CN108593557B - Remote measurement error compensation method based on TE-ANN-AWF (transverse electric field analysis) -based mobile pollution source - Google Patents

Abstract

The invention discloses a remote measurement error compensation method based on a TE-ANN-AWF mobile pollution source. A virtual observation method is provided to realize the multi-element deconstruction of a unit observation sequence, the compensation of a single interference channel virtual observation sequence is realized through an ANN error prediction model, and then the compensated multi-element virtual observation sequence is subjected to fusion reconstruction by adopting a multi-element self-adaptive weighting fusion method. Aiming at the problem of weight convergence in the fusion algorithm, an exponential forgetting method is introduced into the model, and the advantages of good weight estimation capability of TE and self-adaptive adjustment of the weight of AWF are combined, so that the dynamic performance of the error compensation process is improved.

Description

Remote measurement error compensation method based on TE-ANN-AWF (transverse electric field analysis) -based mobile pollution source

Technical Field

The invention designs a remote sensing detection error compensation method for a mobile pollution source based on TE-ANN-AWF, which belongs to the technical field of error compensation of remote sensing detection instruments for the mobile pollution source.

Background

The mobile pollution source refers to a source that discharges air pollutants without a stationary device, such as a motor vehicle, a mobile construction machine, a ship, an airplane, and the like that discharge exhaust gas during movement. The pollution of mobile sources, particularly heavy diesel trucks, commercial gasoline vehicles, old automobiles and engineering machinery vehicles, has become a main source of air pollution and is an important cause of urban ultrafine particulate matters and photochemical smog pollution. The world health organization in 2012 has promoted diesel exhaust from suspected carcinogens to clear carcinogens. In order to effectively treat the mobile pollution source, especially to identify and control the high pollution discharge motor vehicle, the emission of the mobile pollution source needs to be effectively detected in real time.

At present, the detection technology of the mobile pollution source is various, such as reflecting the pollution degree of the atmosphere through plant growth or determining the concentration of the pollutant through chemical detection, but the methods are difficult to perform real-time online detection on the mobile pollution source. Remote sensing is a fast and efficient method of detecting mobile sources of pollution. The method is based on the precise analysis of the optical absorption spectrum of the gas, and the concentration of the gas is inverted according to the absorption properties of the gas components in the environment in ultraviolet, visible and infrared spectrum bands. In 1988, the first Remote Sensing monitoring system (RSD) using non-dispersive infrared technology (NDIR) was developed by the university of denver, usa, and was capable of simultaneously detecting emission concentrations of CO2, CO, and HC in the exhaust gas of a motor vehicle. In the 90 s of the 20 th century, the university of denver developed a remote sensing monitoring system for measuring the concentration of NO by using an ultraviolet absorption technology (Ultra Violet, UV), and the problem of water vapor absorption during NDIR measurement was overcome. Subsequently, MD-LaserTech developed NO and HC remote sensing systems based on the ultraviolet Differential technology (UV-DOAS). Due to the fact that the emitting wavelength band of a Tunable Diode Laser (TDL) is narrow, the wavelength band which is not interfered can be selected for measuring different measured gas components, and real-time monitoring requirements of high time resolution, high sensitivity, high selectivity and the like are met. Then, the massachusetts institute of technology developed a telemetry system based on the infrared laser differential absorption spectroscopy (tdlas) (tunable diode laser absorption spectrometer) for detecting the excessive emission of mobile pollution sources such as motor vehicles. Currently, remote sensing detection technology has become the mainstream technical means for real-time online detection of gas concentration.

The remote sensing measurement method has high automation degree, and a large number of vehicles passing through the road section can be measured as long as the equipment is erected beside the road. Meanwhile, the method has small influence on traffic. The university of purjohn morse, liriot, uk, TSI corporation, and others, have developed roadside monitoring systems that can detect pollutants including CO, NOx, and others, using technologies based on TDLAS, UV-DOAS, and others. However, the measuring method has limited use conditions and is greatly interfered by the environment, such as the ambient temperature, the humidity, the air pressure, the wind speed and the like, which have important influence on the detection data. And the urban geographic environment is mostly complex and changeable, such as: the urban canyon effect causes a sudden change in airflow. Due to the complexity of the external environment, the German Frounhf physical measurement technology is additionally provided with the measurement of meteorological parameters such as wind speed, wind direction, temperature and humidity, air pressure and the like on the basis of detecting the pollutant parameters, and the pollutant detection result is corrected.

Disclosure of Invention

Aiming at the problem that a remote sensing detection method of a mobile pollution source is easily interfered by an external environment, the invention provides a new error compensation model TE-ANN-AWF by combining three methods of TE transfer entropy, ANN artificial neural network and AWF self-adaptive weighting fusion. In the model, the causal correlation between interference and measurement is quantitatively analyzed by using TE transfer entropy, and a determination method of non-significant causal relationship is introduced. The idea of virtual observation is put forward in the model to realize the multi-element deconstruction of the unit observation sequence, and then the multi-element virtual observation sequence is reconstructed by a multi-element fusion method. The method for introducing the index forgetting into the model combines the advantages of the good weight estimation of the TE and the self-adaptive adjustment of the weight of the AWF, and improves the dynamic performance of the error compensation process.

The technical scheme of the invention is as follows:

the method comprises the following steps: measuring samples under different interference effects are obtained through an environment simulation experiment; based on the experimental measurement sample, performing interference correlation analysis through TE transfer entropy so as to determine a measurement error source and measure the unbalance degree between multiple interferences; the directivity of the TE transfer entropy is utilized to lead out the quantization standard and the judgment method of the non-obvious causal relationship;

step two: acquiring a training sample set of a single interference channel by adopting an environment simulation smoke box experiment platform, and establishing a measurement error prediction model of each interference by a neural network ANN method;

step three: realizing the multivariate deconstruction of the unit observation sequence by a virtual observation method, carrying out error compensation on the deconstructed multivariate virtual observation sequence by an ANN error prediction model under different interferences, and then carrying out fusion reconstruction on the compensated multivariate virtual observation sequence by adopting a multivariate self-adaptive weighting fusion method;

aiming at the problem of weight convergence in the fusion algorithm, an exponential forgetting method is introduced into the model, and the weight estimation capability of TE and the advantage of weight self-adaptive adjustment of the multivariate self-adaptive weighting fusion method are combined, so that the dynamic performance of the error compensation process is improved.

In the first step, TE transfer entropy is introduced to carry out correlation causal analysis on the interference of remote sensing measurement aiming at the characteristic that the interference of an external environment can be detected, and the directivity of the transfer entropy is utilized to introduce a quantitative standard and a judgment method of an insignificant causal relationship;

assuming that the interferences are mutually independent to a certain extent, a measurement sequence under the change of single interference is obtained through a simulation experiment platform, so that the transfer entropy TE from the temperature interference to the measured value is calculated_T->COThe transfer entropy TE of the humidity disturbance to the measured value_H->COTransfer entropy TE of barometric disturbance to measured value_P->COTransfer entropy TE of wind speed disturbance factor to measured value_W->COIn which the maximum backward transfer entropy TE is taken₀As a balance of non-causal relationsA quantity standard;

TE₀＝max{TE_CO->T、TE_CO->H、TE_CO->P、TE_CO->W} (1)。

in the third step, the fusion reconstruction of the compensated multivariate virtual observation sequence by adopting the multivariate adaptive weighting fusion method specifically comprises the following steps: carrying out self-adaptive fusion on the multivariate observation values of all interference channels under the criterion of minimum mean square error; three methods of TE transfer entropy, ANN artificial neural network and AWF self-adaptive weighting fusion are closely combined with each other through a virtual observation method and an exponential forgetting mechanism.

In the third step, an exponential forgetting method is introduced into the model to combine the advantages of good weight estimation capability of TE and adaptive adjustment of AWF weight, specifically

In the TE-ANN model, although the transfer entropy has good weight estimation capability, the weight cannot be adjusted according to errors so as to gradually converge, so that the distribution of the errors also keeps fluctuating and cannot converge; the AWF adaptive weighting fusion algorithm has the advantage that the weight can be gradually converged under the criterion of minimum mean square error without any prior knowledge; in order to combine the good weight estimation advantage of TE with the self-adaptive weight adjustment advantage of AWF, a forgetting mechanism is introduced;

the obtained confidence weight K of the transmission entropy estimation and the optimal weighting factor W according to the minimum mean square error criterion^*Selecting a weighting factor of β_nGet K and W through fusion

As shown in the following formula;

wherein n represents the fusion of the nth observation,

a weighting factor, K, representing a confidence weight, K_nTo representThe nth observation value is used for transmitting the confidence weight value of the entropy estimation,

a weighting factor, W, representing an optimal weighting factor W_n ^*And representing the weight of the AWF after the nth observation value is fused.

Considering the characteristics of stable estimation of the transmission entropy and the self-adaptive adjustment and convergence of the AWF weight, the estimated value of the initial dynamic process of the weight is mainly focused on K_nWhile the steady state process should be focused on W_n ^*And gradually converge to W_n ^*In order to embody the above-mentioned characteristics, the weighting factor is β_nThe following characteristics need to be satisfied:

i represents a natural number; (3)

in order to satisfy the above conditions, the following function is constructed;

d_n＝(1-b)/(1-a·bⁿ)，n＝1，2，3… (4)

wherein b is a forgetting factor, a is an attenuation factor, and 0< b <1< a; the weighting coefficient is obtained from equation (3):

thus, the weight of each channel is obtained, as shown in the formula:

compared with the prior art, the invention has the advantages that:

(1) the invention provides a new error compensation model TE-ANN-AWF by combining three methods of TE transfer entropy, ANN artificial neural network and AWF self-adaptive weighting fusion. Compared with the traditional error compensation method, the method does not need to know a priori multiple interference measurement samples, can effectively compensate the measurement error caused by the external environment interference, and improves the applicability and the anti-interference capability of remote sensing measurement.

(2) According to the characteristic that external interference can be detected, the TE transfer entropy is introduced to carry out correlation causal analysis on the interference of remote sensing measurement, and the directivity of the transfer entropy is utilized to introduce the quantization standard and the judgment method of the non-obvious causal relationship.

(3) The invention introduces an adaptive weighted fusion algorithm AWF, and adaptively fuses the observed values of each interference channel under the criterion of minimum mean square error, thereby ensuring the long-term stability of error compensation.

(4) In order to further improve the dynamic performance of the error compensation process, the invention combines the advantages of the good weight estimation of TE and the self-adaptive adjustment of the weight of AWF by introducing a forgetting mechanism.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a diagram illustrating a comparison of transmission entropy for different interference factors according to the present invention;

FIG. 3 is a diagram of a prediction model of a telemetry error neural network under single interference according to the present invention;

FIG. 4 is a CO measurement error distribution diagram under temperature-concentration according to the present invention;

FIG. 5 is a diagram of the CO measurement error distribution under wind speed-concentration according to the present invention;

FIG. 6 is a diagram showing the error distribution of CO measurement under air pressure-concentration in accordance with the present invention;

FIG. 7 is a diagram illustrating reconstruction of a virtual observation sequence according to the present invention;

FIG. 8 is a diagram of a TE-ANN-AWF error compensation model of the present invention;

Detailed Description

In order to make the technical innovation point realized by the invention easy to understand, the following describes the realization mode of the invention in detail with reference to fig. 1, and the specific steps are as follows:

the method comprises the following steps: and obtaining measurement samples under different interference effects through an environment simulation experiment, and then preprocessing and normalizing the measurement samples. And performing interference correlation analysis through TE transfer entropy based on experimental measurement samples, thereby determining a measurement error source and measuring the degree of imbalance among multiple interferences. And the directivity of the TE transfer entropy is utilized to lead out the quantization standard and the judgment method of the non-significant causal relationship.

Let Xn and Yn be two sequences of environmental interference changes and telemetric observations with discrete states of Xn and Yn at time n, and Xn and Yn may be approximated as steady state markov processes of order k and order l, respectively, then the entropy of transfer from Yn and Xn is defined as follows:

wherein, T_Y→XDenotes the entropy of Transfer of Y to X (Transfer Entroy), u_n＝(x_n+1,x_n,y_n ^(l))，p(u_n) Represents a state x_n+1And the sequence x_n ^(k),y_n ^(l)Probability of simultaneous occurrence; p (x)_n+1|x_n ^(k),y_n ^(l)) Indicating that at time n, x is known_n ^(k)，y_n ^(l)On the premise of (1), x_n+1The conditional probability of (a); p (x)_n+1|x_n ^(k)) Denotes x_n ^(k)Given the known premise of x_n+1When x is a conditional probability of_nWhen the state at a certain moment is completely determined by the historical state of the state, the transfer entropy is zero.

The remote sensing detection is based on the optical absorption principle to finish the detection of the mobile pollution source sewage gas, and the optical signal has the problems of absorption, scattering, beam deflection, beam diffusion and the like. Detection is mostly carried out in an outdoor environment, the measuring process is easily influenced by factors such as temperature, humidity, air pressure, wind speed, wind direction and dust, and the problem is a complex nonlinear dynamics problem under the combined action of a plurality of factors. The transfer entropy can quantitatively measure the linear and nonlinear relations among system variables, has good anti-noise capability, and is often applied to depicting dynamic nonlinear characteristics in a complex system. Therefore, the transfer entropy is selected in the compensation model to perform correlation analysis on the measurement data, which helps to trace back the source of error generation and compensate the error more reasonably and accurately.

In order to verify the effectiveness of the compensation model, CO is selected as a target detection object, the measurement environment of temperature, humidity, air pressure and wind speed changes is simulated through an environment simulation experiment platform, and the target object is measured by adopting remote measuring equipment. Transfer entropy is adopted in the compensation model to measure the imbalance degree between multiple interferences. Assuming that the interferences are mutually independent to a certain extent, a measurement sequence under the change of single interference is obtained through a simulation experiment platform, so that the transfer entropy TE from the temperature interference to the measured value is calculated_T->CO, transfer entropy TE of humidity disturbance to measured value_H->CO, transfer entropy TE of barometric disturbance to measured value_P->CO, transfer entropy TE of wind speed disturbance factors to measured values_W->CO, with maximum reverse transfer entropy TE0 taken as a measure of non-causal relationship.

TE₀＝max{TE_CO->T、TE_CO->H、TE_CO->P、TE_CO->W}

As can be seen from FIG. 2, the transfer entropy TE of wind speed, temperature, barometric pressure to CO measurement_W->CO、TE_T->CO、TE_P->COAre clearly greater than the transfer entropy TE of humidity to CO measurement_H->COAnd the transfer entropy TE of humidity to CO measurement_H->COAnd reverse transfer entropy TE₀The difference is not large. From the information theory perspective, the information contained in the measurement sequence can be obviously explained from the wind speed, temperature and air pressure interference sequence, and the explaining part can be obtained from the humidity sequence to be smaller. Therefore, the wind speed, the temperature and the air pressure have obvious causal association on the measurement result, namely, the three environmental factors have larger interference on the measurement, and the proportion of the three factors in the measurement error is larger. From this it can be seen the transfer entropy TE of the humidity to the measurement_H->COAnd reverse transfer entropy TE₀Very close, reflecting that there is no obvious causal relationship of humidity to CO measurements. The effect of humidity may thus not be taken into account in the compensation of the CO measurement.

Step two: acquiring a training sample set of a single interference channel by adopting an environment simulation smoke box experiment platform, and establishing a measurement error prediction model of each interference by a neural network ANN method;

according to the graph shown in FIG. 3, the prediction model of the neural network for the CO gas telemetry error under temperature interference is shown. The telemetering error is not only influenced by interference factors, but also the absolute value of the error is influenced by the real concentration of the gas to be detected. Therefore, the input data of the neural network is the standard gas concentration n and the temperature t, and the output data is the measurement error e. And (4) selecting 7 hidden layer numbers according to a hidden layer point selection method of the forward network and the effect of actually processing data. Through smog chamber environmental simulation platform, fixed other factors regulate and control the incasement temperature to this training sample under obtaining single temperature interference. Similarly, a neural network prediction model under wind speed interference and air pressure interference can be established. Fig. 4-6 are error distributions for a test sample under single temperature, single air pressure, and single wind speed disturbances, respectively.

After three prediction models of temperature, wind speed and air pressure are established, error prediction can be respectively carried out on the measured values under certain temperature, wind speed and air pressure, and then the three prediction errors are summed to obtain a final compensation value.

Step three: according to the TE-ANN-AWF model structure diagram shown in FIG. 8, the transfer entropy TE, the neural network ANN and the adaptive weighting fusion AWF are combined for final estimation of the disturbance measurement value through virtual observation deconstruction and an exponential forgetting mechanism.

1) Firstly, realizing the multivariate deconstruction of a unit observation sequence by a virtual observation method, carrying out corresponding error compensation on the deconstructed multivariate virtual observation sequence by an ANN error prediction model under different interferences, and then carrying out fusion reconstruction on the compensated multivariate virtual observation sequence by adopting a multivariate self-adaptive weighting fusion method AWF.

Aiming at an ANN error prediction model, the real concentration of the gas to be detected directly influences the error distribution. In fact, the actual concentration of the gas to be measured cannot be known, and only approximate estimation can be performed through a historical sequence, which also causes inaccurate predicted measurement errors. Therefore, the error compensation values for the respective channels are directly added, and the effect is not obvious. According to fig. 7, in order to apply the method of data fusion to the error compensation model, the observation sequence needs to be deconstructed. For this purpose, the concept of virtual observation is first introduced.

For example, the remote sensing detection of CO is interfered by temperature, air pressure and wind speed in the environment, and if the mutual coupling of the three interference factors on the measurement result is small, the error component can be regarded as additive noise. Thus, the measured value can be regarded as represented by the following formula, where Y is the measured value, yr is the true value, Wt, Ww, Wp are the environmental interference noise, and θ is the measurement random noise.

Y＝y_r+W_t+W_w+W_p+θ

Wherein, Wt, Ww, Wp are the measurement error of single interference, which can be predicted by the single interference ANN model.

The measured value at a single temperature disturbance is Yt, and it can be considered as a value excluding both of Ww and Wp, as shown in the following equation.

Y_t＝y_r+W_t+θ＝Y-W_w-W_p

It is clear that the measured value Yt at temperature single interference does not exist in practice. In fact, it is a reconstruction of the original observations and is therefore referred to as a "virtual observation". Similarly, the measured value Yp under the single disturbance of the air pressure and the measured value Yw under the single disturbance of the wind speed can be obtained as shown in the following formula.

Y_w＝y_r+W_w+θ＝Y-W_t-W_p

Y_p＝y_r+W_p+θ＝Y-W_t-W_w

After the observation is deconstructed by the concept of virtual observation, reconstruction is also needed. Wind speed has a greater influence on the measurement results than temperature, barometric pressure, especially when wind speed is greater than 5 m/s. Obviously, the confidence of the measured value at this time should be minimal. To express the magnitude of this confidence, a transitive entropy is introduced to express the confidence of the three virtual observations. It can be known from the transmission entropy analysis that the larger the transmission entropy of the interference is, the stronger the causal relationship of the interference measurement is, and the stronger the interference is on the measurement result. The confidence of the virtual observations is thus inversely proportional to the transfer entropy. Meanwhile, in order to keep the total weight of 1, the weights of the three virtual observations whose confidence levels are different need to be calculated, and the confidence levels of the three virtual observations can be obtained as follows.

Wherein TE_T、TE_P、TE_WCan be estimated according to the principle of transfer entropy, and K_T、K_P、K_WSatisfying the following equation.

K_t+K_p+K_w＝1

And reconstructing by using the estimated confidence degrees of different virtual observations as the weight values of the virtual observations. The measurement results after reconstruction are shown in the following formula.

2) Secondly, aiming at the problem of weight convergence in the fusion algorithm, an exponential forgetting method is introduced to combine the advantages of good weight estimation capability of TE and self-adaptive adjustment of the weight of AWF, so that the dynamic performance of the error compensation process is improved.

In the TE-ANN model, although the transfer entropy has a good capability of weight estimation, the weight cannot be adjusted according to the error so as to gradually converge, so that the distribution of the error also keeps fluctuating and cannot converge. The AWF adaptive weighting fusion algorithm has the advantage that the weight can be gradually converged under the criterion of minimum mean square error without any prior knowledge. In order to combine the advantages of good weight estimation of TE and the advantages of adaptive adjustment of AWF weight, a forgetting mechanism is introduced.

Pre-entropy of the obtained transferEstimated confidence weight K and optimal weighting factor W according to minimum mean square error criterion^*Selecting a weighting coefficient { β n }, and adding K to W^*The fusion was carried out as shown in the following formula.

Where n represents the fusion of the nth observation.

Considering the characteristics of the smooth estimation of the transmission entropy and the adaptive adjustment and convergence of the weight of the AWF, the estimated value of the initial dynamic process of the weight is mainly referred to Kn, and the steady-state process is mainly referred to Wn and gradually converges to Wn. In order to embody the above-described characteristics, the weighting coefficients { β n } need to satisfy the following characteristics:

in order to satisfy the above conditions, the following function is constructed.

d_n＝(1-b)/(1-a·bⁿ)，n＝1，2，3…

Wherein b is a forgetting factor, a is an attenuation factor, and 0< b <1< a. By

The available weighting coefficients:

β_n ^K＝d_n，β_n ^W＝1-d_n

therefore, the weight of each channel can be obtained, as shown in the formula:

wherein Wn ^ satisfies the following formula, and the obtained new weight Wn ^ is used as a new weight to replace the original Wn ^.

The above examples are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.

Claims (4)

1. The method for compensating the telemetering error of the mobile pollution source based on the TE-ANN-AWF specifically comprises the following steps:

the method comprises the following steps: measuring samples under different interference effects are obtained through an environment simulation experiment; based on the experimental measurement sample, performing interference correlation analysis through TE transfer entropy so as to determine a measurement error source and measure the unbalance degree between multiple interferences; the directivity of the TE transfer entropy is utilized to lead out the quantization standard and the judgment method of the non-obvious causal relationship; ignoring interference factors which have non-significant causal relationship with the measurement result in the subsequent step;

step two: acquiring a training sample set of a single interference channel by adopting an environment simulation smoke box experiment platform, and establishing a measurement error prediction model of each interference by a neural network ANN method;

step three: realizing the multivariate deconstruction of the unit observation sequence by a virtual observation method, carrying out error compensation on the deconstructed multivariate virtual observation sequence by an ANN error prediction model under different interferences, and then carrying out fusion reconstruction on the compensated multivariate virtual observation sequence by adopting a multivariate self-adaptive weighting fusion method;

aiming at weight convergence in the fusion algorithm, an exponential forgetting method is introduced into the model to combine the weight pre-estimation capability of TE and the weight self-adaptive adjustment of the multivariate self-adaptive weighting fusion method, so that the dynamic performance of the error compensation process is improved.

2. The TE-ANN-AWF-based mobile pollution source telemetry error compensation method of claim 1, wherein: in the first step, TE transfer entropy is introduced to carry out correlation causal analysis on the interference of remote sensing measurement aiming at the characteristic that the interference of an external environment can be detected, and the directivity of the transfer entropy is utilized to introduce a quantitative standard and a judgment method of an insignificant causal relationship;

assuming that the interferences are mutually independent to a certain extent, a measurement sequence under the change of single interference is obtained through a simulation experiment platform, so that the transfer entropy TE from the temperature interference to the measured value is calculated_T->COThe transfer entropy TE of the humidity disturbance to the measured value_H->COTransfer entropy TE of barometric disturbance to measured value_P->COTransfer entropy TE of wind speed disturbance factor to measured value_W->COIn which the maximum backward transfer entropy TE is taken₀As a measure of non-causal relationships;

TE₀＝max{TE_CO->T、TE_CO->H、TE_CO->P、TE_CO->W} (1)。

3. the TE-ANN-AWF-based mobile pollution source telemetry error compensation method of claim 1, wherein: in the third step, the fusion reconstruction of the compensated multivariate virtual observation sequence by adopting the multivariate adaptive weighting fusion method specifically comprises the following steps: carrying out self-adaptive fusion on the multivariate observation values of all interference channels under the criterion of minimum mean square error; three methods of TE transfer entropy, ANN artificial neural network and AWF self-adaptive weighting fusion are closely combined with each other through a virtual observation method and an exponential forgetting mechanism.

4. The TE-ANN-AWF-based mobile pollution source telemetry error compensation method of claim 1, wherein: in the third step, an exponential forgetting method is introduced into the model to combine the TE weight estimation capability and the AWF weight adaptive adjustment, and the method specifically comprises the following steps:

the obtained confidence weight K of the transmission entropy estimation and the optimal weighting factor W according to the minimum mean square error criterion^*Selecting a weighting factor of β_nH, mixing K and W^*Carrying out fusion to obtain

As shown in the following formula;

wherein n represents the fusion of the nth observation,

a weighting factor, K, representing a confidence weight, K_nRepresenting the confidence weight of the transmission entropy estimation of the nth observed value,

represents the optimal weighting factor W^*Weighting coefficient of W_n ^*Representing the weight of the AWF after the nth observation value is fused;

considering the characteristics of stable estimation of the transmission entropy and the self-adaptive adjustment and convergence of the AWF weight, the estimated value of the initial dynamic process of the weight is mainly focused on K_nWhile the steady state process should be focused on W_n ^*And gradually converge to W_n ^*In order to embody the above-mentioned characteristics, the weighting factor is β_nThe following characteristics need to be satisfied:

β_i＝β_i-1b；0<b<1；

i represents a natural number; (3)

in order to satisfy the above conditions, the following function is constructed;

d_n＝(1-b)/(1-a·bⁿ)，n＝1，2，3…(4)

wherein b is a forgetting factor, a is an attenuation factor, and 0< b <1< a; the weighting coefficient is obtained from equation (3):

thus, the weight of each channel is obtained, as shown in the formula:

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