement data, thereby eliminating the deviation caused by error accumulation while maintaining the smoothness of the temperature measurement data curve.

[0015] Preferably, step S1:

[0016] The temperature state equation of the temperature measurement object is T k =T k-1 +u k-1 +w k ,

[0017] Among them, T k Represents the temperature of the object at the kth moment, T k-1 represents the temperature of the object at the k-1th moment, u k-1 is the temperature change trend between time k-1 and time k, according to the heating power P heat and leakage heat power P loss The difference between the values ​​of and the total heat capacity C of the temperature measurement object, that is, u k-1 =dt*(P heat,k-1 -P loss,k-1 ) / C, where dt is the sampling time interval for temperature measurement, P heat,k-1 Usually determined according to the power of the heating source, P loss,k-1 It can be calculated based on the temperature difference between the temperature measurement object and the environment and the thermal resistance, that is, P loss,k-1 =(T k-1 -T atm,k-1 ) / R, where T atm,k-1 is the ambient temperature, R is the thermal resistance between the temperature measurement object and the environment;

[0018] w k is the white noise error of the temperature state equation, which obeys Gaussian distribution and has a variance of W k ;

[0019] The temperature observation equation of the temperature measurement object is Z k =X k +v k , where Z k is the temperature measurement value, X k is the display value of the temperature measuring instrument, v k To measure white noise, its variance is V k .

[0020] Preferably, step S2:

[0021] The thermal model parameters that need to be determined include the total heat capacity C of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment, and the sampling time interval dt; wherein the total heat capacity C of the temperature measurement object is determined according to the geometric parameters and physical parameters of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment is determined by experimental testing, and the sampling time interval dt is determined according to the data acquisition frequency;

[0022] The optimal Kalman filter parameters that need to be determined include the mean square error of the measurement error V k , system error mean square error W k , and regression coefficient B; where the measurement error mean square error V k Determined according to the mean square error of the temperature measurement data under constant temperature conditions; k After that, we try to find the appropriate mean square error W of the system error by multiple attempts. k The temperature measurement noise is made small enough; the regression coefficient B is used to reduce the temperature measurement deviation value without significantly reducing the noise suppression effect.

[0023] Preferably, step S3:

[0024] Arrange temperature measuring thermocouples on the temperature measurement object according to requirements, set the sampling time interval dt in the data acquisition system, start the data acquisition system, and save the temperature measurement data to the storage.

[0025] Preferably, step S4:

[0026] At the kth moment, the measured data X k Perform standard Kalman filtering and mean filtering;

[0027] Among them, the mean filter is

[0028] In the standard Kalman filtering process, the temperature prior estimate is first calculated

[0029] Then calculate the temperature prior estimated covariance and the Kalman gain coefficient

[0030] Afterwards, update the temperature posterior estimated covariance

[0031] Finally, the standard Kalman filter temperature posterior estimate is calculated

[0032] Preferably, step S5:

[0033] When W k If the value is too small, the standard Kalman filter method tends to over-rely on the inaccurate state equation, resulting in temperature estimation errors;

[0034] At each temperature measurement moment, the standard Kalman filter result is converged to the mean filter result in a small amount of information fusion in, To optimize the temperature posterior estimate of the Kalman filter, B is the regression coefficient of the mean filter result.

[0035] The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples of the present invention has the following beneficial effects: compared with the mean filtering method, the method of the present invention can greatly improve the temperature measurement accuracy; compared with the standard Kalman filtering method, when the thermal model parameters and the filtering parameters are inaccurate, the method of the present invention can correct and eliminate the temperature measurement deviation through the mean filtering result, reduce the risk of temperature measurement deviation, and the method of the present invention can obtain higher temperature measurement accuracy than the standard Kalman filtering by reasonable value selection; specifically:

[0036] 1. Use thermocouples to measure the precise temperature data of the target object. The thermocouples are in a strong and changeable electromagnetic interference environment, and the temperature measurement accuracy is required to reach the mK level;

[0037] 2. It is necessary to establish the temperature state equation and observation equation of the temperature measurement object, and perform preliminary filtering on the temperature data through standard Kalman filtering;

[0038] 3. It is necessary to perform mean filtering on the temperature data at the same time, correct the result of the standard positive Kalman filter by the mean filtering result, and output the information fusion result as the best estimate in real time;

[0039] 4. When the thermal model deviation is large, the mean square error of the Kalman filter is allowed to be W. k Taking a smaller value can improve the suppression effect of temperature measurement glitches without significantly increasing the temperature measurement deviation.

Brief Description of the Drawings

[0040] Figure 1This is a diagram of the implementation steps of an optimized Kalman filter method for improving the accuracy of thermocouple temperature measurement.

[0041] Figure 2 It is a schematic diagram of the prototype of the thermocouple precision temperature measurement and control principle.

[0042] Figure 3 It is a schematic diagram of the filtering effect in the rapid heating section of the prototype of the thermocouple precision temperature measurement and control principle.

[0043] Figure 4 This is a schematic diagram of the filtering effect of the small temperature fluctuation section of the prototype of the thermocouple precision temperature measurement and control principle. [Specific implementation method]

[0044] The present invention will be further described below in conjunction with embodiments and with reference to the accompanying drawings.

[0045] Example

[0046] This embodiment implements an optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples.

[0047] The method of this embodiment belongs to the field of spacecraft temperature measurement technology, and can effectively reduce the deviation of filtering results caused by inaccurate thermal model parameters, and improve the temperature measurement accuracy and precision of thermocouples.

[0048] The method of this embodiment optimizes the standard Kalman filter method, reduces the temperature measurement deviation when the thermal model parameters and Kalman filter parameters are inaccurate, improves the temperature measurement accuracy, and the adaptability and stability of the temperature measurement system in complex and changeable engineering application environments.

[0049] The specific technical features of the method in this embodiment are as follows:

[0050] 1) Use thermocouples to measure the precise temperature data of the target object. The thermocouples are in a strong and variable electromagnetic interference environment, and the temperature measurement accuracy is required to reach the mK level;

[0051] 2) It is necessary to establish the temperature state equation and observation equation of the temperature measurement object, and perform preliminary filtering on the temperature data through standard Kalman filtering;

[0052] 3) It is necessary to perform mean filtering on the temperature data at the same time, correct the result of the standard positive Kalman filter by the mean filtering result, and output the information fusion result as the best estimate in real time;

[0053] 4) When the thermal model deviation is large, the method of this embodiment allows the system error mean square error W of the Kalman filter to be k Taking a smaller value can improve the suppression effect of temperature measurement glitches without significantly increasing the temperature measurement deviation.

[0054] Figure 1This is a diagram of the implementation steps of the optimized Kalman filter method to improve the accuracy of thermocouple temperature measurement. Figure 1 As shown, the specific implementation steps of the method in this embodiment are as follows:

[0055] 1. Establish the temperature state equation and observation equation of the temperature measurement object

[0056] The temperature state equation of the temperature measurement object is:

[0057] T k =T k-1 +u k-1 +w k

[0058] Where T k Represents the temperature of the object at the kth moment, T k-1 Represents the temperature of the object at the k-1th moment. k-1 is the temperature change trend between time k-1 and time k, according to the heating power P heat and leakage heat power P loss The difference between and the total heat capacity C of the temperature measurement object is determined by:

[0059] u k-1 =dt*(P heat,k-1 -P loss,k-1 ) / C

[0060] Where dt is the sampling time interval for temperature measurement.

[0061] P heat,k-1 Usually determined according to the power of the heating source, P loss,k-1 It can be calculated based on the temperature difference between the temperature measurement object and the environment and the thermal resistance, that is,

[0062] P loss,k-1 =(T k-1 -T atm,k-1 ) / R

[0063] Where T atm,k-1 is the ambient temperature, and R is the thermal resistance between the temperature measurement object and the environment.

[0064] w k is the white noise error of the temperature state equation, which obeys Gaussian distribution and has a variance of W k .

[0065] The temperature observation equation of the temperature measurement object is:

[0066] Z k =X k +v k

[0067] Where Z k is the temperature measurement value, Xk is the display value of the temperature measuring instrument, v k To measure white noise, its variance is V k .

[0068] 2. Determine the thermal model parameter values ​​and optimize the Kalman filter parameter values

[0069] The thermal model parameters that need to be determined include the total heat capacity C of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment, and the sampling time interval dt. Among them, R needs to be determined through experimental testing, the total heat capacity C is determined based on the geometric parameters and physical parameters of the temperature measurement object, and the sampling time interval dt is determined based on the data acquisition frequency.

[0070] The optimized Kalman filter parameters that need to be determined include the mean square error of the system error W k , measurement error mean square error V k , and regression coefficient B. Among them, the measurement error mean square error V k Determined based on the mean square error of the temperature measurement data under constant temperature conditions. k After that, we try to find the appropriate mean square error W of the system error by multiple attempts. k Make the temperature measurement noise small enough. Generally speaking, by increasing W k , which can increase the stability of the Kalman filter and make it less prone to deviation, but it will reduce the noise suppression effect. k The value can improve the suppression effect of temperature measurement noise, but it is easy to cause temperature measurement deviation. The regression coefficient B is used to reduce the temperature measurement deviation value without significantly reducing the noise suppression effect. The recommended value is 0.01. You can increase this value appropriately to enhance stability, or reduce this value to enhance noise suppression effect.

[0071] 3. Collect temperature measurement data of thermocouples

[0072] Arrange temperature measuring thermocouples on the temperature measuring object according to the requirements, set the sampling time interval dt in the data acquisition system, start the data acquisition system, and save the temperature measurement data to the storage.

[0073] 4. Perform real-time standard Kalman filtering and real-time mean filtering on the temperature measurement data

[0074] At the kth moment, the measured data X k Perform standard Kalman filtering and mean filtering. Among them, the mean filtering method is

[0075]

[0076] In the standard Kalman filtering process, the prior estimate is first calculated

[0077]

[0078] Then calculate the prior estimated covariance and the Kalman gain coefficient K k

[0079]

[0080]

[0081] Afterwards, the posterior estimated covariance is updated

[0082]

[0083] Finally, the standard Kalman filter posterior estimate is calculated

[0084]

[0085] 5. Perform information fusion on the filtering results to obtain the filtering result at the kth moment

[0086] When W k If the value is too small, the standard Kalman filter method tends to over-rely on the inaccurate state equation, resulting in temperature estimation errors. This error will continue to accumulate during the temperature measurement process, causing the temperature measurement results to deviate from the actual temperature, resulting in a decrease in temperature measurement accuracy.

[0087] Therefore, at each temperature measurement moment, the method of this embodiment converges the standard Kalman filter result to the mean filter result by a small margin, eliminating the deviation caused by error accumulation while maintaining the smoothness of the curve, so that the final filter result is always close to the measured value. The information fusion method of this part is

[0088]

[0089] in, That is, it is the posterior estimation value of the optimized Kalman filtering method described in the method of this embodiment, and B is the regression coefficient of the mean filtering result. When it is 0, the optimized Kalman filtering will be restored to the standard Kalman filtering.

[0090] Next, the temperature control measurement experiment of the thermocouple principle prototype is introduced.

[0091] Figure 2 This is a schematic diagram of the prototype of the thermocouple precision temperature measurement and control principle. Figure 2As shown in the figure, the temperature measurement object is the internal temperature of a cubic copper block with a side length of 6 cm. There is a small hole with a diameter of 6 mm and a depth of 3 cm in the center of the top surface of the copper block. The temperature measuring ends of the thermocouple and thermistor are placed at the bottom of the small hole and fixed by thermal conductive glue. Among them, the thermocouple is used for temperature measurement, and its real-time temperature measurement results are used as the basis for temperature control. The high-precision thermistor has been calibrated and is used to compare, analyze and judge the temperature measurement and control effects of the thermocouple. The copper block is placed on a foam insulation board, with a thin film heater on the bottom and an acrylic windshield on the outside. The temperature data of the thermocouple is collected by a data logger and temporarily stored in a storage device. The temperature data collection time interval is 1s. In the figure, 1 is a thermocouple, 2 is a thermistor, 3 is a copper cube, 4 is a thin film heater, 5 is a foam insulation board, and 6 is an acrylic windshield.

[0092] The model parameters can be determined based on the above information and experimental results. Among them, the sampling time interval dt = 1s, the total heat capacity of the temperature measurement object C = 754.8J / K, and the thermal resistance R between the temperature measurement object and the indoor air environment is 11K / W. The standard deviation of the thermocouple temperature measurement noise is about 35mK, so the measurement mean square error V K The value is 1.225E-3.

[0093] Figure 3 It is a schematic diagram of the filtering effect in the rapid heating section of the prototype of the thermocouple precision temperature measurement and control principle. Figure 4 This is a schematic diagram of the filtering effect of the small temperature fluctuation section of the thermocouple precision temperature measurement and control principle prototype. Figure 3 , Figure 4 As shown, after trying, the system error mean square error W k When the temperature is 1E-8 or less, the burr structure of the standard Kalman filter result curve can be as low as the mK level; however, due to the accumulation of state equation errors, the Kalman filter result has obvious deviations at this time. Correspondingly, the mean filter and standard Kalman filter results are shown in the figure. In the rapid heating stage and the small temperature fluctuation stage, the standard deviation of the noise of the mean filter result is 19.9mK and 22.2mK respectively, W k =1E-8, the standard Kalman filter noise is very small, but the result deviation is as high as about 20mK. After information fusion, the deviation of the filtering result is greatly reduced, and the standard deviation of the noise is as low as 2.7mK and 2.2mK respectively. At the same time, compared with W k =1E-7 curve shows that compared with the standard Kalman simply by increasing W k The value reduces the deviation. The method of this embodiment has a smaller burr structure and a smaller filtering deviation, and can achieve higher-precision temperature measurement.

[0094] In summary, the method of this embodiment overcomes the deficiencies of the above-mentioned prior art and achieves the above-mentioned technical effects through the following principles:

[0095] Thermocouples have a series of advantages such as low cost, fast response, good consistency, no self-heating, and no need for power supply, but the temperature measurement is easily disturbed by the external environment, resulting in large temperature measurement noise, and it is difficult to use for precise temperature control in complex environments. Mean filtering, median filtering, limiting filtering and other filtering methods as well as W k The standard Kalman filter with a larger value cannot suppress the temperature measurement noise well. k If the value is too small, the temperature measurement result will easily rely too much on the inaccurate state equation, resulting in temperature estimation error. This error will continue to accumulate during the temperature measurement process, causing the temperature measurement result to deviate from the actual temperature;

[0096] In this embodiment, a smaller W is first used. k The standard Kalman filter is used to perform standard Kalman filtering on the thermocouple temperature measurement data to obtain a good noise suppression effect; then, at each temperature measurement moment, the standard Kalman filter result is converged to the mean filter result by a small margin to eliminate the deviation caused by error accumulation, so that the final filter result is always close to the measured value; the information fusion method for this part is

[0097]

[0098] in, That is, it is the a posteriori estimation value of the optimized Kalman filtering method described in the method of this embodiment.

[0099] Compared with the mean filtering method, the method of this embodiment can greatly improve the temperature measurement accuracy; compared with the standard Kalman filtering method, when the thermal model parameters and the filtering parameters are inaccurate, the temperature measurement deviation can be eliminated by correcting the mean filtering results, thereby reducing the risk of temperature measurement deviation; and, by reasonably taking values, a higher temperature measurement accuracy than the standard Kalman filtering can be obtained.

[0100] A person of ordinary skill in the art can understand that all or part of the steps to implement the above embodiments can be completed by hardware, or can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, wherein the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0101] The above is only a preferred embodiment of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and supplements without departing from the principle of the present invention. These improvements and supplements should also be regarded as the scope of protection of the present invention.

Claims

1. An optimized Kalman filtering method for improving the accuracy of thermocouple temperature measurement, characterized in that The following steps are involved: S1. Establish the temperature state equation and observation equation of the temperature measurement object; S2, determining the thermal model parameter values ​​and optimizing the Kalman filter parameter values; S3, collecting temperature measurement data of thermocouples; S4, performing real-time standard Kalman filtering and real-time mean filtering on the temperature measurement data; S5. At each temperature measurement moment, the real-time standard Kalman filter and real-time mean filter results are fused, and the real-time standard Kalman filter results are slightly converged to the real-time mean filter results to obtain the optimized Kalman filter posterior estimate of the temperature measurement data, thereby eliminating the deviation caused by error accumulation while maintaining the smoothness of the temperature measurement data curve.

2. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 1 is characterized in that Step S1: The temperature state equation of the temperature measurement object is T k =T k-1 +u k-1 +w k , Among them, T k Represents the temperature of the object at the kth moment, T k-1 represents the temperature of the object at the k-1th moment, u k-1 is the temperature change trend between time k-1 and time k, according to the heating power P heat and leakage heat power P loss The difference between the values ​​of and the total heat capacity C of the temperature measurement object, that is, u k-1 =dt*(P heat,k-1 -P loss,k-1 ) / C, where dt is the sampling time interval for temperature measurement, P heat,k-1 Usually determined according to the power of the heating source, P loss,k-1 It can be calculated based on the temperature difference between the temperature measurement object and the environment and the thermal resistance, that is, P loss,k-1 =(T k-1 -T atm,k-1 ) / R, where T atm,k-1 is the ambient temperature, R is the thermal resistance between the temperature measurement object and the environment; w k is the white noise error of the temperature state equation, which obeys Gaussian distribution and has a variance of W k ; The temperature observation equation of the temperature measurement object is Z k =X k +v k , where Z k is the temperature measurement value, X k is the display value of the temperature measuring instrument, v k To measure white noise, its variance is V k .

3. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 2 is characterized in that Step S2: The thermal model parameters that need to be determined include the total heat capacity C of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment, and the sampling time interval dt; wherein the total heat capacity C of the temperature measurement object is determined according to the geometric parameters and physical parameters of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment is determined by experimental testing, and the sampling time interval dt is determined according to the data acquisition frequency; The optimal Kalman filter parameters that need to be determined include the mean square error of the measurement error V k , system error mean square error W k , and regression coefficient B; where the measurement error mean square error V k Determined according to the mean square error of the temperature measurement data under constant temperature conditions; k After that, we try to find the appropriate mean square error W of the system error by multiple attempts. k The temperature measurement noise is made small enough; the regression coefficient B is used to reduce the temperature measurement deviation value without significantly reducing the noise suppression effect.

4. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 3 is characterized in that Step S3: Arrange temperature measuring thermocouples on the temperature measurement object according to requirements, set the sampling time interval dt in the data acquisition system, start the data acquisition system, and save the temperature measurement data to the storage.

5. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 4 is characterized in that Step S4: At the kth moment, the measured data X k Perform standard Kalman filtering and mean filtering; Among them, the mean filter is In the standard Kalman filtering process, the temperature prior estimate is first calculated Then calculate the temperature prior estimated covariance and the Kalman gain coefficient Afterwards, update the temperature posterior estimated covariance Finally, the standard Kalman filter temperature posterior estimate is calculated 6. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 5 is characterized in that Step S5: When W k If the value is too small, the standard Kalman filter method tends to over-rely on the inaccurate state equation, resulting in temperature estimation errors; At each temperature measurement moment, the standard Kalman filter result is converged to the mean filter result in a small amount of information fusion in, To optimize the temperature posterior estimate of the Kalman filter, B is the regression coefficient of the mean filter result.

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