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 PDFInfo
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Abstract
Description
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when any inertia sensitive element breaks down output exception value, the navigation results that system exports is by no longer valid.Therefore in traditional strapdown inertial navitation system (SINS), the fault of any inertia device is equal to scrapping of whole system, and the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 systemlevel redundancy and device level redundancy two kinds.Systemlevel 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 systemlevel redundancy strategy.Compared with platformtype 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 systemlevel redundancy, device level oblique redundant mode has greater advantage in volume power consumption and cost, becomes the firstselection 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 systemlevel 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 threeaxle 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:
1tilting RSINS configuration mode selects module 2IMU data configuration module 3calibrating parameters to select module
4revolving table position and rate selection module 5calibrating parameters resolve module 6calibration 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 _{b}y _{b}z _{b}for system ontology is connected coordinate system; H _{i}represent the axis of ith sensor, H _{i}following 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 _{i}axle, X _{b}axle, Y _{b}axle, Z _{b}unit vector on axle, α _{i}represent h _{i}at X _{b}Y _{b}projection vector in plane and X _{b}the angle of axle, β _{i}represent h _{i}with X _{b}Y _{b}the 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 _{i}with δ β _{i}, as shown in Figure 2.Suppose sensor axis H _{i}' at X _{b}Y _{b}projection vector in plane and X _{b}the angle of axle is α _{i}', with X _{b}Y _{b}the 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 _{i}and β _{i}'=β _{i}+ δ β _{i}substitution formula (2), ignores second order (δ α in a small amount _{i}δ 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 _{i}represent the original pulse amount that ith (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 _{x}x _{y}x _{z}] ^{t}, for gyroscope, X represents angular velocity vector, and for accelerometer, X represents acceleration, x _{x}x _{y}x _{z}represent the component of X along system ontology coordinate system respectively; H=[h _{1}, h _{2}..., h _{i}... h _{n}] ^{t}expression system ideal installs matrix, wherein, and h _{i}ith (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}' ith (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 _{1}b _{2}b _{n}] ^{t}represent zero inclined vector of n sensor; K=diag [k _{1}k _{2}k _{n}] represent the diagonal matrix be made up of the constant multiplier of n sensor, separately have:
δα＝diag[δ _{α}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}；
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 threeaxle 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 _{i}represent output original pulse, zero inclined error and the constant multiplier of ith gyroscope or accelerometer respectively.。
Formula (5) is written as following form:
Wherein:: hi _{1,}h _{i2}, h _{i3}represent vector h respectively _{i}in first, second, the 3rd element, p _{i1}, p _{i2}, p _{i3}represent vector p respectively _{i}in first, second, the 3rd element, q _{i1}, q _{i2}, q _{i3}represent vector q respectively _{i}in 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:
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 _{i}with δ β _{i}there is unique solution:
X _{l}refer to the x value under l diverse location;
(1) threeaxle table position is determined
Suppose that housing axle at original state threeaxle table is along DongXi to, center axle along southnorth orientation, inner axis along skyground to, tilting RSINS system ontology coordinate system is along eastnorthdirection, sky.Accessibility 24 positions of now three shaft positions/rate table are as shown in table 1.
24 positions that table 1 threeaxle table can forward to
Z:g represents: now the zaxis of system ontology coordinate system is towards sky, and local gravitational acceleration component in zaxis 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 zaxis of system ontology coordinate system is towards ground, and local gravitational acceleration component in zaxis isg;
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 org, 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 yaxis be arranged in sky, local to 8 positions select any position, any position is selected in 8 positions that xaxis 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 _{i1}to m _{i4}represent 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:
In formula:
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 _{ie}as 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
Rotationalangular velocity of the earth ω _{ie}projection vector in local geographic coordinate system (eastnorthsky coordinate system) is ω _{ie}=[0 ω _{n}ω _{u}] ^{t}, wherein ω _{n}=ω _{ie}cos (L), ω _{u}=ω _{ie}sin (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 _{n}ω _{u}] ^{T}+b _{i}
2, ground, the southeast:
m _{i2}＝k _{i}(h _{i}+δα _{i}·p _{i}+δβ _{i}·q _{i})·[0 ω _{n}ω _{u}] ^{T}+b _{i}
3, Dong Tiannan:
m _{i3}＝k _{i}(h _{i}+δα _{i}·p _{i}+δβ _{i}·q _{i})·[0 ω _{u}ω _{n}] ^{T}+b _{i}
4, southwest, sky:
m _{i4}＝k _{i}(h _{i}+δα _{i}·p _{i}+δβ _{i}·q _{i})·[ω _{u}0 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:
In formula:
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 _{ie}as 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 _{b}the rotating speed of axle towards east with ω rotates forward, at t _{1}moment Y _{b}axle 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 _{b}with Z _{b}all angular velocity of axle sensitivity respectively integration can obtain:
ω _{n}=ω _{ie}cos (L), ω _{u}=ω _{ie}sin (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 _{b}and Z _{b}respectively 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:
As the formula (7), matrix Λ is nonsingular 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 amountintrinsic 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 redundancytype 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:
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.
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