CN111444663A - Kalman tracking loop design method, Kalman tracking loop, space vehicle - Google Patents

Abstract

The invention belongs to the technical field of aerospace craft measurement and control communication, and discloses a Kalman tracking loop design method, a Kalman tracking loop and an aerospace craft.A time-varying plasma sheath model is established and the amplitude attenuation and the phase shift of a received signal under a plasma sheath are calculated; establishing an autoregressive model of amplitude attenuation and calculating the statistical characteristic of phase shift; designing a state equation and an observation equation of a Kalman filter; designing a novel Kalman tracking loop of the hypersonic aircraft; analyzing the amplitude attenuation and the phase shift of a received signal under a plasma sheath channel, calculating an autoregressive model of the amplitude attenuation and the statistical characteristics of the phase shift, and designing a Kalman filter suitable for the plasma sheath channel; and considering the amplitude attenuation of the received signal under the action of the plasma sheath in the design of a tracking loop, and establishing a Kalman filter for simultaneously tracking the amplitude attenuation and the phase of the received signal. The method provides a new idea for the stable signal tracking of the hypersonic aircraft.

Description

Kalman tracking loop design method, Kalman tracking loop, space vehicle

technical field

The invention belongs to the technical field of aerospace vehicle measurement and control communication, in particular to a Kalman tracking loop design method, a Kalman tracking loop, and an aerospace vehicle, in particular to a new Kalman tracking loop design method for a hypersonic aircraft.

Background technique

At present, the fast flying speed and large maneuvering range of the near space hypersonic vehicle make the received signal of the receiver have a large Doppler frequency shift and high-order derivative. In addition, when a hypersonic vehicle penetrates the atmosphere, the plasma sheath covering the surface of the aircraft will absorb, reflect and scatter electromagnetic waves, and the electromagnetic signal will have severe amplitude attenuation and phase shift after passing through the plasma sheath. . Therefore, the design of the carrier tracking loop of hypersonic vehicle is challenged by multiple factors such as large dynamic Doppler frequency offset, severe amplitude attenuation and phase shift.

At present, there are two main types of carrier tracking methods in the field of measurement and control communication: one is a tracking loop based on a traditional phase-locked loop (PLL), and the other is a tracking loop based on a Kalman filter. The existing tracking loops based on these two types of methods have excellent performance in general application scenarios, but cannot achieve robust carrier tracking in large dynamic Doppler and plasma sheath channels. The first type of method does not consider the influence of the amplitude noise of the received signal, and the bandwidth of the loop filter is a constant value. Large dynamic Doppler requires a larger bandwidth of the loop filter of the phase-locked loop, and low signal-to-noise ratio requires loop filtering. Due to the small bandwidth of the device, the contradiction between large bandwidth and high precision cannot be balanced, and the carrier tracking capability of the traditional phase-locked loop drops sharply in the state of high dynamic, low signal-to-noise ratio and severe plasma sheath amplitude attenuation. In the second type of method, in order to solve the contradiction between large dynamics and low signal-to-noise ratio, Kalman filter is introduced. At present, only large dynamic Doppler is considered, and its state variables are usually carrier phase, Doppler frequency, and Doppler acceleration. Although it can better solve the large dynamic tracking problem, it does not consider the influence of signal amplitude attenuation on the tracking loop in the plasma sheath channel.

Through the above analysis, the existing problems and defects in the prior art are:

(1) The existing tracking loop has a large dynamic Doppler under the dual harsh conditions of a large dynamic Doppler and a plasma sheath channel, which requires a large loop bandwidth, and a low signal-to-noise ratio requires a small loop bandwidth.

(2) The traditional tracking loop uses the bandwidth of the loop filter as a fixed value, which cannot balance the contradiction between large bandwidth and high precision.

(3) The traditional tracking loop works in the scenario where the signal amplitude attenuation can generally be ignored, or the attenuation is a fixed value. The amplitude attenuation of the received signal of the hypersonic aircraft has fast time variation. The effects of amplitude decay are extremely vulnerable to loss of lock.

The difficulty of solving the above problems and defects is as follows:

The signal received by the hypersonic vehicle is severely attenuated due to the action of the plasma sheath. The traditional tracking loop ignores the amplitude attenuation of the received signal during the tracking process, and can only overcome the influence of the large dynamic Doppler frequency offset and Doppler acceleration on the received signal. In a high-level environment, the attenuation of the received signal amplitude will cause the phase-locked loop to lose its lock, which cannot be ignored. How to consider the amplitude attenuation of the received signal in the loop design is the difficulty and focus of the phase-locked loop to achieve stable carrier tracking under the plasma sheath.

The significance of solving the above problems and defects is:

The invention provides a Kalman tracking loop design method, realizes robust tracking of received signals in a hypersonic environment, and provides a new idea for the design of receiver tracking loops with severe amplitude attenuation.

SUMMARY OF THE INVENTION

Aiming at the problems existing in the prior art, the present invention provides a Kalman tracking loop design method, a Kalman tracking loop, and a space vehicle.

The present invention is realized by a Kalman tracking loop design method, the Kalman tracking loop design method establishes a time-varying plasma sheath model and calculates the amplitude attenuation and phase shift of the received signal under the plasma sheath; Establish the autoregressive model of amplitude attenuation and the statistical characteristics of phase shift; design the state equation and observation equation of the Kalman filter; design a new Kalman tracking loop for hypersonic aircraft; through the amplitude attenuation of the received signal under the plasma sheath channel and phase shift, calculate the autoregressive model of amplitude attenuation and the statistical characteristics of phase shift, and design a Kalman filter suitable for the plasma sheath channel; consider the amplitude attenuation of the received signal under the action of the plasma sheath into the tracking loop In the design, a Kalman filter is built that tracks both the amplitude attenuation and the phase of the received signal.

Further, the Kalman tracking loop design method includes:

使用双高斯模型确定时不变的等离子体鞘套信道的电子密度模型Ne(z_m)；或者通过RAM-C实测数据确定不同飞行高度上的时不变的等离子体鞘套信道的电子密度模型Ne(z_m)；在时不变电子信道基础上加入时变抖动Δ建立时变等离子体鞘套电子密度模型Ne(z_m,t_n)，根据均匀等离子体中电磁波传输理论计算信号穿过等离子体鞘套之后的幅度衰减r(t_n)和相移

The first step is to establish a time-varying plasma sheath electron density model to solve the amplitude attenuation r(t _n ) and phase shift of the received signal

Use the double Gaussian model to determine the time-invariant plasma sheath channel electron density model Ne(z _m ); or determine the time-invariant plasma sheath channel electron density model at different flight heights through RAM-C measured data Ne(z _m ); on the basis of the time-invariant electron channel, the time-varying jitter Δ is added to establish a time-varying plasma sheath electron density model Ne(z _m , t _n ), and the signal passing through the plasma is calculated according to the electromagnetic wave transmission theory in uniform plasma. Amplitude decay r(t _n ) and phase shift after plasma sheath

和方差

输入仿真得到的接收信号的幅度衰减r(t_n)和相移

使用Levinson-Durbin算法求解得到自回归模型的一次迭代系数α_2,1、二次迭代系数α_2,2和迭代噪声方差σ_ν，得到接收信号幅度衰减的自回归模型，使用输入相移计算其均值

和方差

The second step is to establish an autoregressive model r'(t _n ) after the amplitude attenuation of the received signal is removed and the mean value is removed, and the statistical characteristics of the phase shift, that is, the mean value of the phase shift, are calculated.

and variance

Enter the simulated amplitude attenuation r(t _n ) and phase shift of the received signal

The first iteration coefficient α _2,1 , the second iteration coefficient α _2,2 and iterative noise variance σ _ν of the autoregressive model are obtained by using the Levinson-Durbin algorithm to obtain the autoregressive model of the amplitude attenuation of the received signal, and the input phase shift is used to calculate its mean

and variance

和方差

设计状态变量包括接收信号幅度衰减和相位的Kalman滤波器的状态方程X_n＝AX_n-1+BY_n-1+W_n-1和观测方程Z_n＝H_nX_n+V_n；The third step is to design the Kalman filter, input the phase noise υ _1,n generated by the tracking loop circuit, the Doppler frequency noise υ _2,n , the Doppler acceleration noise υ _3,n The covariance matrix Q, the phase detection The covariance matrix R of the observed noise at the output of the receiver, the receiver integration time T _s , the first iteration coefficient α _2,1 , the second iteration coefficient α _2,2 and the iterative noise variance σ of the autoregressive model of the received signal amplitude attenuation and mean removal _ν , the mean amplitude attenuation mean(r(t _n )), the mean value of the phase shift of the received signal

and variance

The design state variables include the state equation X _n =AX _n-1 +BY _n-1 +W _n-1 and the observation equation Z _n =H _n X _n +V _n of the Kalman filter of the received signal amplitude attenuation and phase;

The fourth step, input the state equation of the Kalman filter: X _n =AX _n-1 +BY _n-1 +W _n-1 and the observation equation: Z _n =H _n X _n +V _n , the actual output of the phase detector The observation value Z _n , the initial value X ₀ of the observation vector, the initial value P ₀ of the covariance matrix of the observation vector, the initial phase θ _vco of the local oscillator and the Doppler frequency offset w _d after coarse acquisition, the loop update time T _s , the Kalman filter tracking loop under the plasma sheath channel is realized according to the tracking steps of the Kalman filter loop.

Further, the first step of calculating and establishing the amplitude attenuation and phase shift under the time-varying plasma sheath channel includes:

(1) Calculate the specific distribution of the plasma sheath electron density with the surface of the aircraft at a fixed time, using the data measured by NASA's RAM-C or the double Gaussian distribution:

Input the thickness of the surface plasmon sheath during the flight of the hypersonic vehicle is Z, the layer of the plasma sheath is M, the thickness of each layer is d _m , the peak electron density ne _,max , and the first Gaussian function influence parameter σ ₁ and the second Gaussian function influence parameter σ ₂ take a fixed value, z _T is the thickness of the plasma sheath, z _B is the thickness of the boundary layer, and the electron density model Ne(z _m ) of the time-invariant plasma sheath channel is determined. ;

(2) Calculate the electron density distribution of the time-varying plasma sheath, and generate a non-stationary colored noise n(t _n ) with a standard deviation of 1, and add the jitter factor Δ of the electron density on the basis of the time-varying plasma sheath , the electron density distribution of the time-varying plasma sheath is established as:

Ne(z _m ,t _n )=Ne(z _m )*[1+Δ*n(t _n )];

输入等离子体的碰撞频率ν_en，入射电磁波的角频率ω，光速c，计算每一层的信号幅度衰减系数,和相移系数：(3) Calculate the amplitude attenuation coefficient and phase shift coefficient of each layer: According to the electromagnetic wave propagation theory in uniform plasma, input ε ₀ is the absolute dielectric constant in vacuum, me is the free electron mass, _e is the free electron charge number, Finding the Eigenfrequencies of Time-Varying Plasma

Enter the collision frequency ν _en of the plasma, the angular frequency ω of the incident electromagnetic wave, the speed of light c, and calculate the signal amplitude attenuation coefficient and phase shift coefficient for each layer:

(4) Calculate the amplitude attenuation and phase shift of the signal passing through the entire plasma sheath as:

和方差

包含以下步骤：Further, in the second step, an autoregressive model r'(t _n ) is established after the amplitude attenuation of the received signal is removed and the mean value is removed, and the statistical characteristic of the phase shift, that is, the mean value of the phase shift is calculated.

and variance

Contains the following steps:

(1) Remove the mean value of the obtained amplitude attenuation: the mean value of the signal amplitude attenuation is mean(r(t _n )), and the signal amplitude attenuation after removing the mean value is r′(t _n )=r(t _n )-mean( r(t _n )), the data r′(t _n ) after removing the mean is expressed as:

r'(t _n )=α _2,1 r(t _n-1 )+α _2,2 r(t _n-2 )+v(n);

Use the Levinson-Durbin algorithm to solve the Gaussian white noise v(n) with the first iteration coefficient α _2,1 , the second iteration coefficient α _2,2 , and the variance σ _ν ;

和方差

(2) Calculate the statistical characteristics of the phase shift: input the simulation results of the phase shift, the phase shift obeys the Gaussian distribution function, and solve the mean value of the input phase shift according to the statistical characteristics of the Gaussian distribution function

and variance

Further, the third step Kalman filter design includes:

电路产生的噪声υ_1,n，则n时刻接收信号和本地振荡器的真实相位差Δθ_n表示为：(1) Determine the expression of the real phase difference Δθ _n between the input signal and the local oscillator at time n: According to the real phase difference Δθ _n-1 at the previous time, the Doppler frequency ωd _n-1 and the Doppler frequency at the previous time Phase noise generated by the Le acceleration wan _-1 and the plasma sheath channel

The noise υ _1,n generated by the circuit, then the real phase difference Δθ _n between the received signal and the local oscillator at time n is expressed as:

(2) Determine the state equation of the Kalman filter: According to the autoregressive model and the dynamic equation, the state equation of the Kalman filter that simultaneously tracks the amplitude attenuation and the carrier phase is obtained as:

(3) Determine the observation equation of the Kalman filter: the observation variable Z _n is the output U ₀ (t _n ) _i and U ₀ (t _n ) _q of the phase detector plus the observation noise, which is expressed as:

Express the observation equation in linear form, that is, linearize the output h(X _n ) of the phase detector.

Further, the outputs U ₀ (t _n ) _i and U ₀ (t _n ) _q of the phase detector:

1) Considering the speed and computational complexity of the phase detector, the unfiltered output of the phase detector is expressed as:

θ _e (t _n )=y(t _n )×U _VCO ;

Where y(t _n ) is the received signal, and U _VCO is the carrier signal generated by the local oscillator;

2) Take the expression of θ _e (t _n ) after passing through the low-pass filter as the final output of the phase detector:

Further, the method for realizing linearization of the observation equation includes:

表示为Z_n＝H_nX_n+V_n，求解H_n方法为：

求得：Linearization converts the observation vector Z _n by the formula

Expressed as Z _n =H _n X _n +V _n , the method for solving H _n is:

Get:

Further, the realization of the tracking of the Kalman filter loop in the fourth step includes:

(1) Pre-estimate with the optimal value of the state vector at the previous moment

(2) Pre-estimation error variance

(3) Kalman filter gain calculation

(4) Optimal state vector

(5) Update error variance P _n =[1-K _n H _n ]P _n,n-1 ;

(6) Update the oscillation frequency of the local oscillator w _vco,n =w _d +ωd _n-1 and the initial phase θ _vco,n =Δθ _n-1

Another object of the present invention is to provide a Kalman tracking loop obtained by the Kalman tracking loop design method, wherein the Kalman tracking loop includes a phase detector, a Kalman filter, and a local oscillator; considering the signal Amplitude attenuation Kalman filter after passing through the plasma sheath.

Another object of the present invention is to provide a spacecraft equipped with the Kalman tracking loop.

Combined with all the above technical solutions, the advantages and positive effects of the present invention are as follows: the present invention establishes a time-varying plasma sheath model and calculates the amplitude attenuation and phase shift of the received signal under the plasma sheath; establishes an autoregressive amplitude attenuation The model calculates the statistical characteristics of the phase shift; on this basis, the state equation and observation equation of the Kalman filter are designed; a new Kalman tracking loop for the hypersonic vehicle is designed. The invention avoids the problem of losing lock caused by ignoring the amplitude attenuation of the traditional phase-locked loop tracking under the plasma sheath, and provides a new idea for the stable tracking of the signal of the hypersonic aircraft. Aiming at the fast measurement, control and tracking requirements of high-speed aircraft, the present invention designs a new tracking loop based on Kalman filtering while considering the amplitude attenuation and phase shift of the received signal and the large dynamic Doppler frequency offset under complex channel conditions.

The invention analyzes the amplitude attenuation and phase shift of the received signal under the plasma sheath channel, calculates the autoregressive model of the amplitude attenuation and the statistical characteristics of the phase shift, designs a Kalman filter suitable for the plasma sheath channel, and realizes high Design of a new Kalman filter loop under the aircraft plasma sheath channel.

The invention takes the amplitude attenuation of the received signal under the action of the plasma sheath into consideration in the design of the tracking loop, establishes a Kalman filter that simultaneously tracks the amplitude attenuation and phase of the received signal, and avoids the loop caused by the severe amplitude attenuation of the received signal Loss of lock problem; the traditional loop filter is replaced by a Kalman filter. During the working process, its bandwidth is not a fixed value but is adjusted to an optimal value in real time, and there is no large dynamic Doppler in the traditional loop filter. And the bandwidth design conflict problem caused by low signal-to-noise ratio. The amplitude attenuation, phase shift and related parameters of the received signal of the hypersonic aircraft can be stored in the receiver in advance, and the tracking loop only stores the value of the last moment during operation, so the algorithm has good real-time performance.

Description of drawings

FIG. 1 is a flowchart of a method for designing a Kalman tracking loop provided by an embodiment of the present invention.

FIG. 2 is a structural diagram of a Kalman tracking loop provided by an embodiment of the present invention.

FIG. 3 is a diagram of a time-varying plasma density layering model provided by an embodiment of the present invention.

FIG. 4 is a graph of amplitude attenuation under a plasma sheath provided by an embodiment of the present invention.

FIG. 5 is a phase shift diagram under a plasma sheath provided by an embodiment of the present invention.

FIG. 6 is a result diagram of the phase tracking of the Kalman tracking loop in Embodiment 1 to Embodiment 7 provided by the embodiment of the present invention.

FIG. 7 is a phase tracking result diagram of a Kalman tracking loop when the aircraft flies at 71 km according to an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

Aiming at the problems existing in the prior art, the present invention provides a Kalman tracking loop design method, a Kalman tracking loop, and an aerospace vehicle. The present invention will be described in detail below with reference to the accompanying drawings.

As shown in FIG. 1 , the Kalman tracking loop design method provided by the embodiment of the present invention includes the following steps:

S101: Determine the time-varying plasma model to calculate the amplitude attenuation and phase shift of the received signal;

S102: Calculate the statistical characteristics of the autoregressive model and the phase shift after the amplitude attenuation is removed from the mean;

S103: Design a Kalman filter that considers both the amplitude attenuation and the phase of the state variable and the observed variable;

S104: Design a Kalman filter tracking loop under the plasma sheath.

The technical solutions of the present invention will be further described below with reference to specific embodiments.

Example 1

The current tracking loops are designed for application scenarios where the signal amplitude attenuation is negligible. The received signal amplitude attenuation is severe in the plasma sheath channel of the hypersonic aircraft. At this time, the traditional tracking loop is very easy to lose lock. The invention simulates and analyzes the amplitude attenuation and phase shift of the signal under the time-varying plasma, and obtains the autoregressive model of the amplitude attenuation and the statistical characteristics of the phase shift. On this basis, the Kalman filter considering the signal amplitude attenuation and phase shift is designed , The present invention realizes a new Kalman tracking loop design method for hypersonic aircraft.

The new Kalman tracking loop design method under the plasma sheath channel of the hypersonic aircraft provided by the present invention includes the following steps:

使用双高斯模型确定时不变的等离子体鞘套信道的电子密度模型Ne(z_m)。或者通过RAM-C实测数据确定不同飞行高度上的时不变的等离子体鞘套信道的电子密度模型Ne(z_m)。在时不变电子信道基础上加入时变抖动Δ建立时变等离子体鞘套电子密度模型Ne(z_m,t_n)。根据均匀等离子体中电磁波传输理论计算信号穿过等离子体鞘套之后的幅度衰减r(t_n)和相移

The first step is to establish a time-varying plasma sheath electron density model and solve the amplitude attenuation r(t _n ) and phase shift of the received signal

The electron density model Ne(z _m ) for the time-invariant plasma sheath channel was determined using a double Gaussian model. Alternatively, the electron density model Ne(z _m ) of the time-invariant plasma sheath channel at different flight heights can be determined from the measured data of RAM-C. A time-varying plasma sheath electron density model Ne(z _m , t _n ) is established by adding time-varying jitter Δ on the basis of the time-invariant electron channel. Calculate the amplitude attenuation r(t _n ) and phase shift of the signal after passing through the plasma sheath according to the theory of electromagnetic wave transmission in homogeneous plasma

The invention calculates the amplitude attenuation and phase shift of the received signal after passing through the plasma sheath by establishing a time-varying plasma sheath electron density distribution model, so as to subsequently establish an amplitude attenuation autoregressive model and calculate the phase shift statistical characteristics.

和方差

输入仿真得到的接收信号的幅度衰减r(t_n)和相移

使用Levinson-Durbin算法求解自回归模型的一次迭代系数α_2,1、二次迭代系数α_2,2和迭代噪声方差σ_ν，得到去除均值之后的幅度衰减自回归模型：The second step is to establish an autoregressive model r'(t _n ) after the amplitude attenuation of the received signal is removed and the mean value is removed, and the statistical characteristics of the phase shift, that is, the mean value of the phase shift, are calculated.

and variance

Enter the simulated amplitude attenuation r(t _n ) and phase shift of the received signal

Use the Levinson-Durbin algorithm to solve the first iteration coefficient α _2,1 , the second iteration coefficient α _2,2 and iterative noise variance σ _ν of the autoregressive model, and obtain the amplitude decay autoregressive model after removing the mean:

r'(t _n )=α _2,1 r(t _n-1 )+α _2,2 r(t _n-2 )+v(n);

和方差

Calculate its mean using the input phase shift

and variance

The invention establishes a corresponding autoregressive model for the amplitude attenuation of the signal, and expresses the amplitude attenuation except the mean value as a second-order iterative method, so that it is possible to consider the amplitude attenuation and the phase into the state variables when designing the state equation of the Kalman filter. . Calculate the statistical characteristics of the signal phase shift under the influence of the plasma sheath, which provides the basis for the Kalman filter design.

和方差

设计状态变量包括接收信号幅度衰减和相位的Kalman滤波器的状态方程X_n＝AX_n-1+BY_n-1+W_n-1和观测方程Z_n＝H_nX_n+V_n。其中状态方程具体表示为：The third step is to design the Kalman filter: input the phase noise υ _1,n generated by the tracking loop circuit, the Doppler frequency noise υ _2,n , the Doppler acceleration noise υ _3,n covariance matrix Q, phase detection The covariance matrix R of the observed noise at the output of the receiver, the receiver integration time T _s , the first iteration coefficient α _2,1 , the second iteration coefficient α _2,2 and the iterative noise variance σ of the autoregressive model of the received signal amplitude attenuation and mean removal _ν , the mean amplitude attenuation mean(r(t _n )), the mean value of the phase shift of the received signal

and variance

The design state variables include the state equation _Xn =AXn _-1 +BYn _-1 + _{Wn -1} and the observation equation Zn= _{HnXn + Vn} for the Kalman filter of the received signal amplitude attenuation and phase. The state equation is specifically expressed as:

The observation equation is specifically expressed as:

By analyzing the amplitude attenuation and phase shift characteristics of the received signal under the plasma sheath channel, the invention designs the state equation and the observation equation that the state variable and the observation variable include the signal amplitude attenuation and phase shift at the same time, so that the Kalman filter considers the amplitude attenuation The mathematical model is more in line with the real state when the signal is tracked.

The fourth step is to realize the new Kalman tracking loop: input the state equation of the Kalman filter: X _n =AX _n-1 +BY _n-1 +W _n-1 and the observation equation: Z _n =H _n X _n +V _n , the actual observation quantity Z _n output by the phase detector, the initial value X ₀ of the observation vector, the initial value P ₀ of the covariance matrix of the observation vector, the initial phase θ _vco of the local oscillator and the Doppler frequency offset w after coarse acquisition _d , the loop update time T _s , the new Kalman loop tracking of the hypersonic vehicle is realized according to the tracking steps of the Kalman filter loop:

1) Pre-estimate with the optimal value of the state vector at the previous moment

2) Pre-estimated error variance

3) Kalman filter gain calculation

4) Optimal state vector

5) Update error variance P _n =[1-K _n H _n ]P _n,n-1 ;

6) Update the oscillation frequency w _vco,n =w _d +ωd _n-1 and the initial phase θ _vco,n =Δθ _n-1 of the generated signal of the local oscillator.

The present invention provides the overall design idea of the new Kalman tracking loop of the hypersonic aircraft, and the structure of the tracking loop is shown in FIG. 2 . It consists of a phase detector, a Kalman filter, and a local oscillator. The amplitude attenuation of the signal after passing through the plasma sheath is taken into account in the design of the Kalman filter, so that the mathematical model of the tracking loop is more in line with the actual tracking situation, and the stable tracking of the signal carrier can also be achieved in the case of severe amplitude attenuation.

Example 2

包括如下步骤：The design method of the new Kalman tracking loop for hypersonic aircraft is the same as that in Example 1, and the amplitude attenuation r(t _n ) and phase shift of the signal after passing through the plasma sheath are calculated

It includes the following steps:

The first step is to establish the electron density distribution of the time-varying plasma sheath as shown in Figure 3: For a fixed time, the electron density distribution Ne(z) that changes with the thickness of the plasma sheath can be expressed as:

where _{n e,max} represents the maximum electron density of the dynamic plasma sheath; z _B is the boundary layer position; z _T is the thickness of the plasma sheath _; According to the data collected by Project C, when the flying height of the aircraft is 30km, the influence of the plasma sheath on the received signal reaches the worst state. At this time, ne _,max = 7.7×10 ¹⁸ m ^-3 , z _T = 15cm , z _B =5 cm, σ ₁ =1, σ ₂ =0.5. After obtaining Ne(z) at a fixed time, the time-varying model of plasma electron density can be expressed as:

Ne(z,t)=Ne(z)*[1+Δ*n(t)];

where Δ is the relative jitter strength of electrons in the plasma, and its value is generally between 0-20%, in this patent the value is 10%, and n(t) is the non-stationary colored noise with a standard deviation of 1.

The second step is to calculate the time-varying plasma sheath characteristic frequency ω _p (z _m , t _n ): the input _Ne (z _m , t _n ) represents the electron density of the m-th layer of plasma at the time of t _n , and the free electron charge Number _e =1.6×10 ⁻¹⁹ C, absolute dielectric constant in vacuum ε ₀ =8.854×10 ⁻¹² F/m, free electron mass me = 9.1×10 ⁻³¹ kg. The time-varying plasma sheath characteristic frequency ω _p (z _m , t _n ) can be specifically expressed as:

The third step is to calculate the amplitude attenuation coefficient α(z _m , t _n ) and phase shift β(z _m , t _n ) of each layer after delamination: input the time-varying plasma sheath eigenfrequency ω _p (z _m , t _n ) ), the collision frequency of the plasma is ν _en =5GHz, the angular frequency of the incident electromagnetic wave is ω=2π×30×10 ⁹ rad/s, and the speed of light is c=3×10 ⁸ m/s. According to the electromagnetic wave propagation theory in homogeneous plasma, the amplitude attenuation coefficient α(z _m , t _n ) and phase shift β(z _m , t _n ) of the m- _th layer at time t n are expressed as follows:

输入等离子体鞘套每层的幅度衰减系数α(z_m,t_n)和相移β(z_m,t_n)。信号穿过等离子体后的整体幅度衰减r(t_n)和相移

表示为：The fourth step is to calculate the amplitude attenuation r(t _n ) and phase shift of the signal under the plasma sheath channel

Enter the amplitude decay coefficient α(z _m ,t _n ) and the phase shift β(z _m ,t _n ) for each layer of the plasma sheath. Overall amplitude attenuation r(t _n ) and phase shift of the signal after passing through the plasma

Expressed as:

The simulated amplitude attenuation under the plasma sheath channel is shown in Figure 4. The phase shift is shown in Figure 5.

Example 3

和方差

包括如下步骤：A new Kalman tracking loop design method for hypersonic vehicles. Same as Embodiment 1 to Embodiment 2, establish the autoregressive model r'(t _n ) after the amplitude attenuation of the received signal and remove the mean value, and calculate the phase shift statistical characteristics, that is, the mean value of the phase shift

and variance

It includes the following steps:

The first step is to de-average the obtained signal amplitude attenuation r(t _n ) to obtain r′(t _n ):

r'(t _n )=r(t _n )-mean(r(t _n ));

The second step is to establish an autoregressive model for the data r'(t _n ) after removing the mean: use the second-order autoregressive model:

r'(t _n )=α _2,1 r(t _n-1 )+α _2,2 r(t _n-2 )+v(n);

where v(n) is a Gaussian distribution subject to variance σ _ν , σ _ν , α _2,1 , α _2,2 are all parameters to be solved, input r′(t _n ) obtained in the first step, and use Levinson- The Durbin algorithm solves the parameter results:

计算最恶劣飞行环境下的相移的均值

方差

为：The third step is to calculate the statistical characteristics of the phase shift caused by the plasma sheath: the existing research shows that the statistical characteristics of the phase shift under the plasma sheath channel are Gaussian

Calculate the mean value of the phase shift for the worst flight conditions

variance

for:

Example 4

The design method of the new Kalman tracking loop of the hypersonic aircraft is the same as that of Embodiment 1 to Embodiment 3, and the equation of state for calculating and designing the Kalman filter includes the following steps:

The first step is to establish the receiver signal model y(t _n ) as:

包括由粗捕获之后剩余多普勒频偏和多普勒加速度引起的相位、受等离子鞘套影响的相位噪声和初始相位；

是接收机产生的噪声服从均值为0方差为

的高斯分布。即

where r(t _n ) is the amplitude attenuation produced by the plasma sheath; A is the amplitude of the original signal, which is set to 1 in this patent to simplify the operation; the carrier phase

Including phase due to residual Doppler frequency offset and Doppler acceleration after coarse acquisition, phase noise and initial phase due to plasma sheath;

is that the noise generated by the receiver obeys the mean of 0 and the variance is

Gaussian distribution. which is

The second step is to calculate the phase detector output U ₀ (t _n ): considering the real-time nature of the tracking loop and the complexity of the algorithm, the phase detector of the traditional PLL tracking loop generally uses the local oscillator signal and the received signal to be multiplied by the received signal. The result of the low pass filter is used as the output of the phase detector. The result of multiplying the local oscillator generated signal U _VCO and the received signal y(t _n ) θ _e (t _n ) is expressed as:

θ _e (t _n )=y(t _n )×U _VCO ;

It includes low-frequency components and high-frequency components. After passing θ _e (t _n ) through the low-pass filter, the in-phase and quadrature components output by the phase detector can be expressed as follows, where Δθ _n is the received signal and the signal generated by the local oscillator True Phase Difference:

电路产生的噪声υ_1,n，该时刻的Δθ_n可以估计为：The third step is to estimate the phase difference Δθ _n between the received signal and the signal generated by the local oscillator: input the optimal phase difference Δθ _n-1 estimated by the Kalman filtering tracking loop at the previous moment, and the Dopp in the T _s time period Le frequency ωd _n-1 , Doppler acceleration wa _n-1 and phase noise due to plasma

The noise υ _1,n generated by the circuit, Δθ _n at this moment can be estimated as:

表示的相位差估计方法、动力学方程。将状态变量定义为[Δθ_n ωd_n wa_n r′ r′_n-1]^T，则新型Kalman滤波器的状态方程X_n＝AX_n-1+BY_n-1+W_n-1表示为：The fourth step is to design the state equation of the Kalman filter X _n =AX _n-1 +BY _n-1 +W _n-1 : Different from the traditional Kalman filter tracking loop, the state variables in the state equation also include the signal's Phase information Δθ _n and amplitude attenuation information r'(t _n ). The combined formula r'(t _n )=α _2,1 r(t _n-1 )+α _2,2 r(t _n-2 )+v(n) represents the amplitude decay autoregressive model after removing the mean, the formula

Represented phase difference estimation method, dynamic equation. Defining the state variable as [Δθ _n ωd _n wa _n r′ r′ _n-1 ] ^T , the state equation of the new Kalman filter X _n =AX _n-1 +BY _n-1 +W _n-1 is expressed as:

Example 5

The design method of a new type of Kalman tracking loop for hypersonic aircraft is the same as that of Embodiment 1 to Embodiment 4. The calculation and design of the observation equation Z _n =H _n X _n +V _n of the Kalman filter includes the following steps:

The first step is to determine the observation variable: the observation variable Z _n is the in-phase output U ₀ (t _n ) _i , U ₀ (t _n ) _q of the phase detector plus the observation noise n _i,n , n _q,n , expressed as :

求得：The second step is to establish the observation equation: the linearization of the observation variable is expressed as the form of multiplying the state variable X _n and the observation matrix H _n , and the general method for solving H _n is:

Get:

The specific expression of the observation equation is:

Example 6

The design method of the new Kalman tracking loop of the hypersonic aircraft is the same as that of Embodiment 1 to Embodiment 5, and the design steps of the new Kalman tracking loop of the hypersonic aircraft are calculated as follows:

其中Y_n-1为常值1，

输入跟踪环路的状态变量初始值X₀＝[0 ωd₀ wa₀ 00]^T，其中ωd₀为粗捕获之后的多普勒频偏取值为3KHz，wa₀为初始的多普勒加速度取值为800KHz。A_n,n-1为状态变量在本专利中是定值：The first step is to use the optimal value of the state vector at the previous moment to pre-estimate

where Y _n-1 is a constant value of 1,

The initial value of the state variable of the input tracking loop X ₀ =[0 ωd ₀ wa ₀ 00] ^T , where ωd ₀ is the Doppler frequency offset after rough acquisition, which is 3KHz, and wa ₀ is the initial Doppler acceleration. The value is 800KHz. A _n,n-1 is a state variable which is a fixed value in this patent:

where T _s =8.3×10 ⁻⁷ .

其中A_n,n-1与步骤6.1)的表达式相同，输入初始的

其中

为等离子体鞘套影响下相移的方差

σ_ν为自回归模型中的变量σ_ν＝0.005，σ_1,n、σ_2,n、σ_3,n分别为电路引起的相位噪声、多普勒频偏噪声、多普勒加速度噪声的方差，取值分别为0.1、0.3、0.3。The second step is to pre-estimate the error variance

where A _n,n-1 is the same as the expression in step 6.1), enter the initial

in

is the variance of the phase shift under the influence of the plasma sheath

σ _ν is the variable in the autoregressive model σ _ν = 0.005, σ _1,n , σ _2,n , σ _3,n are the variances of the phase noise, Doppler frequency offset noise, and Doppler acceleration noise caused by the circuit, respectively , the values are 0.1, 0.3, and 0.3, respectively.

其中H_n为观测矩阵，具体表达式为：The third step, Kalman filter gain calculation

where H _n is the observation matrix, and the specific expression is:

的协方差矩阵，具体表示为：where mean(r(n)) is the mean value of the amplitude attenuation caused by the plasma sheath, mean(r(t _n ))=0.2186. R is the observation noise

The covariance matrix of , specifically expressed as:

为接收机的信噪比，取值为0dB，T_s为相关时间。in

is the signal-to-noise ratio of the receiver, the value is 0dB, and T _s is the correlation time.

其中Z_n为实际的观测变量值，h(X_n)是鉴相器的理论输出值。具体表达式为：The fourth step is to solve the optimal state vector

Among them, Z _n is the actual observed variable value, and h(X _n ) is the theoretical output value of the phase detector. The specific expression is:

The fifth step, update the error variance P _n =[1-K _n H _n ]P _n,n-1 .

In the sixth step, the oscillation frequency w _vco,n =ωd _n-1 and the initial phase θ _vco,n =Δθ _n-1 of the generated signal of the local oscillator are updated.

The seventh step, taking T _s as the update time, repeats the first to sixth steps to realize the new Kalman filter carrier tracking loop under the plasma sheath channel.

The technical effects of the present invention will be described in detail below in conjunction with simulation.

1. Simulation conditions:

The thickness of the plasma sheath is 15cm, which is equally divided into 150 parts. The collision frequency inside the plasma is ν _en = 5GHz, the angular frequency of the incident electromagnetic wave is ω = 2π×30×10 ⁹ rad/s, and the Doppler frequency offset at the receiving end is is 3KHz, the Doppler acceleration is 800KHz/s, the receiver integration time T _s is 8×10 ^-7 s, and the signal-to-noise ratio at the receiver is 0dB.

2. Simulation results and analysis:

FIG. 6 is a graph of the tracking results of the carrier phase of the received signal by the new Kalman tracking loop of the hypersonic aircraft in the present embodiment 1 to embodiment 7. The real-time tracking is performed under the situation where the environment where the aircraft is located has the worst influence on the received signal. It can be seen from FIG. 6 that the novel Kalman tracking loop of the present invention can achieve smooth tracking of the carrier phase. Using the method proposed in this patent to track the received signal when the flight altitude is 71km, the result is shown in Figure 7. It can be seen that the phase difference between the received signal and the local carrier at the flight altitude of 71km floats within ±1.5°. Combined with the simulation results, it can be seen that compared with the traditional PLL tracking loop completely out of lock, the new Kalman tracking loop for hypersonic aircraft considering amplitude attenuation can achieve carrier tracking in near space.

The invention discloses a new Kalman tracking loop design scheme for a hypersonic aircraft, which mainly solves the problem of loss of lock of the traditional phase-locked loop tracking loop caused by the attenuation of the received signal amplitude under the plasma sheath channel. The realization process is: establish a time-varying plasma sheath model and calculate the amplitude attenuation and phase shift of the received signal under the plasma sheath; establish an autoregressive model of amplitude attenuation and statistical characteristics of phase shift; on this basis, design a Kalman filter Equations of state and observation equations of aircraft; design of a new Kalman tracking loop for hypersonic vehicles. The invention avoids the problem of losing lock caused by ignoring the amplitude attenuation of the traditional phase-locked loop tracking under the plasma sheath, and provides a new idea for the stable tracking of the signal of the hypersonic aircraft.

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited to this. Any person skilled in the art is within the technical scope disclosed by the present invention, and all within the spirit and principle of the present invention Any modifications, equivalent replacements and improvements made within the scope of the present invention should be included within the protection scope of the present invention.

Claims (10)

1. A Kalman tracking loop design method is characterized in that the Kalman tracking loop design method establishes a time-varying plasma sheath model and calculates amplitude attenuation and phase shift of a received signal under a plasma sheath; establishing an autoregressive model of amplitude attenuation and statistical characteristics of phase shift; designing a state equation and an observation equation of a Kalman filter; designing a novel Kalman tracking loop of the hypersonic aircraft; analyzing the amplitude attenuation and the phase shift of a received signal under a plasma sheath channel, calculating an autoregressive model of the amplitude attenuation and the statistical characteristics of the phase shift, and designing a Kalman filter suitable for the plasma sheath channel; and considering the amplitude attenuation of the received signal under the action of the plasma sheath in the design of a tracking loop, and establishing a Kalman filter for simultaneously tracking the amplitude attenuation and the phase of the received signal.

2. The kalman tracking loop design method according to claim 1, wherein the kalman tracking loop design method comprises:

in the first step, a time-varying plasma sheath electron density model is established to solve the amplitude attenuation r (t) of a received signal_n) And phase shift

Determining an electron density model Ne (z) for a time-invariant plasma sheath channel using a double Gaussian model_m) (ii) a Or determined not to be in the RAM-C measured dataElectron density model Ne (z) of time-invariant plasma sheath channel at fly height_m) (ii) a Time-varying plasma sheath electron density model Ne (z) is established by adding time-varying jitter delta on the basis of time-invariant electron channel_m,t_n) The amplitude attenuation r (t) after the signal passes through the plasma sheath is calculated according to the theory of electromagnetic wave transmission in uniform plasma_n) And phase shift

Secondly, establishing an autoregressive model r' (t) with the amplitude attenuation of the received signal and the mean value removed_n) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift

Sum variance

Inputting the amplitude attenuation r (t) of the simulated received signal_n) And phase shift

Solving by using L evison-Durbin algorithm to obtain one-time iteration coefficient α of autoregressive model_2,1Coefficient of second iteration α_2,2And the iterative noise variance σ_νObtaining an autoregressive model of the amplitude attenuation of the received signal, and calculating the mean value thereof by using the input phase shift

Sum variance

Thirdly, designing a Kalman filter and inputting phase noise upsilon generated by a tracking loop circuit_1,nDoppler frequency noise v_2,nDoppler acceleration noise v_3,nThe covariance matrix Q of the received signal, the covariance matrix R of the observed noise at the output of the phase discriminator, and the integration time of the receiverT_sCoefficient α of one iteration of an autoregressive model with mean value removed by signal amplitude attenuation_2,1Coefficient of second iteration α_2,2And the iterative noise variance σ_νAmplitude decay mean (r (t)_n) Average of received signal phase shifts)

Sum variance

State equation X for a Kalman filter for designing state variables including amplitude attenuation and phase of a received signal_n＝AX_n-1+BY_n-1+W_n-1And observation equation Z_n＝H_nX_n+V_n；

Fourthly, inputting a state equation of the Kalman filter: x_n＝AX_n-1+BY_n-1+W_n-1And the observation equation: z_n＝H_nX_n+V_nActual observed value Z of phase discriminator output_nInitial value X of the observation vector₀Initial value P of covariance matrix of observation vector₀Initial phase θ of local oscillator_vcoAnd Doppler frequency offset w after coarse acquisition_dLoop update time T_sAnd realizing a Kalman filter tracking loop under a plasma sheath channel according to the tracking step of the Kalman filter loop.

3. The method of kalman tracking loop design according to claim 2, wherein the first step of time varying plasma sheath channel amplitude attenuation and phase shift calculation setup includes:

(1) calculating the specific distribution of plasma sheath electron density at fixed times along the aircraft surface, using NASA's RAM-C measured data or a double Gaussian distribution:

input high ultrasoundThe thickness of the surface plasma sheath is Z and the plasma sheath is layered into M during the flying process of the fast aircraft, wherein the thickness of each layer is d_mPeak electron density n_e,maxThe first Gaussian function influencing parameter σ₁And a second Gaussian function influence parameter σ₂Taking the value as a constant value, z_TIs the plasma sheath thickness, z_BFor boundary layer thickness, an electron density model Ne (z) of the time invariant plasma sheath channel is determined_m)；

(2) Calculating the electron density distribution of the time-varying plasma sheath to produce a non-stationary colored noise n (t) with a standard deviation of 1_n) Adding a jitter factor delta of the electron density on the basis of the time-invariant plasma sheath, and establishing a time-variant plasma sheath electron density distribution as follows:

Ne(z_m,t_n)＝Ne(z_m)*[1+Δ*n(t_n)]；

(3) calculating the amplitude attenuation coefficient and the phase shift coefficient of each layer: according to the electromagnetic wave propagation theory in the uniform plasma, inputting₀Is the absolute dielectric constant in vacuum, m_eCalculating the characteristic frequency of the time-varying plasma according to the mass of free electrons and the number of charges of free electrons

Collision frequency v of input plasma_enThe angular frequency ω of the incident electromagnetic wave, the speed of light c, the signal amplitude attenuation coefficient for each layer, and the phase shift coefficient:

(4) the amplitude attenuation and phase shift of the signal across the entire plasma sheath were calculated:

4. the method of Kalman tracking loop design of claim 2 wherein the second step builds an autoregressive model r' (t) with the received signal amplitude attenuated and mean removed_n) Calculating statistical characteristics of the phase shift, i.e. the mean value of the phase shift

Sum variance

Comprises the following steps:

(1) the resulting amplitude attenuation is de-averaged: solving the mean of the signal to mean (r (t)_n) The averaged signal is subtracted r' (t)_n)＝r(t_n)-mean(r(t_n) Mean-removed data r' (t)_n) Using an autoregressive model as:

r′(t_n)＝α_2,1r(t_n-1)+α_2,2r(t_n-2)+v(n)；

solving one-iteration coefficient α by using L evison-Durbin algorithm_2,1Coefficient of second iteration α_2,2Variance is σ_νWhite gaussian noise v (n);

(2) calculating the statistical properties of the phase shift: inputting simulation result of phase shift, the phase shift obeys Gaussian distribution function, and solving the mean value of the input phase shift according to the statistical characteristics of the Gaussian distribution function

Sum variance

5. The Kalman tracking loop design method of claim 2, wherein the third step of Kalman filter design includes:

(1) determining the sum local oscillator true phase difference Δ θ of the input signal at time n_nExpression (c): true phase difference Δ θ from the previous time instant_n-1Doppler frequency ω d at the previous time_n-1Doppler acceleration wa_n-1Phase noise generated by plasma sheath channel

Noise v generated by the circuit_1,nThen the true phase difference delta theta between the received signal and the local oscillator at time n_nExpressed as:

(2) determining a state equation of the Kalman filter: obtaining a Kalman filter state equation for simultaneously tracking amplitude attenuation and carrier phase according to an autoregressive model and a kinetic equation as follows:

(3) determining an observation equation of a Kalman filter: observed variable Z_nIs output U of the phase discriminator₀(t_n)_i、U₀(t_n)_qPlus observation noise, expressed as:

expressing the observation equation in linear form, i.e. the output h (X) of the phase detector_n) And (6) linearization is carried out.

6. The Kalman tracking loop design method of claim 5, wherein the output of the phase detector, U₀(t_n)_i、U₀(t_n)_q：

(1) Considering the operation speed and the calculation complexity of the phase detector, the output of the phase detector which is not subjected to filtering processing is represented as follows:

θ_e(t_n)＝y(t_n)×U_VCO；

wherein y (t)_n) For receiving signals, U_VCOA carrier signal generated for a local oscillator;

(2) will theta_e(t_n) The result after passing through the low pass filter is taken as the final output of the phase detector:

7. the Kalman tracking loop design method of claim 5, wherein the observation equation linearization implementation method comprises:

linearization: will observe vector Z_nIs composed of

Is represented by Z_n＝H_nX_n+V_nSolving for H_nThe method comprises the following steps:

obtaining:

8. the Kalman tracking loop design method of claim 2, wherein the fourth step of the implementation of tracking of the Kalman filtering loop comprises:

(1) pre-estimation with last moment state vector optimal value

(2) Pre-estimation error variance

(3) Kalman filter gain calculation

(4) Optimal state vector

(5) Updating the error variance P_n＝[1-K_nH_n]P_n,n-1；

(6) Updating the oscillation frequency w of a local oscillator_vco,n＝w_d+ωd_n-1And an initial phase theta_vco,n＝Δθ_n-1。

9. A Kalman tracking loop obtained by the Kalman tracking loop design method according to any one of claims 1 to 8, wherein the Kalman tracking loop includes a phase discriminator, a Kalman filter, and a local oscillator; the amplitude of the signal after passing through the plasma sheath is attenuated into a Kalman filter.

10. An aerospace vehicle carrying the kalman tracking loop of claim 9.

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