CN105548976A - Shipborne radar offshore precision identification method - Google Patents

Abstract

The invention discloses a shipborne radar offshore precision identification method, which relates to the field of spacecraft attitude control ground application. In order to solve the problem that shipborne radar high-precision and high-frequency offshore precision identification can not be realized in the prior art, a star sensor is arranged in the center of three axes of a shipborne radar equipment antenna, and in the case of ship docking, a theodolite calibrates a zero error and a sighting error, and the star sensor calibrates a main point, a focal length and optical distortion parameters; the radar calibrates an axis error, the radar and the star sensor track a spatial object at the same time, the star sensor photographs a radar antenna pointing star map in real time, and according to the optical axis initial pointing, a visual field radius and a visual field range, the optical axis precise attitude of the star sensor, the geocentric vector of the spatial object, the horizon azimuth angle and the pitch angle of the spatial object, and the deck azimuth angle and the pitch angle of the spatial object are calculated. According to the deck pointing of the spatial object, the radar equipment tracks the actually-measured angle of the spatial object, the high-precision star sensor is used for realizing precision identification, and radar precision identification normalization can be realized.

Description

The marine Precision Checkup Method of shipborne radar

Technical field

The present invention relates to Spacecraft Attitude Control Ground Application field, be specifically related to the marine Precision Checkup Method of shipborne radar.Utilize the advantage that star sensor pointing accuracy is high, a High Accuracy Radar measurement of angle benchmark not relying on radar encoder is provided, by synchronized tracking measurement space target, resolves radar pointing accuracy.

Background technology

The high-precision attitude sensor of star sensor to be a kind of with fixed star be reference data, is resolved by the fixed star of diverse location on detection celestial sphere, has independent navigation ability, play an important role in various flight control and attitude measurement process.Star sensor has good concealment, applied widely, reliability is high, precision is high, can the feature of independent all weather operations.

Instrumented tracking and telemetry ship is that its measuring and controlling equipment take boats and ships as platform in order to adapt to guided missile, the development of spacecraft testing and the tracking telemetry and command station arranged at sea.For guaranteeing the measuring accuracy of shipborne radar, must demarcate equipment in good time and calibrate, mainly be divided into calibration in dock and marine calibration two parts.Calibration in dock is basis, can carry out accurate calibration comprehensively, obtain VEC parameter; Marine calibration is carried out in a dynamic condition, utilizes accuracy calibration flight to carry out equipment precision qualification and parametric calibration.But there is cycle length, expend large and organize and coordinate the shortcomings such as difficulty in existing marine accuracy calibration flight, is therefore necessary to find a kind of Precision Checkup Method that can replace accuracy calibration flight, meets the demand of frequent sea trial task.Present stage utilizes boat-carrying transit and instrumentation radar to follow the tracks of the same space target simultaneously, and two groups of measurement data are compared the pointing accuracy obtaining radar electric axis.But the usual visual field of boat-carrying transit is little, generally can only detect fourth class fixed star, and bring deformation of hull error and transit axial system error when data compare, coordinate is felt concerned about on the ground that also cannot resolve extraterrestrial target, and therefore, range of application is restricted.

Summary of the invention

The present invention solves the problem that prior art cannot realize the marine accuracy evaluation to shipborne radar High-precision high-frequency degree, provides a kind of shipborne radar based on Rotating Platform for High Precision Star Sensor marine Precision Checkup Method.

The marine Precision Checkup Method of shipborne radar, the method is realized by following steps:

Step one, at shipborne radar device antenna three axle center strapdown, star sensor SS1 is installed;

When step 2, ship lie up and sit pier, boat-carrying theodolite for calibration is demarcated zero difference and is sighted difference, and described star sensor SS1 demarcates principal point, focal length and optical distortion parameter; Axial system error demarcated by shipborne radar;

Step 3, shipborne radar and star sensor follow the tracks of extraterrestrial target simultaneously, star sensor captured in real-time radar antenna point to star chart, t shipborne radar follow the tracks of extraterrestrial target measure in real time deck system position angle and the angle of pitch be (A _bt, E _bt), form deck coordinate system vector V _bt, shake correction through ship and obtain radar electric axis Horizon system vector V _dPt, to described radar electric axis Horizon system vector V _dPtgeocentric inertial coordinate system vector V is transformed into after carrying out accommodation, Ghandler motion, rotation and precession of the equinoxes correction _cISt, resolve star sensor optical axis initial directional (α _0t, β _0t);

Step 4, the optical axis initial directional (α obtained according to step 3 _0t, β _0t) and the visual field radius R of star sensor, calculate the field range (C of star sensor _α, C _β), adopt the Fast Recognition Algorithm based on nautical star territory, carry out importance in star map recognition, and utilize the corresponding relation of many fixed stars and nautical star in star chart, calculate star sensor optical axis exact posture (α _t, β _t, γ _t), the picpointed coordinate of recycling t extraterrestrial target builds star sensor measurement vector W _t, carry out distortion quadratic fit to described measurement vector and correct, the measurement vector obtained after correcting is W _t', adopt the ground of following formula computer memory target to feel concerned about vector V _t:

$V_t={\left(R_{CIS}^s\right)}^{-1}{W_t}^{\′}$

In formula, for star sensor attitude matrix, CIS is geocentric inertial coordinate system, and s is star sensor coordinate system;

Step 5, vector V is felt concerned about to the ground of the extraterrestrial target described in step 4 _t, after carrying out the conversion of the precession of the equinoxes, nutating, Ghandler motion, earth rotation, obtain extraterrestrial target Horizon system vector, resolve extraterrestrial target Horizon system position angle and the angle of pitch to the described extraterrestrial target Horizon system angle of pitch carry out astronomical refraction correction, obtain the revised extraterrestrial target Horizon system angle of pitch reconstruction attractor target Horizon system vector, then shake correction through ship, the deck obtaining extraterrestrial target mean to, be formulated as:

In formula, for t Attitude matrix, (Ω _t, Ψ _t) for star sensor measure extraterrestrial target deck system position angle and the angle of pitch, b is deck coordinate system, and DP is inertial navigation Horizon system;

Step 6, according to shipborne radar follow the tracks of extraterrestrial target measure in real time deck system position angle and the angle of pitch (A _bt, E _bt), revise the position angle after axial system error and the angle of pitch (A' _bt, E' _bt), adopt star sensor to realize revised position angle and the angle of pitch (A' _bt, E' _bt) carry out accuracy evaluation, be formulated as:

$\left\{\begin{array}{c}{\mathrm{\δA}}_t={\mathrm{\Ω}}_t-A_{bt}^{\′}\\ {\mathrm{\δE}}_t={\mathrm{\Ψ}}_t-E_{bt}^{\′}\end{array}\right.$

In formula, (δ A _t, δ E _t) be the position angle of radar electric axis sensing and the deviation of the angle of pitch.

Beneficial effect of the present invention:

One, propose the marine Precision Checkup Method of a kind of shipborne radar, have the advantages such as precision is high, simple and efficient, the sea trial measure equipment calibration for frequent provides powerful guarantee, can realize the normalization of radar accuracy qualification.

Two, star sensor is arranged on radar antenna, with the high star sensor of pointing accuracy for precision reference, namely a High-precision angle measuring basis not relying on radar encoder is provided, radar and star sensor follow the tracks of extraterrestrial target simultaneously, star chart near star sensor captured in real-time radar antenna points to, resolves radar pointing accuracy, has higher measuring accuracy, orientation, pitching random residual are better than 50 〞, meet radar accuracy qualification requirement.

Three, the present invention is according to star sensor attitude determination principle, resolves shipborne radar precision, achieve real-time automatic measurement, also can complete evaluation work without the need to background context professional person by matrix operation programming.

Four, the present invention utilizes the method for ball rectangle celestial sphere to be divided into 800 ball rectangle little Tian districts, sets up Ge little Tian district navigational star table and star angular distance storehouse.Make full use of radar equipment angle information and reduce hunting zone, determine that the optical axis carries out fast star identification and space target positioning after slightly pointing to, substantially increase data updating rate.

Accompanying drawing explanation

Fig. 1 is star sensor and shipborne radar strapdown scheme of installation in the marine Precision Checkup Method of shipborne radar of the present invention;

Fig. 2 is shipborne radar and star sensor relative coordinate system schematic diagram in the marine Precision Checkup Method of shipborne radar of the present invention;

Fig. 3 is the marine accuracy evaluation schematic diagram of shipborne radar in the marine Precision Checkup Method of shipborne radar of the present invention;

Fig. 4 is that in the marine Precision Checkup Method of shipborne radar of the present invention, inertial navigation horizontal coordinate are tied to geocentric inertial coordinate system transition diagram;

Fig. 5 is corresponding little Tian district, star sensor visual field schematic diagram in the marine Precision Checkup Method of shipborne radar of the present invention;

Fig. 6 is boat-carrying star sensor astronomical refraction correction schematic diagram in the marine Precision Checkup Method of shipborne radar of the present invention.

Embodiment

Embodiment one, composition graphs 1 ~ Fig. 6 illustrate present embodiment, the coordinate system related in present embodiment has CIS-geocentric inertial coordinate system (J2000.0 coordinate system), feel concerned about MT-mean of date equatorial, feel concerned about CT-trae of date Equatorial, ET-pseudo body-fixed system, CTS-body-fixed coordinate system, DP-inertial navigation Horizon system, b-deck coordinate system, s-star sensor coordinate system.Table 1 is the parameter of optical system of star sensor.

Table 1

Basic Eulerian angle rotational transformation matrix R _x(θ), R _y(θ), R _z(θ) represent the matrix formed after X, Y and Z axis are rotated counterclockwise θ angle respectively, there is following canonical form:

$R_x\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\θ}& sin\mathrm{\θ}\\ 0& -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]$

$R_y\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}cos\mathrm{\θ}& 0& -sin\mathrm{\θ}\\ 0& 1& 0\\ \sin \mathrm{\θ}& 0& cos\mathrm{\θ}\end{array}\right]$

$R_z\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}cos\mathrm{\θ}& sin\mathrm{\θ}& 0\\ -sin\mathrm{\θ}& cos\mathrm{\θ}& 0\\ 0& 0& 1\end{array}\right]$

The concrete steps of present embodiment are:

One, install star sensor SS1 at shipborne radar device antenna three axle center strapdown in Fig. 1, confirm that antenna perforate window makes star sensor imaging unobstructed, fixed star is imaged on star sensor CCD target surface by window on antenna.Definition O _b-X _by _bz _bfor inertial navigation deck coordinate system, it is boat-carrying measuring equipment coordinate basis.True origin O _bbe positioned at inertial navigation three axle center, X _baxle points to stem along fore and aft line, Y _bthe vertical deck of axle upwards, Z _baxle and X _baxle, Y _baxle becomes the right-hand rule, points to starboard;

Two, when ship lies up and sits pier, boat-carrying theodolite for calibration is demarcated zero difference and is sighted difference, and described star sensor SS1 demarcates principal point, focal length and optical distortion parameter respectively; Axial system error demarcated by shipborne radar, mainly comprises: the non-orthogonal error of pedestal unlevelness degree, azimuth pitch, ray machine axle deviation, photo electric axis deviation, gravity sag error etc.:

A, transit are demarcated: by fixing 0.2 on testing stand before dispatching from the factory, and " parallel light tube point target, beats the method for change face repeatedly, read-out encoder value, calculates the zero difference of theodolite for calibration, sights difference; During outfield, by clapping azimuth mark, repeatedly beating the method for change face, recalculating the zero difference of theodolite for calibration, sight difference.

The demarcation of B, star sensor comprises the demarcation of principal point, focal length and optical distortion parameter.Before dispatching from the factory, star sensor being arranged on transit four-way platform, aiming at parallel light tube, gather image and extract aiming spot, by repeatedly beating change face method, measuring principal point (X ₀, Y ₀); Rotate transit platform, target is moved at equal intervals in whole visual field, extract many group target locations and encoder values, carry out iteration by calculating Minimum Mean Square Error and go out focal length value f ₀; After principal point, focal length are demarcated, rotate transit platform again, target is moved at equal intervals in visual field, by visual field is divided into several regions, by the method for quadratic fit distortion, calculate the fitting coefficient of regional respectively, thus the accurate correction realized regional aiming spot, shape is as (x, y)=T [u, v], in formula, (x, y) is by the anti-target location true value pushed away of scrambler, (u, v) be the position of target actual extracting, T [] is quadratic fit function.

Optical distortion calibration process is specific as follows:

Demarcate principal point (X ₀, Y ₀), focal distance f ₀after, assuming that transit encoder side parallactic angle, the angle of pitch (A _i, E _i) be effective true value, release the true miss distance of position impact point (Δ x according to following formula is counter _i, Δ y _i):

Δx _i＝tan(A ₀-A _i)*(f ₀*cos(E _i)-Δy*sinE _i)(1)

Δy _i＝(-f ₀*sin(E _i)*cos(A ₀-A _i)+f ₀*cos(E _i)*tanE ₀)/

(2)

(sin(E _i)*tanE ₀+cos(A ₀-A _i)*cosE _i)

In formula, (A ₀, E ₀) be the encoder values of target imaging when principal point place.Obtain the true value (x of impact point _i, y _i):

x _i＝X ₀+Δx _i(3)

y _i＝Y ₀+Δy _i(4)

Set up corresponding relation between impact point true value cell coordinate corresponding to fault image, divide correcting distorted better, adopt the method for picture portion, each Separate Fit goes out the quadratic function coefficient (k in respective region ₁, k ₂, k ₃, k ₄, k ₅, k ₆), (k ₇, k ₈, k ₉, k ₁₀, k ₁₁, k ₁₂):

k ₁+k ₂×v _i+k ₃×v _i ²+k ₄×u _i+k ₅×u _i×v _i+k ₆×u _i ²＝x _i(5)

k ₇+k ₈×v _i+k ₉×v _i ²+k ₁₀×u _i+k ₁₁×u _i×v _i+k ₁₂×u _i ²＝y _i(6)

After trying to achieve fitting coefficient matrix, can put observation championship and revise.

Axial system error demarcated by C, shipborne radar, mainly comprises: the non-orthogonal error of pedestal unlevelness degree, azimuth pitch, orientation zero-bit, pitching zero-bit, ray machine axle deviation, photo electric axis deviation, gravity sag error etc.

Three, shipborne radar and star sensor follow the tracks of extraterrestrial target simultaneously, star chart near star sensor captured in real-time radar antenna points to.

When in Fig. 2, radar electric axis follows the tracks of extraterrestrial target, extraterrestrial target is in the imaging of star sensor target surface.Definition O _bl-X _bly _blz _blfor shipborne radar surving coordinate system (in depressed place timing signal correction pedestal unlevelness degree), with inertial navigation deck coordinate system O _b-X _by _bz _bdifference deformation of hull amount.True origin O _blfor radar three axle center, X _blaxle points to stem along fore and aft line, Y _blthe vertical deck of axle upwards, Z _blaxle and X _blaxle, Y _blaxle becomes the right-hand rule, points to starboard.Definition O _s-X _sy _sz _sfor star sensor image space coordinate system, define different from the star sensor that aerospacecraft is installed, in order to demarcate boat-carrying star sensor coordinate system and radargrammetry coordinate system not coincidence relation better, definition O-YZ is coordinate system between star sensor picture is put down, definition X _sobserved object is pointed to, Y along optical axis direction _saxle is parallel to photo coordinate system Y-axis, along imageing sensor field scan direction upwards, and Z _saxle and X _saxle, Y _saxle becomes the right-hand rule, along imageing sensor direction of line scan to the right, and f ₀for star sensor focal length, (A, E) is respectively Xi Xia position angle, deck corresponding to star sensor optical axis and the angle of pitch.Therefore, the star sensor principal point (X described in step 2 ₀, Y ₀) in star sensor image space coordinate system, be defined as (z ₀, y ₀).

Fig. 3 is that star sensor and shipborne radar Strapdown inertial measurement carry out marine accuracy evaluation principle.Connect firmly star sensor and inertial navigation combines (combining hereinafter referred to as star is used) ship appearance measuring system at radar equipment base, radar equipment pedestal place high precision Attitude is provided.Due to the measurement data of star sensor and shipborne radar equipment, not under the same coordinate system, (the former is geocentric inertial coordinate system, the latter is deck coordinate system), can not directly comparison, star need be utilized to be used to fabricated ship appearance measurement data, first the measurement data of star sensor is revised conversion Horizon system through the precession of the equinoxes, nutating, accommodation etc., then ship appearance data are utilized to be transformed in deck coordinate system, thus the equipment of acquisition angular error information, carry out the marine accuracy evaluation of shipborne radar equipment.

It is (A that shipborne radar follows the tracks of extraterrestrial target real-time deck system angle in t _bt, E _bt), form deck coordinate system vector V _bt, shake correction through ship and obtain radar electric axis Horizon system vector V _dPt:

$V_{DPt}=\left[\begin{array}{c}{X}_{DPt}\\ Y_{DPt}\\ Z_{DPt}\end{array}\right]=\left[\begin{array}{c}\cos \left(A_{DPt}\right)\cos \left(E_{DPt}\right)\\ \sin \left(A_{DPt}\right)\sin \left(E_{DPt}\right)\\ \sin \left(E_{DPt}\right)\end{array}\right]$

$V_{bt}=\left[\begin{array}{c}{X}_{bt}\\ Y_{bt}\\ Z_{bt}\end{array}\right]=\left[\begin{array}{c}cos\left(A_{bt}\right)cos\left(E_{bt}\right)\\ sin\left(A_{bt}\right)cos\left(E_{bt}\right)\\ \sin \left(E_{bt}\right)\end{array}\right]$

$V_{DPt}={\left(R_{DP}^b\right)}^{-1}{V}_{bt}---\left(7\right)$

In formula, (A _dPt, E _dPt) be radar horizon system angle, for Attitude matrix, can be calculated by following formula:

$R_{DP}^b=R_y\left(K_t\right)R_z(-{\mathrm{\ψ}}_t)R_x(-{\mathrm{\θ}}_t)---\left(8\right)$

Wherein, (K _t, ψ _t, θ _t) be used to array output Attitude crab angle, pitch angle and roll angle for equipment base place star.R _x(θ), R _y(θ), R _z(θ) the Eulerian angle rotation matrix formed after X, Y and Z axis are rotated counterclockwise θ angle is represented respectively.

To described reference vector V in Fig. 4 _dPtthrough accommodation, Ghandler motion, rotation, the precession of the equinoxes etc. correction be transformed into geocentric inertial coordinate system reference vector V _cISt:

$V_{CISt}={\left(R_{CIS}^{DP}\right)}^{-1}{V}_{DPt}---\left(9\right)$

In formula, V _cIStfor geocentric inertial coordinate system reference vector:

$V_{CISt}=\left[\begin{array}{c}{X}_{CISt}\\ Y_{CISt}\\ Z_{CISt}\end{array}\right]=\left[\begin{array}{c}\cos \left({\mathrm{\α}}_{0t}\right)\cos \left({\mathrm{\β}}_{0t}\right)\\ \sin \left({\mathrm{\α}}_{0t}\right)\cos \left({\mathrm{\β}}_{0t}\right)\\ \sin \left({\mathrm{\β}}_{0t}\right)\end{array}\right]---\left(10\right)$

Wherein, (α _0t, β _0t) be the sensing of radar geocentric inertial coordinate system.

for t Earth central inertial is tied to Horizon system pose transformation matrix, can be calculated by following formula:

$R_{CIS}^{DP}=R_{CTS}^{DP}{R}_{ET}^{CTS}{R}_{CT}^{ET}{R}_{MT}^{CT}{R}_{CIS}^{MT}---\left(11\right)$

Wherein, for geocentric inertial coordinate system to mean of date equatorial feel concerned about between transition matrix, for mean of date equatorial the earth's core is to the transition matrix felt concerned about of trae of date Equatorial ground, for trae of date Equatorial the earth's core is tied to the transition matrix of pseudo body-fixed system, for pseudo body-fixed system is to the pose transformation matrix of body-fixed coordinate system, for body-fixed coordinate system is tied to the pose transformation matrix between inertial navigation Horizon system.

Below concrete transfer process:

A, precession of the equinoxes correction, the difference of J2000.0 geocentric inertial coordinate system and mean of date equatorial geocentric coordinate system (MT) is caused by the precession of the equinoxes, by the transition matrix of J2000.0 geocentric inertial coordinate system to mean of date equatorial geocentric coordinate system

$R_{CIS}^{MT}=R_z(-z_A)R_y\left({\mathrm{\θ}}_A\right)R_z(-{\mathrm{\ξ}}_A)---\left(12\right)$

In formula,

ξ _A＝2.650545"+2306.083227"T _u+0.2988499"T _u ²

(13)

+0.01801828"T _u ³-0.000005971"T _u ⁴-0.0000003173"T _u ⁵

θ _A＝2004.191903"T _u-0.4294934"T _u ²-0.04182264"T _u ³

(14)

-0.000007089"T _u ⁴-0.0000001274"T _u ⁵

z _A＝-2.650545"+2306.077181"T _u+1.0927348"T _u ²

(15)

+0.01826837"T _u ³-0.000028596"T _u ⁴-0.0000002904"T _u ⁵

T in formula _ufor the Julian century number that terrestrial time is started at.

B, nutating correction, the difference felt concerned about between CT by nutating is caused with feeling concerned about MT and trae of date Equatorial mean of date equatorial, feels concerned about MT mean of date equatorial and feels concerned about the nutating transition matrix of CT to trae of date Equatorial

$R_{MT}^{CT}=R_x(-{\mathrm{\ϵ}}_A-\mathrm{\Δ}\mathrm{\ϵ})R_z(-\mathrm{\Δ}\mathrm{\ψ})R_x\left({\mathrm{\ϵ}}_A\right)---\left(16\right)$

In formula: Δ ε is nutation in obliquity, Δ ψ is nutation of longitude, ε _afor mean obliquity, ε _a=ε-Δ ε, wherein ε considers the ecliptic obliquity of precession of the equinoxes impact, and computing formula is:

ε＝84381.448"-46.8150"T-0.00059"T ²+0.001813"T ³(17)

Δψ＝-(17.1996"+0.01742"T)sinΩ+0.2062"sin2Ω

-(1.3178"+0.00016"T)sin(2F-2D+2Ω)+(18)

(0.1426"-0.00034"T)sin(l')-(0.2274"-0.00002"T)sin(2F+2Ω)

Δε＝(9.2025"+0.00089"T)cosΩ-(0.0895"+0.0005"T)cos2Ω

+(0.5736"+0.00031"T)cos(2F-2D+2Ω)+(0.0977"-0.0005"T)cos(2F+2D)

(19)

L, l', F, D, Ω are respectively angle, the moon flat perigee, angle, the sun flat perigee, the flat lift angle distance of the moon, life straight angle distance and the lunar orbit longitude of ascending node, and specific formula for calculation is as follows:

l＝134°.96340251+1717915923".2178T

(20)

+31".8792T ²+0".051635T ³-0.00024470T ⁴

l＝357°.52910918+129596581".0481T

(21)

-0".5532T ²+0".000136T ³-0.00001149T ⁴

F＝93°.27209062+1739527262".8478T

(22)

-12".7512T ²-0".051635T ³+0".00000417T ⁴

D＝297°.85019547+1602961601".2090T

(23)

-6".3706T ²+0".006593T ³-0".00003169T ⁴

Ω＝125°.04455501-6962890".5431T

(24)

+7".4722T ²+0".007702T ³-0".00005939T ⁴

C, rotation correction, the difference between trae of date Equatorial geocentric coordinate system CT and pseudo body-fixed system ET is caused by earth rotation, and trae of date Equatorial geocentric coordinate is tied to the earth rotation transition matrix of pseudo body-fixed system

$R_{CT}^{ET}=R_z\left(GAST\right)---\left(25\right)$

In formula, GAST is Greenwich apparent time, and computing formula is as follows:

GAST＝6 ^h41 ^m50 ^s.54841+8640184 ^s.812866T _u+0 ^s093104T _u ²-6 ^s.2×10 ^-6T _u ²(26)

GAST＝GMST+Δψcosε(27)

D, Ghandler motion correction, the difference of pseudo body-fixed system ET and body-fixed coordinate system CTS is Ghandler motion, and pseudo body-fixed system is to the Ghandler motion of body-fixed coordinate system CTS matrix

$R_{CT}^{ET}=R_x(-y_p)R_y(-x_p)---\left(28\right)$

Usually, Ghandler motion constant value x _p=y _p=0.4 " calculate.

E, accommodation are revised, and the difference of body-fixed coordinate system CTS and inertial navigation Horizon system DP is caused by geographic position and plumb line deviation, and body-fixed coordinate system CTS is to the Ghandler motion matrix of inertial navigation Horizon system

In formula, for survey station astronomical longitude and latitude, (η ₀, ε ₀) be survey station plumb line deviation, reflect the deviation between measuring station astronomic coordinates and earth coordinates, wherein η ₀for the component of plumb line deviation on prime vertical, ε ₀for the height anomaly of measuring station.

Measure astronomic coordinates with the earth's core earth coordinates (L _on, L _at, H) between transformational relation:

In Practical Project, measurements available station the earth longitude and latitude replaces astronomical longitude and latitude to convert, that is:

$R_{CTS}^{DP}=R_y(-\mathrm{\π}/2)R_x\left(L_{at}\right)R_x(L_{on}-\mathrm{\π}/2)---\left(31\right)$

To described geocentric inertial coordinate system reference vector VCISt, resolve radar geocentric inertial coordinate system by following formula and point to (α _0t, β _0t), as star sensor optical axis initial directional:

$\left\{\begin{array}{c}{\mathrm{\α}}_{0t}={\tan }^{-1}(Y_{CISt}/X_{CISt})\\ {\mathrm{\β}}_{0t}={\sin }^{-1}\left(Z_{CISt}\right)\end{array}\right.---\left(32\right)$

Four, according to optical axis initial directional (α _0t, β _0t) and visual field radius R, calculate the field range (C of star sensor _α, C _β):

$\{\begin{array}{c}{C}_{\mathrm{\α}}\∈({\mathrm{\α}}_{0t}-R/{\mathrm{cos\β}}_{0t},{\mathrm{\α}}_{0t}+R/{\mathrm{cos\β}}_{0t})\\ C_{\mathrm{\β}}\∈({\mathrm{cos\β}}_{0t}-R,{\mathrm{cos\β}}_{0t}+R)\end{array}---\left(33\right)$

The method of ball rectangle is utilized celestial sphere to be divided into 800 ball rectangle little Tian districts in Fig. 5, right ascension and declination are respectively 40 deciles and 20 deciles, each little Tian district represents the span of on right ascension and declination direction 9 °, set up Ge little Tian district navigational star table and star angular distance storehouse, make the number being distributed in nautical star in each visual field meet the needs of normal identification and Attitude Calculation.Install Rotating Platform for High Precision Star Sensor visual field for 4 ° × 4 °, in square visual field, average fixed star number can be obtained by following formula:

$N_{FOV}=6.57e^{1.08M_V}\·\mathrm{\η}---\left(34\right)$

In formula, η is field angle, and the overlayable sky scope in the square visual field for FOV, can be calculated by following formula:

$\mathrm{\η}=\frac{1}{2}-\frac{1}{\mathrm{\π}}arccos\[{\sin }^2(FOV/2)\]---\left(35\right)$

In 4 ° × 4 ° visual fields, average fixed star number is about 42, and star angular distance is individual, and navigational triangle is individual, and 9.0 navigation star databases such as grade are about 120,000 stars, if under star sensor is fully operational in whole day ball recognition mode, observation star must be mated with whole navigation star database, add false recognition rate, data updating rate is also difficult to meet mission requirements simultaneously.Utilize radar equipment angle information to reduce hunting zone, determine that the optical axis carries out local importance in star map recognition after slightly pointing to, can operation time be saved, improve data updating rate.Star sensor square field range span 4 Ge little Tian district in Fig. 5, then import navigation star database and the star angular distance storehouse in this 4 Ge little Tian district, for quick local importance in star map recognition, will greatly improve recognition efficiency and accuracy rate.Adopt the Fast Recognition Algorithm based on nautical star territory, set up the local sky district K vector look-up table that star angular distance is corresponding, utilize the brightest 4 fixed stars in visual field to form 6 groups of star angular distance and carry out matching ratio comparatively, find 4 nautical stars satisfied condition, then identify other fixed star in visual field with shadow matching method.

After completing importance in star map recognition, utilize many fixed stars and nautical star corresponding relation in star chart, adopt Quest-Newton method to calculate star sensor optical axis exact posture (α _t, β _t, γ _t), the picpointed coordinate of recycling t extraterrestrial target builds measurement vector W _t:

$W_t=\frac{{\[f-(y_t-y_0)D(z_t-z_0)D\]}^T}{\sqrt{f^2+{(y_t-y_0)}^2{D}^2+{(z_t-z_0)}^2{D}^2}}---\left(36\right)$

In formula, f ₀for star sensor focal length, (z ₀, y ₀) be the principle point location (pixel number) of imageing sensor, (z _t, y _t) be i-th fixed star picpointed coordinate, imageing sensor pixel dimension is D.Be (z after distortion quadratic fit corrects _t', y _t'), therefore, the measurement vector after correction is W _t':

${W^{\′}}_t=\frac{{\[f_0-(y_t^{\′}-y_0)D(z_t^{\′}-z_0)D\]}^T}{\sqrt{f_0^2+{(y_t^{\′}-y_0)}^2{D}^2+{(z_t^{\′}-z_0)}^2{D}^2}}---\left(37\right)$

Vector V is felt concerned about by the ground of following formula computer memory target _t:

$V_t={\left(R_{CIS}^s\right)}^{-1}{W_t}^{\′}---\left(38\right)$

In formula, for star sensor attitude matrix, can be calculated by following formula:

$R_{CIS}^s=R_y\left({\mathrm{\α}}_t\right)R_z(-{\mathrm{\β}}_t)R_x(-{\mathrm{\γ}}_t)---\left(38\right)$

V _tfor the reference vector of t extraterrestrial target under J2000.0 coordinate system:

Wherein, for coordinate is felt concerned about on the ground of extraterrestrial target to be measured.

Five, vector V is felt concerned about to the ground of described extraterrestrial target _t, obtain extraterrestrial target Horizon system vector through conversion such as the precession of the equinoxes, nutating, Ghandler motion, earth rotations, resolve extraterrestrial target Horizon system position angle, the angle of pitch

In formula, for t Earth central inertial is tied to Horizon system pose transformation matrix, calculated by formula (11). for extraterrestrial target Horizon system position angle, the angle of pitch.

Boat-carrying star sensor works in endoatmosphere, and by the impact of atmospheric refraction during observation space target, apparent place angle and its true place angle of measurement exist certain deviation.Fig. 6 large deviations amount Δ E is the difference of extraterrestrial target Horizon system angle of pitch observed reading and actual value, is astronomical refraction ρ.

To the described Horizon system angle of pitch carry out astronomical refraction correction to obtain

In formula, for the revised Horizon angle of pitch, ρ _tfor the astronomical refraction that t extraterrestrial target is corresponding.

Below the computing method of astronomical refraction:

A, when time, astronomical refraction ρ _tadopt astronomical refraction model in Chinese astronomical almanac:

ρ _t＝(1+α _tA _t+B)ρ ₀(41)

In formula, ρ ₀can following formula be directly utilized to calculate:

ρ ₀＝60.0972468"tanZ++0.0109332tan ²Z

(42)

-0.0729002tan ³Z+0.0018327tan ⁴Z-0.0000107tan ⁵Z

Wherein Z is zenith distance, α _tfor temperature variation multiplier revisory coefficient, can be calculated by following formula:

α _t＝1.0-0.0072027tanZ+0.0133651tan ²Z

(43)

-0.0073417tan ³Z+0.0018700tan ⁴Z-0.0001700tan ⁵Z

A _tfor temperature variation multiplier, relevant with temperature t; B is air pressure variation multiplier, relevant with air pressure P near measuring station:

$\begin{array}{cc}{A}_t=\frac{-0.00383\×t}{1+0.00367\×t},& B=\frac{P}{1013.2472}-1\end{array}---\left(44\right)$

B, when time, still adopt astronomical refraction model, wherein α in Chinese astronomical almanac _t=1.

C, when time, astronomical refraction ρ _tadopt Polkovo astronomical refraction model:

${\mathrm{\ρ}}_t=\frac{P}{1013.25}\×\frac{273.15}{273.15+t}{\mathrm{\ρ}}_0---\left(45\right)$

In formula, ρ ₀can following formula be directly utilized to calculate:

ρ ₀＝60.2293"tanZ-0.06560"tan ³Z

(46)

+0.00016113"tan ⁵Z-2.87"×tan ⁷Z

Will as the Horizon system angle of pitch after correction, reconstruction attractor target Horizon system vector, then shake correction through ship, obtain the deck system vector of extraterrestrial target:

In formula, for t Attitude matrix, calculated by formula (8).(Ω _t, Ψ _t) for star sensor measure extraterrestrial target deck system accurate angle.

Six, extraterrestrial target actual measurement angle (A is followed the tracks of according to radar equipment _bt, E _bt), after revising axial system error be (A ' _bt, E ' _bt):

$\left\{\begin{array}{c}{A}_{bt}^{\′}=A_{bt}-{\mathrm{\β}}_m\sin (A_{bt}-A_m)\tan E_{bt}-{\mathrm{\δ}}_m\tan E_{bt}-\[S_b+C_s+({\mathrm{\ΔU}}_A/C_A)\]\sec E_c\\ E_{bt}^{\′}=E_{bt}-{\mathrm{\β}}_m\sin (A_{bt}-A_m)-C_e-{\mathrm{\ΔE}}_g\cos E_{bt}-({\mathrm{\ΔU}}_E/C_E)\end{array}\right.---\left(48\right)$

In formula, (β _m, A _m) be deep bid maximum inclination and maximum inclination direction; δ _mfor azimuth axis, the non-orthogonal error of pitch axis; S _bfor ray machine deviation; (C _s, C _e) be orientation, pitching photoelectricity deviation; Δ E _gfor antenna gravity sag error; (Δ U _a, Δ U _e) be azimuthal error voltage and pitch error voltage; (C _a, C _e) be orientation branch road directional sensitivity and pitching branch road directional sensitivity.

Rotating Platform for High Precision Star Sensor can be utilized to realize carrying out accuracy evaluation to it:

$\{\begin{array}{c}{\mathrm{\δA}}_t={\mathrm{\Ω}}_t-A_{bt}^{\′}\\ {\mathrm{\δE}}_t={\mathrm{\Ψ}}_t-E_{bt}^{\′}\end{array}---\left(48\right)$

In formula, (δ A _t, δ E _t) be the sensing of radar electric axis deviation, i.e. radar pointing accuracy.

For improving calculation accuracy, adopting repetitive measurement counting statistics to average, effectively can reject the singular value in calculation result, improve radar qualification precision.

Through sea trial checking, present embodiment proposes shipborne radar and is better than 50 〞 relative to star sensor orientation, pitching random residual, meets radar accuracy qualification requirement, illustrates that the method is feasible.

Claims (5)

1. the marine Precision Checkup Method of shipborne radar, it is characterized in that, the method is realized by following steps:

Step one, at shipborne radar device antenna three axle center strapdown, star sensor SS1 is installed;

When step 2, ship lie up and sit pier, boat-carrying theodolite for calibration is demarcated zero difference and is sighted difference, and described star sensor SS1 demarcates principal point, focal length and optical distortion parameter; Axial system error demarcated by shipborne radar;

Step 3, shipborne radar and star sensor follow the tracks of extraterrestrial target simultaneously, star sensor captured in real-time radar antenna point to star chart, t shipborne radar follow the tracks of extraterrestrial target measure in real time deck system position angle and the angle of pitch be (A _bt, E _bt), form deck coordinate system vector V _bt, shake correction through ship and obtain radar electric axis Horizon system vector V _dPt, to described radar electric axis Horizon system vector V _dPtgeocentric inertial coordinate system vector V is transformed into after carrying out accommodation, Ghandler motion, rotation and precession of the equinoxes correction _cISt, resolve star sensor optical axis initial directional (α _0t, β _0t);

Step 4, the optical axis initial directional (α obtained according to step 3 _0t, β _0t) and the visual field radius R of star sensor, calculate the field range (C of star sensor _α, C _β), adopt the Fast Recognition Algorithm based on nautical star territory, carry out importance in star map recognition, and utilize the corresponding relation of many fixed stars and nautical star in star chart, calculate star sensor optical axis exact posture (α _t, β _t, γ _t), the picpointed coordinate of recycling t extraterrestrial target builds star sensor measurement vector W _t, carry out distortion quadratic fit to described measurement vector and correct, the measurement vector obtained after correcting is W _t', adopt the ground of following formula computer memory target to feel concerned about vector V _t:

$V_t={\left(R_{CIS}^s\right)}^{-1}{W}_t^{\′}$

In formula, for star sensor attitude matrix, CIS is geocentric inertial coordinate system, and s is star sensor coordinate system;

Step 5, vector V is felt concerned about to the ground of the extraterrestrial target described in step 4 _t, after carrying out the conversion of the precession of the equinoxes, nutating, Ghandler motion, earth rotation, obtain extraterrestrial target Horizon system vector, resolve extraterrestrial target Horizon system position angle and the angle of pitch to the described extraterrestrial target Horizon system angle of pitch carry out astronomical refraction correction, obtain the revised extraterrestrial target Horizon system angle of pitch reconstruction attractor target Horizon system vector, then shake correction through ship, the deck obtaining extraterrestrial target mean to, be formulated as:

In formula, for t Attitude matrix, (Ω _t, Ψ _t) for star sensor measure extraterrestrial target deck system position angle and the angle of pitch, b is deck coordinate system, and DP is inertial navigation Horizon system;

Step 6, according to shipborne radar follow the tracks of extraterrestrial target measure in real time deck system position angle and the angle of pitch (A _bt, E _bt), revise the position angle after axial system error and the angle of pitch (A' _bt, E' _bt), adopt star sensor to realize revised position angle and the angle of pitch (A' _bt, E' _bt) carry out accuracy evaluation, be formulated as:

$\left\{\begin{array}{c}{\mathrm{\δA}}_t={\mathrm{\Ω}}_t-A_{bt}^{\′}\\ {\mathrm{\δE}}_t={\mathrm{\Ψ}}_t-E_{bt}^{\′}\end{array}\right.$

In formula, (δ A _t, δ E _t) be the position angle of radar electric axis sensing and the deviation of the angle of pitch.

2. the marine Precision Checkup Method of shipborne radar according to claim 1, is characterized in that, in step one, confirms the window of antenna perforate, makes star sensor imaging unobstructed; Extraterrestrial target is imaged on star quick device CCD target surface by window on antenna.

3. the marine Precision Checkup Method of shipborne radar according to claim 1, it is characterized in that, axial system error demarcated by described shipborne radar, mainly comprises: the non-orthogonal error of pedestal unlevelness degree, azimuth pitch, orientation zero-bit, pitching zero-bit, ray machine axle deviation, photo electric axis deviation, gravity sag error.

4. the marine Precision Checkup Method of shipborne radar according to claim 1, is characterized in that, in step 4, and star sensor attitude matrix be formulated as: in formula, R _xr _yr _zrepresent the Eulerian angle rotation matrix being rotated counterclockwise rear formation around X, Y and Z axis respectively;

Basic Eulerian angle rotational transformation matrix R _x(θ), R _y(θ), R _z(θ) represent the matrix formed after X, Y and Z axis are rotated counterclockwise θ angle respectively, there is following canonical form:

$R_x\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\θ}& sin\mathrm{\θ}\\ 0& -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]$

$R_y\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}cos\mathrm{\θ}& 0& -sin\mathrm{\θ}\\ 0& 1& 0\\ \sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right]$

$R_z\left(\mathrm{\θ}\right)=\left[\begin{array}{ccc}cos\mathrm{\θ}& sin\mathrm{\θ}& 0\\ -sin\mathrm{\θ}& cos\mathrm{\θ}& 0\\ 0& 0& 1\end{array}\right].$

5. the marine Precision Checkup Method of shipborne radar according to claim 1, it is characterized in that, in step 4, according to the field range of star sensor, little Tian district, place sequence number is determined by angle, four, square visual field, extract nautical star and star angular distance storehouse in little Tian district, place and be used for fast star identification, and utilize the corresponding relation of many fixed stars and nautical star in star chart, adopt Quest-Newton method to calculate star sensor optical axis exact posture (α _t, β _t, γ _t).