CN102788598B - Error suppressing method of fiber strap-down inertial navigation system based on three-axis rotation - Google Patents

Abstract

The invention provides an error suppressing method of a fiber strap-down inertial navigation system based on three-axis rotation. The error suppressing method comprises the following steps: determining an initial position parameter of a carrier by using a GPS (global positioning system); collecting data output by a fiber-optic gyroscope and a quartz accelerometer; determining attitude information of the carrier according to relationship of output of the accelerometer and gravity acceleration as well as relationship of output of the gyroscope and the rotational angular velocity of the earth, and accomplishing initial alignment of the system; employing an indexing scheme of a rotational period of twelve rotation-stop orders by IMU (inertial measurement unit); converting data generated by the fiber-optic gyroscope and the quartz accelerometer after rotation of the IMU to be in navigation coordinate system to obtain a modulation format of constant deviation of an inertial unit; updating a strap-down matrix Cs<n> by utilizing an output value omega<ls><s> of the fiber-optic gyroscope; and calculating position information of the carrier after the IMU is rotated and modulated. With the adoption of the error suppressing method disclosed by the invention, constant deviation of the inertial unit in three-axis direction can be modulated, thereby navigation positioning precision is improved.

Description

Fiber strapdown inertial navigation system system error inhibiting method based on three axle rotations

(1) technical field

What the present invention relates to is a kind of measuring method, in particular a kind of fiber strapdown inertial navigation system system error inhibiting method based on three axle rotations.

(2) background technology

Inertial navigation is to utilize inertia sensitive element (gyroscope and accelerometer) to measure line motion and the angular motion in carrier relative inertness space, and under known starting condition, calculates the navigational parameters such as speed, position and attitude of carrier with computing machine.It relies on the Sensitive Apparatus of self to complete navigation task completely, without relying on any external information, also not to any energy of external radiation, is a kind of autonomous navigational system completely, therefore have advantages of good concealment, anti-interference, be not subject to any meteorological condition restriction.In addition, inertial navigation system also has that data updating rate is high, short-term accuracy is high and the feature of good stability.Just because of above advantage, it is widely applied at Aeronautics and Astronautics, navigation and a lot of civil area.In strapdown inertial navigation system, all inertance elements are directly installed on carrier, what inertance element was exported is exactly that carrier is with respect to angular velocity and the acceleration of inertial space, by computing machine, the acceleration information recording under carrier coordinate system is transformed into navigation coordinate system and carries out again navigation calculation, be equivalent to utilize gyroscope output data in computing machine, to build the reference that a mathematical platform is calculated as navigation.

Optical fibre gyro is as a kind of novel angular rate sensor, compare with traditional gyroscope (liquid floated gyroscope, dynamically tuned gyro, DTG, electrostatic gyro), there is significant advantage: 1) due to without any rotary part, thereby firm in structure, anti-vibration, shock resistance, resistance to large overload, reliability is high.Simultaneity factor is low in energy consumption, does not need preheating, and start-up time is short, and does not need maintenance, and the life-span is long; 2) because optical fiber is nonmetallic materials, so radiation resistance, strong interference immunity, stable performance, can work in comparatively severe electromagnetic environment; 3) because the area of sensitivity with fiber optic loop is directly proportional, can by increasing the way of the fiber optic loop number of turns, increase the area of fiber optic loop, the sensitivity that improves gyro, so volume is little, simple in structure, processing technology is simple and cost is low; 4) dynamic range is large, and the latch-up phenomenon while there will not be low rate, and direct output digit signals, be convenient to utilize computing machine to carry out system in combination.

In strapdown inertial navigation system, people have promoted the fast development of inertia device for the lasting research that forms the inertia devices such as the gyroscope of Inertial Measurement Unit and accelerometer.But device precision is higher, further the cost of boost device precision is just larger.In inertia device precision, reach after certain requirement, the performance that adopts the method for compensation inertia device deviation further to improve system is to realize of more high precision navigation to realize approach.The compensation method of inertance element has two kinds: the one, and utilize external information to compensate correction, another kind method is the self compensation of inertia device deviation, rotation modulation technology is a kind of method of self compensation, by around an axle or a plurality of axle rotator inertia measuring units (IMU), navigation error is modulated, reach and control the object that navigation accuracy is dispersed, improved to navigation error.

Single-shaft-rotation only can compensate the normal value deviation of inertia device in two sensitive axes directions; Although twin shaft rotation can compensate the normal value deviation of inertia device in three sensitive axes directions, cannot avoid the negative effect of carrier angular motion to rotation modulation technology.Therefore, how three axle rotation compensation modes reasonable in design have important meaning for the navigation accuracy of further raising fiber strapdown inertial navigation system system.

(3) summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of fiber strapdown inertial navigation system system error inhibiting method based on three sensitive axes rotations of Inertial Measurement Unit is provided.

Technical solution of the present invention is: a kind of fiber strapdown inertial navigation system system error inhibiting method based on three axle rotations, it is characterized in that adopting three axle transposition schemes of Inertial Measurement Unit to isolate carrier angular motion completely, make the relative geographic coordinate system of Inertial Measurement Unit static, avoid carrier angular motion for the negative influence that adopts Inertial Measurement Unit rotation modulation technology, can determine that inertia device is often worth the inhibition form of deviation, to realize more high-precision navigation.Its concrete steps are as follows:

(1) by GPS, determine the initial position parameters of carrier, they are bound to navigational computer;

(2) strapdown inertial navitation system (SINS) is carried out preheating preparation, gathers the data of fibre optic gyroscope and quartz accelerometer output and data are processed;

(3) 12 of IMU employings turn and stop the transposition scheme that order is a swing circle (as accompanying drawing 2);

Order 1, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from A point _s; Order 2, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from B point _s; Order 3, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from C point _s; Order 4, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from A point _s; Order 5, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from C point _s; Order 6, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from B point _s; Order 7, IMU clockwise rotates 180 ° of in-position B, stand-by time T from A point _s; Order 8, IMU clockwise rotates 180 ° of in-position C, stand-by time T from B point _s; Order 9, IMU clockwise rotates 180 ° of in-position A, stand-by time T from C point _s; Order 10, IMU clockwise rotates 180 ° of in-position C, stand-by time T from A point _s; Order 11, IMU clockwise rotates 180 ° of in-position B, stand-by time T from C point _s; Order 12, IMU clockwise rotates 180 ° of in-position A, stand-by time T from B point _s; IMU rotates sequential loop according to this to carry out.

(4) data that after Inertial Measurement Unit rotation, gyroscope generates are transformed under carrier coordinate system, obtain the modulation format that inertia device is often worth deviation;

Suppose that the gyroscope constant value drift in IMU horizontal direction is respectively ε _xand ε _y.Under carrier quiescent conditions, because tri-positions of A, B, C that IMU pauses are symmetrical with respect to navigation coordinate system, therefore, on three fixed positions within three axle transposition cycles, three gyro drifts are fastened projection at navigation coordinate the attitude error causing must meet:

$3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_C=0$

$3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_C=0$

$3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_C=0$

According to the rotation in IMU tri-axle scheme of rotation, exist the symmetry problem of rotation, ignore the impact of carrier movement with local geographic coordinate system as a reference, 12 order transposition schemes can be expressed as:

Process 1: order 1,6,7,12, in the rotation period of formation, the gyroscopic drift of x, y axle is ox at navigation coordinate _ny _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}A}=0$

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}A}=0$

Wherein, the time of each rotation process is counted T _z, around the responsive coordinate axis of Inertial Measurement Unit rotate counterclockwise into+, clockwise rotate into-.

Process 2: order 2,5,8,11, in the rotation period of formation, the gyroscopic drift of y, z axle is oy at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}B}=0$

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}B}=0$

Process 3: order 3,4,9,10, in the rotation period of formation, the gyroscopic drift of x, z axle is ox at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}C}=0$

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}C}=0$

It is exactly the value that periodically changes strapdown matrix that 12 order turn the process of stopping, make three gyrostatic sensitive axes in a rotation period along center of rotation symmetrical (as accompanying drawing 3).Proved that intuitively 12 order turn in the process of stopping, gyroscope is often worth deviation Relative Navigation coordinate system to be modulated completely, and the navigation accuracy of system is not exerted an influence.In like manner complete turning in the cycle of stopping, symmetrical due to three fixed positions and rotation process, can obtain that Inertial Measurement Unit stops and transposition process in accelerometer zero drift in the similar effect effect of navigation coordinate system.

(5) output valve under IMU coordinate system by gyroscope bring in strapdown inertial navigation system, adopt equivalent rotating vector method to strapdown matrix upgrade:

${\mathrm{\&omega;}}_{\mathrm{ns}}^s={\mathrm{\&omega;}}_{\mathrm{is}}^s-{\left(C_s^n\right)}^T({\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)$

Wherein: for the component of rotational-angular velocity of the earth under navigation system; for navigation coordinate is the motion angular velocity of the relatively spherical coordinate system component under navigation system; for the motion angular velocity of the IMU Relative Navigation coordinate system component on IMU coordinate system.

If the equivalent rotating vector differential equation of IMU coordinate system Relative Navigation coordinate system is:

$\stackrel{\&CenterDot;}{\mathrm{\&Phi;}}={\mathrm{\&omega;}}_{\mathrm{ns}}^s+\frac{1}{2}\mathrm{\&Phi;}\&times;{\mathrm{\&omega;}}_{\mathrm{ns}}^s+\frac{1}{12}\mathrm{\&Phi;}\&times;(\mathrm{\&Phi;}\&times;{\mathrm{\&omega;}}_{\mathrm{ns}}^s)$

According to angular velocity solve equivalent rotating vector and replace hypercomplex number solution,

$q=\cos \frac{\mathrm{\&Phi;}}{2}+\frac{\mathrm{\&Phi;}}{\left|\mathrm{\&Phi;}\right|}\sin \frac{\mathrm{\&Phi;}}{2}$

Due to q=q ₀+ q ₁i+q ₂j+q ₃k, i, j, k are direction vector.So attitude matrix renewal process be:

$C_s^n=\left[\begin{array}{ccc}{q}_0^2+q_1^2-q_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{q}_2+q_0{q}_3)& q_0^2-q_1^2+q_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& q_0^2-q_1^2-q_2^2+q_3^2\end{array}\right]$

(6) utilize the output valve of quartz accelerometer and the attitude matrix of step (5) calculating calculate the position of carrier after IMU rotation modulation.

1) calculate the lower acceleration f of navigation system ⁿ:

$f^n=C_s^n{f}_{\mathrm{is}}^s$

2) calculate the position of carrier:

According to t ₁carrier east orientation horizontal velocity V constantly _x(t ₁) and north orientation horizontal velocity V _y(t ₁), ask for t ₂carrier positions is constantly:

3) calculate carrier positions error:

Wherein: λ ₀the longitude and the latitude that represent respectively initial time carrier present position; Δ λ represents respectively the latitude of carrier, the variable quantity of longitude; R _n, R _mthe radius-of-curvature that represents respectively earth meridian circle, prime vertical; t ₁, t ₂two the adjacent time points in process that resolve for inertial navigation system.

The present invention's advantage is compared with prior art: the present invention has broken in traditional strapdown inertial navitation system (SINS) IMU and carrier and has been connected and causes system navigation accuracy to be subject to the constraint of inertia device deviation effects, propose a kind of inertia device that IMU is stopped around three fixing position rotatings of the sensitive axes of three directions of carrier and be often worth deviation modulation scheme, the method can often be worth deviation by all inertia devices modulates, and effectively improves navigation and positioning accuracy.

The effect useful to the present invention is described as follows:

Under VC++ simulated conditions, the method is carried out to emulation experiment:

Carrier remains static, the error model parameters of IMU tri-position 12 order rotation-stop schemes:

The dead time of three positions: T _s=5 minutes;

The time consuming while rotating 180 °: T _z=12 seconds;

Rotate in the process of 180 °, the Acceleration and deceleration time in each transposition is respectively 4 seconds;

Carrier initial position: 45.7796 ° of north latitude, 126.6705 ° of east longitudes;

Initial attitude error angle: three initial attitude error angles are zero;

Equatorial radius: R _e=6378393.0 meters;

Ellipsoid degree: e=3.367e-3;

By the available earth surface acceleration of gravity of universal gravitation: g ₀=9.78049;

Rotational-angular velocity of the earth (radian per second): 7.2921158e-5;

Gyro drift: 0.01 degree/hour;

Accelerometer bias: 10 ^-4g ₀;

Constant: π=3.1415926;

Utilize the described method of invention to obtain carrier positions graph of errors as shown in Figure 4.Result shows that IMU tri-position 12 order turn under the condition of stopping, and adopts the inventive method can obtain higher positioning precision.

(4) accompanying drawing explanation

Fig. 1 is a kind of fiber strapdown inertial navigation system system error inhibiting method process flow diagram based on three axle rotations of the present invention;

Fig. 2 is the fiber strapdown inertial navigation system system IMU rotation-stop scheme detailed step figure based on three axle rotations of the present invention;

Fig. 3 is that the fiber strapdown inertial navigation system system IMU based on three axle rotations of the present invention turns stopping time constant value drift azimuth distribution;

Contrast experiment's curve of carrier positioning error when Fig. 4 is the carrier positions error of the fiber strapdown inertial navigation system system based on three axles rotations of the present invention and IMU stationary state.

(5) embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in detail:

(1) by GPS, determine the initial position parameters of carrier, they are bound to navigational computer;

(2) strapdown inertial navitation system (SINS) is carried out preheating preparation, gathers the data of fibre optic gyroscope and quartz accelerometer output and data are processed;

(3) 12 of IMU employings turn and stop the transposition scheme that order is a swing circle (as accompanying drawing 2);

Order 1, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from A point _s; Order 2, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from B point _s; Order 3, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from C point _s; Order 4, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from A point _s; Order 5, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from C point _s; Order 6, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from B point _s; Order 7, IMU clockwise rotates 180 ° of in-position B, stand-by time T from A point _s; Order 8, IMU clockwise rotates 180 ° of in-position C, stand-by time T from B point _s; Order 9, IMU clockwise rotates 180 ° of in-position A, stand-by time T from C point _s; Order 10, IMU clockwise rotates 180 ° of in-position C, stand-by time T from A point _s; Order 11, IMU clockwise rotates 180 ° of in-position B, stand-by time T from C point _s; Order 12, IMU clockwise rotates 180 ° of in-position A, stand-by time T from B point _s; IMU rotates sequential loop according to this to carry out.

(4) data that after Inertial Measurement Unit rotation, gyroscope generates are transformed under carrier coordinate system, obtain the modulation format that inertia device is often worth deviation;

Suppose that the gyroscope constant value drift in IMU horizontal direction is respectively ε _xand ε _y.Under carrier quiescent conditions, because tri-positions of A, B, C that IMU pauses are symmetrical with respect to navigation coordinate system, therefore, on three fixed positions within three axle transposition cycles, three gyro drifts are fastened projection at navigation coordinate the attitude error causing must meet:

$3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_C=0$

$3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_C=0---\left(1\right)$

$3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_C=0$

According to the rotation in IMU tri-axle scheme of rotation, exist the symmetry problem of rotation, ignore the impact of carrier movement with local geographic coordinate system as a reference, 12 order transposition schemes can be expressed as:

Process 1: order 1,6,7,12, in the rotation period of formation, the gyroscopic drift of x, y axle is ox at navigation coordinate _ny _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}A}=0$

$\left(2\right)$

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}A}=0$

Wherein, the time of each rotation process is counted T _z, around the responsive coordinate axis of Inertial Measurement Unit rotate counterclockwise into+, clockwise rotate into-.

Process 2: order 2,5,8,11, in the rotation period of formation, the gyroscopic drift of y, z axle is oy at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}B}=0$

$\left(3\right)$

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}B}=0$

Process 3: order 3,4,9,10, in the rotation period of formation, the gyroscopic drift of x, z axle is ox at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}C}=0$

$\left(4\right)$

${\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}C}=0$

It is exactly the value that periodically changes strapdown matrix that 12 order turn the process of stopping, make three gyrostatic sensitive axes in a rotation period along center of rotation symmetrical (as accompanying drawing 3).Proved that intuitively 12 order turn in the process of stopping, gyroscope is often worth deviation Relative Navigation coordinate system to be modulated completely, and the navigation accuracy of system is not exerted an influence.In like manner complete turning in the cycle of stopping, symmetrical due to three fixed positions and rotation process, can obtain that Inertial Measurement Unit stops and transposition process in accelerometer zero drift in the similar effect effect of navigation coordinate system.

(5) output valve under IMU coordinate system by gyroscope bring in strapdown inertial navigation system, adopt equivalent rotating vector method to strapdown matrix upgrade:

${\mathrm{\&omega;}}_{\mathrm{ns}}^s={\mathrm{\&omega;}}_{\mathrm{is}}^s-{\left(C_s^n\right)}^T({\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)---\left(5\right)$

Wherein: for the component of rotational-angular velocity of the earth under navigation system; for navigation coordinate is the motion angular velocity of the relatively spherical coordinate system component under navigation system; for the motion angular velocity of the IMU Relative Navigation coordinate system component on IMU coordinate system.

If the equivalent rotating vector differential equation of IMU coordinate system Relative Navigation coordinate system is:

$\stackrel{\&CenterDot;}{\mathrm{\&Phi;}}={\mathrm{\&omega;}}_{\mathrm{ns}}^s+\frac{1}{2}\mathrm{\&Phi;}\&times;{\mathrm{\&omega;}}_{\mathrm{ns}}^s+\frac{1}{12}\mathrm{\&Phi;}\&times;(\mathrm{\&Phi;}\&times;{\mathrm{\&omega;}}_{\mathrm{ns}}^s)---\left(6\right)$

According to angular velocity solve equivalent rotating vector and replace hypercomplex number solution,

$q=\cos \frac{\mathrm{\&Phi;}}{2}+\frac{\mathrm{\&Phi;}}{\left|\mathrm{\&Phi;}\right|}\sin \frac{\mathrm{\&Phi;}}{2}---\left(7\right)$

Due to q=q ₀+ q ₁i+q ₂j+q ₃k, i, j, k are direction vector.So attitude matrix renewal process be:

$C_s^n=\left[\begin{array}{ccc}{q}_0^2+q_1^2-q_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{q}_2+q_0{q}_3)& q_0^2-q_1^2+q_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& q_0^2-q_1^2-q_2^2+q_3^2\end{array}\right]---\left(8\right)$

(6) utilize the output valve of quartz accelerometer and the attitude matrix of step (5) calculating calculate the position of carrier after IMU rotation modulation.

1) calculate the lower acceleration f of navigation system ⁿ:

$f^n=C_s^n{f}_{\mathrm{is}}^s---\left(9\right)$

2) calculate the position of carrier:

According to t ₁carrier east orientation horizontal velocity V constantly _x(t ₁) and north orientation horizontal velocity V _y(t ₁), ask for t ₂carrier positions is constantly:

3) calculate carrier positions error:

Wherein: λ ₀the longitude and the latitude that represent respectively initial time carrier present position; Δ λ represents respectively the latitude of carrier, the variable quantity of longitude; R _n, R _mthe radius-of-curvature that represents respectively earth meridian circle, prime vertical; t ₁, t ₂two the adjacent time points in process that resolve for inertial navigation system.

Claims (1)

1. the fiber strapdown inertial navigation system system error inhibiting method rotating based on three axles, is characterized in that comprising the following steps:

(1) by GPS, determine the initial position parameters of carrier, they are bound to navigational computer;

(2) strapdown inertial navitation system (SINS) is carried out preheating preparation, gathers the data of fibre optic gyroscope and quartz accelerometer output and data are processed;

(3) 12 of IMU employings turn and stop the transposition scheme that order is a swing circle;

Order 1, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from A point around U axle _s; Order 2, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from B point around E axle _s; Order 3, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from C point around N axle _s; Order 4, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from A point around N axle _s; Order 5, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from C point around E axle _s; Order 6, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from B point around U axle _s; Order 7, IMU clockwise rotates 180 ° of in-position B, stand-by time T from A point around U axle _s; Order 8, IMU clockwise rotates 180 ° of in-position C, stand-by time T from B point around E axle _s; Order 9, IMU clockwise rotates 180 ° of in-position A, stand-by time T from C point around N axle _s; Order 10, IMU clockwise rotates 180 ° of in-position C, stand-by time T from A point around N axle _s; Order 11, IMU clockwise rotates 180 ° of in-position B, stand-by time T from C point around E axle _s; Order 12, IMU clockwise rotates 180 ° of in-position A, stand-by time T from B point around U axle _s; All to look over and determine from the direction over against coordinate axis counterclockwise and clockwise; IMU rotates sequential loop according to this to carry out;

(4) data that after IMU rotation, gyroscope generates are transformed under carrier coordinate system, obtain the modulation format that inertia device is often worth deviation;

Gyroscope constant value drift in IMU horizontal direction is respectively ε _xand ε _y, under carrier quiescent conditions, because tri-positions of A, B, C that IMU pauses are symmetrical with respect to navigation coordinate system, therefore, on three fixed positions within three axle transposition cycles, three gyro drifts are fastened projection at navigation coordinate the attitude error causing must meet:

$\begin{array}{c}3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_C=0\\ 3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_C=0\\ 3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_A+3{\left({\&Integral;}_0^{T_S}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_B+3{\left({\&Integral;}_0^{T_s}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_C=0\end{array}$

According to the rotation in IMU tri-axle scheme of rotation, exist the symmetry problem of rotation, ignore the impact of carrier movement with local geographic coordinate system as a reference, 12 order transposition schemes are expressed as:

Process 1: order 1,6,7,12, in the rotation period of formation, the gyroscopic drift of x, y axle is ox at navigation coordinate _ny _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

$\begin{array}{c}{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}A}=0\\ {\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}A}=0\end{array}$

Wherein, the time of each rotation process is counted T _z, around the responsive coordinate axis of IMU rotate counterclockwise into+, clockwise rotate into-;

Process 2: order 2,5,8,11, in the rotation period of formation, the gyroscopic drift of y, z axle is oy at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

$\begin{array}{c}{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_y^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}B}=0\\ {\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{B\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}B}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{B\stackrel{-}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}B}=0\end{array}$

Process 3: order 3,4,9,10, in the rotation period of formation, the gyroscopic drift of x, z axle is ox at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

$\begin{array}{c}{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}C}=0\\ {\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{A\stackrel{+}{\&RightArrow;}C}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\&RightArrow;}A}+{\left({\&Integral;}_0^{T_z}{\mathrm{\&epsiv;}}_z^n\mathrm{dt}\right)}_{A\stackrel{-}{\&RightArrow;}C}=0\end{array}$

It is exactly the value that periodically changes strapdown matrix that 12 order turn the process of stopping, and makes three gyrostatic sensitive axes symmetrical along center of rotation in a rotation period; Proved that intuitively 12 order turn in the process of stopping, gyroscope is often worth deviation Relative Navigation coordinate system to be modulated completely, and the navigation accuracy of system is not exerted an influence; In like manner complete turning in the cycle of stopping, symmetrical due to three fixed positions and rotation process, obtain that IMU stops and transposition process in accelerometer zero drift identical at the action effect of navigation coordinate system;

(5) output valve under IMU coordinate system by gyroscope bring in strapdown inertial navitation system (SINS), adopt equivalent rotating vector method to strapdown matrix upgrade:

${\mathrm{\&omega;}}_{\mathrm{ns}}^s={\mathrm{\&omega;}}_{\mathrm{is}}^s-{\left(C_s^n\right)}^T({\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)$

Wherein: for the component of rotational-angular velocity of the earth under navigation coordinate system; for navigation coordinate is the motion angular velocity of the relatively spherical coordinate system component under navigation coordinate system; for the motion angular velocity of the IMU Relative Navigation coordinate system component on IMU coordinate system;

The equivalent rotating vector differential equation of IMU coordinate system Relative Navigation coordinate system is:

$\stackrel{\&CenterDot;}{\mathrm{\&Phi;}}={\mathrm{\&omega;}}_{\mathrm{ns}}^s+\frac{1}{2}\mathrm{\&Phi;}\&times;{\mathrm{\&omega;}}_{\mathrm{ns}}^s+\frac{1}{12}\mathrm{\&Phi;}\&times;(\mathrm{\&Phi;}\&times;{\mathrm{\&omega;}}_{\mathrm{ns}}^s)$

According to angular velocity solve equivalent rotating vector and replace hypercomplex number solution,

$q=\cos \frac{\mathrm{\&Phi;}}{2}+\frac{\mathrm{\&Phi;}}{\left|\mathrm{\&Phi;}\right|}\sin \frac{\mathrm{\&Phi;}}{2}$

Due to q=q ₀+ q ₁i+q ₂j+q ₃k, i, j, k are direction vector, so attitude matrix renewal process be:

$C_s^n=\left[\begin{array}{ccc}{q}_0^2+q_1^2-q_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{q}_2+q_0{q}_3)& q_0^2-q_1^2+q_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& q_0^2-q_1^2-q_2^2+q_3^2\end{array}\right]$

(6) utilize the output valve of quartz accelerometer and the attitude matrix of step (5) calculating calculate the position of carrier after IMU rotation modulation;

1) calculate the lower acceleration f of navigation coordinate system ⁿ:

$f^n=C_s^n{f}_{\mathrm{is}}^s$

2) calculate the position of carrier:

According to t ₁carrier east orientation horizontal velocity V constantly _x(t ₁) and north orientation horizontal velocity V _y(t ₁), ask for t ₂carrier positions is constantly:

3) calculate carrier positions error:

Wherein: λ ₀the longitude and the latitude that represent respectively initial time carrier present position; Δ λ represents respectively the latitude of carrier, the variable quantity of longitude; R _n, R _mthe radius-of-curvature that represents respectively earth meridian circle, prime vertical; t ₁, t ₂two the adjacent time points in process that resolve for strapdown inertial navitation system (SINS).