CN103593509A - Method for analyzing plasma-sheath-caused multipath interference on aircraft surfaces - Google Patents

Abstract

The invention discloses a method for analyzing plasma-sheath-caused multipath interference on aircraft surfaces. The method includes firstly, using a flow field distribution file to input frequency, direction and power of navigation signals; calculating according to the MUSIC algorithm and the decorrelation algorithm to acquire interference signals. Direction of arrival is estimated based on the MUSIC algorithm of the decorrelation processing technology, so that the method is applicable to judgment on influence magnitude of the multipath interference in satellite navigation systems. Since multipath magnitude and incoming direction can be estimated, the method can support for eliminating multipath influences.

Description

The multipath interference analysis method that a kind of aircraft surface is produced by plasma sheath

Technical field

The invention belongs to Satellite Navigation Technique field, be specifically related to the multipath interference analysis method that a kind of aircraft surface is produced by plasma sheath.

Background technology

Aircraft is reentried to the process of landing and is called the process of reentering.Reenter in process, hypersonic aircraft and atmospheric interaction form arc detached shock wave before aircraft, and after shock wave, gas temperature sharply raises and presents " high-temperature effect ", air molecule generation dissociation, ionization reaction; Meanwhile, the ablation under high temperature, high hot-fluid effect of the solar heat protection ablator of aircraft surface, is discharged into aircraft around in flow field by ablation resultant, has formed the various complicated Flow Field that reenters of composition.Reentering Flow Field is an ionized gas, when ionisation of gas degree acquires a certain degree, ionized gas shows the collective behavior that plasma has and becomes plasma, now reenters Flow Field and is also called the coated flow field of plasma, reenters plasma or plasma sheath.Reenter the formation of plasma, make the power attenuation of Electromagnetic Wave Propagation, and make electromagnetic wave produce reflection, refraction and scattering.

Signal produces multiple reflections through after plasma sheath between aircraft surface and plasma sheath, thereby causes multipath effect.The multipath effect here refers to GPS receiver except directly receiving satellite-signal, still may receive after plasma sheath transmitting, through different travel paths, arrives aerial signal.Thereby the positioning error forming, multipath effect can reduce the positioning precision of receiver, and lengthened in the processing time, at WAAS(Wide Area Augmentation System) and DGPS(Difference Global Positioning System) in system, multipath effect error will cause propagation of error, user's positioning precision in seriously reduction system.

The method that also there is no to analyze multipath effect in existing plasma sheath model, if can effectively estimate the multipath effect that plasma sheath produces, will play important effect for eliminating the impact of multipath.

Summary of the invention

The object of this invention is to provide the multipath interference analysis method that a kind of aircraft surface is produced by plasma sheath, solved the problem that existing plasma sheath model can not be analyzed multipath effect.

The technical solution adopted in the present invention is, the multipath interference analysis method that a kind of aircraft surface is produced by plasma sheath is specifically implemented according to following steps:

Step 1: first use Flow Field Distribution file, the frequency of input navigation signal, direction, power;

Step 2: adopt MUSIC algorithm to conciliate related algorithm and calculate undesired signal.

Feature of the present invention is also,

Step 2 wherein is specifically implemented according to following steps:

Input needs the plasma distribution file of prediction, use FDTD numerical value emulation method, plasma is pressed to input file to distribute within the specific limits, according to frequency, direction, the power of the navigation measurement and control signal of setting, be the signal of feed-in, at the aircraft surface of simulating, M observation station is set, position between observation station is less than half wavelength, by FDTD numerical evaluation, go out each observation station, the signal Xp receiving, p is the number of sampled point;

M unit observation station is divided into several submatrixs, and the array number of each submatrix is m, and information source number is K, and submatrix number p, has M=p+m-1;

Get first submatrix for reference battle array, i submatrix reception data are:

$X_i^f\left(k\right)=[x_i,x_{i+1},\·\·\·,x_{i-m+1}]={\mathrm{AD}}^{(i-1)}s\left(k\right)+n_i\left(k\right),$

Wherein

Φ is the phase differential between adjacent array element, so corresponding to the covariance matrix of this submatrix be:

$\begin{array}{c}{R}_i^f=E\left[X_i^f{\left(X_i^f\right)}^H\right]={\mathrm{AD}}^{(i-1)}{R}_s{\left(D^{(i-1)}\right)}^H{A}^H+{\mathrm{\σ}}^2{I}_m\\ ={\mathrm{AD}}^{(i-1)}{R}_s{D}^{-(i-1)}{A}^H+{\mathrm{\σ}}^2{I}_m\end{array},$

In formula, I _mfor m rank unit matrix, R _sfor signal autocorrelation matrix, the covariance matrix of all submatrixs is got to average, the covariance matrix after being processed, that is:

$R^f=\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{R}_i^f=A\left(\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{D}^{(i-1)}{R}_s{D}^{-(i-1)}\right)A^H+{\mathrm{\σ}}^2{I}_m,$

Estimate that input covariance matrix is:

${\hat{R}}_x=R^f,$

Covariance matrix is carried out to feature decomposition:

${\hat{R}}_{x}V=\mathrm{V\Λ},$

In formula, Λ=diag{ λ ₀..., λ _m-1, λ ₀>=...>=λ _m-1for eigenwert, V=[q ₀..., q _m-1] be

the matrix that characteristic of correspondence vector forms;

Utilize the tuple L of little eigenwert to determine Signal estimation number:

$\hat{K}=M-L,$

And then determine noise subspace V _n;

Calculate MUSIC spatial spectrum:

${\hat{P}}_{\mathrm{MUSIC}}\left(\mathrm{\θ}\right)=\frac{a^H\left(\mathrm{\θ}\right)a\left(\mathrm{\θ}\right)}{a^H\left(\mathrm{\θ}\right)V_n{V}_n^{H}a\left(\mathrm{\θ}\right)},$

In formula, V _n=[q _k..., q _m-1];

Find out

's

individual peak-peak, except maximum peak value, obtains other multipath interference radiating way and estimates.

The invention has the beneficial effects as follows, the MUSIC algorithm that the present invention is based on the relevant treatment technology of solution carries out direction of arrival estimation, is suitable for judging in satellite navigation system the application that affects size of multipath effect.And can estimate multipath size and come to, for removing multi-path influence, provide support.

Accompanying drawing explanation

Fig. 1 is plane wave vertical incidence ideal plasma schematic diagram;

Fig. 2 is the analyses of Multipath Effects result that ideal plasma produces;

Fig. 3 is actual plasma sheath electron density distribution figure;

Fig. 4 is the analyses of Multipath Effects result that actual plasma sheath produces.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

The multipath interference analysis method that aircraft surface of the present invention is produced by plasma sheath, carries out numerical modeling to existing plasma sheath (can measure or emulation obtains model data), analyzes the multipath undesired signal that this plasma sheath exists.At aircraft surface, place receiving antenna array element (numerical simulation), the incident wave of navigation signal frequency is set, see through after plasma sheath, antenna array receives signal, adopts and separates coherent algorithm, and the order of signal covariance matrix is effectively restored.Then apply MUSIC algorithm computer memory spectrum, find out a plurality of peak-peaks of signal, obtain multipath Interference Estimation, determine the multipath interference radiating way that plasma sheath produces.Specifically according to following steps, implement:

Step 1: first use Flow Field Distribution file, the frequency of input navigation signal, direction, power.

Step 2: adopt MUSIC algorithm to conciliate related algorithm and calculate undesired signal.

In the method, the plasma distribution file that needs prediction by input, use FDTD numerical value emulation method, plasma is pressed to input file to distribute within the specific limits, according to frequency, direction, the power of the navigation measurement and control signal of setting, for the signal (can be j signal s) of feed-in, at the aircraft surface of simulating, M observation station is set, the position between observation station is less than half wavelength.By FDTD numerical evaluation, go out each observation station, the signal Xp receiving, p is the number of sampled point.

M unit observation station is divided into several submatrixs, and the array number of each submatrix is m, and information source number is K, and submatrix number p, has M=p+m-1.

Get first submatrix for reference battle array, i submatrix reception data are

$X_i^f\left(k\right)=[x_i,x_{i+1},\·\·\·,x_{i-m+1}]={\mathrm{AD}}^{(i-1)}s\left(k\right)+n_i\left(k\right)---\left(1\right)$

Wherein Φ is the phase differential between adjacent array element, so corresponding to the covariance matrix of this submatrix be

$\begin{array}{c}{R}_i^f=E\left[X_i^f{\left(X_i^f\right)}^H\right]={\mathrm{AD}}^{(i-1)}{R}_s{\left(D^{(i-1)}\right)}^H{A}^H+{\mathrm{\σ}}^2{I}_m\\ ={\mathrm{AD}}^{(i-1)}{R}_s{D}^{-(i-1)}{A}^H+{\mathrm{\σ}}^2{I}_m\end{array}---\left(2\right)$

In formula, I _mfor m rank unit matrix, R _sfor signal autocorrelation matrix.Covariance matrix to all submatrixs is got average, the covariance matrix after being processed, that is:

$R^f=\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{R}_i^f=A\left(\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{D}^{(i-1)}{R}_s{D}^{-(i-1)}\right)A^H+{\mathrm{\σ}}^2{I}_m---\left(3\right)$

(1) estimate that input covariance matrix is

${\hat{R}}_x=R^f---\left(4\right)$

(2) covariance matrix is carried out to feature decomposition

${\hat{R}}_{x}V=\mathrm{V\Λ}---\left(5\right)$

In formula, Λ=diag{ λ ₀..., λ _m-1, λ ₀>=...>=λ _m-1for eigenwert, V=[q ₀..., q _m-1] be

the matrix that characteristic of correspondence vector forms.

(3) utilize the tuple L of little eigenwert to determine Signal estimation number:

$\hat{K}=M-L---\left(6\right)$

And then determine noise subspace V _n.

(4) calculate MUSIC spatial spectrum:

${\hat{P}}_{\mathrm{MUSIC}}\left(\mathrm{\θ}\right)=\frac{a^H\left(\mathrm{\θ}\right)a\left(\mathrm{\θ}\right)}{a^H\left(\mathrm{\θ}\right)V_n{V}_n^{H}a\left(\mathrm{\θ}\right)}---\left(7\right)$

In formula, V _n=[q _k..., q _m-1].

(5) find out 's individual peak-peak, except maximum peak value, obtains other multipath interference radiating way and estimates.

Embodiment 1

Numerical value emulation method is used FDTD, and computation model as shown in Figure 1 plasma (in Fig. 1 3.) starting point coordinate is (1,30), and terminal point coordinate is (1000,330), with aircraft surface angle α=16.7 °.Plasma thickness is 6cm(12 * dy).FDTD zoning is total up to 400 * 1000 grids, in PML(Fig. 1 2.) thickness is 10 grids, mesh generation dx=dy=0.5cm, uniform plasma body thickness 6cm(12 * dy) be positioned at y direction 30～41 grids, plasma collision frequency υ=1e10Hz, electron density ne=10 ¹⁷m ^-3.Aircraft surface (in Fig. 1 5.) is positioned at y direction 19 grids.Each antenna (in Fig. 1 4.) is spaced apart 9cm, and coordinate is respectively (50,20), (68,20), (86,20), (104,20), (122,20), (140,20), (158,20), (176,20).It is gps signal centre frequency 1.57542GHz plane wave (in Fig. 1 1.) that institute adds source.When direction of arrival is estimated, adopt MUSIC algorithm, and signal is carried out to the relevant processing of forward direction smoothing solution, wherein total array number is M=8, submatrix array number m=4.As can be seen from Figure 20 ° is direct wave, 2 α=-33.4 °, and the incoming wave of 3 α=-66.8 ° three directions, and energy reduces with the increase of angle, this and theoretical analysis result are in full accord.And it is next to being-33.4 ° and-66.8 ° to know that thus multipath disturbs.

Embodiment 2

Numerical value emulation method is used FDTD, the actual plasma that computation model imports as shown in Figure 3 (in Fig. 3 3.)) thickness is 10 grids, mesh generation dx=dy=0.5cm, plasma collision frequency υ=1e9Hz, electron density ne=10 ¹⁸m ^-3.Aircraft surface (in Fig. 3 5.) is positioned at y direction, length 2m.Each antenna (in Fig. 3 4.) is spaced apart 9cm, and coordinate is respectively (50,20), (68,20), (86,20), (104,20), (122,20), (140,20), (158,20), (176,20).It is 1.57542GHz plane wave (in Fig. 3 1.) that institute adds source.When direction of arrival is estimated, adopt MUSIC algorithm, and signal is carried out to the relevant processing of forward direction smoothing solution, wherein total array number is M=8, submatrix array number m=4.As can be seen from Figure 4 21.7 °, 59.2 ° is multipath interference radiating way.

Inventive point of the present invention is that FDTD emulation gathers on the basis of M bay signal, adopts the level and smooth MUSIC algorithm of forward direction can accurately estimate multipath interference radiating way.The direction that finally can find multipath to disturb by the combination of several algorithms.Find after direction, just have a lot of methods that are easy to can eliminate multipath interference such as wave beam synthetic method etc.

Claims (2)

1. the multipath interference analysis method that aircraft surface is produced by plasma sheath, is characterized in that, specifically according to following steps, implements:

Step 1: first use Flow Field Distribution file, the frequency of input navigation signal, direction, power;

Step 2: adopt MUSIC algorithm to conciliate related algorithm and calculate undesired signal.

2. the multipath interference analysis method that aircraft surface according to claim 1 is produced by plasma sheath, is characterized in that, described step 2 is specifically implemented according to following steps:

Input needs the plasma distribution file of prediction, use FDTD numerical value emulation method, plasma is pressed to input file to distribute within the specific limits, according to frequency, direction, the power of the navigation measurement and control signal of setting, be the signal of feed-in, at the aircraft surface of simulating, M observation station is set, position between observation station is less than half wavelength, by FDTD numerical evaluation, go out each observation station, the signal Xp receiving, p is the number of sampled point;

M unit observation station is divided into several submatrixs, and the array number of each submatrix is m, and information source number is K, and submatrix number p, has M=p+m-1;

Get first submatrix for reference battle array, i submatrix reception data are:

$X_i^f\left(k\right)=[x_i,x_{i+1},\·\·\·,x_{i-m+1}]={\mathrm{AD}}^{(i-1)}s\left(k\right)+n_i\left(k\right),$

Wherein

Φ is the phase differential between adjacent array element, so corresponding to the covariance matrix of this submatrix be:

$\begin{array}{c}{R}_i^f=E\left[X_i^f{\left(X_i^f\right)}^H\right]={\mathrm{AD}}^{(i-1)}{R}_s{\left(D^{(i-1)}\right)}^H{A}^H+{\mathrm{\σ}}^2{I}_m\\ ={\mathrm{AD}}^{(i-1)}{R}_s{D}^{-(i-1)}{A}^H+{\mathrm{\σ}}^2{I}_m\end{array},$

In formula, I _mfor m rank unit matrix, R _sfor signal autocorrelation matrix, the covariance matrix of all submatrixs is got to average, the covariance matrix after being processed, that is:

$R^f=\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{R}_i^f=A\left(\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{D}^{(i-1)}{R}_s{D}^{-(i-1)}\right)A^H+{\mathrm{\σ}}^2{I}_m,$

Estimate that input covariance matrix is:

$\widehat{R_x}=R^f,$

Covariance matrix is carried out to feature decomposition:

$\widehat{R_x}V=\mathrm{V\Λ},$

In formula, Λ=diag{ λ ₀..., λ _m-1, λ ₀>=...>=λ _m-1for eigenwert, V=[q ₀..., q _m-1] be the matrix that characteristic of correspondence vector forms;

Utilize the tuple L of little eigenwert to determine Signal estimation number:

$\hat{K}=M-L,$

And then determine noise subspace V _n;

Calculate MUSIC spatial spectrum:

${\hat{P}}_{\mathrm{MUSIC}}\left(\mathrm{\θ}\right)=\frac{a^H\left(\mathrm{\θ}\right)a\left(\mathrm{\θ}\right)}{a^H\left(\mathrm{\θ}\right)V_n{V}_n^{H}a\left(\mathrm{\θ}\right)},$

In formula, V _n=[q _k..., q _m-1];

Find out

's

individual peak-peak, except maximum peak value, obtains other multipath interference radiating way and estimates.

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