CN103245359B - A kind of inertial sensor fixed error real-time calibration method in inertial navigation system - Google Patents

A kind of inertial sensor fixed error real-time calibration method in inertial navigation system Download PDF

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CN103245359B
CN103245359B CN201310142701.4A CN201310142701A CN103245359B CN 103245359 B CN103245359 B CN 103245359B CN 201310142701 A CN201310142701 A CN 201310142701A CN 103245359 B CN103245359 B CN 103245359B
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CN103245359A (en
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彭惠
王东升
张承
许建新
王融
熊智
刘建业
赵慧
柏青青
王洁
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南京航空航天大学
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Abstract

The invention discloses a kind of inertial sensor fixed error real-time calibration method in inertial navigation system, the method comprises the following steps: first set up the solid error model of inertial sensor in space vehicle dynamic flight course, fixed error comprises alignment error and scale factor error; In traditional IMU random error model and the basis of solid error model set up, set up the filter state equation and the linear measurement equation of position, speed and attitude that comprise inertial sensor fixed error subsequently; Finally in space vehicle dynamic flight course, real-time dynamic calibration and correction are carried out to inertial sensor solid error, obtain the inertial navigation system navigation results after inertial sensor solid error compensation correction.This method can realize demarcation and the correction of inertial sensor alignment error and scale factor error in inertial navigation system in the dynamic flying process of aircraft, effectively improves inertial navigation system performance, is suitable for engineer applied.

Description

A kind of inertial sensor fixed error real-time calibration method in inertial navigation system

Technical field

The invention discloses a kind of inertial sensor fixed error real-time calibration method in inertial navigation system, belong to inertial navigation inertial sensor errors calibration technique field.

Background technology

In recent years, along with the development of course of new aircraft, the requirement of navigational system performance is improved day by day.Inertial navigation system have precision in short-term high, export the core navigation message unit that the outstanding advantages such as continuous and completely autonomous must be following course of new aircraft.

The measuring error of inertial sensor (IMU-gyroscope and accelerometer) is the principal element affecting inertial navigation system precision.In conventional I MU error model, often think and its solid error-alignment error and scale factor error full remuneration after static demarcating only comprise Random Drift Error in imu error.And in space vehicle dynamic flight course, being affected the body deformation caused can not overlap causing the axis of IMU completely with body axis by vibratory impulse, flow perturbation etc., and then alignment error and scale factor error is caused to enlarge markedly.If these errors can not carry out calibration compensation in space vehicle dynamic flight course will affect navigation accuracy to a great extent.

The demarcation that traditional imu error scaling method utilizes turntable to carry out position test and speed trial in indoor to realize alignment error and scale factor error more.But in space vehicle dynamic flight course, due to environmental impact, tradition utilizes the scaling method of turntable will be no longer applicable.In space vehicle dynamic flight course, tradition only for its random error, does not consider the impact of its solid error such as alignment error and scale factor error to the error correction of inertial sensor.And affect due to airborne vibration etc. the alignment error that causes and scale factor error will affect inertial navigation system precision to a great extent, must demarcate and compensating approach it.Therefore, study a kind of in space vehicle dynamic flight course the scaling method to inertial sensor solid error, effectively can improve the inertial navigation system precision in space vehicle dynamic flight course, will outstanding using value be had.

Summary of the invention

The object of the invention is to the solid error modeling and the real-time calibration method that propose a kind of inertial navigation system inertial sensor, to meet the high-precision requirement to navigational system in space vehicle dynamic flight course.

The present invention for solving the problems of the technologies described above by the following technical solutions, a kind of inertial sensor fixed error real-time calibration method in inertial navigation system, described method concrete steps are as follows:

Step 1, set up the solid error model of inertial sensor, comprise accelerometer scale factor error matrix and gyrostatic scale factor error matrix:

Accelerometer scale factor error matrix is δ K a=diag [δ K axδ K ayδ K az], wherein, δ K ax, δ K ay, δ K azbe respectively the scale factor error of X-axis, Y-axis and Z axis accelerometer; Accelerometer alignment error matrix is δA = 0 δA z - δA y - δA z 0 δA x δA y - δA x 0 , Wherein, δ A x, δ A y, δ A zbe respectively the fix error angle of X-axis, Y-axis and Z axis accelerometer; δ K aall be taken as arbitrary constant with δ A, X, Y, Z tri-accelerometer error models of axle are identical, as follows:

δ K · A = 0 δ A · = 0

In above formula, for scale factor error matrix delta K afirst order derivative, for the first order derivative of alignment error matrix delta A;

Gyrostatic scale factor error matrix is δ K g=diag [δ K gxδ K gyδ K gz], δ K gx, δ K gy, δ K gzbe respectively the scale factor error of X-axis, Y-axis and Z axis gyro; Gyro misalignment matrix is δG = 0 δG z - δG y - δG z 0 δG x δG y - δG x 0 , δ G x, δ G y, δ G zbe respectively the alignment error of X-axis, Y-axis and Z axis gyro; Scale factor error and alignment error are all taken as arbitrary constant, and X, Y, Z tri-gyro error models of axle are identical, as follows:

δ K · G = 0 δ G · = 0

In above formula, for scale factor error matrix delta K gfirst order derivative, for the first order derivative of alignment error matrix delta G;

Step 2, in the alignment error of step 1 couple IMU and the basis of scale factor error modeling, using the alignment error of IMU and scale factor error as system state variables, build the filter status equation based on inertial sensor total state error model and position, speed and attitude linearization measurement equation:

Systematic state variable X based on inertial sensor total state error modeling is:

X=[φ Eφ Nφ UδV EδV NδV UδL δλ δh ε bxε byε bzε rxε ryε rzxyzδA xδA yδA zδK AxδK AyδK AzδG xδG yδG zδK GxδK GyδK Gz] T

In above formula, φ e, φ n, φ ube respectively the east orientation in inertial navigation system, north orientation and sky to platform error angle quantity of state; δ V e, δ V n, δ V ube respectively the east orientation in INS errors, north orientation and sky to velocity error quantity of state; δ L, δ λ, δ h are respectively latitude error quantity of state, longitude error quantity of state and height error quantity of state in inertial navigation system; ε bx, ε by, ε bzbe respectively the constant value drift error state amount of the X-axis in inertial navigation system, Y-axis, Z-direction gyro; ε rx, ε ry, ε rzbe respectively the gyro single order Markov drift error quantity of state of X-axis, Y-axis and Z-direction; ▽ x, ▽ y, ▽ zbe respectively the inclined error state amount of accelerometer single order Markov zero of X-axis, Y-axis and Z-direction; δ A x, δ A y, δ A zbe respectively the alignment error quantity of state of accelerometer in X-axis in inertial navigation system, Y-axis and Z-direction; δ K ax, δ K ay, δ K azbe respectively the scale factor error quantity of state of accelerometer in X-axis in inertial navigation system, Y-axis and Z-direction; δ G x, δ G y, δ G zbe respectively the alignment error quantity of state of gyro on X-axis in inertial navigation system, Y-axis and Z axis three directions; δ K gx, δ K gy, δ K gzfor the scale factor error quantity of state of gyro in X-axis, Y-axis and Z-direction in inertial navigation system;

Set up the error state equation of inertial navigation system, shown in (4):

X · ( t ) = F ( t ) X ( t ) + G ( t ) W ( t )

In above formula, X (t) is system state variables; for the first order derivative of state variable X (t); F (t) is system matrix; G (t) is noise figure matrix; W (t) is noise matrix;

Adopt Department of Geography upper/lower positions, speed and attitude linearization Observation principle, set up satellite navigation position detection amount under Department of Geography, speed observed quantity and the linearization measurement equation between star sensor attitude observation and INS errors quantity of state:

Z ( t ) = Z p ( t ) Z v ( t ) Z φ ( t ) = H p ( t ) H v ( t ) H φ ( t ) X ( t ) + V p ( t ) V v ( t ) V φ ( t )

In above formula, Z p(t), Z v(t), Z φt () is respectively position, speed and attitude and measures vector; H p(t), H v(t), H φt () is respectively position, speed and attitude and measures matrix of coefficients; V p(t), V v(t), V φt () is respectively position, speed and attitude observation noise matrix;

Step 3, on the basis of step 2, system state equation and measurement equation are carried out to the renewal of sliding-model control and quantity of state, measurement amount, realize the demarcation to IMU alignment error and scale factor error and compensation.

Further, to the demarcation of IMU alignment error and scale factor error and compensation described in step 3, its concrete steps are:

(301) by filter status equation and measurement equation sliding-model control:

X(k)=Φ(k,k-1)X(k-1)+Γ(k,k-1)W(k-1)

Z(k)=H(k)X(k)+V(k)

In above formula, X (k) is t kmoment system state amount; X (k-1) is t k-1moment system state amount; Φ (k, k-1) is t k-1moment is to t ktime etching system state-transition matrix; Γ (k, k-1) is t k-1moment is to t ktime etching system noise drive matrix; W (k-1) is t ktime etching system noise matrix; Z (k) is t ktime the position of etching system, speed and attitude observation matrix; H (k) is t kthe position in moment, speed and attitude measure matrix of coefficients; V (k) is t kthe noise matrix of the position in moment, speed and attitude observation;

(302) according to formula (8), formula (9), formula (10), formula (11), the INS errors quantity of state of step (301) part and the measurement of covariance information are upgraded:

P(k,k-1)=Φ(k,k-1)P(k-1,k-1)Φ(k,k-1) T+Γ(k,k-1)Q(k)Γ(k,k-1) T

K(k)=P(k,k-1)H(k) T[H(k)P(k,k-1)H(k) T+R(k)] -1

X(k)=X(k,k-1)+K(k)[Z(k)-H(k)X(k,k-1)]

P(k,k)=[I-K(k)H(k)]P(k,k-1)

In above-mentioned formula, P (k, k-1) is t k-1moment is to t kmoment one-step prediction covariance matrix; P (k-1, k-1) is t k-1moment filter state estimate covariance matrix; Q (k) is t ktime etching system noise covariance matrix; Κ (k) is t kmoment filter gain matrix; R (k) is t kmoment position, speed and attitude measurement noise covariance matrix; X (k, k-1) is t k-1moment is to t kmoment one-step prediction quantity of state; P (k, k) is t kmoment filter state estimate covariance matrix; I is the unit matrix identical with P (k, k) dimension;

(303) the quantity of state X (k, k) that filtering exports is judged, if the predicted value of quantity of state X (k, k) is stablized, complete demarcation, obtain the calibration result to IMU alignment error and scale factor error, enter step (304); If predicted value is unstable, then returns step (302) and continue to carry out predicted estimate to state value;

(304) after the calibration result obtained IMU alignment error and scale factor error in step (303), temporary calibration value, utilize calibration value to compensate correction to IMU alignment error and scale factor error, correct and complete within a navigation calculation cycle, error compensation correcting algorithm is:

f b = [ I - δK A - δA ] ( f ~ b - ▿ b ) ω ib b = [ I - δK G - δG ] ( ω ~ ib b - ϵ b )

In above formula, the acceleration that the accelerometer being respectively error exports and the angular speed that gyroscope exports; f b, be respectively the acceleration after getting rid of error and angular speed; ▽ bfor the Random Drift Error of accelerometer, ε bfor the Random Drift Error of gyro.

The present invention is on the basis to inertial sensor errors modeling, the real-time calibration to inertial sensor solid error can be realized in space vehicle dynamic flight course, the result utilizing demarcation to obtain can carry out real-Time Compensation to inertial sensor errors, adopt the present invention significantly can reduce INS errors and can effectively improve inertial navigation system precision, be applicable to engineer applied.

Accompanying drawing explanation

Fig. 1 is inertial navigation system inertial sensor solid error real-time calibration method structural drawing of the present invention.

Fig. 2 demarcates flight path used.

Fig. 3 is the process alignment error calibration result of X-axis, Y-axis and Z axis gyro.

Fig. 4 is the scale factor error calibration result of X-axis, Y-axis and Z axis gyro.

Fig. 5 is the process alignment error calibration result of X-axis, Y-axis and Z axis accelerometer.

Fig. 6 is the scale factor error calibration result of X-axis, Y-axis and Z axis accelerometer.

Fig. 7 is the inertial navigation attitude error after inertial sensor solid error calibration compensation.

Fig. 8 is the inertial navigation velocity error after inertial sensor solid error calibration compensation.

Fig. 9 is the inertial navigation site error after inertial sensor solid error calibration compensation.

Embodiment

Be described in further detail technical scheme of the present invention below in conjunction with accompanying drawing: as shown in Figure 1, inertial sensor solid error real-time calibration side of the present invention ratio juris is: the measurement of gyro and accelerometer exports and is respectively and wherein all contain stationarity and random error. and f bbe through the revised angular speed of error compensation and the acceleration information navigation calculation module for inertial navigation system.Total state error modeling module sets up alignment error and the scale factor error model of IMU on the basis of traditional error model, builds filter state amount and the state equation of INS errors; Meanwhile, according to attitude, speed and position linearity Observation principle under Department of Geography, set up the linearization measurement equation of speed under Department of Geography, position and attitude, realize the real-time calibration to inertial sensor alignment error and scale factor error; Utilize the result of demarcating to compensate and correct at the solid error of imu error correcting module to IMU, can effectively improve inertial navigation system precision.

The specific embodiment of the present invention is as follows:

1. set up inertial sensor solid error model

(1.1) accelerometer error model

In strapdown inertial navigation system, because FLIGHT VEHICLE VIBRATION can cause gyroscope and accelerometer all to there is alignment error and scale factor error.Ignore high-order nonlinear error term, the error model of accelerometer is:

δf b=[δK A+δA]f b+▽ b(1)

In formula (1), δ K a=diag [δ K axδ K ayδ K az] be the scale factor error of accelerometer;

▽=[▽ xyz] tfor zero inclined error of accelerometer; δA = 0 δA z - δA y - δA z 0 δA x δA y - δA x 0 For the fix error angle matrix of accelerometer;

The scale factor error δ K of accelerometer aall be taken as arbitrary constant with alignment error δ A, zero inclined error ▽ of accelerometer is taken as first-order Markov process: and the error model of supposition three axis accelerometers is identical:

δ K · A = 0 δ A · = 0 ▿ · = - 1 T a ▿ + w a - - - ( 2 )

(1.2) gyroscope error model

Similar with accelerometer error modeling method, the error model of gyro is:

δω ib b = [ δK G + δG ] ω ib b + ϵ b - - - ( 3 )

In formula (3), δ K g=diag [δ K gxδ K gyδ K gz] be the scale factor error matrix of gyro; δG = 0 δG z - δG y - δG z 0 δG x δG y - δG x 0 For the fix error angle matrix of gyro; Gyrostatic scale factor error and

Alignment error is all taken as arbitrary constant, assuming that the error model of three axle gyros is identical, obtains:

δ K · G = 0 δ G · = 0 - - - ( 4 )

Gyroscopic drift error ε b=[ε xε yε z] tbe taken as

ε=ε br+w g(5)

In formula (5), for arbitrary constant, for first-order Markov process, w gfor white noise.

2. set up the kalman filter models based on total state error model

(2.1) the quantity of state equation of INS errors is set up

" right, front, on " (X, Y, Z) direction that to choose body axis system (b system) be body, chooses navigational coordinate system (n system) for sky, northeast (ENU) geographic coordinate system.System state variables based on total state error modeling is:

X=[φ Eφ Nφ UδV EδV NδV UδL δλ δh ε bxε byε bzε rxε ryε rzxyzδA xδA yδA zδK AxδK AyδK AzδG xδG yδG zδK GxδK GyδK Gz] T

(6)

In formula (6), φ e, φ n, φ ube respectively the east orientation in inertial navigation system, north orientation and sky to platform error error angle quantity of state; δ V e, δ V n, δ V ube respectively the east orientation in INS errors, north orientation and sky to velocity error quantity of state; δ L, δ λ, δ h represent latitude error quantity of state, longitude error quantity of state and height error quantity of state in inertial navigation system; ε bx, ε by, ε bzbe respectively the constant value drift error state amount of the X-axis in inertial navigation system, Y-axis, Z-direction gyro; ε rx, ε ry, ε rzbe respectively the gyro single order Markov drift error quantity of state of X-axis, Y-axis and Z-direction; ▽ x, ▽ y, ▽ zbe respectively the inclined error state amount of accelerometer single order Markov zero of X-axis in inertial navigation system, Y-axis and Z-direction; δ A x, δ A y, δ A zfor the alignment error quantity of state of accelerometer in X-axis, Y-axis and Z-direction in inertial navigation system; δ K ax, δ K ay, δ K azfor the scale factor error quantity of state of accelerometer in X-axis, Y-axis and Z-direction in inertial navigation system; δ G x, δ G y, δ G zfor the alignment error quantity of state of gyro on three directions of X-axis, Y-axis and Z axis in inertial navigation system; δ K gx, δ K gy, δ K gzfor the scale factor error quantity of state of gyro in X-axis, Y-axis and Z-direction in inertial navigation system;

Set up the error state equation of inertial navigation system, shown in (7):

X · ( t ) = F ( t ) X ( t ) + G ( t ) W ( t ) - - - ( 7 )

In formula (7), X (t) is system state variables, for the first order derivative of state variable X (t); F (t) is system matrix, G (t) for noise figure matrix, W (t) be noise matrix.

According to the inertial sensor errors model set up in step 1, system matrix F (t) corresponding with formula (6) and formula (7) is:

F ( t ) = FN ( t ) 9 × 9 FS ( t ) 9 × 9 Fs ( t ) 9 × 12 0 9 × 9 FM ( t ) 9 × 9 0 9 × 12 0 12 × 30 - - - ( 8 )

In formula (8), FN (t) 9 × 9for the relational matrix between corresponding 9 inertial navigation system navigational parameters (attitude, speed and position), its nonzero term element is:

FN ( 1,2 ) = ω ie sin L + V E R N + h tan L FN ( 1,3 ) = - ( ω ie cos L + V E R N + h ) FN ( 1,5 ) = - 1 R M + h FN ( 2,1 ) = - ( ω ie sin L + V E R N + h tan L ) FN ( 2,3 ) = - V N R M + h FN ( 2,4 ) = 1 R N + h FN ( 2,7 ) = - ω ie sin L

FN ( 3,1 ) = ω ie cos L + V E R N + h FN ( 3,2 ) = V N R M + h FN ( 3,4 ) = tan L R N + h FN ( 3,7 ) = ω ie cos L + V E R N + h sec 2 L

FN ( 4,2 ) = - f u FN ( 4,3 ) = f n FN ( 4,4 ) = V N tan L - V U R N + h FN ( 4,5 ) = 2 ω ie sin L + V E R N + h tan L FN ( 4,6 ) = - ( 2 ω ie cos L + V E R N + h ) FN ( 4,7 ) = 2 ω ie ( V U sin L + V N cos L ) + V E V N R N + h sec 2 L

FN ( 5,1 ) = f u FN ( 5,3 ) = - f e FN ( 5,4 ) = - 2 ( ω ie sin L + V E R N + h tan L ) FN ( 5,5 ) = - V U R M + h FN ( 5,6 ) = - V N R M + h FN ( 5,7 ) = - ( 2 V E ω ie cos L + V E 2 R N + h sec 2 L ) FN ( 6,1 ) = - f n FN ( 6,2 ) = f e FN ( 6,4 ) = 2 ( ω ie cos L + V E R N + h ) FN ( 6,5 ) = 2 V N R M + h FN ( 6,7 ) = - 2 V E ω ie sin L

FN ( 7,5 ) = 1 R M + h FN ( 8,4 ) = sec L R N + h FN ( 8,7 ) = V E R FN ( 9,6 ) = 1

R mfor earth radius of curvature of meridian, R nfor earth radius of curvature in prime vertical; f e, f n, f ufor east orientation, north orientation and sky to acceleration.

In formula (8), FS ( t ) = C b n C b n 0 3 × 3 0 3 × 3 0 3 × 3 C b n 0 3 × 9 , for body is tied to the transition matrix of geographic coordinate system

Fs ( t ) 9 × 12 = 0 3 × 6 F 1 ( t ) 3 × 3 F 3 ( t ) 3 × 3 F 2 ( t ) 3 × 3 F 4 ( t ) 3 × 3 0 3 × 6 0 3 × 12 - - - ( 9 )

In formula (9):

F 1 ( t ) = - C 12 ω ibz b + C 13 ω iby b C 11 ω ibz b - C 13 ω ibx b - C 11 ω iby b + C 12 ω ibx b - C 22 ω ibz b + C 23 ω iby b C 21 ω ibz b - C 23 ω ibx b - C 21 ω iby b + C 22 ω ibx b - C 32 ω ibz b + C 33 ω iby b C 31 ω ibz b - C 33 ω ibx b - C 31 ω iby b + C 32 ω ibx b ,

F 2 ( t ) = C 12 f z b - C 13 f y b - C 11 f z b + C 13 f x b C 11 f y b - C 12 f x b C 22 f z b - C 23 f y b - C 21 f z b + C 23 f x b C 21 f y b - C 22 f x b C 32 f z b - C 33 f y b - C 31 f z b + C 33 f x b C 31 f y b - C 32 f x b

F 3 ( t ) = - C 11 ω ibx b - C 12 ω iby b - C 13 ω ibz b - C 21 ω ibx b - C 22 ω iby b - C 23 ω ibz b - C 31 ω ibx b - C 32 ω iby b - C 33 ω ibz b , F 4 ( t ) = C 11 f x b C 12 f y b C 13 f z b C 21 f x b C 22 f y b C 23 f z b C 31 f x b C 32 f y b C 33 f z b

Wherein: 3 are tied to the transition matrix of geographic coordinate system for body, f b = f x b f y b f z b T For accelerometer is in the output of body system, ω ib b = ω ibx b ω iby b ω ibz b T For gyro exports the projection of fastening at body.

In formula (8), the relational matrix between inertial sensor errors is:

FM ( t ) = Diag 0 0 0 - 1 T gx - 1 T gy - 1 T gz - 1 T ax - 1 T ay - 1 T az - - - ( 10 )

System noise matrix is:

W=[w gxw gyw gzw rxw ryw rzw axw ayw az] (11)

Error coefficient matrix:

G ( t ) = C b n 0 3 × 3 0 3 × 3 0 9 × 3 0 9 × 3 0 9 × 3 0 3 × 3 I 3 × 3 0 3 × 3 0 3 × 3 0 3 × 3 I 3 × 3 - - - ( 12 )

(2.2) determination of measurement equation

Adopt attitude, speed and position linearity Observation principle under Department of Geography, set up satellite navigation speed under Department of Geography, position and star sensor attitude observation and step 2.1) in linearization measurement equation between INS errors quantity of state:

Z ( t ) = Z p ( t ) Z v ( t ) Z φ ( t ) = H p ( t ) H v ( t ) H φ ( t ) X ( t ) + V p ( t ) V v ( t ) V φ ( t ) - - - ( 13 )

In formula, Z p(t), Z v(t) and Z φt () is that position, speed and attitude measure vector.H p(t), H v(t), H φt () is position, speed and attitude measure matrix of coefficients, and position, speed and attitude observation noise matrix are V p(t), V v(t) and V φ(t).3. the real-time calibration of inertial sensor solid error compensates

(3.1) by filter status equation and measurement equation sliding-model control:

X(k)=Φ(k,k-1)X(k-1)+Γ(k,k-1)W(k-1) (14)

Z(k)=H(k)X(k)+V(k) (15)

In formula (15), X (k) is t kmoment system state amount; X (k-1) is t k-1moment system state amount; Φ (k, k-1) is t k-1moment is to t ktime etching system state-transition matrix; Γ (k, k-1) is t k-1moment is to t ktime etching system noise drive matrix; W (k-1) is t ktime etching system noise matrix; Z (k) is t ktime the position of etching system, speed and attitude observation matrix; H (k) is t kthe position in moment, speed and attitude measure matrix of coefficients; V (k) is t kthe noise matrix of the position in moment, speed and attitude observation.

(3.2) according to formula (16), formula (17), formula (18), formula (19) sub-paragraphs 3.1) part ins error quantity of state and covariance information measurement upgrade:

P(k,k-1)=Φ(k,k-1)P(k-1,k-1)Φ(k,k-1) T+Γ(k,k-1)Q(k)Γ(k,k-1) T

(16)

K(k)=P(k,k-1)H(k) T[H(k)P(k,k-1)H(k) T+R(k)] -1(17)

X(k)=X(k,k-1)+K(k)[Z(k)-H(k)X(k,k-1)] (18)

P(k,k)=[I-K(k)H(k)]P(k,k-1) (19)

Wherein, P (k, k-1) is t k-1moment is to t kmoment one-step prediction covariance matrix; P (k-1, k-1) is t k-1moment filter state estimate covariance matrix; Q (k) is t ktime etching system noise covariance matrix; Κ (k) is t kmoment filter gain matrix; R (k) is t kmoment position, speed and attitude measurement noise covariance matrix; X (k, k-1) is t k-1moment is to t kmoment one-step prediction quantity of state; P (k, k) is t kmoment filter state estimate covariance matrix;

I is the unit matrix identical with P (k, k) dimension;

(3.3) the quantity of state X (k, k) that filtering exports is judged, if the predicted value of quantity of state is stablized, then complete demarcation and enter step (3.4) if predicted value is unstable, then return step (3.2) and continue to carry out predicted estimate to state value.

(3.4), after the calibration result obtained IMU alignment error and scale factor error in step (3.3), temporary calibration value, utilizes this calibration value to compensate correction to IMU alignment error and scale factor error, corrects and complete within a navigation calculation cycle.Error compensation correcting algorithm is:

f b = [ I - δK A - δA ] ( f ~ b - ▿ b ) ω ib b = [ I - δK G - δG ] ( ω ~ ib b - ϵ b ) - - - ( 20 )

In formula (20), δ K a, δ A, ▽ bbe respectively the scale factor error of accelerometer, alignment error and zero partially, δ K g, δ G, ε bfor the scale factor error of gyro, alignment error and random zero partially, obtain by calibration process.

(3.5) after step (3.4) completes the alignment error of IMU and scale factor error rectification building-out, do not re-use wave filter and enter pure-inertial guidance system operating mode.

In order to correctness and the validity of the solid error modeling and scaling method of verifying the inertial navigation system inertial sensor that invention proposes, adopt the inventive method Modling model, carry out matlab simulating, verifying.The flight track adopted when Fig. 2 is checking, to the alignment error of inertial sensor and the calibration result of scale factor error as shown in Fig. 3, Fig. 4, Fig. 5, Fig. 6.

In space vehicle dynamic flight course, utilize calibration result to compensate and correct IMU alignment error and scale factor error, inertial navigation result after compensation with carry out contrast verification without the inertial navigation navigation results compensated, the result is as shown in Fig. 7, Fig. 8, Fig. 9.

In Fig. 3, Fig. 4, Fig. 5, Fig. 6, solid black lines represents calibration result of the present invention, and red dot-and-dash line is setting value.As can be seen from the figure demarcate the time used at about 20s to IMU alignment error and scale factor error, calibration result is consistent with setting value.In Fig. 7, Fig. 8, Fig. 9, solid black lines representative does not compensate the pure inertial navigation navigation results of IMU solid error, and red dot-and-dash line representative compensates the pure inertial navigation navigation results after IMU solid error.As can be seen from Fig. 7, Fig. 8, Fig. 9, utilize after correcting the alignment error of IMU and scale factor error the calibration result of IMU alignment error and scale factor error, INS errors obviously reduces, and has useful engineer applied and is worth.

Claims (2)

1. an inertial sensor fixed error real-time calibration method in inertial navigation system, it is characterized in that, described method concrete steps are as follows:
Step 1, set up the solid error model of inertial sensor, comprise accelerometer scale factor error matrix and gyrostatic scale factor error matrix:
Accelerometer scale factor error matrix is δ K a=diag [δ K axδ K ayδ K az], wherein, δ K ax, δ K ay, δ K azbe respectively the scale factor error of X-axis, Y-axis and Z axis accelerometer; Accelerometer alignment error matrix is δA = 0 δA z - δA y - δA z 0 δA x δA y - δA x 0 , Wherein, δ A x, δ A y, δ A zbe respectively the fix error angle of X-axis, Y-axis and Z axis accelerometer; δ K aall be taken as arbitrary constant with δ A, X, Y, Z tri-accelerometer error models of axle are identical, as follows:
δ K . A = 0 δ A . = 0
In above formula, for scale factor error matrix delta K afirst order derivative, for the first order derivative of alignment error matrix delta A;
Gyrostatic scale factor error matrix is δ K g=diag [δ K gxδ K gyδ K gz], δ K gx, δ K gy, δ K gzbe respectively the scale factor error of X-axis, Y-axis and Z axis gyro; Gyro misalignment matrix is δG = 0 δG z - δG y - δG z 0 δG x δG y - δG x 0 , δ G x, δ G y, δ G zbe respectively the alignment error of X-axis, Y-axis and Z axis gyro; Scale factor error and alignment error are all taken as arbitrary constant, and X, Y, Z tri-gyro error models of axle are identical, as follows:
δ K . G = 0 δ G . = 0
In above formula, for scale factor error matrix delta K gfirst order derivative, for the first order derivative of alignment error matrix delta G;
Step 2, in the alignment error of step 1 couple IMU and the basis of scale factor error modeling, using the alignment error of IMU and scale factor error as system state variables, build the filter status equation based on inertial sensor total state error model and position, speed and attitude linearization measurement equation:
Systematic state variable X based on inertial sensor total state error modeling is:
X = φ E φ N φ U δV E δV N δV U δL δλ δh ϵ bx ϵ by ϵ bz ϵ rx ϵ ry ϵ rz ▿ x ▿ y ▿ z δA x δA y δA z δK Ax δK Ax δK Az δG x δG y δG z δK Gx δK Gy δK Gz T
In above formula, φ e, φ n, φ ube respectively the east orientation in inertial navigation system, north orientation and sky to platform error angle quantity of state; δ V e, δ V n, δ V ube respectively the east orientation in INS errors, north orientation and sky to velocity error quantity of state; δ L, δ λ, δ h are respectively latitude error quantity of state, longitude error quantity of state and height error quantity of state in inertial navigation system; ε bx, ε by, ε bzbe respectively the constant value drift error state amount of the X-axis in inertial navigation system, Y-axis, Z-direction gyro; ε rx, ε ry, ε rzbe respectively the gyro single order Markov drift error quantity of state of X-axis, Y-axis and Z-direction; be respectively the inclined error state amount of accelerometer single order Markov zero of X-axis in inertial navigation system, Y-axis and Z-direction; δ A x, δ A y, δ A zbe respectively the alignment error quantity of state of accelerometer in X-axis in inertial navigation system, Y-axis and Z-direction; δ K ax, δ K ay, δ K azbe respectively the scale factor error quantity of state of accelerometer in X-axis in inertial navigation system, Y-axis and Z-direction; δ G x, δ G y, δ G zbe respectively the alignment error quantity of state of gyro on X-axis in inertial navigation system, Y-axis and Z axis three directions; δ K gx, δ K gy, δ K gzfor the scale factor error quantity of state of gyro in X-axis, Y-axis and Z-direction in inertial navigation system;
Set up the error state equation of inertial navigation system, be shown below:
X . ( t ) = F ( t ) X ( t ) + G ( t ) W ( t )
In above formula, X (t) is system state variables; for the first order derivative of state variable X (t); F (t) is system matrix; G (t) is noise figure matrix; W (t) is noise matrix;
Adopt Department of Geography upper/lower positions, speed and attitude linearization Observation principle, set up satellite navigation position detection amount under Department of Geography, speed observed quantity and the linearization measurement equation between star sensor attitude observation and INS errors quantity of state:
Z ( t ) = Z p ( t ) Z v ( t ) Z φ ( t ) = H p ( t ) H v ( t ) H φ ( t ) X ( t ) + V p ( t ) V v ( t ) V φ ( t )
In above formula, Z p(t), Z v(t), Z φt () is respectively position, speed and attitude and measures vector; H p(t), H v(t), H φt () is respectively position, speed and attitude and measures matrix of coefficients; V p(t), V v(t), V φt () is respectively position, speed and attitude observation noise matrix;
Step 3, on the basis of step 2, system state equation and measurement equation are carried out to the renewal of sliding-model control and quantity of state, measurement amount, realize the demarcation to IMU alignment error and scale factor error and compensation.
2. inertial sensor fixed error real-time calibration method in a kind of inertial navigation system as claimed in claim 1, is characterized in that, to the demarcation of IMU alignment error and scale factor error and compensation described in step 3, its concrete steps are:
(301) by filter status equation and measurement equation sliding-model control:
X(k)=Φ(k,k-1)X(k-1)+Γ(k,k-1)W(k-1)
Z(k)=H(k)X(k)+V(k)
In above formula, X (k) is t kmoment system state amount; X (k-1) is t k-1moment system state amount; Φ (k, k-1) is t k-1moment is to t ktime etching system state-transition matrix; Γ (k, k-1) is t k-1moment is to t ktime etching system noise drive matrix; W (k-1) is t ktime etching system noise matrix; Z (k) is t ktime the position of etching system, speed and attitude observation matrix; H (k) is t kthe position in moment, speed and attitude measure matrix of coefficients; V (k) is t kthe noise matrix of the position in moment, speed and attitude observation;
(302) according to the following formula the INS errors quantity of state of step (301) part and the measurement of covariance information are upgraded:
P(k,k-1)=Φ(k,k-1)P(k-1,k-1)Φ(k,k-1) T+Γ(k,k-1)Q(k)Γ(k,k-1) T
K(k)=P(k,k-1)H(k) T[H(k)P(k,k-1)H(k) T+R(k)] -1
X(k)=X(k,k-1)+K(k)[Z(k)-H(k)X(k,k-1)]
P(k,k)=[I-K(k)H(k)]P(k,k-1)
In above-mentioned formula, P (k, k-1) is t k-1moment is to t kmoment one-step prediction covariance matrix; P (k-1, k-1) is t k-1moment filter state estimate covariance matrix; Q (k) is t ktime etching system noise covariance matrix; Κ (k) is t kmoment filter gain matrix; R (k) is t kmoment position, speed and attitude measurement noise covariance matrix; X (k, k-1) is t k-1moment is to t kmoment one-step prediction quantity of state; P (k, k) is t kmoment filter state estimate covariance matrix; I is the unit matrix identical with P (k, k) dimension;
(303) to the quantity of state X (k that filtering exports, k) judge, if the predicted value of quantity of state X (k, k) is stablized, complete demarcation, obtain the calibration result to IMU alignment error and scale factor error, enter step (304); If predicted value is unstable, then returns step (302) and continue to carry out predicted estimate to state value;
(304) after the calibration result obtained IMU alignment error and scale factor error in step (303), temporary calibration value, calibration value is utilized to compensate correction to IMU alignment error and scale factor error, correct and complete within a navigation calculation cycle, error compensation correcting algorithm is:
f b = [ I - δK A - δA ] ( f ~ b - ▿ b ) ω ib b = [ I - δK G - δG ] ( ω ~ ib b - ϵ b )
In above formula, the acceleration that the accelerometer being respectively error exports and the angular speed that gyroscope exports; f b, be respectively the acceleration after getting rid of error and angular speed; for the Random Drift Error of accelerometer, ε bfor the Random Drift Error of gyro.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105865446A (en) * 2016-05-25 2016-08-17 南京航空航天大学 Inertia altitude channel damping Kalman filtering method based on atmosphere assistance

Families Citing this family (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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CN104101362B (en) * 2014-06-24 2017-02-15 湖北航天技术研究院总体设计所 Flexible SIMU system model based on-line compensation method for scale factors of gyroscope
CN104122412B (en) * 2014-07-29 2016-08-24 北京机械设备研究所 A kind of accelerometer scaling method based on Beidou II velocity information
CN104215262A (en) * 2014-08-29 2014-12-17 南京航空航天大学 On-line dynamic inertia sensor error identification method of inertia navigation system
CN105136166B (en) * 2015-08-17 2018-02-02 南京航空航天大学 A kind of SINS error model emulation mode of specified inertial navigation positional precision
CN105203129B (en) * 2015-10-13 2019-05-07 上海华测导航技术股份有限公司 A kind of inertial nevigation apparatus Initial Alignment Method
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CN108507568A (en) * 2017-02-27 2018-09-07 华为技术有限公司 The method, apparatus and integrated navigation system of compensation temperature drift error
CN106996778B (en) * 2017-03-21 2019-11-29 北京航天自动控制研究所 Error parameter scaling method and device
CN108562288A (en) * 2018-05-08 2018-09-21 北京航天时代激光导航技术有限责任公司 A kind of Laser strapdown used group of system-level online self-calibration system and method
CN109655081A (en) * 2018-12-14 2019-04-19 上海航天控制技术研究所 The in-orbit self-adapting correction method of optical system of star sensor parameter and system

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101221046A (en) * 2008-01-22 2008-07-16 南京航空航天大学 Error processing method for output signal of optic fiber gyroscope component

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR101106048B1 (en) * 2010-01-20 2012-01-19 국방과학연구소 Method for calibrating sensor errors automatically during operation, and inertial navigation using the same

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101221046A (en) * 2008-01-22 2008-07-16 南京航空航天大学 Error processing method for output signal of optic fiber gyroscope component

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
SINS/GPS/CNS Information Fusion System Based on Improved Huber Filter with Classified Adaptive Factors for High-speed UAVs;Rong Wang etc;《IEEE》;20120426;第441-446页 *
一种提高车载定位定向系统定位精度的方法;王东升等;《中国惯性技术学报》;20120430;第20卷(第2期);第187-191页 *
捷联惯性传感器多余度配置的误差标定技术研究;华冰等;《传感器技术》;20051231;第24卷(第5期);第31-33页 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105865446A (en) * 2016-05-25 2016-08-17 南京航空航天大学 Inertia altitude channel damping Kalman filtering method based on atmosphere assistance

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