CN101937080A - Method for rapidly measuring speed of flying target by fixed single station - Google Patents

Abstract

The invention discloses a method for rapidly measuring the speed vector of a flying target by a fixed single station. The method comprises the following steps of: directly sending a beacon signal to a land station or indirectly reflecting a detection signal of an irradiator on the premise of assuming that an aerocraft linearly moves at a constant speed and reaches a measuring node (3) from a measuring node (1) and through a measuring node (2); continuously measuring the signal for at least three cycles by the land station with the Doppler frequency shift measuring function to derive the operation speed of the aerocraft through the following formula shown in the specification, wherein the method can accurately measure and calculate the operation speed of the aerocraft in a short time so as to favorably improve the measurement and control performance of the land station. The method is practically used for directly detecting the operation speed vector of a spacecraft. The method of the invention is simple and can also be directly applied to the passive positioning of a signal station under the condition that the central frequency of a target radiation signal is captured.

Description

A kind of method of airbound target speed being measured fast by fixing single station

Technical field

The invention belongs to the radio survey technical field, be specifically related to a kind ofly, aerial moving target velocity is carried out the method for fast detecting by single measuring station based on Doppler shift measurement.

Background technology

Simply directly utilize Doppler effect only can obtain radial velocity.Usually.In three dimensions, obtain the velocity of moving target for utilizing a fixing single station, just must carry out the measurement of six Doppler shifts at least to target.

Test the speed fast and have the important engineering application value in single station.For example, to the fast accurate problems of measurement in single station of spacecraft speed, at least, the observation area at single station is big, and is not equipped with the inconsistent error of bringing because of terminal-station apparatus.For the near-earth orbit satellite, tracking telemetry and command station has only tens minutes to the visible observation time of satellite, and for survey of deep space, just can reach needed precision after also must measuring to sufficiently long segmental arc, as only utilizing land station to survey the deep space spacecraft perpendicular to the speed on the direction of visual lines, then must from a couple of days continuous recording radially doppler data, analyze and obtain.

Summary of the invention:

At the deficiency that prior art exists, the present invention is based on Doppler's principle and provided a kind of method of the speed of airflight target being measured fast by fixing single station.

Goal of the invention of the present invention is achieved through the following technical solutions:

Under the condition of aircraft uniform motion, the one, obtain the Doppler shift between adjacent measured node and the ratio relation of target tangential velocity by means of Doppler shift rate of change expression formula; The 2nd, utilized the velocity identical relation, i.e. the quadratic sum that square is constantly equal to each node place radial velocity and tangential velocity of flying speed; The 3rd, utilize the relational expression between radial velocity and Doppler shift.

Under the condition of distance that satisfies between land station and aircraft, separate the measure formula that these relational expressions just can obtain the aircraft travelling speed by connection greater than detect cycle internal object flying distance.The mathematical expression definition that further utilizes doppler changing rate to the ratio of doppler changing rate be similar to simplify after, can obtain the only relevant formula that tests the speed with the frequency displacement parameter.

Specifically may further comprise the steps:

Step 1, suppose aircraft, arrive 3 through 2, or stand erectly earthward and receive and send beacon signal from measured node 1 along the straight line uniform motion, or the detectable signal of indirect reference irradiator;

Step 2, have Doppler shift and rate of change measurement function,, just can try to achieve the travelling speed of aircraft by following formula then by the continuous coverage at least three cycles as land station:

$v=\mathrm{\&lambda;}\sqrt{\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d^2-\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}{\mathrm{<figure-callout\; id="1"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d^1}{1-\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}}}---\left(1\right)$

In the formula: λ is the signal radiation wavelength; f _DiDoppler shift for the measured node place;

Ratio for Doppler shift rate of change between adjacent node.

According to the definition of doppler changing rate, under the situation that waits time difference measurement, between adjacent node the ratio of Doppler shift rate of change can by the Doppler frequency difference between adjacent node than institute approximate evaluation:

Spacecraft is under the condition that moves along a straight line in approximate supposition short distance, and the given measure formula of the present invention also can directly apply to the speed detection to the deep space spacecraft that moves along elliptical orbit.

Further, under the condition that the centre frequency of target emanation signal has been recorded, method of the present invention also can directly apply to single station passive location.At this moment, by the f that concerns between the centre frequency of Doppler shift, beacon signal and the measured value _t=f ₀± f _d, directly the problem of testing the speed can be converted into the measurement of actual frequency values is calculated, and wherein the ratio of doppler changing rate just can be converted into the ratio of surveying frequency difference between adjacent node:

Wherein: f _TiPractical frequency value for land station's receiver.

Different with the existing single station passive location algorithm of frequency domain and spatial information (si) that must utilize simultaneously, the present invention is by setting up the frequency between adjacent measured node and the ratio relation of speed thereof, just can be under the situation that need not angle and rate of change metrical information thereof, only measure the speed that can try to achieve target by frequency difference, thus the position that estimates target that just can be further sane.

Method proposed by the invention should be able to further obtain higher measuring accuracy by iterative computation and Filtering Processing, and improves the measurement that expands to the non-state that travels at the uniform speed by algorithm.

In addition,, as utilize the Doppler shift rate of change, then only can realize testing the speed, and measuring accuracy also can be improved by twice measurement only from theoretical analysis.The advantage of measuring for three times just is not need to extract doppler changing rate, and only can obtain result comparatively accurately by real time frequency measurement.

The present invention brings following beneficial effect:

1, the mode that can measure with single station at short notice accurately measuring and calculating obtain the travelling speed of aircraft, thereby help to improve the observing and controlling performance of speed of detection and land station.

2, method is simple, does not need to extract doppler changing rate, only can obtain results of measuring comparatively accurately by continuous three real time frequency measurements.

3, the inventive method also has expansibility: under the condition that the centre frequency of target emanation signal has been acquired, this method also can directly apply to single station passive location.Different with the existing single station passive location algorithm of frequency domain and spatial information (si) that must utilize simultaneously, the present invention is by setting up the frequency between adjacent measured node and the ratio relation of speed thereof, just can be under the situation that need not angle and rate of change metrical information thereof, only measure the speed that can try to achieve target by frequency difference, thus the position that estimates target that just can be further sane.

4,, then can effectively reduce the operation and the maintenance cost of spacecraft as being applied to survey of deep space.

Description of drawings

Fig. 1: the fixing geometric relationship figure that directly tests the speed of single-station Doppler.

Fig. 2: relative error curve: different detection times.

Fig. 3: relative error curve: different radial distances.

Fig. 4: satellite orbit operation synoptic diagram.

Fig. 5: the simulation error of spacecraft speed measure formula when different flying distance.

Fig. 6: the simulation error of spacecraft speed measure formula when differing heights.

Fig. 7, the spacecraft measuring error curve when different flying distance.

Embodiment

How further specify the present invention below in conjunction with accompanying drawing 1-Fig. 7 realizes.

Embodiment

A kind of only based on the frequency measurement technology, utilize fixing singly standing erectly to connect the method for surveying aerial moving target velocity, and use by direct detection to the spacecraft travelling speed, the embodiment of this kind method has been described.Fig. 1 has provided the geometric relationship that fixing single-station Doppler directly tests the speed; Fig. 2 has schematically provided the movement locus of uniform motion satellite; Fig. 3 has provided for different detection times, and speed measuring and calculating value is with the relative error change curve of angle of lead; Fig. 4 has provided for different radial distances, and speed measuring and calculating value is with the relative error change curve of angle of lead; Fig. 5 provided spacecraft when different flying distance the speed measure formula with respect to the error simulation calculated curve of theoretical value; Fig. 6 provided spacecraft when different flying height the speed measure formula with respect to the error simulation calculated curve of theoretical value; Fig. 7 has provided the measuring error curve of spacecraft speed measure formula when different flying distance.

Simply directly utilize Doppler effect only can obtain radial velocity.Usually.In three dimensions, obtain the velocity of moving target for utilizing a fixing single station, just must carry out the measurement of six Doppler shifts at least to target.

The present invention is based on Doppler's principle research and provided and a kind ofly only the radiation signal of airborne aircraft is carried out the method that continuous three real-time frequency measurements can be surveyed the velocity that obtains its heading by fixing single station.

1, measurement model

Fixedly the geometric relationship of the direct speed-measuring method of single-station Doppler as shown in Figure 1.Suppose the measured target linear uniform motion, arrive from measured node 1 at 3 o'clock through 2, fixation measuring station, ground is carried out continuous three fixed cycles and is measured.

2, the ratio of adjacent node doppler changing rate

According to the definition of Doppler shift rate of change, two adjacent measured node places can list respectively on the aircraft running orbit:

In the formula: λ is a wavelength; r _iBe radial distance; v _tBe tangential velocity.

The ratio of Doppler type frequency displacement rate of change is between this two adjacent node:

The ratio that can be obtained between the radial distance of this two adjacent node by sine is again:

$\frac{r_2}{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1}=\frac{\sin {\mathrm{\&beta;}}_1}{\sin {\mathrm{\&beta;}}_2}=\frac{v\sin {\mathrm{\&beta;}}_1}{v\sin {\mathrm{\&beta;}}_2}=\frac{v_{t1}}{v_{t2}}---\left(4\right)$

In the formula: v is the flying speed of carrier aircraft.

Promptly under the condition of aircraft uniform motion, the ratio of the radial distance of two nodes equals the ratio of end points tangential velocity, and its generation is returned formula (3):

$q=\frac{v_{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">t</figure-callout>}2}^3}{v_{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">t</figure-callout>}1}^3}---\left(5\right)$

On the other hand, utilize basic definition: And because of fixed cycle detects, the adjacent time difference is near equating, so that the ratio of the doppler changing rate between adjacent node can be similar to by the ratio of Doppler frequency difference is represented:

3, speed analytic expression

If v _rBe radial velocity, according to the relation between speed and component:

With the Doppler shift equation: λ f _d=v _r, can obtain by formula (5):

$\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}[v^2-{\left(\mathrm{\&lambda;}{f}_{d1}\right)}^2]=v^2-{\left(\mathrm{\&lambda;}{f}_{d2}\right)}^2---\left(7\right)$

After putting in order:

${\mathrm{\&lambda;}}^2({\mathrm{<figure-callout\; id="2"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d^2-\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}{\mathrm{<figure-callout\; id="1"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d^1)=(1-\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2})v^2---\left(8\right)$

Therefrom can solve the flying speed of aircraft:

$v=\mathrm{\&lambda;}\sqrt{\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d^2-\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}{\mathrm{<figure-callout\; id="1"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d^1}{1-\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}}}---\left(9\right)$

4, analog computation

The purpose of mathematical simulation calculation is to verify the correctness of institute's derived expression, and the method that this paper takes to utilize theoretical value to replace measured value is carried out analog computation.

Preestablish wavelength X, angle of lead θ earlier ₁, radial distance r ₁, target flying speed v and detection time interval of delta t, target moving distance L is approximately equidistant, and presses L=v Δ t and calculate.Make θ ₁In the zone of regulation, change continuously, just can calculate the angle of lead β of each measured node position thus successively by geometric relationship shown in Figure 1 _iWith radial distance r _i, and calculate Doppler shift f corresponding to each radial distance _DiTheoretical value.

On this basis, just can be according to resulting formula (9) the measuring and calculating speed of deriving, and it is made comparisons with original theoretical value and obtain the relative error of calculation.Under the situation that does not add explanation, the parameter that measuring and calculating is got is: wavelength: λ=0.5m, radial distance: r ₀=100km, the speed of measured target: v=100m/s, detection time interval: Δ t=0.5s.

Fig. 2 has provided for different detection times, and speed measuring and calculating value is with the relative error change curve of angle of lead.Fig. 3 has provided for different radial distances, and speed measuring and calculating value is with the relative error change curve of angle of lead.Therefrom as seen, the sum of errors time span is directly proportional.In fact, be implication between tested distance and the detection time, for example, when radial distance diminished, for obtaining littler error, detection time also should reduce accordingly.

Analog computation proves that the variation of the movement velocity of measuring table and wavelength and relative error is irrelevant.

5 application examples

The direct application that single-station Doppler tests the speed is exactly a travelling speed of measuring spacecraft orbit.Doppler range rate measurement orbit determination system has equipment and constitutes advantages such as simple, that maneuverability is high, the cloth station is flexible, but Doppler effect is only relevant with radial velocity, could obtain the speed of spacecraft orbit in real time so generally need multistation to work simultaneously.As by the synthetic orbital velocity of direction cosine rate of change, need three land stations to work simultaneously usually and could obtain the travelling speed of spacecraft.As by the synthetic orbital velocity of direction cosine rate of change, then need to use three measuring stations could obtain the orbital velocity of spacecraft in real time usually; As position and the speed parameter that establishes an equation by range rate and separate target, can use six ground survey stations to realize testing the speed in real time in theory, then can only need two or above research station to carry out six times on the Project Realization and independently measure.

For multistation is measured, the advantage that tests the speed in single station is self-evident, in fact, for the near-earth orbit satellite, tracking telemetry and command station has only tens minutes to the visible observation time of satellite, and for survey of deep space, just can reach needed precision after also must measuring sufficiently long segmental arc, as only utilizing land station to survey the deep space spacecraft perpendicular to the speed on the direction of visual lines, then must from a couple of days continuous recording radially doppler data, analyze and obtain.

The measurement model that directly tests the speed to the Doppler of spacecraft in fixing single station as shown in Figure 4.Suppose that the earth is a spherosome, its radius R=6400km, the dotted line in the synoptic diagram are the running orbit of spacecraft, and its flying height is H, flies at a constant speed around the earth, and land station is positioned at the S place, and O is the earth centre of sphere.Suppose marker be housed on the spacecraft that the fixed cycle emission is used for the signal that usefulness detects in land station, as radial distance r _iFixed cycle detection range l when spacecraft moves, then the circular motion among Fig. 4 just can be reduced to straight line shown in Figure 1 and move by approximate.

(1) analog computation

Earlier wavelength X given in advance, the range ability l (or detect cycle T) of satellite, flying height H, flying speed v by given angle of elevation alpha (equal to have determined angle ∠ ASO=α+90 °), calculate radial distance r then from triangle Δ ASO ₁, and solve the complementary angle ∠ SAO of angle of lead simultaneously, just can solve angle of lead β perpendicular to the characteristic of track running direction thus according to orbit altitude ₁=90 °-∠ SAO just can solve radial distance r subsequently successively from each triangle Δ SAB, Δ ABC ₂And r ₃, subtended angle Δ β ₁With Δ β ₂, and angle of lead β ₂And β ₃Be Doppler shift value that can each measured node place of more accurate calculating, note also simultaneously and must calculate the subtended angle θ of each node with respect to the earth's core, be used for the bending of modifying factor track and to the influence that angle of lead produced, concrete grammar is the correction that two angles of lead at measured node place, back is all given-0.5 θ.

On this basis, just can press

Acquisition is in the theoretical value of the Doppler shift of each node place beacon signal.

Calculate the measuring and calculating value of satellite velocities then according to the resulting speed analytic equation (9) of deriving, and obtain the relative error of calculation by comparing with theoretical set-point.And calculating is to simulate the correctness of the measure formula when satellite is in aerial diverse location by the angle of elevation alpha that changes land station's sight line.

Fig. 5 has at first provided the analog computation graph of errors of measuring and calculating speed when different flying distance, and satellite altitude is 500km, according to the theoretical flying speed 7000m/s of reference, gets respectively corresponding to the flying distance that is 1,2,3 second measuring period and carries out analog computation.Obviously, draw because measure formula is a hypothesis with approximate straight line motion, so can see that the distance of operation is long more, the error at place, the high elevation angle just increases thereupon, and occurs dispersing near 90 ° the time, so be the clear of figure.The elevation angle is only got 80 °.

Fig. 6 has provided satellite is calculated speed when differing heights analog computation graph of errors, and wherein flying distance is set to 7000m.Graph of errors shape during with different flying distance is similar, and when spending near 90 at the elevation angle, relative error has the tendency of dispersing fast.Graphic presentation, orbit altitude are high more, and graph of errors is just all the more smooth.

Analog computation and error analysis show, and be shorter at signal wavelength, and the elevation angle is less than 70 degree, under the moderate situation of detect cycle, utilizes the given measure formula of the present invention promptly can obtain velocity measurement comparatively accurately in real time.

(2) error analysis

According to theory of errors, be by each frequency measurement error component of frequency displacement being asked partial differential can try to achieve the measuring and calculating speed formula:

$\frac{\&PartialD;v}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d}=\frac{\mathrm{\&lambda;}}{3}\frac{u}{{(1-u)}^2}\sqrt{\frac{1-\mathrm{<figure-callout\; id="2"\; label="u\; f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">u</figure-callout>}}{f_d^{}}}[{\mathrm{<figure-callout\; id="2"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d+(4-3u)f_{d1}]---\left(10\right)$

$\frac{\&PartialD;v}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d}=\frac{\mathrm{\&lambda;}}{3{(1-u)}^2}\sqrt{\frac{1-\mathrm{<figure-callout\; id="2"\; label="u\; f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">u</figure-callout>}}{f_d^{}}}[3(1-u)f_{d2}-\frac{(1+q)}{\sqrt[3]{q}}({\mathrm{<figure-callout\; id="1"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d+f_{d2})]---\left(11\right)$

$\frac{\&PartialD;v}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d}=\frac{\mathrm{\&lambda;}}{3}\sqrt{\frac{1-\mathrm{<figure-callout\; id="2"\; label="u\; f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">u</figure-callout>}}{f_d^{}}}\frac{({\mathrm{<figure-callout\; id="2"\; label="f\; d"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">f</figure-callout>}}_d+f_{d1})}{\sqrt[3]{q}}---\left(12\right)$

In the formula: $u=\sqrt[3]{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000205454400011.png,HSA00000205454400031.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}.$

The relative measurement Error Calculation formula of measuring and calculating speed is:

$\frac{{\mathrm{\&sigma;}}_v}{{\mathrm{\&sigma;}}_f}=\sqrt{\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{\left(\frac{\&PartialD;v}{\&PartialD;f_{\mathrm{di}}}\right)}^2}---\left(13\right)$

Wherein: σ _fIt is the root-mean-square value of the measuring error of Doppler shift.

From each error formula as seen, measuring error and wavelength are directly proportional, and the existing setting frequency of operation of using according to satellite is 5GHz, and establishes the root-mean-square value σ of frequency displacement measuring error _f=10 ^-5The measuring error curve display when different flying distance that Fig. 7 is given, flying distance is big more, and measuring error is more little.The also visible elevation angle has minimum measuring error in 45 ° of-55 ° of scopes from figure.In addition, analysis also shows, reduces satellite altitude and also helps to improve measuring accuracy.

Claims (2)

1. method of airbound target speed being measured fast by fixing single station, this method may further comprise the steps:

1), suppose aircraft along the straight line uniform motion, arrive 3 from measured node 1 through 2, or stand erectly earthward and receive and send beacon signal, or the detectable signal of indirect reference irradiator;

2), land station only need have the Doppler shift measurement function, by the continuous coverage at least three cycles, just can be tried to achieve the travelling speed of aircraft by following formula:

In the formula: λ is the signal radiation wavelength; f _DiDoppler shift for the measured node place; Q is the ratio of Doppler shift rate of change between adjacent node, and according to the definition of doppler changing rate, and under the situation that waits time difference measurement, the ratio of Doppler shift rate of change can be by the ratio approximate evaluation of the Doppler frequency difference between adjacent node between adjacent node:

3), under the known situation of signal center frequency, by the f that concerns between the centre frequency of Doppler shift, beacon signal and the measured value _t=f ₀± f _d, directly the problem of testing the speed can be converted into the measurement calculating to the actual frequency values of radiation signal, and have this moment:

Wherein: f _TiPractical frequency value for land station's receiver.

2. a kind of method of airbound target speed being measured fast by fixing single station according to claim 1 is characterized in that: the described method of the airbound target velocity being measured fast by fixing single station can further obtain higher measuring accuracy by iterative computation and Filtering Processing.

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