CN102788598A - 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 by utilizing an output value 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 error inhibition method based on three 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 error inhibition method based on three rotations.

(2) background technology

Inertial navigation is to utilize inertia sensitive element (gyroscope and accelerometer) to measure the line motion and the angular motion in carrier relative inertness space, and under known starting condition, goes out the navigational parameters such as speed, position and attitude of carrier with COMPUTER CALCULATION.It relies on the Sensitive Apparatus of self to accomplish navigation task fully, need not to rely on any external information, also not to any energy of external radiation, is a kind of autonomous navigational system fully, therefore has good concealment, anti-interference, the advantage that do not receive any meteorological condition restriction.In addition, inertial navigation system also has the characteristics of data updating rate height, short-term accuracy height and good stability.Just because of above advantage, it has obtained widespread use at Aeronautics and Astronautics, navigation and a lot of civil area.In strapdown inertial navigation system; All inertance elements are directly installed on the carrier; What inertance element was exported is exactly angular velocity and the acceleration of carrier with respect to inertial space; By computing machine the acceleration information that records under the carrier coordinate system is transformed into navigation coordinate system and carries out navigation calculation again, be equivalent to utilize the gyroscope output data in computing machine, to make up of the reference of a mathematical platform as navigation calculating.

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); Has significant advantage: 1) owing to have no rotary part; Thereby firm in structure, anti-vibration, shock resistance, anti-big overload, reliability is high.Simultaneity factor is low in energy consumption, does not need preheating, and start-up time is short, and need not keep in repair, and the life-span is long; 2) because optical fiber is nonmetallic materials, so radiation resistance, strong interference immunity, stable performance can work in the comparatively abominable electromagnetic environment; 3) owing to the area of sensitivity with fiber optic loop is directly proportional, can increase the area of fiber optic loop through the way that increases the fiber optic loop number of turns, the sensitivity that improves gyro, so volume is little, simple in structure, processing technology is simple and cost is low; 4) dynamic range is big, the latch-up phenomenon in the time of can not low rate occurring, and can directly export digital signal, be convenient to utilize computing machine to carry out system in combination.

In the strapdown inertial navigation system, people have promoted the fast development of inertia device for the lasting research of inertia devices such as gyroscope that constitutes Inertial Measurement Unit and accelerometer.But the device precision is high more, and further the cost of boost device precision is just big more.After the inertia device precision reached certain requirement, the performance that adopts the next further improvement of the method system of compensation inertia device deviation was to realize a more realization approach of high precision navigation.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; The rotation modulation technique is a kind of method of self compensation; Through around an axle or a plurality of rotator inertia measuring units (IMU), navigation error is modulated, reach the purpose that navigation accuracy is dispersed, improved to the control navigation error.

The single shaft rotation only can compensate the normal value deviation of inertia device on two sensitive axes directions; Though the twin shaft rotation can compensate the normal value deviation of inertia device on three sensitive axes directions, can't avoid the negative effect of carrier angular motion to the rotation modulation technique.Therefore, how reasonable in design three rotation compensation modes have important meaning for the navigation accuracy of further raising fiber strapdown inertial navigation system.

(3) summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiency of prior art, a kind of fiber strapdown inertial navigation system error inhibition 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 error inhibition method based on three rotations; It is characterized in that adopting three transposition schemes of Inertial Measurement Unit to come to isolate fully the carrier angular motion; Make the relative geographic coordinate system of Inertial Measurement Unit static; Avoid the carrier angular motion for the negative influence of adopting Inertial Measurement Unit rotation modulation technique, can confirm that inertia device often is worth the inhibition form of deviation, to realize more precise navigation.Its concrete steps are following:

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

(2) SINS carries out preheating and prepares, and gathers data that fibre optic gyroscope and quartz accelerometer export and data are handled;

(3) IMU adopts 12 commentaries on classics to stop the transposition scheme that order is a swing circle (like accompanying drawing 2);

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

(4) data-switching that Inertial Measurement Unit rotation back gyroscope is generated obtains the modulation format that inertia device often is worth deviation under carrier coordinate system;

Suppose that the gyroscope constant value drift on the IMU horizontal direction is respectively ε _xAnd ε _yUnder the carrier quiescent conditions; Because three positions of A, B, C that IMU pauses are with respect to navigation coordinate system symmetry; Therefore on three fixed positions in one three transposition cycles, three gyroscope constant value drifts are fastened the attitude error that projection causes at navigation coordinate and must be satisfied:

$3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_A+3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_B+3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_C=0$

$3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_A+3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_B+3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_C=0$

$3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_A+3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_B+3{\left({\∫}_0^{T_s}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_C=0$

Exist the symmetry problem of rotation according to the rotation in three scheme of rotation of IMU, ignore the influence of carrier movement and 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces is zero, that is:

${\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\→}B}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{B\stackrel{+}{\→}A}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\→}B}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{B\stackrel{-}{\→}A}=0$

${\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{A\stackrel{+}{\→}B}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\→}A}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{A\stackrel{-}{\→}B}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\→}A}=0$

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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces is zero, that is:

${\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{B\stackrel{+}{\→}C}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{C\stackrel{+}{\→}B}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{B\stackrel{-}{\→}C}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_y^n\mathrm{dt}\right)}_{C\stackrel{-}{\→}B}=0$

${\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{B\stackrel{+}{\→}C}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\→}B}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{B\stackrel{-}{\→}C}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\→}B}=0$

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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces is zero, that is:

${\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{C\stackrel{+}{\→}A}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{A\stackrel{+}{\→}C}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{C\stackrel{-}{\→}A}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_x^n\mathrm{dt}\right)}_{A\stackrel{-}{\→}C}=0$

${\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{C\stackrel{+}{\→}A}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{A\stackrel{+}{\→}C}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{C\stackrel{-}{\→}A}+{\left({\∫}_0^{T_z}{\mathrm{\ϵ}}_z^n\mathrm{dt}\right)}_{A\stackrel{-}{\→}C}=0$

It is exactly the value that periodically changes the strapdown matrix that 12 order change the process of stopping, make three gyrostatic sensitive axes in a rotation period along center of rotation be symmetrically distributed (like accompanying drawing 3).Having proved intuitively that one 12 order changes stops in the process, and gyroscope often is worth the relative navigation coordinate of deviation system by modulation fully, and the navigation accuracy of system is not exerted an influence.In like manner stop in the cycle a complete commentaries on classics because the symmetrical distribution of three fixed positions and rotation process, can obtain that Inertial Measurement Unit stops and the transposition process in the accelerometer zero drift in the similar effect effect of navigation coordinate system.

(5) output valve of gyroscope under the IMU coordinate system brought in the strapdown inertial navigation system, adopts the equivalent rotating vector method that strapdown matrix

is upgraded:

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

Wherein:

is the component of rotational-angular velocity of the earth under navigation system;

is the component of motion angular velocity under navigation system of spherical coordinate system relatively for navigation coordinate;

is the component of motion angular velocity on the IMU coordinate system of the relative navigation coordinate of IMU system.

If the equivalent rotating vector differential equation of the relative navigation coordinate of IMU coordinate system system is:

$\stackrel{\·}{\mathrm{\Φ}}={\mathrm{\ω}}_{\mathrm{ns}}^s+\frac{1}{2}\mathrm{\Φ}\×{\mathrm{\ω}}_{\mathrm{ns}}^s+\frac{1}{12}\mathrm{\Φ}\×(\mathrm{\Φ}\×{\mathrm{\ω}}_{\mathrm{ns}}^s)$

Solve the rotating vector of equivalence and replace hypercomplex number to separate according to angular velocity

$q=\cos \frac{\mathrm{\Φ}}{2}+\frac{\mathrm{\Φ}}{\left|\mathrm{\Φ}\right|}\sin \frac{\mathrm{\Φ}}{2}$

Because q=q ₀+ q ₁I+q ₂J+q ₃K, i, j, k are direction vector.Therefore the renewal process of attitude matrix

is:

$C_s^n=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3+q_0{q}_2)\\ 2(q_1{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2+q_0{q}_3)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3+q_0{q}_1)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2+{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2\end{array}\right]$

(6) the use of quartz accelerometer output value

and Step (5) the calculated attitude matrix

calculated after IMU rotation modulated carrier position.

1) calculates the acceleration f down of navigation system ⁿ:

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

2) position of calculating 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 the carrier positions error:

Wherein:

λ ₀Longitude and the latitude of representing initial time carrier present position respectively; Δ λ representes the latitude of carrier, the variable quantity of longitude respectively; R _N, R _MThe radius-of-curvature of representing earth meridian circle, prime vertical respectively; t ₁, t ₂Two the adjacent time points in the process that resolve for inertial navigation system.

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

Effect to the present invention is useful is explained as follows:

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

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

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

The time that consumes when rotating 180 °: T _z=12 seconds;

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

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

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

Equatorial radius: R _e=6378393.0 meters;

Ellipsoid degree: e=3.367e-3;

The earth surface acceleration of gravity that can get by universal gravitation: g ₀=9.78049;

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

The gyroscope constant value drift: 0.01 degree/hour;

Accelerometer bias: 10 ^-4g ₀

Constant: π=3.1415926;

It is as shown in Figure 4 to utilize the said method of invention to obtain the carrier positions graph of errors.The result shows that the 12 order commentaries on classics of IMU three positions stops under the condition, adopts the inventive method can obtain high orientation precision.

(4) description of drawings

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

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

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

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

(5) embodiment

Describe in detail below in conjunction with the accompanying drawing specific embodiments of the invention:

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

(2) SINS carries out preheating and prepares, and gathers data that fibre optic gyroscope and quartz accelerometer export and data are handled;

(3) IMU adopts 12 commentaries on classics to stop the transposition scheme that order is a swing circle (like accompanying drawing 2);

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

(4) data-switching that Inertial Measurement Unit rotation back gyroscope is generated obtains the modulation format that inertia device often is worth deviation under carrier coordinate system;

Suppose that the gyroscope constant value drift on the IMU horizontal direction is respectively ε _xAnd ε _yUnder the carrier quiescent conditions; Because three positions of A, B, C that IMU pauses are with respect to navigation coordinate system symmetry; Therefore on three fixed positions in one three transposition cycles, three gyroscope constant value drifts are fastened the attitude error that projection

causes at navigation coordinate and must be satisfied:

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

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

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

Exist the symmetry problem of rotation according to the rotation in three scheme of rotation of IMU, ignore the influence of carrier movement and 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 the strapdown matrix that 12 order change the process of stopping, make three gyrostatic sensitive axes in a rotation period along center of rotation be symmetrically distributed (like accompanying drawing 3).Having proved intuitively that one 12 order changes stops in the process, and gyroscope often is worth the relative navigation coordinate of deviation system by modulation fully, and the navigation accuracy of system is not exerted an influence.In like manner stop in the cycle a complete commentaries on classics because the symmetrical distribution of three fixed positions and rotation process, can obtain that Inertial Measurement Unit stops and the transposition process in the accelerometer zero drift in the similar effect effect of navigation coordinate system.

(5) output valve of gyroscope under the IMU coordinate system brought in the strapdown inertial navigation system, adopts the equivalent rotating vector method that strapdown matrix

is upgraded:

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

Wherein:

is the component of rotational-angular velocity of the earth under navigation system;

is the component of motion angular velocity under navigation system of spherical coordinate system relatively for navigation coordinate;

is the component of motion angular velocity on the IMU coordinate system of the relative navigation coordinate of IMU system.

If the equivalent rotating vector differential equation of the relative navigation coordinate of IMU coordinate system system is:

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

Solve the rotating vector of equivalence and replace hypercomplex number to separate according to angular velocity

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

Because q=q ₀+ q ₁I+q ₂J+q ₃K, i, j, k are direction vector.Therefore the renewal process of attitude matrix is:

$C_s^n=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3+q_0{q}_2)\\ 2(q_1{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2+q_0{q}_3)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3+q_0{q}_1)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2+{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000768634200012.png,HSA00000768634200022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2\end{array}\right]---\left(8\right)$

(6) the use of quartz accelerometer output value

and Step (5) the calculated attitude matrix

calculated after IMU rotation modulated carrier position.

1) calculates the acceleration f down of navigation system ⁿ:

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

2) position of calculating 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 the carrier positions error:

Wherein: λ ₀Longitude and the latitude of representing initial time carrier present position respectively;

Δ λ representes the latitude of carrier, the variable quantity of longitude respectively; R _N, R _MThe radius-of-curvature of representing earth meridian circle, prime vertical respectively; t ₁, t ₂Two the adjacent time points in the process that resolve for inertial navigation system.

Claims (5)

1. fiber strapdown inertial navigation system error inhibition method based on three rotations is characterized in that may further comprise the steps:

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

(2) SINS carries out preheating and prepares, and gathers data that fibre optic gyroscope and quartz accelerometer export and data are handled;

(3) IMU adopts 12 commentaries on classics to stop the transposition scheme that order is a swing circle (like accompanying drawing 2);

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

(4) data-switching that Inertial Measurement Unit rotation back gyroscope is generated obtains the modulation format that inertia device often is worth deviation under carrier coordinate system;

Suppose that the gyroscope constant value drift on the IMU horizontal direction is respectively ε _xAnd ε _yUnder the carrier quiescent conditions; Because three positions of A, B, C that IMU pauses are with respect to navigation coordinate system symmetry; Therefore on three fixed positions in one three transposition cycles, three gyroscope constant value drifts are fastened the attitude error that projection causes at navigation coordinate and must be satisfied:

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

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

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

Exist the symmetry problem of rotation according to the rotation in three scheme of rotation of IMU, ignore the influence of carrier movement and 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 the strapdown matrix that 12 order change the process of stopping, make three gyrostatic sensitive axes in a rotation period along center of rotation be symmetrically distributed (like accompanying drawing 3).Having proved intuitively that one 12 order changes stops in the process, and gyroscope often is worth the relative navigation coordinate of deviation system by modulation fully, and the navigation accuracy of system is not exerted an influence.In like manner stop in the cycle a complete commentaries on classics because the symmetrical distribution of three fixed positions and rotation process, can obtain that Inertial Measurement Unit stops and the transposition process in the accelerometer zero drift in the similar effect effect of navigation coordinate system.

(5) output valve

of gyroscope under the IMU coordinate system brought in the strapdown inertial navigation system, adopts the equivalent rotating vector method that strapdown matrix

is upgraded:

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

Wherein:

is the component of rotational-angular velocity of the earth under navigation system;

is the component of motion angular velocity under navigation system of spherical coordinate system relatively for navigation coordinate; is the component of motion angular velocity on the IMU coordinate system of the relative navigation coordinate of IMU system.

If the equivalent rotating vector differential equation of the relative navigation coordinate of IMU coordinate system system is:

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

Solve the rotating vector of equivalence and replace hypercomplex number to separate according to angular velocity

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

Because q=q ₀+ q ₁I+q ₂J+q ₃K, i, j, k are direction vector.Therefore the renewal process of attitude matrix

is:

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

(6) the use of quartz accelerometer output value

and steps (5) calculation of attitude matrix

calculated after IMU rotation modulated carrier position.

1) calculates the acceleration f down of navigation system ⁿ:

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

2) position of calculating 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 the carrier positions error:

Wherein:

λ ₀Longitude and the latitude of representing initial time carrier present position respectively;

Δ λ representes the latitude of carrier, the variable quantity of longitude respectively; R _N, R _MThe radius-of-curvature of representing earth meridian circle, prime vertical respectively; t ₁, t ₂Two the adjacent time points in the process that resolve for inertial navigation system.

2. the fiber strapdown inertial navigation system error inhibition method based on three rotations according to claim 1 is characterized in that adopting 12 commentaries on classics to stop the transposition scheme that order is a swing circle IMU, specifically comprises the steps:

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

3. the fiber strapdown inertial navigation system error inhibition method based on three rotations according to claim 1; The data-switching that it is characterized in that Inertial Measurement Unit rotation back gyroscope is generated is under carrier coordinate system; Obtain the modulation format that inertia device often is worth deviation, specifically comprise the steps:

Suppose that the gyroscope constant value drift on the IMU horizontal direction is respectively ε _xAnd ε _yUnder the carrier quiescent conditions; Because three positions of A, B, C that IMU pauses are with respect to navigation coordinate system symmetry; Therefore on three fixed positions in one three transposition cycles, three gyroscope constant value drifts are fastened the attitude error that projection causes at navigation coordinate and must be satisfied:

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

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

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

Exist the symmetry problem of rotation according to the rotation in three scheme of rotation of IMU, ignore the influence of carrier movement and 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 _nDemonstrate the Changing Pattern in positive and negative each week in the plane, the normal value deviation that therefore in the integral process of complete cycle, produces 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 the strapdown matrix that 12 order change the process of stopping, make three gyrostatic sensitive axes in a rotation period along center of rotation be symmetrically distributed (like accompanying drawing 3).Having proved intuitively that one 12 order changes stops in the process, and gyroscope often is worth the relative navigation coordinate of deviation system by modulation fully, and the navigation accuracy of system is not exerted an influence.In like manner stop in the cycle a complete commentaries on classics because the symmetrical distribution of three fixed positions and rotation process, can obtain that Inertial Measurement Unit stops and the transposition process in the accelerometer zero drift in the similar effect effect of navigation coordinate system.

4. the fiber strapdown inertial navigation system error inhibition method based on three rotations according to claim 1; It is characterized in that the output valve

of gyroscope under the IMU coordinate system brought in the strapdown inertial navigation system, adopt the equivalent rotating vector method that strapdown matrix

is upgraded:

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

Wherein:

is the component of rotational-angular velocity of the earth under navigation system;

is the component of motion angular velocity under navigation system of spherical coordinate system relatively for navigation coordinate;

is the component of motion angular velocity on the IMU coordinate system of the relative navigation coordinate of IMU system.

If the equivalent rotating vector differential equation of the relative navigation coordinate of IMU coordinate system system is:

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

Solve the rotating vector of equivalence and replace hypercomplex number to separate according to angular velocity

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

Because q=q ₀+ q ₁I+q ₂J+q ₃K, i, j, k are direction vector.Therefore the renewal process of attitude matrix

is:

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

5. the fiber strapdown inertial navigation system error inhibition method based on three rotations according to claim 1 is characterized in that utilizing the output valve

of quartz accelerometer and the attitude matrix

of step (5) calculating to calculate the position through IMU rotation modulation back carrier.

1) calculates the acceleration f down of navigation system ⁿ:

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

2) position of calculating 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 the carrier positions error:

Wherein:

λ ₀Longitude and the latitude of representing initial time carrier present position respectively;

Δ λ representes the latitude of carrier, the variable quantity of longitude respectively; R _N, R _MThe radius-of-curvature of representing earth meridian circle, prime vertical respectively; t ₁, t ₂Two the adjacent time points in the process that resolve for inertial navigation system.

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