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CN105929419B - A kind of GPS carrier tracking based on BP artificial neural network - Google Patents

A kind of GPS carrier tracking based on BP artificial neural network Download PDF

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CN105929419B
CN105929419B CN201610225689.7A CN201610225689A CN105929419B CN 105929419 B CN105929419 B CN 105929419B CN 201610225689 A CN201610225689 A CN 201610225689A CN 105929419 B CN105929419 B CN 105929419B
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CN105929419A (en
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陈帅
蒋长辉
屈新芬
韩乃龙
陈克振
薄煜明
黄思亮
孔维
孔维一
韩筱
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
    • G01S19/29—Acquisition or tracking or demodulation of signals transmitted by the system carrier including Doppler, related
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent

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Abstract

The invention discloses a kind of GPS carrier trackings based on BP artificial neural network, and steps are as follows: BP ANN first；The phase discriminator of phaselocked loop exports the judgement factor after being computed as carrier tracking loop operating condition, which can accurately reflect carrier tracking loop tracking situation；The judgement factor being calculated is inputted into trained neural network, neural network exports control parameter；Loop filter receives the output of frequency locking ring discriminator and the output of phaselocked loop discriminator, respectively multiplied by the local carrier digital controlled oscillator after corresponding control parameter to control and receive machine, to keep the tenacious tracking to input signal.The method of the present invention establishes the non-linear relation between the loop judgement factor and control parameter using BP artificial neural network algorithm, according to loop tracks situation dynamic regulation closed loop control parameter, tracking performance of the receiver carrier tracking loop under high dynamic environment is significantly improved.

Description

A kind of GPS carrier tracking based on BP artificial neural network
Technical field
The present invention relates to technical field of satellite navigation, a kind of GPS carrier tracking based on BP artificial neural network.
Background technique
GPS is a kind of Global Satellite Navigation System controlled by U.S. Department of Defense, has the advantages that high-precision, round-the-clock. It is widely used in the fields such as geodesic survey, automobile navigation, weapon guidance.For traditional GPS receiver, key technology It is exactly GPS carrier tracking technique, only steadily tracking carrier signal just can be carried out positioning and navigation.And it is general based on locking phase The greatest problem that the carrier tracking loop of ring faces is exactly high dynamic, weak signal and multipath effect etc..Wherein high dynamic problem It is the altitude maneuver due to receiver, causes carrier Doppler shift variation excessively fierce, at this time use the carrier wave of phaselocked loop Track loop is easy to losing lock, causes receiver can not work normally and steadily exports location information.Currently used GPS is carried Wave track loop is using pure phaselocked loop or using the form of frequency locking ring auxiliary phaselocked loop, and this structure is under low dynamic environment With good performance, but the tracer request under being unable to satisfy high dynamic environment.
Summary of the invention
The purpose of the present invention is to provide a kind of GPS carrier trackings based on BP artificial neural network, to improve GPS Tracking performance of the receiver under high dynamic environment.
Technical solution of the invention are as follows: a kind of GPS carrier tracking based on BP artificial neural network, carrier wave with Track loop includes PLL discriminator, FLL discriminator, carrier wave ring wave filter, correlator, frequency mixer, carrier wave NCO, C/A code generator With BP artificial neural network etc., the specific steps are as follows:
Step 1, carrier wave NCO generates sinusoidal signal and cosine signal, GPS digital medium-frequency signal and sinusoidal signal after despreading Frequency mixing processing is carried out into the first frequency mixer and obtains signal i (n), and the GPS digital medium-frequency signal after despreading and cosine signal enter Second frequency mixer carries out Frequency mixing processing and obtains signal q (n)；
Step 2, the i.e. time-code that signal i (n) and local C/A code generator generate carries out relevant treatment by the first correlator Obtain signal ip(n), the i.e. time-code that signal q (n) and local C/A code generator generate carries out relevant treatment by the second correlator Obtain signal qp(n)；
Step 3, it is assumed that in integration interval, carrier frequency difference and phase difference are all constant, signal ip(n)、qp(n) respectively pre- Add up the signal I that sums to obtain in the detection time of integrationP、QP；
Step 4, PLL discriminator is to signal IP、QPIt is handled to obtain local carrier-phase error delta φeIdentification result, FLL discriminator is to signal IP、QPIt is handled to obtain local carrier frequency error delta feIdentification result；
Step 5, the local carrier-phase error delta φ of PLL discriminator outputeAs loop operating condition after converted The factor is adjudicated, the judgement factor handles to obtain closed loop control parameter α by trained BP artificial neural network；
Step 6, the local carrier frequency error delta f of FLL discriminator outputeLocal carrier frequency after being adjusted multiplied by α Rate error delta f, PLL discriminator exports Δ φeLocal carrier-phase error delta φ after being adjusted multiplied by input after 2- α, Δ F, Δ φ incoming carrier ring wave filter is to control carrier wave NCO；
Further, PLL discriminator described in step 4 is to signal IP、QPIt is handled to obtain local carrier-phase error delta φeIdentification result, formula is as follows:
In formula: Δ φeValue range be (- π, π)；
FLL discriminator is to signal IP、QPIt is handled to obtain local carrier frequency error delta feIdentification result, formula is such as Under:
In formula: cross=IP(k-1)QP(k)-IP(k)QP(k-1), dot=IP(k-1)IP(k)-QP(k)QP(k-1), Cross=IP(k-1)QP(k)-IP(k)QP(k-1), dot=IP(k-1)IP(k)-QP(k)QP(k-1), IP(k-1) when being kth -1 Carve IPValue, QPIt (k-1) is -1 moment of kth QPValue, Δ t is the time interval between k-1 moment and k moment.
Further, the local carrier-phase error delta φ of the output of PLL discriminator described in step 5eRing is used as after converted The judgement factor of road operating condition, specific as follows:
E=cos [2 Δ φe]≤1
In formula, e is the judgement factor.
Further, the judgement factor described in step 5 handles to obtain loop control by trained BP artificial neural network Parameter alpha, detailed process is as follows:
(a) initiation parameter: wij,wjk,bj,bk,η,α；
Wherein wijIndicate the connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer, wherein wjk Indicate the connection weight between k-th of neuron of j-th of neuron of hidden layer and output layer, bjIt is j-th of neuron of hidden layer Threshold value, bkIt is k-th of neuron threshold value of output layer, η indicates Learning Step, and α is momentum term；
(b) training sample is inputted:
X=(x1,x2,x3,x4,…,xm)T, y=(y1,y2,…,yn)T；
Wherein x is input vector, and y is output vector, and m indicates input layer number, and n indicates output layer neuron Number；
(c) hidden layer input and output are calculated:
In formula, hijIndicate j-th of neuron input of hidden layer, hoj(k) j-th of neuron output of hidden layer；wijIt indicates Connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer, bjIt is j-th of neuron threshold value of hidden layer； xiIt is input vector；
(d) output layer input and output are calculated:
yok=f (yik)
In formula, yikIndicate k-th of neuron input of output layer, yokIndicate k-th of neuron output of output layer；wjkIt indicates Connection weight between k-th of neuron of j-th of neuron of hidden layer and output layer, bkIt is k-th of neuron threshold value of output layer；
hoj(k) j-th of neuron output of hidden layer；
(e) output layer and hidden layer output error are calculated:
δk=yok(1-yok)(yk-yok),
In formula, δkIndicate output layer output error, δjIndicate hidden layer output error, yiIt is output vector, yokIndicate defeated K-th of neuron output of layer out；hijIndicate j-th of neuron input of hidden layer；wjkIndicate j-th of neuron of hidden layer and defeated Connection weight between k-th of neuron of layer out；
(f) output layer and input layer connection weight and threshold value correction value are calculated:
Δwjk=η δkhij+αΔwjk, Δ θk=-η δk+αΔθk
Δwij=η δjxi+αΔwij, Δ θj=-η δj+αΔθj
In formula, Δ wijWith Δ θjIndicate the connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer Correction value and threshold value correction value；ΔwjkWith Δ θkIt indicates between k-th of neuron of j-th of neuron of hidden layer and output layer The correction value of connection weight and the correction value of threshold value；η indicates Learning Step, and α is momentum term；δkIndicate output layer output error, δj Indicate hidden layer output error；hijIndicate j-th of neuron input of hidden layer, xiIndicate i-th of neuron input value of input layer；
(g) output layer and input layer threshold value and Connecting quantity value are updated:
wjk=wjk+Δwjk, θk=θk+Δθk；wij=wij+Δwij, θj=θj+Δθj
Δ w in formulaijWith Δ θjIndicate the connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer Correction value and threshold value correction value；ΔwjkWith Δ θkIt indicates between k-th of neuron of j-th of neuron of hidden layer and output layer The correction value of connection weight and the correction value of threshold value；
(h) error cost function is calculated:
In formula, error indicates that error cost, n indicate output layer neuron number, yiIt is output vector, yoiIndicate output I-th of neuron output of layer；
Compared with prior art, the present invention its remarkable result is: (1) using loop judgement factor reflection track loop operation Situation adjudicates the size of the factor according to loop to adjust phaselocked loop and frequency locking ring in loop and act on size relatively, gives full play to lock Phase ring and frequency locking ring are respective a little；(2) it is established using BP artificial neural network algorithm non-between the judgement factor and control amount α Linear relationship significantly improves receiver carrier tracking loop and exists according to loop tracks situation dynamic regulation closed loop control parameter Tracking performance under high dynamic environment.
Detailed description of the invention
Fig. 1 is the functional block diagram of the GPS carrier tracking the present invention is based on BP artificial neural network.
Fig. 2 is BP artificial neural network structure figure.
Specific embodiment
The present invention is described in further details below in conjunction with the drawings and specific embodiments.
In carrier tracking loop designs, the biggish loop bandwidth of high dynamic environment needs, and biggish loop bandwidth meeting Cause to introduce more thermal noises, therefore needs to make this contradiction good compromise in receiver loop design.
As shown in Figure 1, 2, the present invention is based on the GPS carrier tracking of BP artificial neural network, carrier tracking loop packets It is artificial to include PLL discriminator, FLL discriminator, carrier wave ring wave filter, correlator, frequency mixer, carrier wave NCO, C/A code generator and BP Neural network etc., is implemented as follows:
The defeated intermediate-freuqncy signal S of GPS receiver radio-frequency front-end in the ideal situationIF(n) mathematical model are as follows:
In formula, A is signal strength, and n indicates the time, and D (n) is navigation message, and C (n) is C/A code, and τ is in transmission process Time delay, ωIFFor intermediate-freuqncy signal SIF(n) frequency, φ (n) are original carrier phase.
Step 1, carrier wave NCO generates sinusoidal signal and cosine signal, GPS digital medium-frequency signal and sinusoidal signal after despreading Frequency mixing processing is carried out into the first frequency mixer and obtains signal i (n), and the GPS digital medium-frequency signal after despreading and cosine signal enter Second frequency mixer carries out Frequency mixing processing and obtains signal q (n):
In formula, (ωIF+ Δ ω) it is the carrier frequency that local oscillator generates, Δ ω is local carrier frequency and input The difference of IF signal frequency, φ0Original carrier phase is generated for local signal.
Step 2, the i.e. time-code that signal i (n) and local C/A code generator generate carries out relevant treatment by the first correlator Obtain signal ip(n), the i.e. time-code that signal q (n) and local C/A code generator generate carries out relevant treatment by the second correlator Obtain signal qp(n):
In formula, A is signal strength, and n indicates the time, and D (n) is navigation message, and C (n) is C/A code, and τ is in transmission process Time delay, φ (n) are original carrier phase, and Δ ω is the difference of the IF signal frequency of local carrier frequency and input, φ0For Local signal generates original carrier phase.
Step 3, it is assumed that in integration interval, carrier frequency difference and phase difference are all constant, signal ip(n)、qp(n) respectively pre- Add up the signal I that sums to obtain in the detection time of integrationP、QP:
In formula, δ is the interval of local C/A code lead-lag, and T is post detection integration, and δ τ is PRN phase error, δ f WithCarrier frequency difference and carrier phase respectively between integration interval initial time local reference signal and input signal Difference, R (τ) are the correlation function of C/A code.
Step 4, PLL discriminator is to signal IP、QPIt is handled to obtain local carrier-phase error delta φeIdentification result, Formula is as follows:
In formula: Δ φeValue range be (- π, π)；
FLL discriminator is to signal IP、QPIt is handled to obtain local carrier frequency error delta feIdentification result, formula is such as Under:
In formula: cross=IP(k-1)QP(k)-IP(k)QP(k-1), dot=IP(k-1)IP(k)-QP(k)QP(k-1), IP It (k-1) is -1 moment of kth IPValue, QPIt (k-1) is -1 moment of kth QPValue, Δ t is the time between k-1 moment and k moment Interval.
Step 5, the local carrier-phase error delta φ of PLL discriminator outputeAs loop operating condition after converted The factor is adjudicated, the judgement factor handles to obtain closed loop control parameter α by trained BP artificial neural network；
The carrier tracking loop operating condition judgement factor calculates: the output of PLL discriminator is run after being computed as loop The judgement factor of situation, the judgement factor can accurately reflect loop tracks situation, adjudicate factor calculation formula:
The judgement factor handles to obtain closed loop control parameter α, specific training process by trained BP artificial neural network It is as follows:
(a) initiation parameter: wij,wjk,bj,bk,η,α；
Wherein wijIndicate the connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer, wherein wjk Indicate the connection weight between k-th of neuron of j-th of neuron of hidden layer and output layer, bjIt is j-th of neuron of hidden layer Threshold value, bkIt is k-th of neuron threshold value of output layer, η indicates Learning Step, and α is momentum term；
(b) training sample is inputted:
X=(x1,x2,x3,x4,…,xm)T, y=(y1,y2,…,yn)T；
Wherein x is input vector, and y is output vector, and m indicates input layer number, and n indicates output layer neuron Number；
(c) hidden layer input and output are calculated:
In formula, hijIndicate j-th of neuron input of hidden layer, hoj(k) j-th of neuron output of hidden layer；wijIt indicates Connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer, bjIt is j-th of neuron threshold value of hidden layer； xiIt is input vector；
(d) output layer input and output are calculated:
yok=f (yik) (12)
In formula, yikIndicate k-th of neuron input of output layer, yokIndicate k-th of neuron output of output layer；wjkIt indicates Connection weight between k-th of neuron of j-th of neuron of hidden layer and output layer, bkIt is k-th of neuron threshold value of output layer；
hoj(k) j-th of neuron output of hidden layer；
(e) output layer and hidden layer output error are calculated:
δk=yok(1-yok)(yk-yok),
In formula, δkIndicate output layer output error, δjIndicate hidden layer output error, yiIt is output vector, yokIndicate defeated K-th of neuron output of layer out；hijIndicate j-th of neuron input of hidden layer；wjkIndicate j-th of neuron of hidden layer and defeated Connection weight between k-th of neuron of layer out；
(f) output layer and input layer connection weight and threshold value correction value are calculated:
Δwjk=η δkhij+αΔwjk, Δ θk=-η δk+αΔθk (14)
Δwij=η δjxi+αΔwij, Δ θj=-η δj+αΔθj (15)
In formula, Δ wijWith Δ θjIndicate the connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer Correction value and threshold value correction value；ΔwjkWith Δ θkIt indicates between k-th of neuron of j-th of neuron of hidden layer and output layer The correction value of connection weight and the correction value of threshold value；η indicates Learning Step, and α is momentum term；δkIndicate output layer output error, δj Indicate hidden layer output error；hijIndicate j-th of neuron input of hidden layer, xiIndicate i-th of neuron input value of input layer；
(g) output layer and input layer threshold value and Connecting quantity value are updated:
wjk=wjk+Δwjk, θk=θk+Δθk；wij=wij+Δwij, θj=θj+Δθj (16)
Δ w in formulaijWith Δ θjIndicate the connection weight between j-th of neuron of i-th of neuron of input layer and hidden layer Correction value and threshold value correction value；ΔwjkWith Δ θkIt indicates between k-th of neuron of j-th of neuron of hidden layer and output layer The correction value of connection weight and the correction value of threshold value；
(h) error cost function is calculated:
In formula, error indicates that error cost, n indicate output layer neuron number, yiIt is output vector, yoiIndicate output I-th of neuron output of layer.
Step 6, the local carrier frequency error delta f of FLL discriminator outputeLocal carrier frequency after being adjusted multiplied by α Rate error delta f, PLL discriminator exports Δ φeLocal carrier-phase error delta φ after being adjusted multiplied by input after 2- α, Δ F, Δ φ incoming carrier ring wave filter is to control carrier wave NCO.
In conclusion the method for the present invention using BP artificial neural network algorithm establish loop judgement the factor and control parameter it Between non-linear relation receiver carrier track is significantly improved according to loop tracks situation dynamic regulation closed loop control parameter Tracking performance of the loop under high dynamic environment.

Claims (4)

1.一种基于BP人工神经网络的GPS载波跟踪方法，其特征在于，载波跟踪环路包括PLL鉴别器、FLL鉴别器、载波环滤波器、相关器、混频器、载波NCO、C/A码发生器和BP人工神经网络，具体步骤如下：1. a GPS carrier tracking method based on BP artificial neural network, is characterized in that, carrier tracking loop comprises PLL discriminator, FLL discriminator, carrier loop filter, correlator, frequency mixer, carrier NCO, C/A Code generator and BP artificial neural network, the specific steps are as follows: 步骤1，载波NCO产生正弦信号和余弦信号，解扩后的GPS数字中频信号与正弦信号进入第一混频器进行混频处理得到信号i(n)，解扩后的GPS数字中频信号与余弦信号进入第二混频器进行混频处理得到信号q(n)；Step 1, the carrier NCO generates a sine signal and a cosine signal, the despread GPS digital intermediate frequency signal and the sine signal enter the first mixer for mixing processing to obtain a signal i(n), and the despread GPS digital intermediate frequency signal and cosine. The signal enters the second mixer for mixing processing to obtain the signal q(n); 步骤2，信号i(n)与本地C/A码发生器生成的即时码通过第一相关器进行相关处理得到信号ip(n)，信号q(n)与本地C/A码发生器生成的即时码通过第二相关器进行相关处理得到信号qp(n)；Step 2, the signal i(n) and the real-time code generated by the local C/A code generator are subjected to correlation processing by the first correlator to obtain the signal i p (n), and the signal q(n) is generated by the local C/A code generator. The real-time code of is obtained by the second correlator for correlation processing to obtain the signal q p (n); 步骤3，假设积分间隔内，载波频率差和相位差都不变，信号ip(n)、qp(n)分别在预检测积分时间内累加求和得信号IP、QP；Step 3, assuming that in the integration interval, the carrier frequency difference and the phase difference are unchanged, and the signals i p (n) and q p (n) are accumulated and summed to obtain the signals IP and Q P in the pre-detection integration time respectively; 步骤4，PLL鉴别器对信号IP、QP进行处理得到本地载波相位误差Δφe的鉴别结果，FLL鉴别器对信号IP、QP进行处理得到本地载波频率误差Δfe的鉴别结果；Step 4, the PLL discriminator processes the signals IP and QP to obtain the discrimination result of the local carrier phase error Δφ e , and the FLL discriminator processes the signals IP and QP to obtain the discrimination result of the local carrier frequency error Δf e ; 步骤5，PLL鉴别器输出的本地载波相位误差Δφe经转换后作为环路运行情况的判决因子，判决因子通过训练好的BP人工神经网络处理得到环路控制参数α；Step 5, the local carrier phase error Δφ e output by the PLL discriminator is converted as the decision factor of the loop operation, and the decision factor is processed by the trained BP artificial neural network to obtain the loop control parameter α; 步骤6，FLL鉴别器输出的本地载波频率误差Δfe乘以α得到调整后的本地载波频率误差Δf，PLL鉴别器输出Δφe乘以2-α后输入得到调整后的本地载波相位误差Δφ，Δf、Δφ输入载波环滤波器以控制载波NCO。Step 6, the local carrier frequency error Δf e output by the FLL discriminator is multiplied by α to obtain the adjusted local carrier frequency error Δf, and the PLL discriminator output Δφ e is multiplied by 2-α and then input to obtain the adjusted local carrier phase error Δφ, Δf, Δφ are input to the carrier loop filter to control the carrier NCO. 2.根据权利要求1所述的基于BP人工神经网络的GPS载波跟踪方法，其特征在于，步骤4中所述PLL鉴别器对信号IP、QP进行处理得到本地载波相位误差Δφe的鉴别结果，公式如下：2. the GPS carrier tracking method based on BP artificial neural network according to claim 1, is characterized in that, described in step 4, the PLL discriminator processes the signal IP, QP and obtains the discrimination of local carrier phase error Δφ e As a result, the formula is as follows: 式中：Δφe的取值范围为(-π,π)；In the formula: the value range of Δφ e is (-π, π); FLL鉴别器对信号IP、QP进行处理得到本地载波频率误差Δfe的鉴别结果，公式如下：The FLL discriminator processes the signals IP and QP to obtain the discrimination result of the local carrier frequency error Δf e . The formula is as follows: 式中：cross＝IP(k-1)QP(k)-IP(k)QP(k-1)，dot＝IP(k-1)IP(k)-QP(k)QP(k-1)，IP(k-1)是第k-1时刻IP的值，QP(k-1)是第k-1时刻QP的值，Δt是k-1时刻和k时刻之间的时间间隔。In the formula: cross=IP (k-1)Q P (k) -IP (k) QP (k-1), dot= IP (k-1) IP (k)-Q P ( k )Q P (k-1), IP (k-1) is the value of IP at the k-1th time, Q P (k-1) is the value of Q P at the k- 1th time, Δt is k-1 The time interval between moment and k moment. 3.根据权利要求1所述的基于BP人工神经网络的GPS载波跟踪方法，其特征在于，步骤5所述PLL鉴别器输出的本地载波相位误差Δφe经转换后作为环路运行情况的判决因子，具体如下：3. the GPS carrier tracking method based on BP artificial neural network according to claim 1 is characterized in that, the local carrier phase error Δφ e of the described PLL discriminator output of step 5 is converted as the decision factor of the loop operation situation ,details as follows: e＝cos[2Δφe]≤1 (3)e=cos[2Δφ e ]≤1 (3) 式中，e为环路运行情况判决因子。In the formula, e is the decision factor of the loop operation condition. 4.根据权利要求1所述的基于BP人工神经网络的GPS载波跟踪方法，其特征在于，步骤5所述判决因子通过训练好的BP人工神经网络处理得到环路控制参数α，具体过程如下：4. the GPS carrier tracking method based on BP artificial neural network according to claim 1, is characterized in that, the described decision factor of step 5 obtains loop control parameter α by trained BP artificial neural network, and concrete process is as follows: (a)初始化参数：wij,wjk,bj,bk,η,β；(a) Initialization parameters: w ij , w jk , b j , b k , η, β; 其中wij表示输入层第i个神经元和隐含层第j个神经元之间的连接权值，其中wjk表示隐含层第j个神经元和输出层第k个神经元之间的连接权值，bj是隐含层第j个神经元阈值，bk是输出层第k个神经元阈值,η表示学习步长，β是动量项；where w ij represents the connection weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer, and w jk represents the connection weight between the j-th neuron in the hidden layer and the k-th neuron in the output layer Connection weight, b j is the threshold of the jth neuron in the hidden layer, b k is the threshold of the kth neuron in the output layer, η represents the learning step size, and β is the momentum term; (b)输入训练样本：(b) Input training samples: x＝(x1,x2,x3,x4,···,xm)T,y＝(y1,y2,···,yn)T；x=(x 1 , x 2 , x 3 , x 4 ,...,x m ) T , y=(y 1 , y 2 ,..., y n ) T ; 其中x是输入向量，y是输出向量，m表示输入层神经元个数，n表示输出层神经元个数；where x is the input vector, y is the output vector, m is the number of neurons in the input layer, and n is the number of neurons in the output layer; (c)计算隐含层输入输出：(c) Calculate the input and output of the hidden layer: 式中，hij表示隐含层第j个神经元输入，hoj(k)表示隐含层第j个神经元输出；wij表示输入层第i个神经元和隐含层第j个神经元之间的连接权值，bj是隐含层第j个神经元阈值；xi表示输入层第i个神经元输入值；In the formula, hi j represents the input of the jth neuron in the hidden layer, ho j (k) represents the output of the jth neuron in the hidden layer; w ij represents the ith neuron in the input layer and the jth neuron in the hidden layer. The connection weights between elements, b j is the threshold of the jth neuron in the hidden layer; x i represents the input value of the ith neuron in the input layer; (d)计算输出层输入输出：(d) Calculate the input and output of the output layer: 式中，yik表示输出层第k个神经元输入，yok表示输出层第k个神经元输出；wjk表示隐含层第j个神经元和输出层第k个神经元之间的连接权值，bk是输出层第k个神经元阈值；hoj(k)表示隐含层第j个神经元输出；In the formula, yi k represents the input of the kth neuron in the output layer, yo k represents the output of the kth neuron in the output layer; w jk represents the connection between the jth neuron in the hidden layer and the kth neuron in the output layer. Weight, b k is the threshold of the kth neuron in the output layer; ho j (k) represents the output of the jth neuron in the hidden layer; (e)计算输出层和隐含层输出误差：(e) Calculate the output layer and hidden layer output errors: 式中，δk表示输出层输出误差，δj表示隐含层输出误差，yk是输出向量中的第k个值，yok表示输出层第k个神经元输出；hij表示隐含层第j个神经元输入；wjk表示隐含层第j个神经元和输出层第k个神经元之间的连接权值；In the formula, δ k is the output error of the output layer, δ j is the output error of the hidden layer, y k is the k-th value in the output vector, yo k is the output of the k-th neuron in the output layer; hi j is the hidden layer The jth neuron is input; w jk represents the connection weight between the jth neuron in the hidden layer and the kth neuron in the output layer; (f)计算输出层和输入层连接权值和阈值修正值：(f) Calculate the connection weights and threshold correction values of the output layer and the input layer: Δwjk＝ηδkhij+βΔwjk，Δθk＝-ηδk+βΔθk (7)Δw jk = ηδ k hi j +βΔw jk , Δθ k =-ηδ k +βΔθ k (7) Δwij＝ηδjxi+βΔwij，Δθj＝-ηδj+βΔθj (8)Δw ij = ηδ j x i +βΔw ij , Δθ j =-ηδ j +βΔθ j (8) 式中，Δwij和Δθj表示输入层第i个神经元和隐含层第j个神经元之间的连接权值的修正值和阈值修正值；Δwjk和Δθk表示隐含层第j个神经元和输出层第k个神经元之间的连接权值的修正值和阈值的修正值；η表示学习步长，β是动量项；δk表示输出层输出误差，δj表示隐含层输出误差；hij表示隐含层第j个神经元输入，xi表示输入层第i个神经元输入值；In the formula, Δw ij and Δθ j represent the correction value and threshold correction value of the connection weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer; Δw jk and Δθ k represent the j-th hidden layer The correction value of the connection weight and the threshold value between each neuron and the kth neuron in the output layer; η represents the learning step size, β is the momentum term; δ k represents the output layer output error, δ j represents the implicit layer output error; hi j represents the input of the jth neuron in the hidden layer, and xi represents the input value of the ith neuron in the input layer; (g)更新输出层和输入层阈值和连接参数值：(g) Update output and input layer thresholds and connection parameter values: wjk＝wjk+Δwjk，θk＝θk+Δθk；wij＝wij+Δwij，θj＝θj+Δθj (9)w jk =w jk +Δw jk , θ k =θ k +Δθ k ; w ij =w ij +Δw ij , θ j =θ j +Δθ j (9) 式中Δwij和Δθj表示输入层第i个神经元和隐含层第j个神经元之间的连接权值的修正值和阈值修正值；Δwjk和Δθk表示隐含层第j个神经元和输出层第k个神经元之间的连接权值的修正值和阈值的修正值；where Δw ij and Δθ j represent the correction value and threshold correction value of the connection weight between the ith neuron in the input layer and the jth neuron in the hidden layer; Δw jk and Δθ k represent the jth neuron in the hidden layer The correction value of the connection weight between the neuron and the kth neuron of the output layer and the correction value of the threshold; (h)计算误差代价函数：(h) Calculate the error cost function: 式中，error表示误差代价，n表示输出层神经元个数，yi是输出向量中的第i个值，yoi表示输出层第i个神经元输出。where error represents the error cost, n represents the number of neurons in the output layer, y i is the ith value in the output vector, and yo i represents the output of the ith neuron in the output layer.
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