CN104897178B - A kind of pair of inertial navigation joint rotation modulation navigation and online relative performance appraisal procedure - Google Patents

Abstract

The present invention discloses a kind of pair of inertial navigation joint rotation modulation navigation and online relative performance appraisal procedure for the problem of inertial navigation performance online assessment.The present invention is defined by coordinate system, joint rotation modulation strategy layout, association system state equation determine, measurement equation determines and the step of Kalman filtering, realizes the online evaluation of inertial navigation performance, improves the effects for covering information fusion between inertial navigation systems more.The present invention can be used for the assessment and the diagnosis of inertial navigation system failure of inertial navigation system relative performance under high accuracy guidanuce condition during boat long, during for boat long under the conditions of the guarantee of navigation accuracy there is positive effect.

Description

A kind of pair of inertial navigation joint rotation modulation navigation and online relative performance appraisal procedure

Technical field

The present invention relates to a kind of inertial navigation performance online appraisal procedure, particularly a kind of pair inertial navigation joint rotation modulation navigation with Online relative performance appraisal procedure.

Background technology

The Inertial Measurement Unit (IMU) of inertial navigation system by gyro, plus table constitute, gyro, plus the precision of table determine The performance of inertial navigation system, inertial navigation performance determines the precision of navigation.Inertial navigation system was all needed before concrete application environment is configured to Performance test is carried out, at present, the test to inertial navigation performance both at home and abroad typically takes two class testings：

1st, device level test.It is main to gyro, plus table carry out single device detection, by the device of test screen high precision come Inertial Measurement Unit is constituted, to meet the application of some high accuracy navigational environments.

2nd, system level testing.System level testing formally mainly is carried out to Inertial Measurement Unit using preceding in inertial navigation system, The pure inertial navigation precision of inertial navigation system is usually investigated in a static condition, additionally, according to the difference of inertial navigation applied environment, in addition it is also necessary to Carry out the system accuracy test under other conditions.

This two class testing is all that, formally using preceding carrying out off-line test, the problem that off-line test is present is in inertial navigation system： Even if off-line test inertial navigation precision is up to standard, but due to gyro when inertial navigation works long hours, plus table zero change occurs partially, can be directly Influence navigation accuracy is connect, inertial navigation failure can be additionally likely to occur, triggers navigational error.It is being independent of the bar of extraneous reference information Under part, how to change gyro, plus table zero be biased capable estimation, and then it is to need to solve to carry out system-level performance online assessment Problem, in existing achievement in research, under conditions of not by oracle, it is impossible to carry out online evaluation to inertial navigation performance.

To ensure reliability, boat-carrying inertial navigation system often redundant configuration (general two sets of carrying), other needs high accuracy are led The inertial navigation system of boat also tends to redundant configuration.Working method is principal and subordinate's backup mode, and only a set of inertial navigation is in running order, its Its system is in Status of Backups, considers from Information Pull angle, and master-slave back-up working method causes the wasting of resources indirectly.How The information of redundant configuration inertial navigation system is comprehensively utilized, and then realization carries out online evaluation to inertial navigation performance, preferably high precision is The navigational parameter of system is the problem for needing to solve, domestic and international not disclosed report as system output.

In CNKI storehouses《A kind of pair of inertial navigation combination navigation method》(Liu Weiren, Wang Ning, Liu Guobin, year great waves, Ai Guangbin；In State's inertial technology journal；2 months the 1st phases in 2014) text discloses and a kind of refers to northern inertial navigation system, stage body orientation rotation using fixation Inertial navigation system carries out information fusion and improves the method for navigation accuracy, but is not involved with proposed a kind of pair of inertial navigation joint Rotation modulation navigates and online relative performance appraisal procedure.

The content of the invention

Problem of the present invention for the assessment of inertial navigation performance online, it is proposed that a kind of pair of inertial navigation joint rotation modulation navigation with Line relative performance appraisal procedure, the method is made different used by the reasonable layout to double ionertial navigation system joint rotation modulation strategy The indexable rule of guiding systems is different, so that inertial navigation system error characteristics have certain complementarity, is measured without the external world Under information condition, error state is chosen, using the difference of inertial navigation system navigational parameter as measurement information, carries out Kalman filtering, To constant value or slowly varying gyroscopic drift, plus table zero be biased capable estimation, and then relative performance to inertial navigation system is estimated.

For the technical solution that the realization present invention is taken is：

A kind of pair of inertial navigation joint rotation modulation navigates and online relative performance appraisal procedure, and its step is：

Step one：Coordinate system is defined, and it is local horizontal geographic coordinate system, reference axis difference to define navigational coordinate system (n systems) North orientation-east orientation-ground is pointed to (N-E-D), carrier coordinate system (b systems) reference axis is respectively along the roll axle-pitch axis-driftage of carrier Axle (preceding-right-under), Inertial Measurement Unit (IMU) coordinate system of inertial navigation system 1,2 is respectively s₁、s₂, the same carrier of reference axis sensing Coordinate system is defined；

Step 2：Joint rotation modulation strategy layout, inertial navigation system 1,2 carries out the order rotation of 4 position 8 rotating around azimuth axis Modulation indexing, indexable rule is different；

Step 3：The determination of association system state equation, takes attitude error of the inertial navigation system 1 with inertial navigation system 2, speed mistake Difference, the state difference of site error are association system state, and 16 error states are：

X=[(φ_N1-φ_N2) (φ_E1-φ_E2) (φ_D1-φ_D2) (δv_N1-δv_N2) (δv_E1-δv_E2)

(δL₁-δL₂) (δλ₁-δλ₂) ε_x1 ε_y1 ε_x2 ε_y2 (ε_z1-ε_z2) ▽_x1 ▽_y1 ▽_x2 ▽_y2]^T (1)

I.e.

X=[φ_N12 φ_E12 φ_D12 δv_N12 δv_E12 δL₁₂ δλ₁₂

ε_x1 ε_y1 ε_x2 ε_y2 ε_z12 ▽_x1 ▽_y1 ▽_x2 ▽_y2]^T

Wherein, subscript T represents the transposition of vector or matrix, φ_N12=(φ_N1-φ_N2)、φ_E12=(φ_E1-φ_E2)、φ_D12 =(φ_D1-φ_D2) it is respectively the difference of inertial navigation system 1 and the attitude error vector of inertial navigation system 2, δ v_N12=(δ v_N1-δv_N2)、δ v_E12=(δ v_E1-δv_E2) it is respectively north orientation, the difference of east orientation speed error of inertial navigation system 1 and inertial navigation system 2, δ L₁₂=(δ L₁- δL₂)、δλ₁₂=(δ λ₁-δλ₂) it is respectively latitude, the difference of longitude error, ε of inertial navigation system 1 and inertial navigation system 2_x1、ε_x2、ε_y1、 ε_y2The respectively gyroscope constant value drift of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1, ε_z12=(ε_z1-ε_z2) be Gyroscope constant value drift of difference from the corresponding day of the IMU of inertial navigation system 1 and inertial navigation system 2 to reference axis (during around azimuth axis single-shaft-rotation, Level add table zero partially, gyroscope constant value drift can be separated, but day to gyroscope constant value drift it is inseparable), ▽_x1、▽_x2、▽_y1、 ▽_y2Respectively the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 plus table constant value zero partially, according to association system shape State determines association system state equation；

Step 4：Measurement equation determines that the velocity error that deduction error in mounting position and lever arm are caused is lacking the external world Under the conditions of reference information, it is corresponding measurement, measurement to take the speed of 1s renewals inertial navigation system 1,2 once and the difference of position For：

Z (t)=[δ v_N1-δv_N2δv_E1-δv_E2δL₁-δL₂δλ₁-δλ₂]^T (2)

Wherein,It is the north orientation speed difference of inertial navigation system 1,2,It is inertial navigation The east orientation speed difference of system 1,2,It is the latitude difference of inertial navigation system 1,2,It is inertial navigation The longitude difference of system 1,2, measurement equation is determined according to state quantity measurement；

Step 5：Kalman filtering, Kalman filter is built according to association system state equation, measurement equation, and 1s enters Row is once measured and updated, and to two sets of respective gyros of inertial navigation system, adds table zero to be biased capable estimation；

Step 6：Inertial navigation performance online is assessed, and according to gyro, adds the inclined estimate of table zero to the relative of inertial navigation system 1,2 Performance is estimated, and zero system less than normal is used as optimum decision system；

Wherein：Inertial navigation system 1,2 described in step 2 carries out the order rotation modulation of 4 position 8 and turns rotating around azimuth axis Position, indexable order method of combination is as follows：

1) inertial navigation system 1,2 is respectively adopted different indexable order layouts

The indexable order of inertial navigation system 1 is(Fig. 2 institutes Show), i.e. 8 order indexing is (shown in Fig. 4)：Order 1, by 180 ° of arrival location of C of location A rotate counterclockwise, stops the Ts times；It is secondary Sequence 2,90 ° of arrival B locations are rotated clockwise by location of C, stop the Ts times；Order 3,180 ° of arrival D are rotated clockwise by B location Position, stops the Ts times；Order 4,90 ° of arrival location As are rotated counterclockwise by D positions, stop the Ts times；Order 5, by location A 180 ° of arrival location of C are rotated counterclockwise, the Ts times are stopped；Order 6, rotates counterclockwise 90 ° and reaches D positions by location of C, stops Ts Time；Order 7,180 ° of arrival B locations are rotated clockwise by D positions, stop the Ts times；Order 8, is rotated clockwise by B location 90 ° of arrival location As, stop the Ts times；

The indexable order of inertial navigation system 2 is(Fig. 3 institutes Show), i.e. 8 order indexing is (shown in Fig. 5)：Order 1, is turned clockwise 180 ° by location A and reaches location of C, stops the Ts times；It is secondary Sequence 2, rotates counterclockwise 90 ° and reaches D positions by location of C, stops the Ts times；Order 3,180 ° of arrival B are rotated counterclockwise by D positions Position, stops the Ts times；Order 4,90 ° of arrival location As are rotated clockwise by B location, stop the Ts times；Order 5, by location A 180 ° of arrival location of C are rotated clockwise, the Ts times are stopped；Order 6,90 ° of arrival B locations are rotated clockwise by location of C, stop Ts Time；Order 7, rotates counterclockwise 180 ° and reaches D positions by B location, stops the Ts times；Order 8, is rotated counterclockwise by D positions 90 ° of arrival location As, stop the Ts times；

2) inertial navigation system 1,2 is using identical indexing order layout, but index time phase shifting

Two sets of inertial navigation systems are usedScheme or UseScheme, but index time phase is different (i.e. Azimuth axis initially points to difference)；

Association system state equation is determined according to association system state described in step 3, its method is as follows：

Association system state equation is：

Wherein,

X (t) is system mode,

It is state-transition matrix, each element is in formula,

Wherein, v_EIt is carrier east orientation speed, v_NIt is carrier north orientation speed, ω_ieIt is rotational-angular velocity of the earth, R_NIt is meridian plane Radius of curvature, R_EIt is chordwise curvature radius, h is carrier height, f_N、f_E、f_DRespectively north orientation, east orientation, to than force value, Respective element (the i of direction cosine matrix between the IMU coordinate systems and geographic coordinate system of inertial navigation 1,2 is represented respectively Row is represented, j represents row)；

It is system noise, wherein, For the gyro of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 exports random noise,The difference of random noise is exported to the gyro of reference axis for the corresponding days of the IMU of inertial navigation system 1 and inertial navigation system 2,Add table output random noise for the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1；

It is system noise matrix, wherein, B₁=A₄,B₂=A₈；

Measurement equation is determined according to state quantity measurement in step 4, its method is as follows：

Measurement equation is：

Z (t)=Hx (t)+ν (t) (4)

Wherein, ν (t) is measurement noise,It is measurement matrix, I_2×2It is second order unit matrix；

During double inertial navigation joint rotation modulation strategy layouts, rotation modulation also includes the dual-axis rotation around azimuth axis and trunnion axis Modulation, now increases the day of inertial navigation system 1,2 to the inclined ε of gyro zero_z1、ε_z2, and inertial navigation system 1,2 day to plus table zero it is inclined ▽_z1、▽_z2, used as association system state, association system state is

Corresponding state equation and measurement equation are built according to association system state, and to gyro, plus table zero be biased row and estimate Meter, according to gyro, adds the inclined estimate of table zero, and online evaluation is carried out to systematic function；

This pair of inertial navigation joint rotation modulation navigation and online relative performance appraisal procedure can be applied to two between the inertial navigation of many sets The assessment of two relative performances, as long as making the indexable rule of different inertial navigation systems different, error has complementarity, can be with United state equation is built respectively, access speed, position difference carry out Kalman filtering as measurement, estimate gyro, add table Zero partially, online evaluation is carried out to systematic function.

Compared with prior art, the beneficial effects of the invention are as follows：

1) the invention comprehensively utilizes the letter of boat-carrying redundant configuration inertial navigation system (carrying two sets of inertial navigation systems in general naval vessel) Breath, changes the present situation that the cold and hot back-up job pattern of current boat-carrying inertial navigation system causes the wasting of resources.

2) by the way that double inertial navigations are combined with the reasonable layout of rotation modulation strategy, the error characteristics of double ionertial navigation system are made to be presented poor Different, the difference with the navigational parameter of double ionertial navigation system builds Kalman filter as measurement information, respective to double ionertial navigation system Gyro, plus table zero be biased capable estimation, according to gyro, plus the inclined estimate of table zero, online evaluation is carried out to systematic function, change mesh Preceding boat-carrying inertial navigation system performance cannot carry out the present situation of online evaluation.

3) effect of information fusion between the inertial navigation systems of set more than improve, bar when diagnosis and length to inertial navigation system failure are navigated The guarantee of navigation accuracy has positive effect under part.

Brief description of the drawings

Fig. 1 is the schematic flow sheet of the inventive method；

Fig. 2 is the order rotation modulation indexing figure of 4 position of single-shaft-rotation 8 of inertial navigation system 1IMU；

Fig. 3 is the order rotation modulation indexing figure of 4 position of single-shaft-rotation 8 of inertial navigation system 2IMU；

Fig. 4 is the order rotation modulation indexing timing diagram of 4 position of single-shaft-rotation 8 of inertial navigation system 1IMU；

Fig. 5 is the order rotation modulation indexing timing diagram of 4 position of single-shaft-rotation 8 of inertial navigation system 2IMU；

Fig. 6 is two sets of top views of inertial navigation system joint rotation modulation indexing sequential；

Fig. 7 is that inertial navigation system 1 is estimated using double inertial navigation joint rotation modulation navigation with online relative performance appraisal procedure The two horizontal gyros zero for arriving are inclined；

Fig. 8 is that inertial navigation system 2 is estimated using double inertial navigation joint rotation modulation navigation with online relative performance appraisal procedure The two horizontal gyros zero for arriving are inclined；

Fig. 9 is that inertial navigation system 1,2 is estimated using the navigation of double inertial navigation joint rotation modulations and online relative performance appraisal procedure Two days for obtaining are to gyro zero-deviation value；

Figure 10 is that inertial navigation system 1 is estimated using double inertial navigation joint rotation modulation navigation with online relative performance appraisal procedure Two levels plus table zero for arriving are inclined；

Figure 11 is that inertial navigation system 2 is estimated using double inertial navigation joint rotation modulation navigation with online relative performance appraisal procedure Two levels plus table zero for arriving are inclined.

Specific embodiment

Below in conjunction with the accompanying drawings to the present invention in a kind of preferred embodiment be described in further detail.

Step one：Coordinate system is defined

Define navigational coordinate system (n systems) be local horizontal geographic coordinate system, reference axis be respectively directed to north orientation-east orientation-ground to (N-E-D), carrier coordinate system (b systems) reference axis is respectively along the roll axle-pitch axis-yaw axis (preceding-right-under) of carrier, inertial navigation Inertial Measurement Unit (IMU) coordinate system of system 1,2 is respectively s₁、s₂, reference axis sensing is with carrier coordinate system definition.

Step 2：Joint rotation modulation strategy layout

Inertial navigation system 1,2 carries out the order rotation modulation indexing of 4 position 8 rotating around azimuth axis, and inertial navigation system 1,2 is respectively adopted Different indexable order layouts；

The indexable order of inertial navigation system 1 is(Fig. 2 institutes Show), i.e. 8 order indexing is (shown in Fig. 4)：Order 1, by 180 ° of arrival location of C of location A rotate counterclockwise, stops the Ts times；It is secondary Sequence 2,90 ° of arrival B locations are rotated clockwise by location of C, stop the Ts times；Order 3,180 ° of arrival D are rotated clockwise by B location Position, stops the Ts times；Order 4,90 ° of arrival location As are rotated counterclockwise by D positions, stop the Ts times；Order 5, by location A 180 ° of arrival location of C are rotated counterclockwise, the Ts times are stopped；Order 6, rotates counterclockwise 90 ° and reaches D positions by location of C, stops Ts Time；Order 7,180 ° of arrival B locations are rotated clockwise by D positions, stop the Ts times；Order 8, is rotated clockwise by B location 90 ° of arrival location As, stop the Ts times；

The indexable order of inertial navigation system 2 is(Fig. 3 institutes Show), i.e. 8 order indexing is (shown in Fig. 5)：Order 1, is turned clockwise 180 ° by location A and reaches location of C, stops the Ts times；It is secondary Sequence 2, rotates counterclockwise 90 ° and reaches D positions by location of C, stops the Ts times；Order 3,180 ° of arrival B are rotated counterclockwise by D positions Position, stops the Ts times；Order 4,90 ° of arrival location As are rotated clockwise by B location, stop the Ts times；Order 5, by location A 180 ° of arrival location of C are rotated clockwise, the Ts times are stopped；Order 6,90 ° of arrival B locations are rotated clockwise by location of C, stop Ts Time；Order 7, rotates counterclockwise 180 ° and reaches D positions by B location, stops the Ts times；Order 8, is rotated counterclockwise by D positions 90 ° of arrival location As, stop the Ts times；

Two sets of inertial navigation systems are rotated according to respective indexable order loop cycle, as inertial navigation system 1 and the IMU of inertial navigation system 2 During using joint rotation modulation, Correspondence orientation Eulerian angles are changed by predetermined rule, as shown in Figure 2 and Figure 3 (Fig. 4, Fig. 5 It is corresponding timing diagram, Fig. 6 is indexable sequential top view), the IMU coordinate systems s of inertial navigation system 1₁IMU with inertial navigation system 2 sits Mark system s₂Between be followed successively by equidirectional and opposite direction.

Step 3：Association system state equation determines

It is association system to take the attitude error of inertial navigation system 1 and inertial navigation system 2, velocity error, the state difference of site error State, 16 error states are：

X=[(φ_N1-φ_N2) (φ_E1-φ_E2) (φ_D1-φ_D2) (δv_N1-δv_N2) (δv_E1-δv_E2)

(δL₁-δL₂) (δλ₁-δλ₂) ε_x1 ε_y1 ε_x2 ε_y2 (ε_z1-ε_z2) ▽_x1 ▽_y1 ▽_x2 ▽_y2]^T (6)

I.e.

X=[φ_N12 φ_E12 φ_D12 δv_N12 δv_E12 δL₁₂ δλ₁₂

ε_x1 ε_y1 ε_x2 ε_y2 ε_z12 ▽_x1 ▽_y1 ▽_x2 ▽_y2]^T

Wherein, subscript T represents the transposition of vector or matrix, φ_N12=(φ_N1-φ_N2)、φ_E12=(φ_E1-φ_E2)、φ_D12 =(φ_D1-φ_D2) it is respectively the difference of inertial navigation system 1 and the attitude error vector of inertial navigation system 2, δ v_N12=(δ v_N1-δv_N2)、δ v_E12=(δ v_E1-δv_E2) it is respectively north orientation, the difference of east orientation speed error of inertial navigation system 1 and inertial navigation system 2, δ L₁₂=(δ L₁- δL₂)、δλ₁₂=(δ λ₁-δλ₂) it is respectively latitude, the difference of longitude error, ε of inertial navigation system 1 and inertial navigation system 2_x1、ε_x2、ε_y1、 ε_y2The respectively gyroscope constant value drift of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1, ε_z12=(ε_z1-ε_z2) be Gyroscope constant value drift of difference from the corresponding day of the IMU of inertial navigation system 1 and inertial navigation system 2 to reference axis (during around azimuth axis single-shaft-rotation, Level add table zero partially, gyroscope constant value drift can be separated, but day to gyroscope constant value drift it is inseparable), ▽_x1、▽_x2、▽_y1、 ▽_y2Respectively the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 plus table constant value zero it is inclined；

Determine that association system state equation is as follows according to association system state,

Association system state equation is：

Wherein,

X (t) is system mode,

X=[φ_N12 φ_E12 φ_D12 δv_N12 δv_E12 δL₁₂ δλ₁₂

ε_x1 ε_y1 ε_x2 ε_y2 ε_z12 ▽_x1 ▽_y1 ▽_x2 ▽_y2]^T

It is state-transition matrix, each element is in formula,

Wherein, v_EIt is carrier east orientation speed, v_NIt is carrier north orientation speed, ω_ieIt is rotational-angular velocity of the earth, R_NIt is meridian plane Radius of curvature, R_EIt is chordwise curvature radius, h is carrier height, f_N、f_E、f_DRespectively north orientation, east orientation, to than force value, Respective element (the i of direction cosine matrix between the IMU coordinate systems and geographic coordinate system of inertial navigation 1,2 is represented respectively Row is represented, j represents row)；

It is system noise, wherein, For the gyro of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 exports random noise,The difference of random noise is exported to the gyro of reference axis for the corresponding days of the IMU of inertial navigation system 1 and inertial navigation system 2,For the table output that adds of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 is made an uproar at random Sound；

It is system noise matrix, wherein, B₁=A₄,B₂=A₈。

Step 4：Measurement equation determines

The velocity error that error in mounting position and lever arm are caused is deducted, under the conditions of extraneous reference information is lacked, 1s is taken The speed of renewal inertial navigation system 1,2 once and the difference of position are corresponding measurement, and measurement is：

Z (t)=[δ v_N1-δv_N2δv_E1-δv_E2δL₁-δL₂δλ₁-δλ₂]^T (8)

Wherein,It is the north orientation speed difference of inertial navigation system 1,2,It is inertial navigation The east orientation speed difference of system 1,2,It is the latitude difference of inertial navigation system 1,2,It is inertial navigation The longitude difference of system 1,2；

Determine that measurement equation is as follows according to state quantity measurement,

Z (t)=Hx (t)+ν (t) (9)

Wherein, ν (t) is measurement noise,It is measurement matrix, I_2×2It is second order unit matrix.

Step 5：Kalman filtering

Kalman filter is built according to association system state equation, measurement equation, 1s is once measured renewal, to two Cover the respective gyro of inertial navigation system, add table zero to be biased capable estimation.

Step 6：Inertial navigation performance online is assessed, and according to gyro, adds the inclined estimate of table zero to the relative of inertial navigation system 1,2 Performance is estimated, and zero system less than normal is used as optimum decision system.

The navigation of double inertial navigation joint rotation modulations can be in kind by Matlab half with online relative performance appraisal procedure effect Emulation experiment is verified that emulation sets as follows：

Two sets of inertial navigation positions are 30 ° of north latitude, and 120 ° of east longitude is in inactive state, are turned according to joint rotation modulation strategy It is dynamic, it is 442s in each position residence time Ts, 180 ° of rotation, 90 ° of time are 8s, and a complete rotation is modulation period 3600s.The horizontal initial attitude angle of two sets of inertial navigations is 0 °, and orientation initial attitude angle is 45 °, and the azimuth of inertial navigation 1 adds 30 " Error, " error, ignores horizontal attitude angle error, while ignoring scale factor error, constant multiplier for the azimuth of inertial navigation 2 addition -30 Nonlinearity erron and alignment error, the influence of lever arm error.

Investigation double inertial navigations joint rotation modulations navigation is inclined to gyro zero with online relative performance appraisal procedure, add table zero inclined Estimation effect.

It is inclined according to following setting addition zero in inertial navigation 1 emulates the gyro angle increment of generation, adds table speed increment data：

X gyros：0.001 °/h Y gyros：- 0.001 °/h Z gyros：-0.0003°/h

X adds table：0.5×10^-5G Y add table：-0.5×10^-5g

It is inclined according to following setting addition zero in inertial navigation 2 emulates the gyro angle increment of generation, adds table speed increment data：

X gyros：- 0.002 °/h Y gyros：0.002 °/h Z gyros：0.0005°/h

X adds table：-1×10^-5G Y add table：1×10^-5g

It to loop independence, ignore day to plus table zero offset error.

Two sets of gyros of inertial navigation, plus table noise be that the incremental data that actual inertial navigation system inactive state down-sampling is obtained is deducted Remainder after average.

Simulation time is set to 72h, and two sets of inertial navigation system sample frequencys are 200Hz, and inertial reference calculation frequency is 100Hz.

Each the inclined estimation condition of horizontal gyro zero and it is used to from two sets of Figure 10, Figure 11 from two sets of inertial navigation systems of Fig. 7, Fig. 8 The guiding systems estimation condition that each level adds table zero inclined can be seen that in 72h simulation times gyro zero partially, plus table zero set partially Value is it is estimated that come, under the conditions of single shaft joint rotation modulation, day can also be estimated to obtain (Fig. 9 to gyro zero-deviation value It is shown), if combining rotation modulation using twin shaft, two sets of respective days of inertial navigation can also be estimated partially to gyro zero, Jin Ergen The gyro zero that obtains according to estimates partially, plus the inclined situation of table zero, it is possible to determine that inertial navigation 1 is preferred inertial navigation system, completes inertial navigation performance Online evaluation.

The above is only the preferred embodiment of the present invention, protection scope of the present invention is not limited in above-described embodiment, all The technical scheme belonged under thinking of the present invention belongs to protection scope of the present invention.It should be pointed out that general for the art For logical technical staff, some improvements and modifications without departing from the principles of the present invention should be contemplated as falling within of the invention Protection domain.

Claims (4)

1. a kind of pair of inertial navigation joint rotation modulation navigates and online relative performance appraisal procedure, it is characterised in that including following step Suddenly：

Step one：Coordinate system is defined, and it is local horizontal geographic coordinate system to define navigational coordinate system (n systems), and reference axis is respectively directed to To (N-E-D), carrier coordinate system (b systems) reference axis is respectively along the roll axle-pitch axis-yaw axis of carrier on north orientation-east orientation-ground (preceding-right-under), Inertial Measurement Unit (IMU) coordinate system of inertial navigation system 1,2 is respectively s₁、s₂, reference axis sensing is with carrier seat The definition of mark system；

Step 2：Joint rotation modulation strategy layout, inertial navigation system 1,2 carries out the order rotation modulation of 4 position 8 rotating around azimuth axis Indexing, indexable rule is different；

Step 3：The determination of association system state equation, takes attitude error, velocity error, the position of inertial navigation system 1 and inertial navigation system 2 The state difference of error is put for association system state, 16 error states are：

X=[(φ_N1-φ_N2) (φ_E1-φ_E2) (φ_D1-φ_D2) (δv_N1-δv_N2) (δv_E1-δv_E2)

(δL₁-δL₂) (δλ₁-δλ₂) ε_x1 ε_y1 ε_x2 ε_y2 (ε_z1-ε_z2) ▽_x1 ▽_y1 ▽_x2 ▽_y2]^T (1)

I.e.

X=[φ_N12 φ_E12 φ_D12 δv_N12 δv_E12 δL₁₂ δλ₁₂

ε_x1 ε_y1 ε_x2 ε_y2 ε_z12 ▽_x1 ▽_y1 ▽_x2 ▽_y2]^T

Wherein, subscript T represents the transposition of vector or matrix, φ_N12=(φ_N1-φ_N2)、φ_E12=(φ_E1-φ_E2)、φ_D12= (φ_D1-φ_D2) it is respectively the difference of inertial navigation system 1 and the attitude error vector of inertial navigation system 2, δ v_N12=(δ v_N1-δv_N2)、δv_E12 =(δ v_E1-δv_E2) it is respectively north orientation, the difference of east orientation speed error of inertial navigation system 1 and inertial navigation system 2, δ L₁₂=(δ L₁-δ L₂)、δλ₁₂=(δ λ₁-δλ₂) it is respectively latitude, the difference of longitude error, ε of inertial navigation system 1 and inertial navigation system 2_x1、ε_x2、ε_y1、 ε_y2The respectively gyroscope constant value drift of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1, ε_z12=(ε_z1-ε_z2) be Gyroscope constant value drift of difference from the corresponding day of the IMU of inertial navigation system 1 and inertial navigation system 2 to reference axis (during around azimuth axis single-shaft-rotation, Level add table zero partially, gyroscope constant value drift can be separated, but day to gyroscope constant value drift it is inseparable), ▽_x1、▽_x2、▽_y1、 ▽_y2Respectively the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 plus table constant value zero partially, according to association system shape State determines association system state equation；

Step 4：Measurement equation determines that the velocity error that deduction error in mounting position and lever arm are caused is lacking extraneous reference Under information condition, it is corresponding measurement to take the speed of 1s renewals inertial navigation system 1,2 once and the difference of position, and measurement is：

Z (t)=[δ v_N1-δv_N2 δv_E1-δv_E2 δL₁-δL₂ δλ₁-δλ₂]^T (2)

Wherein,It is the north orientation speed difference of inertial navigation system 1,2,It is inertial navigation system 1st, 2 east orientation speed difference,It is the latitude difference of inertial navigation system 1,2,It is inertial navigation system 1st, 2 longitude difference, measurement equation is determined according to state quantity measurement；

Step 5：Kalman filtering, Kalman filter is built according to association system state equation, measurement equation, and 1s carries out one Secondary measurement updates, and to two sets of respective gyros of inertial navigation system, adds table zero to be biased capable estimation；

Step 6：Inertial navigation performance online is assessed, according to gyro, plus the inclined estimate of table zero to the relative performance of inertial navigation system 1,2 It is estimated, zero system less than normal is used as optimum decision system.

2. a kind of pair of inertial navigation joint rotation modulation according to claim 1 navigates and online relative performance appraisal procedure, its It is characterised by：

Inertial navigation system 1,2 described in step 2 carries out the order rotation modulation indexing of 4 position 8, indexing time rotating around azimuth axis Sequence method of combination is as follows：

1) inertial navigation system 1,2 is respectively adopted different indexable order layouts

The indexable order of inertial navigation system 1 isThat is 8 order indexing For：Order 1, by 180 ° of arrival location of C of location A rotate counterclockwise, stops the Ts times；Order 2,90 ° are rotated clockwise by location of C B location is reached, the Ts times are stopped；Order 3, rotates clockwise 180 ° and reaches D positions by B location, stops the Ts times；Order 4, by D positions rotate counterclockwise 90 ° of arrival location As, stop the Ts times；Order 5,180 ° of arrival location of C are rotated counterclockwise by location A, Stop the Ts times；Order 6, rotates counterclockwise 90 ° and reaches D positions by location of C, stops the Ts times；Order 7, it is clockwise by D positions 180 ° of arrival B locations are rotated, the Ts times are stopped；Order 8,90 ° of arrival location As are rotated clockwise by B location, stop the Ts times；

The indexable order of inertial navigation system 2 isThat is 8 order indexing For：Order 1, is turned clockwise 180 ° by location A and reaches location of C, stops the Ts times；Order 2,90 ° are rotated counterclockwise by location of C D positions are reached, the Ts times are stopped；Order 3,180 ° of arrival B locations are rotated counterclockwise by D positions, stop the Ts times；Order 4, by B location rotates clockwise 90 ° of arrival location As, stops the Ts times；Order 5,180 ° of arrival location of C are rotated clockwise by location A, Stop the Ts times；Order 6,90 ° of arrival B locations are rotated clockwise by location of C, stop the Ts times；Order 7, it is counterclockwise by B location Rotate 180 ° and reach D positions, stop the Ts times；Order 8,90 ° of arrival location As are rotated counterclockwise by D positions, stop the Ts times；

2) inertial navigation system 1,2 is using identical indexing order layout, but index time phase shifting

Two sets of inertial navigation systems are usedScheme or adopt WithScheme, but different (the i.e. orientation of index time phase Axle initially points to difference)；

Association system state equation is determined according to association system state described in step 3, its method is as follows：

Association system state equation is：

$\stackrel{\·}{x}\left(t\right)=F\left(t\right)x\left(t\right)+G\left(t\right)w\left(t\right)---\left(3\right)$

Wherein,

X (t) is system mode,

$\begin{array}{c}x=\[\begin{array}{ccccccc}{\mathrm{\φ}}_{N12}& {\mathrm{\φ}}_{E12}& {\mathrm{\φ}}_{D12}& {\mathrm{\δv}}_{N12}& {\mathrm{\δv}}_{E12}& {\mathrm{\δL}}_{12}& {\mathrm{\δ\λ}}_{12}\end{array}\\ \begin{array}{ccccccccc}{\mathrm{\ϵ}}_{x1}& {\mathrm{\ϵ}}_{y1}& {\mathrm{\ϵ}}_{x2}& {\mathrm{\ϵ}}_{y2}& {\mathrm{\ϵ}}_{z12}& {\▿}_{x1}& {\▿}_{y1}& {\▿}_{x2}& {\▿}_{y2}\end{array}{\]}^T\end{array};$

It is state-transition matrix, each element is in formula,

$F_u\left(t\right)=\left[\begin{array}{ccccc}{A}_1& A_2& A_3& A_4& 0_{3\×4}\\ A_5& A_6& A_7& 0_{2\×5}& A_8\\ 0_{2\×3}& A_9& A_{10}& 0_{2\×5}& 0_{2\×4}\end{array}\right]$

$A_1=\left[\begin{array}{ccc}0& -\frac{v_E\tan L}{R_E+h}-{\mathrm{\ω}}_{ie}\sin L& \frac{v_N}{R_N+h}\\ \frac{v_E\tan L}{R_E+h}+{\mathrm{\ω}}_{ie}\sin L& 0& {\mathrm{\ω}}_{ie}\cos L+\frac{v_E}{R_E+h}\\ -\frac{v_N}{R_N+h}& -{\mathrm{\ω}}_{ie}\cos L-\frac{v_E}{R_E+h}& 0\end{array}\right]$

$A_2=\left[\begin{array}{cc}0& \frac{1}{R_E+h}\\ -\frac{1}{R_N+h}& 0\\ 0& -\frac{\tan L}{R_E+h}\end{array}\right],A_3=\left[\begin{array}{cc}-{\mathrm{\ω}}_{ie}\sin L& 0\\ 0& 0\\ -{\mathrm{\ω}}_{ie}\cos L-\frac{v_E}{(R_E+h){\cos }^{2}L}& 0\end{array}\right]$

$A_4=\left[\begin{array}{ccccc}-C_{s1}^n(1,1)& -C_{s1}^n(1,2)& C_{s2}^n(1,1)& C_{s2}^n(1,2)& 0\\ -C_{s1}^n(2,1)& -C_{s1}^n(2,2)& C_{s2}^n(2,1)& C_{s2}^n(2,2)& 0\\ 0& 0& 0& 0& -1\end{array}\right],A_5=\left[\begin{array}{ccc}0& -f_D& f_E\\ f_D& 0& -f_N\end{array}\right]$

$A_6=\left[\begin{array}{cc}0& -2{\mathrm{\ω}}_{ie}\sin L-2\frac{v_E\tan L}{R_E+h}\\ \frac{v_E\tan L}{R_E+h}+2{\mathrm{\ω}}_{ie}\sin L& \frac{v_N\tan L}{R_N+h}\end{array}\right]$

$A_7=\left[\begin{array}{cc}-v_E(2{\mathrm{\ω}}_{ie}\cos L+\frac{v_E}{R_E{\cos }^{2}L})& 0\\ 2{\mathrm{\ω}}_{ie}{v}_N\cos L+\frac{v_N{v}_E}{R_E{\cos }^{2}L}& 0\end{array}\right]$

$A_8=\left[\begin{array}{cccc}{C}_{s1}^n(1,1)& C_{s1}^n(1,2)& -C_{s2}^n(1,1)& -C_{s2}^n(1,2)\\ C_{s1}^n(2,1)& C_{s1}^n(2,2)& -C_{s2}^n(2,1)& -C_{s2}^n(2,2)\end{array}\right],A_9=\left[\begin{array}{cc}\frac{1}{R_N+h}& 0\\ 0& \frac{\sec L}{R_E+h}\end{array}\right]$

$A_{10}=\left[\begin{array}{cc}0& 0\\ 0& \frac{v_E\tan L}{R_E\cos L}\end{array}\right]$

Wherein, v_EIt is carrier east orientation speed, v_NIt is carrier north orientation speed, ω_ieIt is rotational-angular velocity of the earth, R_NIt is meridian face curvature Radius, R_EIt is chordwise curvature radius, h is carrier height, f_N、f_E、f_DRespectively north orientation, east orientation, to than force value, The respective element of direction cosine matrix between the IMU coordinate systems and geographic coordinate system of inertial navigation 1,2 is represented respectively, and i represents capable, J represents row；

It is system noise, wherein, For the gyro of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 exports random noise,It is inertial navigation system Difference from the day corresponding with the IMU of inertial navigation system 2 of system 1 to the gyro output random noise of reference axis,For The table that adds of the horizontal axis corresponding with the IMU of inertial navigation system 2 of inertial navigation system 1 exports random noise；

It is system noise matrix, wherein, B₁=A₄,B₂=A₈；

Measurement equation is determined according to state quantity measurement in step 4, its method is as follows：

Measurement equation is：

Z (t)=Hx (t)+ν (t) (4)

Wherein, ν (t) is measurement noise,It is measurement matrix, I_2×2It is second order unit matrix.

3. a kind of pair of inertial navigation joint rotation modulation according to claim 1 navigates and online relative performance appraisal procedure, its It is characterised by：Rotation modulation also includes being modulated around the dual-axis rotation of azimuth axis and trunnion axis, now increases the day of inertial navigation system 1,2 To the inclined ε of gyro zero_z1、ε_z2, and inertial navigation system 1,2 day to plus the inclined ▽ of table zero_z1、▽_z2, as association system state, joint system System state is

$\begin{array}{c}s=\[\begin{array}{cccccc}({\mathrm{\φ}}_{N1}-{\mathrm{\φ}}_{N2})& ({\mathrm{\φ}}_{E1}-{\mathrm{\φ}}_{E2})& ({\mathrm{\φ}}_{D1}-{\mathrm{\φ}}_{D2})& ({\mathrm{\δv}}_{N1}-{\mathrm{\δv}}_{N2})& ({\mathrm{\δv}}_{E1}-{\mathrm{\δv}}_{E2})& ({\mathrm{\δL}}_1-{\mathrm{\δL}}_2)\end{array}\\ \begin{array}{ccccccccccccc}({\mathrm{\δ\λ}}_1-{\mathrm{\δ\λ}}_2)& {\mathrm{\ϵ}}_{x1}& {\mathrm{\ϵ}}_{y1}& {\mathrm{\ϵ}}_{z1}& {\mathrm{\ϵ}}_{x2}& {\mathrm{\ϵ}}_{y2}& {\mathrm{\ϵ}}_{z2}& {\▿}_{x1}& {\▿}_{y1}& {\▿}_{z1}& {\▿}_{x2}& {\▿}_{y2}& {\▿}_{z2}\end{array}{\]}^T\end{array}---\left(5\right)$

Corresponding state equation and measurement equation are built according to association system state, and to gyro, plus table zero be biased capable estimation, root According to gyro, add the inclined estimate of table zero, online evaluation is carried out to systematic function.

4. a kind of pair of inertial navigation joint rotation modulation according to any one of claim 1 to 3 navigates and online relative performance Appraisal procedure, it is characterised in that：The method can be applied to the assessment of relative performance two-by-two between the inertial navigation of many sets.