CN113866732B - Calculation method for short-arc rail measurement capability of single-part radar - Google Patents

Calculation method for short-arc rail measurement capability of single-part radar Download PDF

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CN113866732B
CN113866732B CN202111131259.6A CN202111131259A CN113866732B CN 113866732 B CN113866732 B CN 113866732B CN 202111131259 A CN202111131259 A CN 202111131259A CN 113866732 B CN113866732 B CN 113866732B
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orbit
satellite
radar
error
initial state
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CN113866732A (en
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王家松
王冲
何雨帆
呼延宗泊
方海舰
王丹
房亚男
杜凯
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China Xian Satellite Control Center
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
    • G01S19/37—Hardware or software details of the signal processing chain
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Signal Processing (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a calculation method of single-part radar short-arc rail measurement capability, which comprises the following steps: step 1: setting an initial state vector of a satellite, and simulating a motion orbit and error-free observation data to obtain a simulation standard orbit of the satellite; step 2: obtaining radar observation data with errors based on a Monte Carlo simulation method; step 3: and outputting satellite orbits within the radar observation data period; step 4: and (3) comparing the satellite orbit obtained in the step (3) with the simulation standard orbit in the step (1), carrying out statistical analysis on an orbit comparison result, and obtaining the short arc orbit measurement capability of the single radar through the corresponding relation between orbit determination precision and measurement data errors. The method is efficient in operation and has certain applicability.

Description

Calculation method for short-arc rail measurement capability of single-part radar
Technical Field
The invention belongs to the technical field of aerospace measurement and control, and provides a method for calculating short-arc orbit measurement capability of a single-part radar.
Background
The orbit support of the orbit launching section of the spacecraft, the rescue of the fault satellite and the monitoring of space debris all put higher and higher requirements on the short-time orbit measurement capability of a single radar. The radar equipment acquires the distance, azimuth angle and pitch angle measurement value of the space target relative to the radar by receiving the radio signal reflected by the surface of the space target in a non-cooperative mode, so that the orbit of the space target is rapidly determined. Short arc orbit determination capability of the radar refers to orbit determination capability of the radar in a specified short time, and is characterized by orbit determination precision. The radar which is put into use at present can track a space target for multiple times and compare with the space target precise ephemeris given by a third party to obtain the short arc track measurement capability of the single-part radar. However, the method has three limitations, namely, the method is not suitable for planning design and index demonstration of newly developed radars; secondly, a single radar is required to be arranged for carrying out large-batch tracking measurement on the target, which is not economical and efficient; thirdly, on some special orbits, there is no suitable spatial target to meet the radar tracking measurements.
Disclosure of Invention
The invention aims to provide a calculation method for the short arc rail measurement capability of a single radar, which solves the problems of low applicability and low measurement efficiency of the existing method for obtaining the short arc rail measurement capability of the single radar.
The technical proposal adopted by the invention is that,
A calculation method of single radar short arc rail measurement capability is specifically carried out according to the following steps:
Step 1: setting an initial state vector of a satellite, simulating the motion orbit of the satellite and error-free observation data of ground single-part radar equipment by using an orbit dynamics simulation, and setting an observation period to obtain a simulation standard orbit of the satellite;
Step 2: based on a Monte Carlo simulation method, adding a systematic error and a random error into the observed data to obtain radar observed data with errors;
Step 3: giving a satellite reference initial state quantity, completing orbit determination by using a least square estimation method, obtaining an improved satellite initial state quantity, and outputting a satellite orbit in a radar observation data period;
step 4: and (3) comparing the satellite orbit obtained in the step (3) with the simulation standard orbit in the step (1), and carrying out statistical analysis on an orbit comparison result to obtain the short arc orbit determination precision of the single radar under the condition that the measured data contain errors, and obtaining the short arc orbit determination capability of the single radar through the corresponding relation between the orbit determination precision and the measured data errors.
The present invention is also characterized in that,
In step 1: the error-free observation data includes a data sequence of radar ranging, azimuth and pitch angle measurements.
In step 2, the radar observation data with error is obtained specifically as follows: and (3) respectively adding a systematic error and a random error to the error-free observed data according to the following formula (1):
Wherein Δρ, Δa, Δe are respectively a ranging system error, an azimuth angle system error, and a pitch angle system error, which are all fixed constants; σ (ρ i),σ(Ai),σ(Ei) is the random error sequence of radar ranging, azimuth and pitch, respectively.
The step 3 is specifically as follows: adding an error to the satellite reference initial state quantity to obtain a satellite reference initial state vector, using the satellite reference initial state vector and radar observation data with the error, completing orbit determination by using a least square estimation method to obtain an improved satellite initial state vector, obtaining an orbit sequence corresponding to the satellite in a time period through the improved satellite initial state vector and a satellite dynamics model, and then outputting a satellite orbit in the radar observation data time period.
The step 4 is specifically as follows: analyzing and comparing the satellite orbit output in the step 3 with a simulation standard orbit in the same period of time through the following formula to obtain the three-dimensional orbit determination precision under the condition of the radar measurement data error; and (3) repeating the steps 1-3 for several times in a mode of changing random error sequences of radar ranging, azimuth angle and pitch angle through a Monte Carlo simulation method, finally obtaining an accuracy sequence, and obtaining mathematical expectations of the sequence to obtain the short arc orbit measurement capability of the single radar.
The beneficial effects of the invention are: the method comprises the steps of simulating and generating large batches of single-part radar short-arc measurement data through a Monte Carlo method, determining the track, comparing the track with a standard track, and finally giving out the short-arc track measurement capability of the single-part radar through a statistical analysis comparison result. The short arc in the method means that the long time of the radar in the observation arc section of the space target is less than 1/6 of the orbit period of the space target, and the method generally uses one minute or a few minutes, so that the method has better applicability.
Drawings
FIG. 1 is a schematic diagram of a calculation flow of a calculation method of a single-part radar short-arc rail measurement capability;
FIG. 2 is a schematic diagram of a comparison result of a track without considering radar measurement errors in a method for calculating a single-part radar short arc track measurement capability according to the present invention;
Fig. 3 is a schematic diagram of track comparison results obtained by 100 groups of experiments in the calculation method of the short-arc track measurement capability of the single-part radar.
Detailed Description
The following describes a method for calculating the short arc rail measurement capability of the single-part radar in detail by referring to the accompanying drawings and the specific embodiments.
As shown in fig. 1, the initial state vector of a certain satellite is set asAnd modeling the motion orbit of the satellite by using the orbit dynamics simulation, and setting the observation time to be 1 minute. The satellite motion orbit at this time is called the simulated standard orbit. Then based on Monte Carlo simulation method, adding systematic error and random error to the observed data, and giving a simulation result containing error/>Satellite reference initial state quantity/>I.e.Using least square estimation method, using radar observation data with error to complete orbit determination, obtaining improved satellite initial state quantity/>And outputs satellite orbits over periods of radar observation data. And comparing the satellite orbit with the simulation standard orbit, and carrying out statistical analysis on an orbit comparison result to obtain the single-part radar short-arc orbit determination precision under the condition that the measured data contain errors. And through the corresponding relation between the orbit determination precision and the measured data error, the judgment basis of the single radar short arc orbit determination capability is provided. The specific calculation model is shown in fig. 1:
the following describes a method for calculating the short arc rail measurement capability of the single-part radar in detail through a specific embodiment.
Let the initial epoch t 0 time, the initial state vector of a satellite under the J2000.0 inertial coordinate system beThe satellite's dynamic model takes into account the earth's gravitational field, the gravitational perturbation of the sun and moon, the atmospheric drag, and the solid and sea tides.
Setting t i (i=0, 1,2, m) to be a time sequence with a total length of 1 minute, thereby obtaining a set of satellite simulation standard orbit sequences {(R0,T0,N0),(R1,T1,N1),(R2,T2,N2),...(Rm,Tm,Nm)}. with an arc length of 1 minute, wherein R i,Ti,Ni respectively represents a coordinate component of a satellite in an orbit radial direction under a three-dimensional space coordinate system, a coordinate component along a track direction (also referred to as a flight direction) and a coordinate component along a normal direction at time t i (i=0, 1,2, m). It is set that a radar P somewhere on the ground starts tracking this satellite. According to the radar position and the simulation standard orbit of the satellite, a radar ranging, azimuth angle and pitch angle measurement data sequence {(t0,ρ0,A0,E0),(t1,ρ1,A1,E1),(t2,ρ2,A2,E2),…,(tm,ρm,Am,Em)}, under the error-free condition can be obtained, wherein: ρ i (i=0, 1,2,., m) is the corresponding radar ranging data sequence, a i (i=0, 1,2,., m) is the corresponding radar ranging azimuth data sequence; e i (i=0, 1,2,., m) is a corresponding radar measurement pitch angle data sequence.
The specific calculation process is as follows:
1.1: and (3) adding a systematic error and a random error to the radar measurement data sequence according to the following formula (1).
Wherein Δρ, Δa, Δe are respectively a ranging system error, an azimuth system error, and a pitch system error, which are all fixed constants; σ (ρ i),σ(Ai),σ(Ei) is the random error sequence of radar ranging, azimuth and pitch, respectively.
1.2: For satellite initial state vectorIncrease certain error/>Obtaining satellite reference initial state vector
1.3: Using reference initial state vectorsAnd radar observation data sequence with errorOrbit determination is carried out by utilizing a least square estimation method, and an improved satellite initial state vector/>And pass/>The satellite dynamics model is used to obtain the satellite position at t i (i=0, 1,2, track sequence corresponding to m) moment
1.4: Comparing the satellite orbit output in 1.3 with the simulated standard orbit within the same period, according to the following formula (2):
And (3) carrying out statistical analysis and comparison to obtain three-dimensional orbit determination accuracy L under the condition of radar measurement data error, wherein the orbit determination accuracy of three coordinate directions can be respectively obtained by the following formulas:
1.5: and (3) changing a random error sequence sigma (rho i),σ(Ai),σ(Ei) of radar ranging, azimuth angle and pitch angle by using a Monte Carlo simulation method, and repeating the experimental process of 1 to 4 steps. After 100 iterations of the experiment, a precision sequence { L j }, where j=1, 2,..100, was obtained. The sequence { L j } is mathematically expected, thus giving the short arc orbital capability of a single-part radar.
According to the calculation result:
Setting an initial reference epoch t 0 of the satellite to be 2014, 7, 17, 04:00:00 (UTC time), and an initial state vector of the satellite The corresponding orbit parameters are as follows:
a＝7030000.0m,e＝0.00288,i＝97.00°,Ω＝214.00°,ω＝128.00°,M＝173.10°。
wherein a is a semi-long axis of a satellite orbit, e is eccentricity of the satellite orbit, i is an inclination angle of the satellite orbit, Ω is an ascent and intersection point of the satellite orbit, ω is a near-site radial angle of the satellite orbit, and M is a plane near-site angle of the satellite at time t 0.
The engineering parameters of the set satellites are shown in the following table:
TABLE 1 engineering parameters for satellites
Quality (kg) Frontal area (m 2) Atmospheric resistance coefficient
500.0 10.0 2.1
In the dynamic model, besides the two gravitation of the earth to the satellite, the non-spherical gravitation perturbation of the earth, the atmospheric resistance perturbation, the third gravitation perturbation of the sun and the moon, the solid tide and the sea tide perturbation are considered.
2.1: When radar measurement errors are not considered;
As shown in fig. 2 below, if Δρ, Δa, Δe, and σ (ρ i),σ(Ai),σ(Ei) are all 0 in the above-mentioned formula (1), the radar measurement error is not considered. Since there is no error, 1.5 is not required at this time, and the orbit comparison result obtained by 1.4 is shown as R indicating the radial direction of the satellite orbit, T indicating the tracking direction of the satellite orbit, also called the flight direction, N indicating the normal direction of the satellite orbit, and Total indicating the three-dimensional space position of the satellite.
It can be seen that when measurement errors are not considered, the satellite orbit calculated by the method is not close to the simulation reference orbit, and the three-dimensional space position deviation is less than 0.3m. This error is mainly caused by the computational truncation error of the software and is within the allowed error range, from which it can be seen that our simulated computational flow is correct.
2.2: Consider the measurement bias situation;
As shown in fig. 3, the random error of the ranging data of the radar is set to be 5m, and the random error of the azimuth angle and the pitch angle data is set to be 0.01 degrees; the range system error is 5m, and the azimuth angle and pitch angle system error is 0.01 degrees. Counting 100 groups of track comparison results:
And counting the orbit comparison results obtained by 100 groups of experiments, wherein the orbit determination precision in the radial direction is 302.4m, the orbit determination precision in the track direction is 64.2m, the orbit determination precision in the normal direction is 366.9m, and the position precision of the satellite three-dimensional space is 479.8m. From this, the three-dimensional position error 490m of the short-arc orbital capability of the radar for 1 minute for this type of low-orbit satellite can be given.
According to the method for calculating the short arc orbit measurement capability of the single radar, large batches of short arc measurement data of the single radar are generated through Monte Carlo simulation, orbit determination is carried out, orbit comparison is carried out with a standard orbit, and finally the short arc orbit measurement capability of the single radar is given through a statistical analysis comparison result. The method has higher efficiency and accuracy and better applicability.

Claims (3)

1. A calculation method of single radar short arc rail measurement capability is characterized by comprising the following steps:
Step 1: setting an initial state vector of a satellite, simulating the motion orbit of the satellite and error-free observation data of ground single-part radar equipment by using an orbit dynamics simulation, and setting an observation period to obtain a simulation standard orbit of the satellite;
Step 2: based on a Monte Carlo simulation method, adding a systematic error and a random error into the observed data to obtain radar observed data with errors;
Step 3: giving a satellite reference initial state quantity, completing orbit determination by using a least square estimation method, obtaining an improved satellite initial state quantity, and outputting a satellite orbit in a radar observation data period; the method comprises the following steps: adding an error to the satellite reference initial state quantity to obtain a satellite reference initial state vector, using the satellite reference initial state vector and radar observation data with the error, completing orbit determination by using a least square estimation method to obtain an improved satellite initial state vector, obtaining an orbit sequence corresponding to the satellite in a time period through the improved satellite initial state vector and a satellite dynamics model, and then outputting a satellite orbit in a radar observation data time period;
Step 4: comparing the satellite orbit obtained in the step 3 with the simulation standard orbit in the step 1, carrying out statistical analysis on an orbit comparison result to obtain the short arc orbit determination precision of the single radar under the condition that the measured data contain errors, and obtaining the short arc orbit determination capability of the single radar through the corresponding relation between the orbit determination precision and the measured data errors, wherein the method comprises the following specific steps: and (3) analyzing and comparing the satellite orbit output in the step (3) with a simulation standard orbit in the same period through the following formula:
And (3) carrying out statistical analysis and comparison to obtain three-dimensional orbit determination accuracy L under the condition of radar measurement data error, wherein the orbit determination accuracy of three coordinate directions can be respectively obtained by the following formulas:
Wherein, R i,Ti,Ni represents the coordinate components of the satellite in the radial direction of the orbit in the three-dimensional space coordinate system at the time t i (i=0, 1,2, m), and the orbit sequence corresponding to the time t i (i=0, 1,2, m) is
And (3) repeating the steps 1-3 for several times in a mode of changing random error sequences of radar ranging, azimuth angle and pitch angle through a Monte Carlo simulation method, finally obtaining an accuracy sequence, and obtaining mathematical expectations of the sequence to obtain the short arc orbit measurement capability of the single radar.
2. The method for calculating the short arc rail measurement capability of the single-part radar according to claim 1, wherein in step 1: the error-free observation data includes a data sequence of radar ranging, azimuth and pitch angle measurements.
3. The method for calculating the short arc orbit determination capability of a single-part radar according to claim 2, wherein in step 2, the obtaining of the radar observation data with errors is specifically: and (3) respectively adding a systematic error and a random error to the error-free observed data according to the following formula (1):
Wherein Δρ, Δa, Δe are respectively a ranging system error, an azimuth angle system error, and a pitch angle system error, which are all fixed constants; σ (ρ i),σ(Ai),σ(Ei) is the random error sequence of radar ranging, azimuth and pitch, respectively.
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