CN102927994B - A kind of quick calibrating method of oblique redundant strapdown inertial navigation system - Google Patents

A kind of quick calibrating method of oblique redundant strapdown inertial navigation system Download PDF

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CN102927994B
CN102927994B CN201210404851.3A CN201210404851A CN102927994B CN 102927994 B CN102927994 B CN 102927994B CN 201210404851 A CN201210404851 A CN 201210404851A CN 102927994 B CN102927994 B CN 102927994B
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sky
gyroscope
accelerometer
delta
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CN102927994A (en
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张春熹
宋来亮
晁代宏
周小红
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北京航空航天大学
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Abstract

The invention discloses a kind of oblique redundant strapdown inertial navitation system (SINS) quick calibrating method, comprise step one: describe tilting RSINS and misalignment is installed, provide demarcation measurement equation.Step 2: design tilting RSINS scaling scheme.Step 3: build tilting RSINS Calibration Simulation platform, and utilize emulation platform to verify the accuracy of scaling method.The present invention is based on three shaft positions/rate table and Fast Calibration is carried out to tilting RSINS, utilize respectively four Fa Hesan position, position methods of rotation demarcate redundant accelerometers and gyrostatic zero partially, constant multiplier and install the calibrating parameters such as misalignment, and utilize emulation platform to verify the accuracy of above scaling method.Stated accuracy of the present invention is high, easy and simple to handle, in can meeting, the Fast Calibration demand of the tilting RSINS of low precision, has good engineer applied and is worth.

Description

A kind of quick calibrating method of oblique redundant strapdown inertial navigation system

Technical field

The present invention relates to a kind of quick calibrating method of oblique redundant strapdown inertial navigation system, belong to Aeronautics and Astronautics field of navigation technology.

Background technology

Traditional strapdown inertial navitation system (SINS) scheme is " 3 gyro+3 accelerometer " orthogonal configuration, utilizes the sensitive axes of gyro and accelerometer to build the body coordinate system of inertial navigation system.Whole output informations of gyro and accelerometer will be utilized in inertial reference calculation process.Traditional Methods of Strapdown Inertial Navigation System does not allow inertia sensitive element to produce fault output, and when any inertia sensitive element breaks down output exception value, the navigation results that system exports is by no longer valid.Therefore in traditional strapdown inertial navitation system (SINS), the fault of any inertia device is equal to scrapping of whole system, and the consequence caused is by hardly imaginable.The precision of inertial navigation system and reliability depend on precision and the reliability of inertia sensitive element to a great extent.Improve the raising that the precision of inertia sensitive element and reliability need whole industry and manufacturing industry level, this needs R&D cycle of growing very much and drops into huge financial resources.Under existing commercial production levels condition, Redundancy Design is adopted to be improve the effective way of inertial navigation system reliability.

Redundancy can be divided into system-level redundancy and device level redundancy two kinds.System-level redundancy refers to that one or more sets systems are as backup, and when main system loses efficacy, standby system was started working; Device level redundancy refers to utilize the best configuration of multiple inertia sensitive element to form redundant system, and when one or more component failure, redundancy device still can complete navigation task.Platform INS Inertial physical construction is comparatively complicated, all takes system-level redundancy strategy.Compared with platform-type system, Methods of Strapdown Inertial Navigation System small volume, inertia sensitive element connects firmly with carrier neatly, and without the need to using complicated mechanical support and stable platform, therefore device level redundancy is more suitable for Methods of Strapdown Inertial Navigation System.Redundancy has become one of important method improving strapdown inertial navitation system (SINS) (SINS) reliability and precision.Compare system-level redundancy, device level oblique redundant mode has greater advantage in volume power consumption and cost, becomes the first-selection of redundancy strapdown inertial navitation system (SINS) (RSINS).Tilting RSINS must carry out accurate calibration to sensor before use, to determine zero of each inertial sensor partially, constant multiplier and install the parameters such as misalignment.

Conventional orthogonal type SINS mainly contains discrete and system-level two kinds of scaling methods: separate calibration method directly utilizes the output of gyroscope and accelerometer as observed quantity, generally adopts least square method; Systematic calibration then utilizes the output of gyroscope and accelerometer to carry out navigation calculation, carrys out the error parameter of calibration system using navigation error (site error, velocity error and attitude error) as observed quantity.Because tilting RSINS sensor adopts nonopiate mounting means, its scaling method is different from conventional orthogonal type SINS.

Existing redundancy strapdown inertial navitation system (SINS) timing signal has following weak point:

1, existing domestic discrete scaling method is only applicable to the redundancy strapdown inertial navitation system (SINS) of the lower MEMS composition of precision, and versatility is poor;

2, for current domestic inertia device level, still can not play the advantage of systematic calibration completely, if Kalman filter design is incorrect, each calibrating parameters valuation will be dispersed, and have a strong impact on demarcation performance.

Summary of the invention

The object of the invention is to solve the problem, a kind of quick calibrating method of oblique redundant strapdown inertial navigation system is proposed, utilize respectively four Fa Hesan position, position methods of rotation demarcate redundant accelerometers and gyrostatic zero partially, constant multiplier and install the calibrating parameters such as misalignment, and utilize emulation platform to verify the accuracy of scaling method of the present invention.Stated accuracy of the present invention is high, easy and simple to handle, has good engineer applied and is worth, be applied to inertial sensor zero partially, constant multiplier and installing in the isoparametric identification of misalignment, effectively can pick out parameter, there is very high stated accuracy.

A quick calibrating method for oblique redundant strapdown inertial navigation system, comprises following step:

Step one: describe tilting RSINS and install misalignment, build and demarcate measurement equation;

(1) tilting RSINS installs misalignment description;

(2) build tilting RSINS and demarcate measurement equation;

Step 2: determine tilting RSINS scaling scheme, comprise and determine three-axle table position, accelerometer four position calibration method, determines gyroscope scaling method, adopts gyroscope four position calibration method or gyroscope three position to rotate scaling method;

Step 3: build tilting RSINS Calibration Simulation platform, and the accuracy utilizing the scaling method described in emulation platform checking.

The invention has the advantages that:

(1) the method for the invention is applicable to the demarcation of the tilting RINS of multiple precision, has versatility;

(2) the method for the invention stated accuracy is higher, simple to operate and consuming time short, in can meeting, the Fast Calibration demand of the tilting RSINS of low precision;

(3) the method for the invention is for middle low precision gyroscope instrument, and three positions are rotated scaling method and effectively enhanced gyroscope calibrating parameters observability.

Accompanying drawing explanation

Fig. 1 is the installation relation of ideal transducer of the present invention axis and system ontology coordinate system;

Fig. 2 is the installation relation of real sensor of the present invention axis and system ontology coordinate system;

Fig. 3 is Calibration Simulation platform structure block diagram of the present invention;

Fig. 4 is the regular dodecahedron mounting means of the present invention six redundancy RSINS;

Fig. 5 is method flow diagram of the present invention.

In figure:

1-tilting RSINS configuration mode selects module 2-IMU data configuration module 3-calibrating parameters to select module

4-revolving table position and rate selection module 5-calibrating parameters resolve module 6-calibration result authentication module

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present invention is a kind of quick calibrating method of oblique redundant strapdown inertial navigation system, first gives tilting RSINS(oblique redundant strapdown inertial navigation system) demarcation measurement equation and describe emphatically its install misalignment; Then give accelerometer and gyrostatic four position calibration methods, and propose three positions rotation scaling methods for low precision gyroscope instrument; Finally build tilting RSINS Calibration Simulation platform, describe each functional module effect, and utilize emulation platform to verify the accuracy of above scaling method.

Flow process as shown in Figure 5, comprises following step:

Step one: describe tilting RSINS and install misalignment, build and demarcate measurement equation.

(1) tilting RSINS installs misalignment description

In tilting RSINS, sensor coordinate system (s system) cartesian coordinate systems that not three axles are orthogonal, therefore must export sensor and map to system ontology and to be connected coordinate system (b system), to complete conventional inertial reference calculation.OX as shown in Figure 1 by bz bfor system ontology is connected coordinate system; H irepresent the axis of i-th sensor, H ifollowing mapping relations are had with b cording:

h i=[cos(α i)cos(β i)]·i+[sin(α i)cos(β i)]·j+[sin(β i)]·k (1)

Wherein: h i, i, j, k represent H respectively iaxle, X baxle, Y baxle, Z bunit vector on axle, α irepresent h iat X b-Y bprojection vector in plane and X bthe angle of axle, β irepresent h iwith X b-Y bthe angle of plane.

But in sensor actual installation process, actual sensor axle H can not be ensured i' strictly overlap with desired axis Hi, there is both supposing small angle error δ α iwith δ β i, as shown in Figure 2.Suppose sensor axis H i' at X b-Y bprojection vector in plane and X bthe angle of axle is α i', with X b-Y bthe angle of plane is β i', therefore:

h i'=[cos(α i')cos(β i')]·i+[sin(α i′)cos(β i')]·j+[sin(β i′)]·k (2)

By α i'=α i-δ α iand β i'=β i+ δ β isubstitution formula (2), ignores second order (δ α in a small amount iδ β i), and by sin (δ α i), sin (δ β i) linearly turn to δ α i, δ β i, cos (δ α i), cos (δ β i) be approximately 1, formula (3) can be obtained:

h i'=h i+δα i·p i+δβ i·q i(3)

In formula, p i=[sin (α i) cos (β i)-cos (α i) cos (β i) 0], q i=[-cos (α i) sin (β i)-sin (α i) sin (β i) cos (β i)].

(2) build tilting RSINS and demarcate measurement equation

In actual use, the gyroscope in tilting RSINS and accelerometer export not angular velocity and acceleration true value, but associated umber of pulse or digital quantity, device output valve just can use after having to pass through calibration compensation.Calibrating parameters mainly comprises zero partially, constant multiplier and install misalignment three.In supposing the system, inertial sensor exports and is expressed as M=[m 1, m 2..., m i... m n] t, wherein, m irepresent the original pulse amount that i-th (i ∈ [1, n]) gyroscope or accelerometer export, n represents system redundancy (i.e. the quantity of gyro or accelerometer); System ontology coordinate system responsive to angular velocity or acceleration be expressed as X=[x xx yx z] t, for gyroscope, X represents angular velocity vector, and for accelerometer, X represents acceleration, x xx yx zrepresent the component of X along system ontology coordinate system respectively; H=[h 1, h 2..., h i... h n] texpression system ideal installs matrix, wherein, and h ii-th (i ∈ [1, n]) gyroscope or the accelerometer desirable installation direction vector relative to system ontology coordinate system is described; H'=[h 1', h 2' ..., h i' ... h n'] T represents system actual installation matrix, wherein, h i' i-th (i ∈ [1, n]) gyroscope or the accelerometer actual installation direction vector relative to system ontology coordinate system is described, H'=H+ δ α P+ δ β Q; B=[b 1b 2b n] trepresent zero inclined vector of n sensor; K=diag [k 1k 2k n] represent the diagonal matrix be made up of the constant multiplier of n sensor, separately have:

δα=diag[δ α1,δα 2,…,δα i,…,δα n];

δβ=diag[δβ 1,δβ 2,…,δβ i,…,δβ n];

P=[p 1,p 2,…,p i,…,p n] T

Q=[q 1,q 2,…,q i,…,q n] T

Wherein: now K, P, Q, δ α, δ β, H, H' and B are constant value, tilting RSINS demarcation measurement equation is specially:

M=K(H+δα·P+δβ·Q)·X+B (4)

Step 2: determine tilting RSINS scaling scheme, comprise and determine three-axle table position, accelerometer four position calibration method, determines gyroscope scaling method, adopts gyroscope four position calibration method or gyroscope three position to rotate scaling method.

Suppose the demarcation measurement equation only considering wherein some sensors, as follows:

m i=k i(h i+δα i·p i+δβ i·q i)·x+b i(5)

Wherein: m i, b i, k irepresent output original pulse, zero inclined error and the constant multiplier of i-th gyroscope or accelerometer respectively.。

Formula (5) is written as following form:

m i = x T 1 ( k i · h i 1 + k i · δ α i · p i 1 + k i · δ β i · q i 1 ) ( k i · h i 2 + k i · δ α i · p i 2 + k i · δ β i · q i 2 ) ( k i · h i 3 + k i · δ α i · p i 3 + k i · δ β i · q i 3 ) b i - - - ( 6 )

Wherein:: hi 1,h i2, h i3represent vector h respectively iin first, second, the 3rd element, p i1, p i2, p i3represent vector p respectively iin first, second, the 3rd element, q i1, q i2, q i3represent vector q respectively iin first, second, the 3rd element, x is input value or earth rate, the terrestrial gravitation accekeration of turntable, is normative reference amount.

Oblique redundant strapdown inertial navitation system (SINS) meets α i≠ k pi/2 and β i≠ k pi/2 (k=0, ± 1, ± 2 ...), then have:

rank h i 1 p i 1 q i 1 h i 2 p i 2 q i 2 h i 3 p i 3 q i 3 = 3 - - - ( 7 )

RSINS is positioned over l diverse location, makes earth rate ω ie/ gravity acceleration g is all different at the projection vector x of system ontology coordinate system, and sensor output value is not O entirely, if systematic observation matrix meets following condition, then and k i, δ α iwith δ β ithere is unique solution:

x 1 T 1 x 2 T 1 . . . . . . x l T 1 = 4 - - - ( 8 )

X lrefer to the x value under l diverse location;

(1) three-axle table position is determined

Suppose that housing axle at original state three-axle table is along Dong-Xi to, center axle along south-north orientation, inner axis along sky-ground to, tilting RSINS system ontology coordinate system is along east-north-direction, sky.Accessibility 24 positions of now three shaft positions/rate table are as shown in table 1.

24 positions that table 1 three-axle table can forward to

Z:g represents: now the z-axis of system ontology coordinate system is towards sky, and local gravitational acceleration component in z-axis is that (g is about 9.8m/s to g 2, different in different geographic position, following g definition is identical);

Z:-g represents: now the z-axis of system ontology coordinate system is towards ground, and local gravitational acceleration component in z-axis is-g;

X:g, X:-g, Y:g, Y:-g are identical with above Z axis definition mode.

(2) accelerometer four position calibration method

The observed quantity of accelerometer timing signal is local gravitational acceleration, its in vertical direction component be g or-g, component is 0 in the horizontal direction.By three of RSINS body coordinate system axles respectively towards heaven and earth, accessibility 24 positions of turntable can be divided into 6 groups, as shown in table 1.Accelerometer can utilize at least 4 positions in 24 positions shown in table 1 to demarcate.Supposing the system initial position is positioned at sky, northeast, and the second place goes to ground, the southeast, and two positions output data are got average and can be calibrated accelerometer bias; Again y-axis be arranged in sky, local to 8 positions select any position, any position is selected in 8 positions that x-axis is arranged in direction, the world, can demarcate accelerometer constant multiplier and install misalignment.For any one accelerometer, select sky, northeast, ground, the southeast, Dong Tiannan, four positions, southwest, sky, average after gathering certain segment data and can obtain:

1, sky, northeast:

m i1=k i(h i+δα i·p i+δβ i·q i)·[0 0 g] T+b i

2, ground, the southeast:

m i2=k i(h i+δα i·p i+δβ i·q i)·[0 0 -g] T+b i

3, Dong Tiannan:

m i3=k i(h i+δα i·p i+δβ i·q i)·[0 g 0] T+b i

4, southwest, sky:

m i4=k i(h i+δα i·p i+δβ i·q i)·[g 0 0] T+b i

Wherein: m i1to m i4represent that the accelerometer of four positions exports original pulse amount respectively, therefore accelerometer bias can be expressed as:

b i=(m i1+m i2)/2 (9)

Utilize above four position datas can build following equation:

( m i 1 - m i 2 ) / ( 2 · g ) ( 2 · m i 3 - m i 1 - m i 2 ) / ( 2 · g ) ( 2 · m i 4 - m i 1 - m i 2 ) / ( 2 · g ) = Λ k i k i · δ α i k i · δ β i - - - ( 10 )

In formula:

Λ = h i 3 p i 3 q i 3 h i 2 p i 2 q i 2 h i 1 p i 1 q i 1

Oblique redundant strapdown inertial navitation system (SINS) meets α i≠ k pi/2 and β i≠ k pi/2 (k=0, ± 1, ± 2 ...), then have:

rank(Λ)=3 (11)

Therefore accelerometer constant multiplier and install misalignment by equation (10) obtain unique solution.

(3) determine gyroscope scaling method, adopt gyroscope four position calibration method or gyroscope three position to rotate scaling method, if only with earth rate ω ieas observed quantity, when gyroscope precision higher (bias instaility is about 0.01 °/h magnitude), adopt gyroscope four position calibration method, all the other, adopt gyroscope three position to rotate scaling method, be specially:

1) gyroscope four position calibration method

Rotational-angular velocity of the earth ω ieprojection vector in local geographic coordinate system (east-north-sky coordinate system) is ω ie=[0 ω nω u] t, wherein ω niecos (L), ω uiesin (L), L are local geographic latitude.Get four positions identical with accelerometer timing signal in (2), average and can obtain after gathering any one certain segment data gyrostatic:

1, sky, northeast:

m i1=k i(h i+δα i·p i+δβ i·q i)·[0 ω nω u] T+b i

2, ground, the southeast:

m i2=k i(h i+δα i·p i+δβ i·q i)·[0 -ω nu] T+b i

3, Dong Tiannan:

m i3=k i(h i+δα i·p i+δβ i·q i)·[0 ω un] T+b i

4, southwest, sky:

m i4=k i(h i+δα i·p i+δβ i·q i)·[ω u0 -ω n] T+b i

Therefore gyroscope zero can be expressed as partially:

b i=(m i1+m i2)/2 (12)

Utilize above four position datas can build following equation:

( m i 1 - m i 2 ) / ( 2 · ω n ) ( 2 · m i 3 - m i 1 - m i 2 ) / ( 2 · ω u ) ( 2 · m i 4 - m i 1 - m i 2 ) / ( 2 · ω u ) = Γ · k i k i · δ α i k i · δ β i - - - ( 13 )

In formula:

Γ = h i 2 + h i 3 · tg ( L ) p i 2 + p i 3 · tg ( L ) q i 2 + q i 3 · tg ( L ) h i 2 - h i 3 · ctg ( L ) p i 2 - p i 3 · ctg ( L ) q i 2 - q i 3 · ctg ( L ) h i 1 - h i 3 · ctg ( L ) p i 1 - p i 3 · ctg ( L ) q i 1 - q i 3 · ctg ( L )

Wherein, L represents local geographic latitude.

Oblique redundant strapdown inertial navitation system (SINS) meets α i≠ k pi/2 and β i≠ k pi/2 (k=0, ± 1, ± 2 ...), can as drawn a conclusion:

rank(Г)=3 (14)

Gyroscope scale factor can be obtained by equation (13) and misalignment is installed.

2) scaling method is rotated in gyroscope three position

If only with earth rate ω ieas observed quantity, for middle low precision gyroscope instrument, earth rate zero partially can flood with noise by it, and now four position simple calibrating methods are no longer applicable, must to the larger rotating speed of turntable applying to improve the observability of calibrating parameters.

By the X of system ontology bthe rotating speed of axle towards east with ω rotates forward, at t 1moment Y baxle and north orientation angle are θ, suppose elapsed time t system rotate n week (n=1,2,3 ...), namely turn over angle be 2 π n (n=1,2,3 ...).By Y in time t bwith Z ball angular velocity of axle sensitivity respectively integration can obtain:

ω niecos (L), ω uiesin (L), L are local geographic latitude.Same conclusion can be obtained when diaxon rotates towards east in addition.Therefore gyroscope can be demarcated with three positions rotation scaling methods, and step is as follows:

1, first system is placed in sky, northeast and ground, the southeast and image data asks for gyro zero partially and compensate;

2, by system ontology coordinate axis X b, Y band Z brespectively towards east, and with angular velocity omega uniform rotation integer multiples l, all gyro output valves that cumulative offset zero is to the rear, can obtain following formula:

Σ m i x = 2 π · l · k i · ( h i 1 + δ α i · p i 1 + δ β i · q i 1 ) Σ m i y = 2 π · l · k i · ( h i 2 + δ α i · p i 2 + δ β i · q i 2 ) Σ m i z = 2 π · l · k i · ( h i 3 + δ α i · p i 3 + δ β i · q i 3 ) - - - ( 16 )

As the formula (7), matrix Λ is non-singular matrix, and therefore solve an equation (16) can obtain gyrostatic constant multiplier and install misalignment parameter.

Demarcation is a kind of method of device parameters identification, and device output signal is pulsed quantity, and original output pulsed quantity directly can not be used by inertial navigation system, has to pass through following process:

Actual use amount=installation misalignment matrix * { (original pulse amount-intrinsic zero is worth partially)/device constant multiplier }

Install misalignment, intrinsic zero partially value, constant multiplier three kinds of parameters be not known, by the mode of demarcation by three kinds of parametric solutions, then must compensate obtain actual use amount in above formula.Therefore scaling method embody rule occasion/background that the present invention proposes is exactly redundancy-type fiber optic gyro strapdown inertial navigation system.

Step 3: build tilting RSINS Calibration Simulation platform, and the accuracy utilizing the scaling method described in emulation platform checking.

(1) Calibration Simulation platform is built

As shown in Figure 3, Calibration Simulation platform comprises tilting RSINS configuration mode and selects module 1, IMU data configuration module 2, calibrating parameters to select module 3, revolving table position and rate selection module 4, calibrating parameters to resolve module 5 and calibration result authentication module 6.

Tilting RSINS configuration mode selects module 1 to select as four, five, six oblique redundant RSINS under the different configuration modes such as positive tetrahedron, regular octahedron, regular dodecahedron.

IMU data configuration module 2 produces redundancy IMU data in the tilting RSINS selected, and comprises whole gyroscope and accelerometer original pulse data, and unit to be respectively °/s and m/s 2; .

Calibrating parameters selects module 3 to select calibrating parameters, mainly comprises zero inclined, constant multiplier, installation misalignment, utilizes above parameter and superpose device noise, can build the raw data of redundancy gyroscope and accelerometer.

24 diverse locations that revolving table position and rate selection module 4 select turntable to forward to, and in conjunction with multiple forward and backward speed, produce the redundancy gyroscope under turntable diverse location, speed and accelerometer raw data, this module mainly for generation of calibration process data, for the every calibrating parameters of direct solution.

Calibrating parameters resolve module 5 mainly utilize the calibrating parameters calculation method that describes in step one and step 2 calculate redundancy device zero partially, constant multiplier and install the size of misalignment, and to compare with preset value.

Calibration result authentication module 6 utilizes above calibration result, carries out system initial alignment and inertial navigation performance verification in conjunction with path generator.

(2) simulated conditions is determined

As shown in Figure 4, system comprises 6 redundancy gyroscopes and accelerometer to tilting RSINS system architecture, and the normal direction respectively along 6 planes in regular dodecahedron configures, and this configuration mode has geometrical symmetry.In Fig. 4, XYZ is system ontology coordinate system, M1, M2 and M3 are the mutual vertical plane be made up of body coordinate system three coordinate axis, with ABCDEF, sensor axis represents that (AB is positioned at face M2, and CD is positioned at face M 1, EF is positioned at face M3), folded Space Angle is 2 α=63 ° 26 ' 5.8 ".

According to the configuration mode of Fig. 4, the installation matrix that can obtain system is:

H = sin α - sin α cos α cos α 0 0 0 0 sin α - sin α cos α cos α cos α cos α 0 0 sin α - sin α T

Suppose to adopt the identical redundancy gyroscope of performance and accelerometer, zero partially, scale and to install misalignment all identical.In simulation process, the sampling period is 20ms, and every calibrating parameters is as shown in table 2.

Table 2 redundancy gyroscope and accelerometer calibrating parameters

(3) simulation process and result

Select revolving table position to be sky, northeast, ground, the southeast, Dong Tiannan, four positions, southwest, sky in Calibration Simulation platform, the 5min redundant accelerometers data gathering RSINS output are respectively used for four location positions; Simultaneously by three of the body coordinate system of RSINS system coordinate axis respectively towards east with 20 °/s rotational speed, gather 5min data and be used for gyrostatic three positions and rotate and demarcate.

Table 3 redundant accelerometers four position method calibration result

Table 4 redundancy gyroscope three position method of rotation calibration result

The data of contrast table 3, table 4 and table 2 are known, and the method can more adequately be demarcated zero of tilting RSINS partially, constant multiplier and install misalignment, and whole calibration process is less than 1h and simple to operate, and therefore whole scaling method can take into account rapidity and accuracy.

Claims (2)

1. a quick calibrating method for oblique redundant strapdown inertial navigation system, is characterized in that, comprises following step:
Step one: describe tilting RSINS and install misalignment, build and demarcate measurement equation;
(1) tilting RSINS installs misalignment description
RSINS represents redundancy strapdown inertial navitation system (SINS), and in tilting RSINS, sensor coordinates is s system, and the system ontology coordinate that is connected is b system, OX by bz brepresent that system ontology is connected coordinate system, H irepresent the axis of i-th sensor, H ifollowing mapping relations are had with b cording:
h i=[cos(α i)cos(β i)]·i+[sin(α i)cos(β i)]·j+[sin(β i)]·k (1)
Wherein: h i, i, j, k represent H respectively iaxle, X baxle, Y baxle, Z bunit vector on axle, α irepresent h iat X b-Y bprojection vector in plane and X bthe angle of axle, β irepresent h iwith X b-Y bthe angle of plane;
In sensor practical application, if the actual axial H of sensor i' with the desired axis H of sensor ithere is error delta α iwith δ β i, suppose sensor axis H i' at X b-Y bprojection vector in plane and X bthe angle of axle is α i', with X b-Y bthe angle of plane is β i', therefore:
h i'=[cos(α i')cos(β i')]·i+[sin(α i')cos(β i')]·j+[sin(β i')]·k (2)
By α i'=α i-δ α iand β i'=β i+ δ β isubstitution formula (2), ignores second order (δ α in a small amount iδ β i), and by sin (δ α i), sin (δ β i) linearly turn to δ α i, δ β i, cos (δ α i), cos (δ β i) be approximately 1, obtain formula (3):
h i'=h i+δα i·p i+δβ i·q i(3)
In formula, p i=[sin (α i) cos (β i)-cos (α i) cos (β i) 0], q i=[-cos (α i) sin (β i)-sin (α i) sin (β i) cos (β i)];
(2) build tilting RSINS and demarcate measurement equation
Tilting RSINS demarcates measurement equation and is specially:
M=K(H+δα·P+δβ·Q)·X+B (4)
Wherein: M is the output of inertial sensor in tilting RSINS system, can be expressed as:
M=[m 1,m 2,…,m i,…m n] T
In formula, m irepresent the original pulse amount that i-th gyroscope or accelerometer export, i ∈ [1, n], n represents system redundancy, i.e. the quantity of gyro or accelerometer;
K=diag [k 1k 2k n] represent the diagonal matrix be made up of the constant multiplier of n sensor;
H=[h 1, h 2..., h i... h n] texpression system ideal installs matrix, wherein, and h ii-th gyroscope or the accelerometer desirable installation direction vector relative to system ontology coordinate system is described;
δα=diag[δα 1,δα 2,…,δα i,…,δα n];
δβ=diag[δβ 1,δβ 2,…,δβ i,…,δβ n];
P=[p 1,p 2,…,p i,…,p n] T
Q=[q 1,q 2,…,q i,…,q n] T
X=[x xx yx z] trepresent the angular velocity that system ontology coordinate system sensitivity arrives or acceleration, for gyroscope, X represents angular velocity vector, and for accelerometer, X represents acceleration, x xx yx zrepresent the component of X along system ontology coordinate system respectively;
B=[b 1b 2b n] trepresent zero inclined vector of n sensor;
H'=[h 1', h 2' ..., h i' ... h n'] texpression system actual installation matrix, wherein, h i' i-th gyroscope or the accelerometer actual installation direction vector relative to system ontology coordinate system is described, H'=H+ δ α P+ δ β Q;
Now K, P, Q, δ α, δ β, H, H' and B are constant value;
Step 2: determine tilting RSINS scaling scheme, comprise and determine three-axle table position, accelerometer four position calibration method, determines gyroscope scaling method, adopts gyroscope four position calibration method or gyroscope three position to rotate scaling method;
Suppose the demarcation measurement equation only considering wherein some sensors, as follows:
m i=k i(h i+δα i·p i+δβ i·q i)·x+b i(5)
Wherein: m i, b i, k irepresent output original pulse, zero inclined error and the constant multiplier of i-th gyroscope or accelerometer respectively;
Formula (5) is written as following form:
m i = x T 1 ( k i · h i 1 + k i · δα i · p i 1 + k i · δβ i · q i 1 ) ( k i · h i 2 + k i · δα i · p i 2 + k i · δβ i · q i 2 ) ( k i · h i 3 + k i · δα i · p i 3 + k i · δβ i · q i 3 ) b i - - - ( 6 )
Wherein: h i1, h i2, h i3represent vector h respectively iin first, second, the 3rd element, p i1, p i2, p i3represent vector p respectively iin first, second, the 3rd element, q i1, q i2, q i3represent vector q respectively iin first, second, the 3rd element;
Oblique redundant strapdown inertial navitation system (SINS) meets α i≠ k pi/2 and β i≠ k pi/2, k=0, ± 1, ± 2 ..., then have:
rank ( h i 1 p i 1 q i 1 h i 2 p i 2 q i 2 h i 3 p i 3 q i 3 ) = 3 - - - ( 7 )
RSINS is positioned over l diverse location, makes earth rate ω ie/ gravity acceleration g is all different at the projection vector x of system ontology coordinate system, and sensor output value is not 0 entirely, if systematic observation matrix meets following condition, then and k i, δ α iwith δ β ithere is unique solution:
rank ( x 1 T 1 x 2 T 1 . . . . . . x l T 1 ) = 4 - - - ( 8 )
Wherein: x lrefer to the x value under l diverse location;
(1) three-axle table position is determined
Suppose that housing axle at original state three-axle table is along Dong-Xi to, center axle along south-north orientation, inner axis along sky-ground to, tilting RSINS system ontology coordinate system is along east-north-direction, sky; Accessibility 24 positions of now three shaft positions/rate table are:
When the z-axis of system ontology coordinate system is towards sky, local gravitational acceleration component in z-axis is g, is expressed as z:g, and three shaft positions/rate table accessible position is: sky, northeast, northwest (NW) sky, southwestern sky, east southeast sky;
When the z-axis of system ontology coordinate system is towards sky, local gravitational acceleration component in z-axis is-g, is expressed as z:-g, and three shaft positions/rate table accessible position is: ground, the southeast, Nan Xidi, ground, northwest, east northeast ground;
When the y-axis of system ontology coordinate system is towards sky, local gravitational acceleration component in y-axis is g, is expressed as y:g, and three shaft positions/rate table accessible position is: Dong Tiannan, Bei Tiandong, Xi Tianbei, Nan Tian west;
When the y-axis of system ontology coordinate system is towards sky, local gravitational acceleration component in y-axis is-g, is expressed as y:-g, and three shaft positions/rate table accessible position is: Dong Dibei, west, backlands, Xi Dinan, Nan Didong;
When the x-axis of system ontology coordinate system is towards sky, local gravitational acceleration component in x-axis is g, is expressed as x:g, and three shaft positions/rate table accessible position is: northeast, sky, sky northwest (NW), southwest, sky, sky east southeast;
When the x-axis of system ontology coordinate system is towards sky, local gravitational acceleration component in x-axis is-g, is expressed as x:-g, and three shaft positions/rate table accessible position is: the southeast, ground, east northeast, northwest, Di Nanxi;
(2) accelerometer four position calibration method
The observed quantity of accelerometer timing signal is local gravitational acceleration, its in vertical direction component be g or-g, component is 0 in the horizontal direction; By three of RSINS body coordinate system axles respectively towards heaven and earth, accessibility 24 positions of turntable can be divided into 6 groups; Accelerometer can utilize at least 4 positions in 24 positions to demarcate; For any one accelerometer, select sky, northeast, ground, the southeast, Dong Tiannan, four positions, southwest, sky, average after gathering certain segment data and can obtain:
1, sky, northeast:
m i1=k i(h i+δα i·p i+δβ i·q i)·[0 0 g] T+b i
2, ground, the southeast:
m i2=k i(h i+δα i·p i+δβ i·q i)·[0 0 -g] T+b i
3, Dong Tiannan:
m i3=k i(h i+δα i·p i+δβ i·q i)·[0 g 0] T+b i
4, southwest, sky:
m i4=k i(h i+δα i·p i+δβ i·q i)·[g 0 0] T+b i
Wherein: m i1to m i4represent that the accelerometer of four positions exports original pulse amount respectively, therefore accelerometer bias can be expressed as:
b i=(m i1+m i2)/2 (9)
Utilize above four position datas can build following equation:
( m i 1 - m i 2 ) / ( 2 · g ) ( 2 · m i 3 - m i 1 - m i 2 ) / ( 2 · g ) ( 2 · m i 4 - m i 1 - m i 2 ) / ( 2 · g ) = Λ k i k i · δα i k i · δβ i - - - ( 10 )
In formula:
Λ = h i 3 p i 3 q i 3 h i 2 p i 2 q i 2 h i 1 p i 1 q i 1
Oblique redundant strapdown inertial navitation system (SINS) meets α i≠ k pi/2 and β i≠ k pi/2, k=0, ± 1, ± 2 ..., then have:
rank(Λ)=3 (11)
Therefore accelerometer constant multiplier and install misalignment by equation (10) obtain unique solution;
(3) determine gyroscope scaling method, adopt gyroscope four position calibration method or gyroscope three position to rotate scaling method, if only with earth rate ω ieas observed quantity, when gyroscope precision is higher, adopt gyroscope four position calibration method, all the other, adopt gyroscope three position to rotate scaling method, be specially:
1) gyroscope four position calibration method
Earth rate ω ieprojection vector in local geographic coordinate system is ω ie=[0 ω nω u] t, wherein: ω niecos (L), ω uiesin (L), L are local geographic latitude; Get four positions identical with accelerometer timing signal in above-mentioned steps (2), average and can obtain after gathering any one certain segment data gyrostatic:
1, sky, northeast:
m i1=k i(h i+δα i·p i+δβ i·q i)·[0 ω nω u] T+b i
2, ground, the southeast:
m i2=k i(h i+δα i·p i+δβ i·q i)·[0 -ω nu] T+b i
3, Dong Tiannan:
m i3=k i(h i+δα i·p i+δβ i·q i)·[0 ω un] T+b i
4, southwest, sky:
m i4=k i(h i+δα i·p i+δβ i·q i)·[ω u0 -ω n] T+b i
Therefore gyroscope zero can be expressed as partially:
b i=(m i1+m i2)/2 (12)
Utilize above four position datas can build following equation:
( m i 1 - m i 2 ) / ( 2 · ω n ) ( 2 · m i 3 - m i 1 - m i 2 ) / ( 2 · ω u ) ( 2 · m i 4 - m i 1 - m i 2 ) / ( 2 · ω u ) = Γ · k i k i · δα i k i · δβ i - - - ( 13 )
In formula:
Γ = h i 2 + h i 3 · tg ( L ) p i 2 + p i 3 · tg ( L ) q i 2 + q i 3 · tg ( L ) h i 2 - h i 3 · ctg ( L ) p i 2 - p i 3 · ctg ( L ) q i 2 - q i 3 · ctg ( L ) h i 1 - h i 3 · ctg ( L ) p i 1 - p i 3 · ctg ( L ) q i 1 - q i 3 · ctg ( L )
Wherein, L represents local geographic latitude;
Oblique redundant strapdown inertial navitation system (SINS) meets α i≠ k pi/2 and β i≠ k pi/2, k=0, ± 1, ± 2 ..., then have:
rank(Γ)=3 (14)
Gyroscope scale factor can be obtained by equation (13) and misalignment is installed;
2) scaling method is rotated in gyroscope three position
By the X of system ontology bthe rotating speed of axle towards east with ω rotates forward, at t 1moment Y baxle and north orientation angle are θ, suppose that elapsed time t system rotates n week, (n=1,2,3 ...), namely turn over angle be 2 π n (n=1,2,3 ...); By Y in time t bwith Z ball angular velocity of axle sensitivity respectively integration can obtain:
Wherein, ω niecos (L), ω uiesin (L), L are local geographic latitude; Can obtain same conclusion when diaxon rotates towards east in addition, therefore gyroscope can be demarcated with three positions rotation scaling methods, and step is as follows:
1, first system is placed in sky, northeast and ground, the southeast and image data asks for gyro zero partially and compensate;
2, by system ontology coordinate axis X b, Y band Z brespectively towards east, and with angular velocity omega uniform rotation integer multiples l, all gyro output valves that cumulative offset zero is to the rear, can obtain following formula:
Σ m i x = 2 π · l · k i · ( h i 1 + δα i · p i 1 + δβ i · q i 1 ) Σ m i y = 2 π · l · k i · ( h i 2 + δα i · p i 2 + δβ i · q i 2 ) Σ m i z = 2 π · l · k i · ( h i 3 + δα i · p i 3 + δβ i · q i 3 ) - - - ( 16 )
Shown in (7), matrix Λ is non-singular matrix, and therefore solve an equation (16) can obtain gyrostatic constant multiplier and install misalignment parameter;
Finally obtain zero value, constant multiplier and install misalignment parameter partially of accelerometer, gyrostatic zero to be partially worth, constant multiplier and install misalignment parameter, by above-mentioned parameter, obtain actual use amount, for oblique redundant strapdown inertial navigation system.
2. the quick calibrating method of a kind of oblique redundant strapdown inertial navigation system according to claim 1, is characterized in that, described actual use amount is:
Actual use amount=installation misalignment matrix * { (original pulse amount-zero is worth partially)/device constant multiplier }
Accelerometer, gyrostatic installation misalignment, zero partially value, constant multiplier substitute into above formula respectively, obtain the actual use amount of accelerometer, gyrostatic actual use amount.
CN201210404851.3A 2012-10-23 2012-10-23 A kind of quick calibrating method of oblique redundant strapdown inertial navigation system CN102927994B (en)

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