CN103838968A - Low-elevation-angle tropospheric refraction correction method - Google Patents

Abstract

The invention belongs to the technical field of atmospheric sciences and discloses a low-elevation-angle tropospheric refraction correction method. The low-elevation-angle tropospheric refraction correction method comprises the steps of 1 calculating a ray trajectory of a tropospheric propagated low-elevation-angle measurement signal; 2 establishing a low-elevation-angle tropospheric refraction correction iteration algorithm; 3 confirming a low-elevation-angle tropospheric refraction correction iteration stopping condition; 4 calculating the low-elevation-angle tropospheric refraction correction amount. By adopting the low-elevation-angle tropospheric refraction correction method, the refraction correction accuracy of the low-elevation-angle measurement signal passing through a troposphere is improved, the effects of spaceflight test control, navigational positioning and the like are effectively improved, and technical support is provided for the fields of spaceflight test control, communication and navigation and the like in our country.

Description

A kind of low elevation angle tropospheric refraction modification method

Technical field

The invention belongs to atmospheric science technical field, relate to a kind of low elevation angle tropospheric refraction modification method.

Background technology

The aircraft such as spacecraft, guided missile all will experience atmosphere convection layer, the refraction effect of atmosphere cause delay that electricity (light) ripple is propagated and path bending and cause error, be to improve the effective means of telemetry communication, navigation and positioning accuracy to the error correction of signal communication media.In the practical engineering application such as space flight measurement and control, tropospheric refraction corrected Calculation adopts the refraction model based on atmosphere spherically stratified ionosphere hypothesis, suppose that the earth is ball, atmospheric strument is uniform in the horizontal direction, atmospheric refraction on position angle without impact, only consider range finding and the error correction of the angle of pitch, atmosphere can be divided into concentric thin layer along sphere, and the integration modification methods such as hopfield based on spherically stratified ionosphere are conventional convection current modification methods.

Under this hypothesis of atmosphere sphere Hierachical Basis, the earth is ball, and its mean radius is t _e, the thin layer radius concentric with the earth is r.In troposphere, the calculation of parameter such as thin layer radius (the earth's core distance) the atmospheric temperature in r place, humidity and the air pressure that signal refractive index n (r) is concentric according to the earth obtain, and without loss of generality, in engineering, refractive index n are abbreviated as to the function of r:

n＝n(r) (9)

And electric wave and light wave meet Snell law at the propagation law in space, in the concentric atmosphere thin layer of any one and the earth, set up:

nrcosθ=const (10)

Wherein, n is the refractive index in thin layer, and r is thin layer radius, and θ is the angle of signal ray and thin layer tangent plane, as shown in Figure 1.In Fig. 1

for the earth's core angle, S is geometric distance.

Traditional troposphere integration correction algorithm is generally taking the earth's core on swash travel path apart from as integration variable, its earth's core angle

computing formula be:

Wherein, r ₀for the earth's core distance at survey station place, n ₀for the refractive index at survey station place, E is the apparent elevation angle at survey station place; r _mfor the earth's core distance at target place, n is that the earth's core is apart from the refractive index at r place.When E hour, denominator is tending towards 0 and can makes integral result error very large.Therefore in engineering application, the tropospheric refraction correction of the lower measuring-signal in the low elevation angle (≤10 °) is a technical barrier, and the low elevation angle is that the measurement and control signal direction of survey station transmitting and the angle of horizontal direction are not more than 10 °.

Summary of the invention

The problem that the present invention need to solve is: provide a kind of low elevation angle tropospheric refraction modification method, to improve the correction precision of signal at tropospheric propagation.

For solving the problems of the technologies described above, the present invention proposes a kind of low elevation angle tropospheric refraction modification method, comprises the following steps:

Step 1, set up the ray tracing system of equations of low measurement of elevation signal at tropospheric propagation

Low measurement of elevation signal is as follows in the ray tracing system of equations of tropospheric propagation:

Wherein, to be low measurement of elevation signal propagate the angle of atmospheric envelope tangent plane at the ray of tropospheric propagation and signal to θ, and r is that signal is propagated atmospheric radius, the infinitesimal that ds gets on the ray geometric distance S of tropospheric propagation for signal,

for the earth's core angle between survey station and target, n (r) refractive index that to be signal propagate at atmospheric envelope, R is and the actual propagation path of ds respective signal.

Step 2, set up low elevation angle tropospheric refraction correction iterative algorithm

The thought of iteration correction is to choose suitable step-length, make to revise precision reach demand by iterating, and the low elevation angle tropospheric refraction correction iterative algorithm of foundation is as follows:

2.1, k=0, getting iteration step length is Δ S, obtains iterative initial value system of equations as follows:

Wherein, r ₀for the earth's core distance of survey station, r _afor the earth's core distance of target,

for the earth's core angle of real survey station and target, R ₀for real range finding, θ ₀for signal is propagated atmospheric envelope tangent plane angle, E at real ray and the signal of tropospheric propagation _efor survey station place is without the actual measurement elevation angle of refraction correction.

2.2, k=k+1, obtains the iterative algorithm system of equations of revising in troposphere as follows:

Wherein, r _k, r _k-1be respectively the earth's core distance of iteration k step and k-1 step target, Δ S is iteration step length, θ _k, θ _k-1respectively that iteration k step and k-1 step signal are propagated atmospheric envelope tangent plane angle at ray and the signal of tropospheric propagation,

respectively iteration k step and the survey station of k-1 step and the earth's core angle of target, R _k, R _k-1respectively the range finding of iteration k step and k-1 step, n (r _k), n (r _k-1) be respectively the signal refractive index of iteration k step and k-1 step.

Step 3, determine low elevation angle tropospheric refraction correction stopping criterion for iteration

The checking system of equations that stops low elevation angle tropospheric refraction correction iteration is as follows:

$\left\{\begin{array}{c}{R}_k\≤R_e\\ R_k+n\left(r_k\right)\mathrm{\ΔS}>R_e\end{array}\right.$

Wherein, R _kthe range finding of iteration k step, R _efor the range finding that survey station place is revised without refraction, n (r _k) be the signal refractive index of iteration k step, Δ S is iteration step length.

Step 4, calculate low elevation angle tropospheric refraction correction

Calculate low elevation angle tropospheric refraction correction as follows:

$\left\{\begin{array}{c}\mathrm{\ΔE}=E_e-E_0\\ \mathrm{\ΔR}=R_e-R_0\end{array}\right.$

Wherein Δ E is elevation angle correction, and Δ R is range finding correction, R _ewith E _ebe respectively measured distance and the actual measurement elevation angle revised without refraction at survey station place, R ₀with E ₀be respectively real range finding and the elevation angle.

Wherein, r _afor the earth's core distance of iteration target when initial.R _end,

and θ _endbe respectively the earth's core angle of low elevation angle tropospheric refraction correction iteration target the earth's core while finishing apart from, survey station and target, and the apparent elevation angle at target place, its computing formula is as follows:

Wherein, r _kfor target the earth's core distance of iteration k step, θ _kfor the apparent elevation angle at iteration k step target place, for the earth's core angle of iteration k pacing station and target, R _kfor the range finding of iteration k step, n (r _k) be the refractive index of iteration k step.Δ S _lastfor the step-length of last iteration, its computing formula is as follows:

△S _last=R _e-R _k

Wherein, R _e, R _kbe respectively survey station place without the range finding of refraction correction and the range finding of iteration k step.

The technology of the present invention beneficial effect:

The present invention is on based on atmosphere sphere theory of hierarchies basis, set up the ray tracing system of equations of signal at tropospheric propagation, and research iterative algorithm, set up low elevation angle tropospheric refraction correction iterative algorithm, not only calculate low elevation angle tropospheric refraction modified value, calculated range finding modified value simultaneously, and by theory and experimental verification, adopt the inventive method to realize the low elevation angle of raising signal tropospheric propagation correction precision, for the fields such as China's space flight measurement and control, communication and navigation provide technical support.

Brief description of the drawings

Fig. 1 is that signal is propagated schematic diagram at earth concentric circles thin layer.

Fig. 2 is the low elevation angle of the present invention tropospheric refraction modification method process flow diagram.

Fig. 3 is low measurement of elevation signal tropospheric refraction correction effect figure in the embodiment of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further.

As shown in Figure 2, the low elevation angle of one of the present invention tropospheric refraction modification method, comprises the steps:

Step 1, set up the ray tracing system of equations of low measurement of elevation signal at tropospheric propagation

Low measurement of elevation signal is as follows in the ray tracing system of equations of tropospheric propagation:

Wherein, to be low measurement of elevation signal propagate the angle of atmospheric envelope tangent plane at the ray of tropospheric propagation and signal to θ, and r is that signal is propagated atmospheric radius, the infinitesimal that ds gets on the ray geometric distance S of tropospheric propagation for signal,

for the earth's core angle between survey station and target, n (r) refractive index that to be signal propagate at atmospheric envelope, R is and the actual propagation path of ds respective signal.

In system of equations (1), (1-1) formula, (1-2) formula, (1-3) formula are the signal that obtained by the formula of mentioning in background technology (9) and Fig. 1 ray geometric relationships at tropospheric propagation.

(1-4) formula is by after the differential of formula (10) both sides, then is simplified and obtained by geometric relationship, specific as follows:

To formula (10) both sides simultaneously to ds differential, n=n (r):

By (1-1) formula substitution (2) formula, simplify (1-4) formula that obtains.System of equations (1) can be described under the low elevation angle the uniform measuring-signal of horizontal refraction in the ray tracing of tropospheric propagation.

Step 2, set up low elevation angle tropospheric refraction correction iterative algorithm

The thought of iteration correction is to choose suitable step-length, make to revise precision reach demand by iterating, and the low elevation angle tropospheric refraction correction iterative algorithm of foundation is as follows:

2.1, k=0, getting iteration step length is Δ S, obtains iterative initial value system of equations as follows:

Wherein, r ₀for the earth's core distance of survey station, r _afor the earth's core distance of target,

for the earth's core angle of real survey station and target, R ₀for real range finding, θ ₀for signal is propagated atmospheric envelope tangent plane angle, E at real ray and the signal of tropospheric propagation _efor survey station place is without the actual measurement elevation angle of refraction correction.

2.2, k=k+1, obtains the iterative algorithm system of equations of revising in troposphere as follows:

Wherein, r _k, r _k-1be respectively the earth's core distance of iteration k step and k-1 step target, Δ S is iteration step length, θ _k, θ _k-1respectively that iteration k step and k-1 step signal are propagated atmospheric envelope tangent plane angle at ray and the signal of tropospheric propagation,

respectively iteration k step and the survey station of k-1 step and the earth's core angle of target, R _k, R _k-1respectively the range finding of iteration k step and k-1 step, n (r _k), n (r _k-1) be respectively the signal refractive index of iteration k step and k-1 step.

Step 3, determine low elevation angle tropospheric refraction correction stopping criterion for iteration

The checking system of equations that stops low elevation angle tropospheric refraction correction iteration is as follows:

$\left\{\begin{array}{c}{R}_k\≤R_e\\ R_k+n\left(r_k\right)\mathrm{\ΔS}>R_e\end{array}\right.---\left(5\right)$

Wherein, R _kthe range finding of iteration k step, R _efor the range finding that survey station place is revised without refraction, n (r _k) be the signal refractive index of iteration k step, Δ S is iteration step length.

Step 4, calculate low elevation angle tropospheric refraction correction

Calculate low elevation angle tropospheric refraction correction as follows:

$\left\{\begin{array}{c}\mathrm{\ΔE}=E_e-E_0\\ \mathrm{\ΔR}=R_e-R_0\end{array}\right.---\left(6\right)$

Wherein Δ E is elevation angle correction, and Δ R is range finding correction, R _ewith E _ebe respectively measured distance and the actual measurement elevation angle revised without refraction at survey station place, R ₀with E ₀be respectively real range finding and the elevation angle.

Wherein, r _afor the earth's core distance of iteration target when initial.R _end,

and θ _endbe respectively the earth's core angle of low elevation angle tropospheric refraction correction iteration target the earth's core while finishing apart from, survey station and target, and the apparent elevation angle at target place, its computing formula is as follows:

Wherein, r _kfor target the earth's core distance of iteration k step, θ _kfor the apparent elevation angle at iteration k step target place,

for the earth's core angle of iteration k pacing station and target, R _kfor the range finding of iteration k step, n (r _k) be the refractive index of iteration k step.Δ S _tastfor the step-length of last iteration, its computing formula is as follows:

△S _tast=R _e-R _k

Wherein, R _e, R _kbe respectively survey station place without the range finding of refraction correction and the range finding of iteration k step.

Choose the aloft low elevation angle observing and controlling period of low flyer No. one time, carry out tropospheric refraction correction by above-mentioned steps of the present invention.It is 2 °～8 ° that the optical device of flight period is measured the elevation angle, and finding range is 10km～30km, the about 1.6km of object height.Fig. 3 is the correction effect figure of signal tropospheric refraction.

As shown in Figure 3, the residual error of iterative algorithm and the residual error of measured data are coincide more satisfactory, it is revised residual error and is significantly less than the conventional hopfield model of engineering, shows that iterative algorithm has higher precision for the tropospheric refraction correction of the low elevation angle, possesses engineering practical value.

Claims (1)

1. a low elevation angle tropospheric refraction modification method, is characterized in that: comprise the steps:

Step 1, to set up low measurement of elevation signal as follows in the ray tracing system of equations of tropospheric propagation at the low measurement of elevation signal of ray tracing system of equations of tropospheric propagation:

Wherein, to be low measurement of elevation signal propagate the angle of atmospheric envelope tangent plane at the ray of tropospheric propagation and signal to θ, and r is that signal is propagated atmospheric radius, the infinitesimal that ds gets on the ray geometric distance S of tropospheric propagation for signal,

for the earth's core angle between survey station and target, n (r) refractive index that to be signal propagate at atmospheric envelope, R is and the actual propagation path of ds respective signal;

Step 2, set up low elevation angle tropospheric refraction correction iterative algorithm

2.1, k=0, getting iteration step length is Δ S, obtains iterative initial value system of equations as follows:

Wherein, r ₀for the earth's core distance of survey station, r _afor the earth's core distance of target,

for the earth's core angle of real survey station and target, R ₀for real range finding, θ ₀for signal is propagated atmospheric envelope tangent plane angle, E at real ray and the signal of tropospheric propagation _efor survey station place is without the actual measurement elevation angle of refraction correction;

2.2, k=k+1, obtains the iterative algorithm system of equations of revising in troposphere as follows:

Wherein, r _k, r _k-1be respectively the earth's core distance of iteration k step and k-1 step target, Δ S is iteration step length, θ _k, θ _k-1respectively that iteration k step and k-1 step signal are propagated atmospheric envelope tangent plane angle at ray and the signal of tropospheric propagation,

respectively iteration k step and the survey station of k-1 step and the earth's core angle of target, R _k, R _k-1respectively the range finding of iteration k step and k-1 step, n (r _k), n (r _k-1) be respectively the signal refractive index of iteration k step and k-1 step;

Step 3, determine low elevation angle tropospheric refraction correction stopping criterion for iteration

The checking system of equations that stops low elevation angle tropospheric refraction correction iteration is as follows:

Wherein, R _kthe range finding of iteration k step, R _efor the range finding that survey station place is revised without refraction, n (r _k) be the signal refractive index of iteration k step, Δ S is iteration step length;

Step 4, calculate low elevation angle tropospheric refraction correction

Calculate low elevation angle tropospheric refraction correction as follows:

Wherein, Δ E is elevation angle correction, and Δ R is range finding correction, R _ewith E _ebe respectively measured distance and the actual measurement elevation angle revised without refraction at survey station place, R ₀with E ₀be respectively real range finding and the elevation angle:

Wherein, r _afor the earth's core distance of iteration target when initial.R _end,

and θ _endbe respectively the earth's core angle of low elevation angle tropospheric refraction correction iteration target the earth's core while finishing apart from, survey station and target, and the apparent elevation angle at target place, its computing formula is as follows:

Wherein, r _kfor target the earth's core distance of iteration k step, θ _kfor the apparent elevation angle at iteration k step target place,

for the earth's core angle of iteration k pacing station and target, R _kfor the range finding of iteration k step, n (r _k) be the refractive index of iteration k step, Δ S _tastfor the step-length of last iteration, its computing formula is as follows:

ΔS _last=R _e-R _k

Wherein, R _e, R _kbe respectively survey station place without the range finding of refraction correction and the range finding of iteration k step.

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