CN103234512B - Triaxial air bearing table high-precision attitude angle and angular velocity measuring device - Google Patents

Abstract

The invention discloses a triaxial air bearing table high-precision attitude angle and angular velocity measuring device. According to the invention, an intelligent measuring head, a gyroscope, and a four-side prism are arranged on an instrument platform of the triaxial air bearing table. A laser tracker is arranged below the triaxial air bearing table. Two photoelectric autocollimators are orthogonally arranged below the triaxial air bearing table. During large-angle movement, data of the gyroscopes and the laser tracker are subjected to Kalman filtering fusion, such that angle and angular velocity information of the air bearing table is obtained. During small-angle movement, data of the two photoelectric autocollimators are directly combined, such that angle and angular velocity information of the air bearing table can be obtained. With the device provided by the invention, non-contact, high-precision, and dynamic measuring of the attitude angle and angular velocity of the triaxial air bearing table can be realized. The device is also suitable for attitude angle measuring of a uniaxial air bearing table.

Description

Three-axis air-bearing table table high-precision attitude angle and angular velocity measurement device

Technical field

The present invention relates to measuring technique, is exactly a kind of three-axis air-bearing table table high-precision attitude angle and angular velocity measurement device specifically.

Background technology

The air film that three-axis air-bearing table relies on pressurized air to be formed between air-bearing and bearing seat, simulation stage body is floated, thus realize approximate friction free relative motion condition, with the spacecrafts such as the analog satellite mechanical environment that disturbance torque is very little suffered by outer space.As spacecraft motion simulator, three-axis air-bearing table carries out the performance of Physical Simulation for Satellite Control Systems experimental check system, is the important means in spacecraft development process and method.

Three-axis air-bearing table needs the attitude information such as angle, angular velocity dynamically being provided air floating table by attitude measurement system in process of the test, to complete Control loop, due to the special construction of three-axis air-bearing table, the device (as rotary transformer, inductosyn, photoelectric code disk, grating etc.) in the past measured for turntable is not suitable for the measurement of three-axis air-bearing table, needs to consider new measuring method and device.And in current practical application, the height of attitude measurement system precision is directly connected to the effect of l-G simulation test.

Find through searching document, Chinese invention patent application number: 200610010260.2, patent name is attitude angle of three-axis air-bearing table device and measuring method thereof, this patent is provided with ccd video camera above three-axis air-bearing table, air floating table table top is provided with and measures LED light mark system, theory on computer vision is utilized to combine the range information measuring cursor point part, calculate the relative movement parameters of air floating table table top relative to video camera, but due to the defect on system constructing, measuring accuracy is restricted, thus affects its actual usable range.

Chinese invention patent application number: 200410009086.7, patent name is: rigid space pose measuring apparatus and measuring method thereof, this patent adopts stay-supported scrambler to realize a kind of measurement of rigid space position and attitude of contact, but because three-axis air-bearing table can not allow external touch metering system, because contact brings interference to air floating table, therefore the method is not suitable for the attitude information measurement of three-axis air-bearing table.

(aerospace journal is published at document " three-axis air-bearing table single frame servo angle measurement systematic research ", 1996,17th volume, 4th phase, the page number: 71-74) in, Zhang Xiaoyou, Liu Dun of Harbin Institute of Technology and the Li Jisu etc. of Beijing Control Engineering Inst. propose a kind of single frame servo measurement scheme, this system installs an arc arms that can rotate around air floating table center pedal line on air floating table base, and transportable balladeur train is installed, by the attitude information of the rotation of responsive arc arms and the traverse measurement air floating table of balladeur train thereon.When this system needs to increase complicated mechanical system and sensor system, mechanism is complicated, and engineer applied is more difficult, and its precision is subject to the restriction of mechanical hook-up and sensor, is difficult to reach high precision.

Summary of the invention

The object of the present invention is to provide a kind of three-axis air-bearing table high-precision attitude angle, method for measuring angular velocity and device thereof.

The object of the present invention is achieved like this:

A kind of three-axis air-bearing table table high-precision attitude angle and angular velocity measurement device, comprise laser tracker, intelligence gauge head, gyroscope, two photoelectric auto-collimators, kaleidoscope prism and data processor, under laser tracker is installed on the platform of three-axis air-bearing table, intelligence gauge head is fixed on the platform of three-axis air-bearing table, intelligence gauge head has target positioning system, laser tracker coordinates intelligent gauge head to follow the tracks of and determines the three-dimensional distance of the three-dimensional perspective that intelligent gauge head rotates and movement, gyroscope and kaleidoscope prism are fixed on the platform of three-axis air-bearing table, two photoelectric auto-collimators are orthogonal be positioned over three-axis air-bearing table platform under, and the optical axis of these two photoelectric auto-collimators aims at the adjacent normal surface of two of kaleidoscope prism respectively, data processor receives laser tracker, the angle of gyroscope and two photoelectric auto-collimators and angular velocity data row relax of going forward side by side exports the attitude angle of air floating table and angular velocity information, when three-axis air-bearing table is ± 55 ° of polarizers of big angle scope motions, the data acquisition Kalman filtering fusion method of gyroscope and laser tracker obtains attitude angle and the angular velocity information of three-axis air-bearing table, directly combine according to the data of two photoelectric auto-collimators the attitude angle and angular velocity information that obtain three-axis air-bearing table when three-axis air-bearing table is ± 0.1 ° of small angle range motion.

The present invention also has following feature:

1, when three-axis air-bearing table is ± 55 ° of polarizers of big angle scope motions, the data acquisition Kalman filtering fusion method of gyroscope and laser tracker obtains attitude angle and the angular velocity information of three-axis air-bearing table as above, and its method step is as follows:

Step one: adopt deviation hypercomplex number and gyroscopic drift composition six-vector, as the irredundant expression of filter state, the measurement equation of wave filter is obtained by the output of laser tracker, and system state equation is as follows:

$\left\{\begin{array}{c}\stackrel{\·}{X}\left(t\right)=F\left(t\right)X\left(t\right)+\mathrm{GW}\left(t\right)\\ Z\left(t\right)=H\left(t\right)X\left(t\right)+D\left(t\right)V\left(t\right)\end{array}\right.---\left(1\right)$

Obtain after discretize:

$\left\{\begin{array}{c}{X}_k={\mathrm{\Φ}}_{k,k-1}{X}_{k-1}+{\mathrm{\Γ}}_{k-1}{W}_{k-1}\\ Z_k=H_k{X}_k+D_k{V}_k\end{array}\right.---\left(2\right)$

Wherein:

${\mathrm{\Φ}}_{k,k-1}=I_{6\×6}+F\·T+\frac{T^2}{2}{F}^2,$

${\mathrm{\Γ}}_{k,k-1}=(I_{6\×6}\·T+\frac{T^2}{2}F+\frac{T^3}{6}{F}^2)G,$

$H_k=\left[I_{3\×3}{0}_{3\×3}\right],D_k=C_{\mathrm{bs}}^l---\left(3\right)$

Wherein, X represents selected state vector, F (t) represents system matrix, and G (t) represents system noise matrix, and W (t) represents system noise, Z (t) represents that wave filter measures input, D (t) represents measurement noise matrix, and V (t) represents measurement noise, Φ and Γ is system matrix after discretize and system noise matrix, T is sampling time interval for measuring the transition matrix being tied to body series;

Step 2: filtering process

First state updating is carried out according to following formula:

$\left[\begin{array}{c}{\hat{Q}}_{e,k/k-1}\\ \mathrm{\Δ}{\hat{b}}_{k/k-1}\end{array}\right]={\mathrm{\Φ}}_{k,k-1}\left[\begin{array}{c}{\hat{Q}}_{e,k-1}\\ \mathrm{\Δ}{\hat{b}}_{k-1}\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{\hat{Q}}_{e,k}\\ \mathrm{\Δ}{\hat{b}}_k\end{array}\right]=\left[\begin{array}{c}{\hat{Q}}_{e,k/k-1}\\ \mathrm{\Δ}{\hat{b}}_{k/k-1}\end{array}\right]+K_k[Q_{\mathrm{el}}-{\hat{Q}}_{e,k/k-1}]---\left(6\right)$

${\hat{b}}_k^{+}={\hat{b}}_k^{-}+\mathrm{\Δ}{\hat{b}}_k---\left(8\right)$

Then, filtering renewal is carried out according to following formula:

$P_{k/k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+{\mathrm{\Γ}}_{k-1}{Q}_{k-1}{\mathrm{\Γ}}_{k-1}^T---\left(9\right)$

$R_k=C_{\mathrm{bs}}^l\·N_{g,k}^l\·{(C_{\mathrm{bs}}^l\·N_{g,k}^l)}^T---\left(10\right)$

$K_k=P_{k/k-1}{H}_k^T{(H_k{P}_{k/k-1}{H}_k^T+R_k)}^{-1}---\left(11\right)$

P _k＝(1-K _kH _k)P _k/k-1(12)

$Q_k=W_k{W}_k^T---\left(13\right)$

Wherein, q _elrepresent deviation hypercomplex number, q _lrepresent hypercomplex number observed reading, represent hypercomplex number estimated value, Q _erepresent the vector portion of deviation hypercomplex number, b represents gyroscopic drift, represent that laser tracker measures the vector portion being tied to the error in measurement of body series, P represents filter error covariance matrix, and K represents filter gain matrix, and Q is system noise variance matrix, and R is measuring noise square difference battle array.

2, as above when three-axis air-bearing table directly combines according to the data of two photoelectric auto-collimators the attitude angle and angular velocity information that obtain three-axis air-bearing table with during ± 0.1 ° of small angle range motion, method is: two orthogonal placements of photoelectric auto-collimator, every platform photoelectric auto-collimator obtains bidimensional measurement data, the measurement data that first photoelectric auto-collimator obtains is (a1, b1), and the measurement data that the second photoelectric auto-collimator obtains is (a2, b2), according to the position relationship of two photoelectric auto-collimators, b1 and a2 is corresponding, so final measurement data should be (a1, b1, b2), the measurement of angular velocity adopts the mode of angular difference to obtain, wherein a1 is the angle of the one dimension optical axis deflection of the first photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is a1, and b1 is the angle of another dimension optical axis deflection of the first photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is b1, a2 is the angle of the one dimension optical axis deflection of the second photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is a2, and b2 is the angle of another dimension optical axis deflection of the second photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is b2.

The invention provides a kind of can attitude angle, the angular velocity information of kinetic measurement three-axis air-bearing table, and interference can not be produced to three-axis air-bearing table, measuring equipment is installed simple, can realize three-axis air-bearing table attitude angle, contactless, the high precision of angular velocity, kinetic measurement.The present invention is also for the accurate measurement of single axle table attitude angle, angular velocity.

Accompanying drawing explanation

Fig. 1 is three-axis air-bearing table attitude angle, angular velocity measurement system composition schematic diagram;

Fig. 2 is photoelectric auto-collimator and kaleidoscope prism position view;

Embodiment

Below in conjunction with accompanying drawing citing, the invention will be further described.

Embodiment 1: composition graphs 1, the present invention's 1. 1 kinds of three-axis air-bearing table table high-precision attitude angle and angular velocity measurement device, comprise laser tracker 1, intelligence gauge head 2, gyroscope 3, two photoelectric auto-collimators 4, kaleidoscope prism 5 and data processor 6, under laser tracker 1 is installed on the platform of three-axis air-bearing table, intelligence gauge head 2 is fixed on the platform of three-axis air-bearing table, intelligence gauge head 2 has target positioning system, laser tracker 1 coordinates intelligent gauge head 2 to follow the tracks of and determine that intelligent gauge head 2 the rotates three-dimensional perspective of (usually together with will recording object and being fixed on) and the three-dimensional distance of movement, gyroscope 3 and kaleidoscope prism 4 are fixed on the platform of three-axis air-bearing table, two photoelectric auto-collimators 4 are orthogonal be positioned over three-axis air-bearing table platform under, and the optical axis of these two photoelectric auto-collimators 4 aims at the adjacent normal surface of two of kaleidoscope prism respectively, data processor 6 receives laser tracker 1, the angle of gyroscope 3 and two photoelectric auto-collimators 4 and angular velocity data row relax of going forward side by side exports the attitude angle of air floating table and angular velocity information, when three-axis air-bearing table is to obtain attitude angle and the angular velocity information of three-axis air-bearing table by Kalman filtering fusion method by the data of gyroscope 3 and laser tracker 1 during the motion of ± 55 ° of polarizers of big angle scope, when three-axis air-bearing table directly combines according to the data of two photoelectric auto-collimators 4 the attitude angle and angular velocity information that obtain three-axis air-bearing table with during ± 0.1 ° of small angle range motion.

A kind of three-axis air-bearing table high-precision attitude angle measuring method, concrete steps are as follows:

Step one: open device power supply (DPS), carries out next step after each equipment preheating completes;

Step 2: during polarizers of big angle scope motion, the data of gyroscope and laser tracker merge the angle and the angular velocity information that obtain air floating table by Kalman filtering;

Step 3: the angle and the angular velocity information that obtain air floating table during small angle range motion by the data fusion of two photoelectric auto-collimators.

In addition, the present invention utilizes gyro, laser tracker and photoelectric auto-collimator to combine and realizes the attitude angle of three-axis air-bearing table and the measurement of angular velocity.During use, laser tracking head is arranged on the support under air floating table, intelligence gauge head is arranged on air floating table platform and moves together with stage body, the visual field demand between laser tracker optical axis and intelligent gauge head target ball will be ensured during installation, to ensure that test macro does not lose measurement degree of freedom in the course of the work, laser tracker calculates the attitude information of intelligent gauge head relative to follower head in real time according to measurement data, these data by network cable transmission to data processor.

Photoelectric auto-collimator can select corresponding product according to the actual requirements, the ELCOMAT3000 type photoelectric auto-collimator that such as German Muler company produces, measuring accuracy can reach 0.1 "; every platform photoelectric auto-collimator can measure the attitude angle change of two axis (horizontal direction and vertical direction); the measurement of (± 1000 " scope is interior) three-dimension altitude angle just can realize the Three Degree Of Freedom low-angle of platform with two photoelectric auto instrument under, and measuring accuracy is better than 1 ".

Kaleidoscope prism used on platform need to be arranged on platform near outer to ensure visual field.In experimentation, prism moves together with the platform of air floating table, two autocollimators are installed out of office on mounting base, its optical axis aims at the orthogonal reflecting surface of two of this prism respectively, every platform autocollimator can measure the bidimensional attitude information of prism, just can provide the Three Degree Of Freedom attitude angle of platform according to the measurement data of two photoelectric auto instrument.

The measurement of angular velocity is realized by high accuracy gyroscope, because the drift of gyro can not be ignored, when reality uses, adopts the attitude information of laser tracker and the attitude information of photoelectric auto-collimator regularly to revise the output of gyro.The control system of air floating table can complete speed closed loop by gyro, positional information after the output integration of gyro, consider the drift of gyro, can be revised by laser tracker for a long time, after the measurement range entering autocollimator, directly carry out closed-loop control by the output of autocollimator.

Embodiment 2:

Composition graphs 2, the present invention utilizes the installation relation of two photoelectric auto-collimators and prism to do following explanation:

Prism used should be arranged on platform near outer to ensure visual field.In experimentation, prism moves together with the platform of air floating table, the optical axis relation of being orthogonal of two autocollimators is installed out of office on pedestal, its light pipe aims at the orthogonal reflecting surface of two of this prism respectively, every platform autocollimator can measure the bidimensional attitude information of prism, just can provide the Three Degree Of Freedom attitude angle of platform according to the measurement data of two photoelectric auto instrument.

In addition, the concrete numerical value of above-mentioned mentioned " low-angle " range of movement (its representative value usually get ± 0.1 °) can be determined according to the model of concrete photoelectric auto-collimator, if what select is the ELCOMAT3000 type photoelectric auto-collimator that German Muler company produces, due to the useful range of this equipment be ± 1000 ", such small-angle movement just refer to range of movement be ± 1000 ", and photoelectric auto-collimator only has just has data when prism can return effective image, when therefore installing, photoelectric auto-collimator should be arranged on the final alignment district of specific tasks, stable region is entered like this by large closed-loop control air floating table, prism also enters the workspace of photoelectric auto-collimator just.

Embodiment 3:

The present invention utilize the Kalman filtering of laser tracker and gyro merge obtain wide-angle run time attitude information, concrete steps are as follows:

Step one: adopt deviation hypercomplex number and gyroscopic drift composition six-vector, as the irredundant expression of filter state, the measurement equation of wave filter can be obtained by the output of laser tracker.If system state equation is as follows:

$\left\{\begin{array}{c}\stackrel{\·}{X}\left(t\right)=F\left(t\right)X\left(t\right)+\mathrm{GW}\left(t\right)\\ Z\left(t\right)=H\left(t\right)X\left(t\right)+D\left(t\right)V\left(t\right)\end{array}\right.---\left(1\right)$

Obtain after discretize:

$\left\{\begin{array}{c}{X}_k={\mathrm{\Φ}}_{k,k-1}{X}_{k-1}+{\mathrm{\Γ}}_{k-1}{W}_{k-1}\\ Z_k=H_k{X}_k+D_k{V}_k\end{array}\right.---\left(2\right)$

Wherein:

${\mathrm{\Φ}}_{k,k-1}=I_{6\×6}+F\·T+\frac{T^2}{2}{F}^2,$

${\mathrm{\Γ}}_{k,k-1}=(I_{6\×6}\·T+\frac{T^2}{2}F+\frac{T^3}{6}{F}^2)G,$

$H_k=\left[I_{3\×3}{0}_{3\×3}\right],D_k=C_{\mathrm{bs}}^l---\left(3\right)$

Wherein, X represents selected state vector, F (t) represents system matrix, and G (t) represents system noise matrix, and W (t) represents system noise, Z (t) represents that wave filter measures input, D (t) represents measurement noise matrix, and V (t) represents measurement noise, Φ and Γ is system matrix after discretize and system noise matrix, T is sampling time interval for measuring the transition matrix being tied to body series.

Step 2: filtering process

First state updating is carried out according to following formula:

$\left[\begin{array}{c}{\hat{Q}}_{e,k/k-1}\\ \mathrm{\Δ}{\hat{b}}_{k/k-1}\end{array}\right]={\mathrm{\Φ}}_{k,k-1}\left[\begin{array}{c}{\hat{Q}}_{e,k-1}\\ \mathrm{\Δ}{\hat{b}}_{k-1}\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{\hat{Q}}_{e,k}\\ \mathrm{\Δ}{\hat{b}}_k\end{array}\right]=\left[\begin{array}{c}{\hat{Q}}_{e,k/k-1}\\ \mathrm{\Δ}{\hat{b}}_{k/k-1}\end{array}\right]+K_k[Q_{\mathrm{el}}-{\hat{Q}}_{e,k/k-1}]---\left(6\right)$

${\hat{b}}_k^{+}={\hat{b}}_k^{-}+\mathrm{\Δ}{\hat{b}}_k---\left(8\right)$

Then, filtering renewal is carried out according to following formula:

$P_{k/k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+{\mathrm{\Γ}}_{k-1}{Q}_{k-1}{\mathrm{\Γ}}_{k-1}^T---\left(9\right)$

$R_k=C_{\mathrm{bs}}^l\·N_{g,k}^l\·{(C_{\mathrm{bs}}^l\·N_{g,k}^l)}^T---\left(10\right)$

$K_k=P_{k/k-1}{H}_k^T{(H_k{P}_{k/k-1}{H}_k^T+R_k)}^{-1}---\left(11\right)$

P _k＝(1-K _kH _k)P _k/k-1(12)

$Q_k=W_k{W}_k^T---\left(13\right)$

Wherein, q _elrepresent deviation hypercomplex number, q _lrepresent hypercomplex number observed reading, represent hypercomplex number estimated value, Q _erepresent the vector portion of deviation hypercomplex number, b represents gyroscopic drift, represent that laser tracker measures the vector portion being tied to the error in measurement of body series, P represents filter error covariance matrix, and K represents filter gain matrix, and Q is system noise variance matrix, and R is measuring noise square difference battle array.

In addition, the representative value of the large moving range that the present invention mentions is ± 55 °, and the measurement range of laser tracker ripe at present all can meet the demands.

Embodiment 4:

The present invention utilize the data fusion of two photoelectric auto-collimators obtain small angle range run time attitude information, concrete grammar is as follows:

Two orthogonal placements of photoelectric auto-collimator, every platform photoelectric auto-collimator can obtain bidimensional measurement data, assuming that the measurement data that photoelectric auto-collimator I obtains is (a1, b1), and the measurement data that photoelectric auto-collimator II obtains is (a2, b2), according to the position relationship of two photoelectric auto-collimators, b1 and a2 is corresponding, so final measurement data should be (a1, b1, b2), the measurement of angular velocity adopts the mode of angular difference to obtain.Wherein a1 is the angle of the one dimension optical axis deflection of photoelectric auto-collimator I, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is a1, and b1 is the angle of another dimension optical axis deflection of photoelectric auto-collimator I, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is b1.A2 is the angle of the one dimension optical axis deflection of photoelectric auto-collimator II, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is a2, and b2 is the angle of another dimension optical axis deflection of photoelectric auto-collimator II, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is b2.

Claims (3)

1. a three-axis air-bearing table table high-precision attitude angle and angular velocity measurement device, comprise laser tracker (1), intelligence gauge head (2), gyroscope (3), two photoelectric auto-collimators (4), kaleidoscope prism (5) and data processor (6), it is characterized in that: under laser tracker (1) is installed on the platform of three-axis air-bearing table, intelligence gauge head (2) is fixed on the platform of three-axis air-bearing table, intelligence gauge head (2) has target positioning system, laser tracker (1) coordinates intelligent gauge head (2) to follow the tracks of and determines the three-dimensional distance of the three-dimensional perspective that intelligent gauge head (2) rotates and movement, gyroscope (3) and kaleidoscope prism (4) are fixed on the platform of three-axis air-bearing table, two photoelectric auto-collimators (4) are orthogonal be positioned over three-axis air-bearing table platform under, and the optical axis of these two photoelectric auto-collimators (4) aims at the adjacent normal surface of two of kaleidoscope prism respectively, data processor (6) receives laser tracker (1), the angle of gyroscope (3) and two photoelectric auto-collimators (4) and angular velocity data row relax of going forward side by side exports the attitude angle of air floating table and angular velocity information, obtain attitude angle and the angular velocity information of three-axis air-bearing table by the data acquisition Kalman filtering fusion method of gyroscope (3) and laser tracker (1) when three-axis air-bearing table is in the motion of ± 55 ° of polarizers of big angle scope, directly combine according to the data of two photoelectric auto-collimators (4) the attitude angle and angular velocity information that obtain three-axis air-bearing table when three-axis air-bearing table is ± 0.1 ° of small angle range motion.

2. a kind of three-axis air-bearing table table high-precision attitude angle according to claim 1 and angular velocity measurement device, it is characterized in that: described attitude angle and the angular velocity information obtaining three-axis air-bearing table when three-axis air-bearing table is ± 55 ° of polarizers of big angle scope motions by the data acquisition Kalman filtering fusion method of gyroscope (3) and laser tracker (1), its method step is as follows:

Step one: adopt deviation hypercomplex number and gyroscopic drift composition six-vector, as the irredundant expression of filter state, the measurement equation of wave filter is obtained by the output of laser tracker, and system state equation is as follows:

$\left\{\begin{array}{c}\stackrel{\·}{X}\left(t\right)=F\left(t\right)X\left(t\right)+G\left(t\right)W\left(t\right)\\ Z\left(t\right)=H\left(t\right)X\left(t\right)+D\left(t\right)V\left(t\right)\end{array}\right.---\left(1\right)$

Obtain after discretize:

$\left\{\begin{array}{c}{X}_k={\mathrm{\Φ}}_{k,k-1}{X}_{k-1}+{\mathrm{\Γ}}_{k-1}{W}_{k-1}\\ Z_k=H_k{X}_k+D_k{V}_k\end{array}\right.---\left(2\right)$

Wherein:

${\mathrm{\Φ}}_{k,k-1}=I_{6\×6}+F\·T+\frac{T^2}{2}{F}^2,$

${\mathrm{\Γ}}_{k,k-1}=(I_{6\×6}\·T+\frac{T^2}{2}F+\frac{T^3}{6}{F}^2)G,$

$H_k=\left[\begin{array}{cc}{I}_{3\×3}& 0_{3\×3}\end{array}\right],D_k=C_{\mathrm{bs}}^l---\left(3\right)$

Wherein, the state vector selected by X (t) represents, represent 1 order derivative of state vector X (t), I _{6 × 6}represent 6 × 6 dimension vector of unit length battle arrays, I _{3 × 3}represent 3 × 3 dimension vector of unit length battle arrays, 0 _{3 × 3}represent 3 × 3 dimension null vector battle arrays, H (t) represents observing matrix, F (t) represents system matrix, G (t) represents system noise matrix, W (t) represents system noise, Z (t) represents that wave filter measures input, D (t) represents measurement noise matrix, V (t) represents measurement noise, X, H, D, V, F, G, W is respectively X (t), H (t), D (t), V (t), F (t), G (t), vector after the discretize of W (t), Φ and Γ is system matrix after discretize and system noise matrix, T is sampling time interval, for measuring the transition matrix being tied to body series,

Step 2: filtering process

First state updating is carried out according to following formula:

$q_{\mathrm{el}}={\hat{q}}^{-1}\⊗q_l---\left(4\right)$

$\left[\begin{array}{c}{\hat{Q}}_{e,k/k-1}\\ {\mathrm{\Δ}\hat{b}}_{k/k-1}\end{array}\right]={\mathrm{\Φ}}_{k,k-1}\left[\begin{array}{c}{\hat{Q}}_{e,k-1}\\ \mathrm{\Δ}{\hat{b}}_{k-1}\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{\hat{Q}}_{e,k}\\ \mathrm{\Δ}{\hat{b}}_k\end{array}\right]=\left[\begin{array}{c}{\hat{Q}}_{e,k/k-1}\\ \mathrm{\Δ}{\hat{b}}_{k/k-1}\end{array}\right]+K_k{[Q}_{\mathrm{el}}-{\hat{Q}}_{e,k/k-1}]---\left(6\right)$

${\hat{q}}^{+}=q\⊗\{1-{\hat{Q}}_e\}---\left(7\right)$

${\hat{b}}_k^{+}={\hat{b}}_k^{-}+\mathrm{\Δ}{\hat{b}}_k---\left(8\right)$

Then, filtering renewal is carried out according to following formula:

$P_{k/k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+{\mathrm{\Γ}}_{k-1}{Q}_{k-1}{\mathrm{\Γ}}_{k-1}^T---\left(9\right)$

$R_k=C_{\mathrm{bs}}^l\·N_{g,k}^l\·{(C_{\mathrm{bs}}^l\·N_{g,k}^l)}^T---\left(10\right)$

$K_k=P_{k/k-1}{H}_k^T{(H_k{P}_{k/k-1}{H}_k^T+R_k)}^{-1}---\left(11\right)$

P _k＝(1-K _kH _k)P _k/k-1(12)

$Q_k=W_k{W}_k^T---\left(13\right)$

Wherein, q _elrepresent deviation hypercomplex number, q _lrepresent hypercomplex number observed reading, represent hypercomplex number estimated value, Q _erepresent the vector portion of deviation hypercomplex number, b represents gyroscopic drift, represent that laser tracker measures the vector portion being tied to the error in measurement of body series, P represents filter error covariance matrix, and K represents filter gain matrix, and Q is system noise variance matrix, and R is measuring noise square difference battle array, H _krepresent the observing matrix in k moment, W _krepresent the system noise in k moment, P _krepresent the filter error covariance matrix in k moment, R _krepresent the measuring noise square difference battle array in k moment, Q _krepresent the value of vector portion in the k moment of hypercomplex number, P _k/k-1represent that filter error covariance matrix utilizes the k-1 moment to the predicted value in k moment, represent the estimated value of the vector portion of deviation hypercomplex number.

3. a kind of three-axis air-bearing table table high-precision attitude angle according to claim 1 and angular velocity measurement device, it is characterized in that: described directly combines according to the data of two photoelectric auto-collimators (4) the attitude angle and angular velocity information that obtain three-axis air-bearing table when three-axis air-bearing table is ± 0.1 ° of small angle range motion, method is: two orthogonal placements of photoelectric auto-collimator, every platform photoelectric auto-collimator obtains bidimensional measurement data, the measurement data that first photoelectric auto-collimator obtains is (a1, b1), and the measurement data that the second photoelectric auto-collimator obtains is (a2, b2), according to the position relationship of two photoelectric auto-collimators, b1 and a2 is corresponding, so final measurement data should be (a1, b1, b2), the measurement of angular velocity adopts the mode of angular difference to obtain, wherein a1 is the angle of the one dimension optical axis deflection of the first photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is a1, and b1 is the angle of another dimension optical axis deflection of the first photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is b1, a2 is the angle of the one dimension optical axis deflection of the second photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is a2, and b2 is the angle of another dimension optical axis deflection of the second photoelectric auto-collimator, the angular deviation which represent prismatic reflection Mian Yugai road optical axis reference field is b2.