CN105698822B - Initial Alignment Method between autonomous type inertial navigation based on reversed Attitude Tracking is advanced - Google Patents
Initial Alignment Method between autonomous type inertial navigation based on reversed Attitude Tracking is advanced Download PDFInfo
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Abstract
Initial Alignment Method between a kind of autonomous type inertial navigation based on reversed Attitude Tracking is advanced, it includes the following steps：First, transition reference frame is established；2nd, during carrier movement, rough attitude matrix is calculated according to sensor subsystem sampled data；3rd, Nonlinear Tracking Differentiator processing odometer velocity differentials；4th, using the sensor subsystem sampled data of storage, reversed Attitude Tracking calculates initial alignment start time attitude matrix；5th, inertial navigation resolving is carried out using the sensor subsystem sampled data of storage, establishes Kalman filter and carry out fine alignment, obtain accurate attitude matrix and carrier positions information；The method of the invention, sensor sample data is taken full advantage of, under conditions of carrier initial position is just known that, you can realize that the running posture battle array that precisely aligns obtains and position navigation, carrier maneuverability is substantially increased, is Initial Alignment Method between effective traveling.
Description
One, the technical field
The invention provides an autonomous inertial navigation initial alignment method based on reverse attitude tracking, relates to an inertial navigation initial alignment method, and belongs to the technical field of inertial navigation initial alignment.
Second, background Art
The initial alignment between the inertial navigation travels refers to a technology for completing the initial alignment of an inertial navigation system during the movement of a carrier, and therefore, the initial alignment is one of the technologies for the initial alignment of a moving base. The inertial navigation marching initial alignment technology has immeasurable significance and effect on enhancing the mobility and the quick response capability of the carrier. Therefore, how to achieve initial alignment during carrier motion is a considerable issue to be studied.
Different from the traditional static base initial alignment environment, in the carrier motion state, the position, the speed, the acceleration and the angular velocity of the carrier are constantly changed, and the influence on the initial alignment is mainly embodied as follows: on one hand, the linear motion can change parameters such as ground acceleration, coriolis acceleration and the like in the inertial navigation basic equation at any moment, so that the accurate information of the gravity acceleration can not be measured by utilizing the output data of the accelerometer in the motion state; on the other hand, the vibration of the carrier under the motion condition causes the interference angular velocity to have a wide frequency band, the signal-to-noise ratio of the output signal of the gyroscope is low, and useful information of the alignment of the earth rotation angular velocity cannot be extracted from the output data of the gyroscope.
Therefore, under the condition of carrier motion, initial alignment cannot be carried out by only depending on direct measurement information of a gyroscope and an accelerometer, and distance measurement or speed measurement information needs to be introduced to compensate the influence of harmful acceleration on initial alignment precision in the motion process. At present, the inertial navigation inter-travel alignment method mainly includes a strapdown compass method, an inertial system alignment method, an optimal estimation alignment method, and the like. The strapdown compass method applies a mature classical control theory method to realize initial alignment between advances, has a simple principle but long alignment time and is sensitive to low-frequency interference of a gyroscope, and needs to select appropriate control parameters according to a motion environment. The inertial system alignment method takes an inertial space as a middle transition coordinate system to isolate the interference of angular motion of the carrier on initial alignment, but the method only simply processes measurement errors, so that the alignment accuracy is not high and the position information of the carrier cannot be acquired. The optimal estimation alignment method establishes an inertial navigation error equation, uses the speed measurement information of speed measurement sensors such as a speedometer and the like as measurement information to carry out Kalman (Kalman) filtering, and estimates key errors such as a platform misalignment angle and the like so as to realize initial alignment between advances. The method is mostly based on an inertial navigation linearization error model, and can be carried out only by acquiring a rough initial attitude matrix under a static condition, so that the mobility advantage of the carrier is weakened to a certain extent.
It can be seen that each of the methods has its features and applicability. In order to obtain a rough attitude matrix in the motion process and realize high-precision attitude alignment and position navigation, the invention provides an autonomous inertial navigation inter-travel alignment method based on reverse attitude tracking by taking odometer speed sampling data as alignment auxiliary information. The method can realize the high-precision initial alignment between the inertial navigation travels under the condition of only knowing the initial position.
Third, the invention
Aiming at the problems in the prior art, the invention provides an autonomous inertial navigation inter-marching initial alignment method based on reverse attitude tracking. Firstly, in the carrier movement process, the speed measurement information of the odometer is used as assistance to carry out coarse alignment to obtain a coarse attitude matrix, and meanwhile, the sampling data of the inertia measurement element (comprising a gyroscope and an accelerometer) and the odometer are stored. And then carrying out reverse attitude tracking to obtain an attitude matrix at the initial alignment starting moment. And finally, on the basis, Kalman filtering fine alignment is carried out by utilizing the stored inertial measurement element sampling data and the odometer speed sampling data. And finally, high-precision attitude alignment and position navigation are realized.
The invention provides an autonomous inertial navigation inter-traveling initial alignment method based on reverse attitude tracking, which is used for a vehicle-mounted inertial navigation system. The relationship between them is: the sampling data of the sensor subsystem are respectively transmitted to the data storage module and the rough alignment calculation module; the rough alignment calculation module calculates a rough initial attitude matrix and transmits the rough initial attitude matrix to the reverse attitude tracking calculation module; the reverse attitude tracking calculation module carries out reverse attitude tracking by utilizing the sensor data of the data storage module and transmits the calculation result to the fine alignment calculation module. And the fine alignment calculation module performs fine alignment calculation by using the data of the data storage module to obtain a fine alignment attitude matrix and a position navigation result.
The invention provides an autonomous inertial navigation inter-traveling initial alignment method based on reverse attitude tracking, which specifically comprises the following steps:
the method comprises the following steps: establishing a transition reference coordinate system;
four important transitional reference coordinate systems established by the whole alignment algorithm are an initial moment inertial coordinate system (i)0System), global coordinate system at initial time (e)0System), initial time navigation coordinate system (n)0System) and initial time carrier coordinate system (i)b0System), which is defined as follows:
(1) initial moment inertial frame (i)0Series)
At the beginning of the initial alignment, OXi0In the local meridian plane, parallel to the equatorial plane; OZi0Pointing to the direction of the earth rotation axis; OYi0And OXi0And OZi0Forming a right-handed spiral coordinate system; after the initial alignment starts, i0The system three axes are invariant with respect to the inertial space;
(2) global coordinate system of initial time (e)0Series)
The earth coordinate system at the initial moment takes the earth center as the origin of the coordinate system, OXe0Pointing in the local meridian direction in the equatorial plane; OZi0Pointing to the direction of the earth rotation axis; OYi0And OXi0And OZi0Forming a right-handed spiral coordinate system; the coordinate system is stationary relative to the earth's surface;
(3) initial time navigation coordinate system (n)0Series)
Taking an east-north-sky navigation coordinate system of the initial alignment starting time as an initial time navigation coordinate system; after the initial alignment begins, the coordinate system is stationary relative to the earth's surface;
(4) initial time carrier coordinate system (i)b0Series)
Taking a right-front-upper carrier coordinate system of the initial alignment starting moment as an initial moment carrier coordinate system; after the initial alignment begins, the coordinate system is stationary relative to the inertial space;
step two: in the motion process of the carrier, calculating a rough attitude matrix according to the sampling data of the sensor subsystem;
with i0Is a transitional reference coordinate system, a navigation coordinate system (n system) is relative to a carrier coordinate system (b system) in terms of an attitude matrixThe calculation is divided into two parts, and the calculation process is shown as the formula (1)
Wherein,n is relative to i0A transformation matrix of the system;is i0Is a transformation matrix relative to b;
a calculation matrix
By a transitional reference coordinate system n0System e0The calculation process of the matrix can be divided into four parts, namely:
in the formula,a transformation matrix for n with respect to a geographic coordinate system (e system);is e is relative to n0A transformation matrix of the system;
is n0Is relative to e0A transformation matrix of the system;is e0Is relative to i0A transformation matrix of the system;
since the carrier position cannot be accurately obtained in the coarse alignment module, equation (2) is approximated as:
wherein,
in the formula, L0The geographic latitude at the beginning of the initial alignment; omegaieThe rotational angular velocity of the earth; Δ t is the current time t and the initial alignment start time tstartA time difference of (a), i.e. t-tstart(ii) a When formula (4-5) is substituted into formula (3), it is possible to obtain:
b calculating matrix
With ib0Is a transitional reference coordinate system, i0Is relative to the transformation matrix of the b systemThe calculation of (a) is divided into two parts, namely:
wherein,is i0Is relative to ib0A transformation matrix of the system;is ib0Is a transformation matrix relative to b;
the matrix can be directly obtained by the attitude matrix differential equation (8) by utilizing the measured angular velocity of the gyroscope
In the formula, due to ib0Is a reaction of with i0The system is stationary with respect to the inertial frame (i system), so that the angular velocity of the inertial measurement unit can be used to sample the dataDirect substitutionIn addition, at the initial alignment start time, ib0Is coincident with b, so that the matrixThe integral calculation initial value is a unit matrix I3×3；
Matrix arrayThe calculation of the method needs to use the slow drift property of the earth gravity acceleration in an inertial system; the calculation method is as follows:
ib0a series of and i0The systems are stationary with respect to the inertial space and thus, it is easy to know the matrixIs a constant value matrix; for carrier velocityThe derivation on both sides can be obtained:
wherein,is the component of the carrier acceleration in the n system;is the component of the carrier acceleration in the b system;
substituting the inertial navigation basic equation into the inertial navigation basic equation, wherein the inertial navigation basic equation can be rewritten into a form shown in a formula (10);
wherein, gnIs the component of the earth gravity acceleration in the n system;is the component of the rotational angular velocity of the earth in the n system;is the angular velocity of rotation of n relative to i; f. ofnSampling the component of the data in the n system for the specific force of the inertia measuring element;
differential equation of known attitude matrixWhereinB is a rotational angular velocity relative to n. Substituting this into (10) yields:
in the formula,negligible, the above formula is further rewritten as formula (12);
wherein, gbIs the component of the earth gravity acceleration in the b system; f. ofbSampling data for the specific force of the inertial measurement unit; v. ofbData sampling with odometer speedConstructed velocity measurement vectorReplacing; whileVector differentiation with odometer speed measurementReplacing; it should be noted that, since the odometer speed sampling data contains noise and direct differentiation amplifies the noise to cause a decrease in alignment accuracy, it is necessary to use a tracking differentiator pairDifferential processing to obtain a signal with less noise interference
To obtain a matrixNeed to pass throughgbAnd gn(ii) an important relation (13);
wherein the component g of the acceleration of the earth's gravity under bn＝[0 0 -g]TIs a known amount; matrix arrayAll can be derived from previous calculations, hence the matrixThe solution of (2) is only needed to construct three vectors which are not in the same plane according to the formula (13);
in order to construct a vector and weaken noise at the same time, the two sides of equation (13) are integrated to obtain:
in the formula,
obtaining a transformation matrixIt is necessary to pass through gbAnd gnSignificant relation between
Wherein,all can be obtained by the previous calculation; integrating the two sides of the above formula to obtain
Take two moments t1And t2Integral value ofAndthenCan be calculated by formula (17);
up to this point, during the movement of the carrier, the initial alignment end time t can be calculated by using equations (6), (8) and (17)endCoarse attitude matrix ofHowever, the accuracy of the attitude matrix is not high, and the position of the carrier cannot be acquired at the moment, so that the sampling data of the sensor needs to be stored for further processing;
step three: the tracking differentiator processes the speedometer differentiation;
order toThere is the following non-linear tracking differentiator
wherein r is a tracking differentiator parameter, v (t) is a signal to be tracked containing noise, and the signal is odometer speed sampling data;
therefore, the speedometer differential of the milemeter with smaller pollution degree of the interfered noise can be obtained;
step four: utilizing the stored sampling data of the sensor subsystem to perform reverse attitude tracking calculation on an attitude matrix at the initial alignment starting moment;
the inverse attitude tracking algorithm is to obtain the attitude matrix by coarse alignmentReversely calculating to the initial alignment starting moment to obtain an attitude matrixTo lay the foundation for subsequent fine alignment and position determination;
the carrier attitude is represented by a quaternion q, and the calculation of the attitude can be obtained by a quaternion differential equation (20);
wherein,
in the formula,is the component of the angular velocity of b in b relative to n;is the component of the rotational angular velocity of the earth in the n system;is the component of the angular velocity of n relative to the earth coordinate system (e system) in n system;
in the forward solution of the attitude, the attitude quaternion q (k) at the last moment k and the gyroscope sampling data at the moment k +1 are utilizedSolving an attitude quaternion q (k +1) at the moment of k + 1; the calculation process adopts a Picard solution method; the Picard solution is a common method for solving attitude quaternion by using angle increment, and the three-order approximate calculation formula is as follows:
in the formula, TsAn attitude update period;
Δθ(k+1)＝||Δθ(k+1)|| (25)
in the backward attitude tracking calculation, the attitude quaternion q (k +1) at the moment k +1 and the inertial measurement element angular velocity sampling data at the moment k are knownSolving an attitude quaternion q (k) at the moment k; therefore, formula (23) is rewritten to formula (26);
wherein,
considering that after coarse alignment the position information of the carrier is not known, thereforeIs approximately taken asMeanwhile, in order to improve the calculation precision of delta theta (k), the speed sampling data of the odometer is used for calculationThe calculation process is as follows:
wherein,
to this end, the attitude matrix can be expressed by equations (26), (27) and (28)Tracking back to the initial alignment start time to obtainThereby laying a foundation for the next fine alignment;
step five: carrying out inertial navigation resolving by using the stored sampling data of the sensor subsystem, establishing a Kalman filter for fine alignment, and acquiring accurate attitude matrix and carrier position information;
a. inertial navigation solution and odometer position estimation
At the latitude L of the initial alignment start time0Longitude λ, longitude0Height h0And reverse attitude tracking resultsIn order to solve the initial value, the stored sensor sampling data is used for carrying out attitude, speed and position calculation to obtain an inertial navigation calculation position p ═ L lambda h at each sampling point]TInertial navigation resolving speedInertial navigation resolving attitude matrixAnd the estimated position p of the odometerD＝[LDλDhD]TAnd estimate the speed
b. Constructing a model of the filtering state
Taking the n system as a reference coordinate system of inertial navigation, the filtering state model is as follows:
in the formula,is the inertial navigation platform misalignment angle; delta vnInertial navigation speed error; deltapInertial navigation position error; epsilon is the null shift of the inertial navigation gyroscope;is an inertia guideZero offset of the aeronautical accelerometer; δ pDCalculating a position error for the odometer; delta KDScale factor error for odometer; known equatorial radius R of the eartheMatrix M1To M6Respectively as follows:
M2＝M′+M″ (32)
M4＝(vn×)·(2M′+M″) (34)
filter state model is abbreviated as
Wherein, the system state transition matrix F belongs to R19×19The matrix is specifically shown as a formula (38); g is a system noise transfer array; w is system noise;
c. building a metrology model
Calculating the inertial navigation calculated position p and the odometer calculated position pDThe difference is used as a measurement vector Z, and the error of the calculated position caused by the noise measured by the odometer is established as the measurement noise of the measurement model;
Z＝p-pD＝δp-δpD+V＝H·X+V (39)
wherein H is a measurement transfer matrix, and H is [0 ]3×6I3×303×6-I3×303×1](ii) a V is position measurement noise; the measurement vector Z is [ L-L ═ LDλ-λDh-hD]T；
Finally, the inertial navigation attitude matrix which is estimated by the filter and is corrected and solved by the inertial navigation errorObtaining an accurate inertial navigation attitude matrixMeanwhile, the accurate calculated position p of the odometer can be obtainedD(ii) a And the accurate attitude alignment and position navigation of inertial navigation are realized.
In step two, the sensor subsystem comprises an inertial measurement element and an odometer. The inertial measurement element measures the angular velocity and specific force of the carrier relative to an inertial space to obtain angular velocity and specific force sampling data; the odometer measures the speed of the carrier to obtain carrier speed sampling data.
Through the steps, the autonomous inertial navigation inter-travelling initial alignment method based on the reverse attitude tracking fully utilizes the sampling data of the sensor, can realize accurate alignment attitude array acquisition and position navigation during travelling under the condition of only knowing the initial position of the carrier, greatly improves the mobility of the carrier, and is an effective inter-travelling initial alignment method.
The invention has the advantages that:
(1) the invention provides an autonomous inertial navigation inter-advancing initial alignment method based on reverse attitude tracking, which organically combines coarse alignment and fine alignment through the reverse attitude tracking, fully utilizes sampling data of a sensor subsystem, and can realize acquisition of an accurate alignment attitude matrix and position navigation;
(2) the invention provides an autonomous inertial navigation inter-marching initial alignment method based on reverse attitude tracking, which utilizes Kalman filtering fine alignment to optimally estimate inertial measurement element errors (accelerometer zero offset and gyroscope zero drift) and odometer scale factor errors and can provide compensation parameters for subsequent navigation calculation;
(3) the invention provides an autonomous inertial navigation inter-marching initial alignment method based on reverse attitude tracking, which can realize attitude alignment and position navigation under the condition of only knowing the position of the initial alignment starting moment of a carrier, greatly improves the maneuvering performance of the carrier and has good application prospect;
description of the drawings
Fig. 1 is a schematic structural diagram of the autonomous inertial navigation inter-traveling initial alignment method based on reverse attitude tracking according to the present invention.
FIG. 2 is a block diagram of the process of the present invention.
The numbers, symbols and codes in the figures are explained as follows:
1-sensor subsystem 2-data storage module 3-coarse alignment calculation module
4-reverse attitude tracking calculation module and 5-fine alignment calculation module
101-inertial measurement unit 102-odometer
201-data storage Unit
301-coarse alignment calculation Unit
401-backward attitude tracking calculation unit
501-inertial navigation resolving unit 502-odometer position calculation unit 503-Kalman filtering unit
-angular velocity fbSpecific force-vehicle speed measured by odometer
-attitude matrix determined by the coarse alignment calculation module
-attitude matrix determined by the inverse attitude tracking calculation module
p-inertial navigation solution position pD-odometer reckoning position-fine alignment determined alignment attitude matrix
Fifth, detailed description of the invention
The present invention will be described in further detail below with reference to the accompanying drawings.
The invention provides an autonomous inertial navigation inter-marching initial alignment method based on reverse attitude tracking. Firstly, in the carrier movement process, coarse alignment is carried out by using speed measurement information of a speedometer as assistance to obtain a coarse gestureState matrixWhile preserving the inertial measurement unit and odometer sample data. Then, the attitude matrix of the initial alignment starting moment is obtained by carrying out reverse attitude trackingAnd finally, on the basis, Kalman filtering fine alignment is carried out by utilizing the stored inertial measurement element sampling data and the odometer speed sampling data. Finally, acquiring a high-precision alignment attitude matrixAnd the carrier position navigation is realized.
Referring to fig. 1, the invention provides an autonomous inertial navigation inter-traveling initial alignment method based on reverse attitude tracking, which comprises a sensor subsystem 1, a data storage module 2, a coarse alignment calculation module 3, a reverse attitude tracking calculation module 4 and a fine alignment calculation module 5.
Sampled data for sensor subsystem systemRespectively transmitted to the data storage module 2 and the coarse alignment calculation module 3; the rough alignment calculation module 3 calculates a rough initial attitude matrixAnd transmits it to the backward attitude tracking calculation module 4; the backward attitude tracking calculation module 4 performs backward attitude tracking by using the sensor data of the data storage module 2, and calculates the calculation resultTo the fine alignment calculation module 5. The fine alignment calculation module 5 performs fine alignment calculation by using the data of the data storage module 2 to obtain a fine alignment attitude matrixAnd a position navigation result.
Referring to fig. 2, the invention provides an autonomous inertial navigation inter-traveling initial alignment method based on reverse attitude tracking, which specifically comprises the following steps:
the method comprises the following steps: establishing a transition reference coordinate system;
four important transitional reference coordinate systems established by the whole alignment algorithm are an initial moment inertial coordinate system (i)0System), global coordinate system at initial time (e)0System), initial time navigation coordinate system (n)0System) and initial time carrier coordinate system (i)b0System), which is defined as follows:
(1) initial moment inertial frame (i)0Series)
At the beginning of the initial alignment, OXi0In the local meridian plane, parallel to the equatorial plane; OZi0Pointing to the direction of the earth rotation axis; OYi0And OXi0And OZi0Forming a right-handed spiral coordinate system; after the initial alignment starts, i0The system three axes are invariant with respect to the inertial space;
(2) global coordinate system of initial time (e)0Series)
The earth coordinate system at the initial moment takes the earth center as the origin of the coordinate system, OXe0Pointing in the local meridian direction in the equatorial plane; OZi0Pointing to the direction of the earth rotation axis; OYi0And OXi0And OZi0Forming a right-handed spiral coordinate system; the coordinate system is stationary relative to the earth's surface;
(3) initial time navigation coordinate system (n)0Series)
Taking an east-north-sky navigation coordinate system of the initial alignment starting time as an initial time navigation coordinate system; after the initial alignment begins, the coordinate system is stationary relative to the earth's surface;
(4) initial time carrier coordinate system (i)b0Series)
Taking a right-front-upper carrier coordinate system of the initial alignment starting moment as an initial moment carrier coordinate system; after the initial alignment begins, the coordinate system is stationary relative to the inertial space;
step two: in the motion process of the carrier, calculating a rough attitude matrix according to the sampling data of the sensor subsystem;
with i0Is a transitional reference coordinate system, a navigation coordinate system (n system) is relative to a carrier coordinate system (b system) in terms of an attitude matrixThe calculation is divided into two parts, and the calculation process is shown as the formula (1)
Wherein,n is relative to i0A transformation matrix of the system;is i0Is a transformation matrix relative to b;
a calculation matrix
By a transitional reference coordinate system n0System e0The calculation process of the matrix can be divided into four parts, namely:
in the formula,a transformation matrix for n with respect to a geographic coordinate system (e system);is e is relative to n0A transformation matrix of the system;is n0Is relative to e0A transformation matrix of the system;is e0Is relative to i0A transformation matrix of the system;
since the carrier position cannot be accurately obtained in the coarse alignment module, equation (2) is approximated as:
wherein,
in the formula, L0The geographic latitude at the beginning of the initial alignment; omegaieThe rotational angular velocity of the earth; Δ t is the current time t and the initial alignment start time tstartA time difference of (a), i.e. t-tstart(ii) a When formula (4-5) is substituted into formula (3), it is possible to obtain:
b calculating matrix
With ib0Is a transitional reference coordinate system, i0Is relative to the transformation matrix of the b systemThe calculation of (a) is divided into two parts, namely:
wherein,is i0Is relative to ib0A transformation matrix of the system;is ib0Is a transformation matrix relative to b;
the matrix can be directly obtained by the attitude matrix differential equation (8) by utilizing the measured angular velocity of the gyroscope
In the formula, due to ib0Is a reaction of with i0The system is stationary with respect to the inertial frame (i system), so that the angular velocity of the inertial measurement unit can be used to sample the dataDirect substitutionIn addition, at the initial alignment start time, ib0Is coincident with b, soMatrix arrayThe integral calculation initial value is a unit matrix I3×3；
Matrix arrayThe calculation of the method needs to use the slow drift property of the earth gravity acceleration in an inertial system; the calculation method is as follows:
ib0a series of and i0The systems are stationary with respect to the inertial space and thus, it is easy to know the matrixIs a constant value matrix; for carrier velocityThe derivation on both sides can be obtained:
wherein,is the component of the carrier acceleration in the n system;is the component of the carrier acceleration in the b system;
substituting the inertial navigation basic equation into the inertial navigation basic equation, wherein the inertial navigation basic equation can be rewritten into a form shown in a formula (10);
wherein, gnIs the component of the earth gravity acceleration in the n system;is the component of the rotational angular velocity of the earth in the n system;is the angular velocity of rotation of n relative to i; f. ofnSampling the component of the data in the n system for the specific force of the inertia measuring element;
differential equation of known attitude matrixWhereinB is a rotational angular velocity relative to n. Substituting this into (10) yields:
in the formula,negligible, the above formula is further rewritten as formula (12);
wherein, gbIs the component of the earth gravity acceleration in the b system; f. ofbSampling data for the specific force of the inertial measurement unit; v. ofbData sampling with odometer speedConstructed velocity measurement vectorReplacing; whileVector differentiation with odometer speed measurementReplacing; it should be noted that, since the odometer speed sampling data contains noise and direct differentiation amplifies the noise to cause a decrease in alignment accuracy, it is necessary to use a tracking differentiator pairDifferential processing to obtain a signal with less noise interference
To obtain a matrixIt is necessary to pass through gbAnd gn(ii) an important relation (13);
wherein the component g of the acceleration of the earth's gravity under bn＝[0 0 -g]TIs a known amount; matrix arrayAll can be derived from previous calculations, hence the matrixThe solution of (2) is only needed to construct three vectors which are not in the same plane according to the formula (13);
in order to construct a vector and weaken noise at the same time, the two sides of equation (13) are integrated to obtain:
in the formula,
obtaining a transformation matrixIt is necessary to pass through gbAnd gnSignificant relation between
Wherein,all can be obtained by the previous calculation; integrating the two sides of the above formula to obtain
Take two moments t1And t2Integral value ofAndthenCan be calculated by formula (17);
up to this point, during the movement of the carrier, the initial alignment end time t can be calculated by using equations (6), (8) and (17)endCoarse attitude matrix ofHowever, the accuracy of the attitude matrix is not high, and the position of the carrier cannot be acquired at the moment, so that the sampling data of the sensor needs to be stored for further processing;
step three: the tracking differentiator processes the speedometer differentiation;
order toThere is the following non-linear tracking differentiator
wherein r is a tracking differentiator parameter, v (t) is a signal to be tracked containing noise, and the signal is odometer speed sampling data;
therefore, the speedometer differential of the milemeter with smaller pollution degree of the interfered noise can be obtained;
step four: utilizing the stored sampling data of the sensor subsystem to perform reverse attitude tracking calculation on an attitude matrix at the initial alignment starting moment;
the inverse attitude tracking algorithm is to obtain the attitude matrix by coarse alignmentReversely calculating to the initial alignment starting moment to obtain an attitude matrixTo lay the foundation for subsequent fine alignment and position determination;
the carrier attitude is represented by a quaternion q, and the calculation of the attitude can be obtained by a quaternion differential equation (20);
wherein,
in the formula,is the component of the angular velocity of b in b relative to n;is the component of the rotational angular velocity of the earth in the n system;is the component of the angular velocity of n relative to the earth coordinate system (e system) in n system;
in the forward solution of the attitude, the attitude quaternion q (k) at the last moment k and the gyroscope sampling data at the moment k +1 are utilizedSolving an attitude quaternion q (k +1) at the moment of k + 1; the calculation process adopts a Picard solution method; the Picard solution is a common method for solving attitude quaternion by using angle increment, and the three-order approximate calculation formula is as follows:
in the formula, TsAn attitude update period;
Δθ(k+1)＝||Δθ(k+1)|| (25)
in the backward attitude tracking calculation, the attitude quaternion q (k +1) at the moment k +1 and the inertial measurement element angular velocity sampling data at the moment k are knownSolving an attitude quaternion q (k) at the moment k; therefore, formula (23) is rewritten to formula (26);
wherein,
considering that after coarse alignment the position information of the carrier is not known, thereforeIs approximately taken asMeanwhile, in order to improve the calculation precision of delta theta (k), the speed sampling data of the odometer is used for calculationThe calculation process is as follows:
wherein,
to this end, the attitude matrix can be expressed by equations (26), (27) and (28)Tracking back to the initial alignment start time to obtainThereby laying a foundation for the next fine alignment;
step five: carrying out inertial navigation resolving by using the stored sampling data of the sensor subsystem, establishing a Kalman filter for fine alignment, and acquiring accurate attitude matrix and carrier position information;
a. inertial navigation solution and odometer position estimation
At the latitude L of the initial alignment start time0Longitude λ, longitude0Height h0And reverse attitude tracking resultsIn order to solve the initial value, the stored sensor sampling data is used for carrying out attitude, speed and position calculation to obtain an inertial navigation calculation position p ═ L lambda h at each sampling point]TInertial navigation resolving speedInertial navigation resolving attitude matrixAnd the estimated position p of the odometerD＝[LDλDhD]TAnd estimate the speed
b. Constructing a model of the filtering state
Taking the n system as a reference coordinate system of inertial navigation, the filtering state model is as follows:
in the formula,is the inertial navigation platform misalignment angle; delta vnInertial navigation speed error; δ p is the inertial navigation position error; epsilon is the null shift of the inertial navigation gyroscope;zero bias for inertial navigation accelerometers; δ pDCalculating a position error for the odometer; delta KDScale factor error for odometer; known equatorial radius R of the eartheMatrix M1To M6Respectively as follows:
M2＝M′+M″ (32)
M4＝(vn×)·(2M′+M″) (34)
filter state model is abbreviated as
Wherein, the system state transition matrix F belongs to R19×19The matrix is specifically shown as a formula (38); g is a system noise transfer array; w is system noise;
c. building a metrology model
Calculating the inertial navigation calculated position p and the odometer calculated position pDThe difference is used as a measurement vector Z, and the error of the calculated position caused by the noise measured by the odometer is established as the measurement noise of the measurement model;
Z＝p-pD＝δp-δpD+V＝H·X+V (39)
wherein H is a measurement transfer matrix, and H is [0 ]3×6I3×303×6-I3×303×1](ii) a V is position measurement noise; the measurement vector Z is [ L-L ═ LDλ-λDh-hD]T；
Finally, the inertial navigation attitude matrix which is estimated by the filter and is corrected and solved by the inertial navigation errorObtaining an accurate inertial navigation attitude matrixMeanwhile, the accurate calculated position p of the odometer can be obtainedD(ii) a And the accurate attitude alignment and position navigation of inertial navigation are realized.
In step two, the sensor subsystem comprises an inertial measurement element and an odometer. The inertial measurement element measures the angular velocity and specific force of the carrier relative to an inertial space to obtain angular velocity and specific force sampling data; the odometer measures the speed of the carrier to obtain carrier speed sampling data.
Through the steps, the autonomous inertial navigation inter-travelling initial alignment method based on the reverse attitude tracking fully utilizes the sampling data of the sensor, can realize accurate alignment attitude array acquisition and position navigation during travelling under the condition of only knowing the initial position of the carrier, greatly improves the mobility of the carrier, and is an effective inter-travelling initial alignment method.
Claims (2)
1. An autonomous inertial navigation inter-marching initial alignment method based on reverse attitude tracking is characterized in that: it comprises the following steps:
the method comprises the following steps: establishing a transition reference coordinate system;
four important transitional reference coordinate systems established by the whole alignment algorithm are an initial moment inertial coordinate system i0Global coordinate system of system and initial time e0Navigation coordinate system of system and initial time, i.e. n0System and initial time carrier coordinate system ib0It is defined as follows:
(1) initial moment inertial frame i0Is a system
At the beginning of the initial alignment, OXi0In the local meridian plane, parallel to the equatorial plane; OZi0Pointing to the direction of the earth rotation axis; OYi0And OXi0And OZi0Forming a right-handed spiral coordinate system; after the initial alignment starts, i0The system three axes are invariant with respect to the inertial space;
(2) global coordinate system of initial time e0Is a system
The earth coordinate system at the initial moment takes the earth center as the origin of the coordinate system, OXe0Pointing in the local meridian direction in the equatorial plane; OZe0Pointing to the direction of the earth rotation axis; OYe0And OXe0And OZe0Forming a right-handed spiral coordinate system; the coordinate system is stationary relative to the earth's surface;
(3) initial time navigation coordinate system n0Is a system
Taking an east-north-sky navigation coordinate system of the initial alignment starting time as an initial time navigation coordinate system; after the initial alignment begins, the coordinate system is stationary relative to the earth's surface;
(4) initial time carrier coordinate system ib0Is a system
Taking a right-front-upper carrier coordinate system of the initial alignment starting moment as an initial moment carrier coordinate system; after the initial alignment begins, the coordinate system is stationary relative to the inertial space;
step two: in the motion process of the carrier, calculating a rough attitude matrix according to the sampling data of the sensor subsystem;
with i0Is a transitional reference coordinate system, a navigation coordinate system, namely n system, is relative to a carrier coordinate system, namely b system attitude matrixThe calculation is divided into two parts, and the calculation process is shown as the formula (1)
Wherein,n is relative to i0A transformation matrix of the system;is i0Is a transformation matrix relative to b;
a calculation matrix
By a transitional reference coordinate system n0System e0The calculation process of the matrix can be divided into four parts, namely:
in the formula,a transformation matrix of n relative to the terrestrial coordinate system, i.e. e;is e is relative to n0A transformation matrix of the system;is n0Is relative to e0A transformation matrix of the system;is e0Is relative to i0A transformation matrix of the system;
since the carrier position cannot be accurately obtained in the coarse alignment module, equation (2) is approximated as:
wherein,
in the formula, L0The latitude of the earth at the beginning of the initial alignment; omegaieThe rotational angular velocity of the earth; Δ t is the current time t and the initial alignment start time tstartA time difference of (a), i.e. t-tstart(ii) a Substituting the formula (4) and the formula (5) into the formula (3) to obtain:
b calculating matrix
With ib0Is a transitional reference coordinate system, i0Is relative to the transformation matrix of the b systemThe calculation of (a) is divided into two parts, namely:
wherein,is i0Is relative to ib0A transformation matrix of the system;is ib0Is a transformation matrix relative to b;
differentiation of the measured angular velocity by the attitude matrix using inertial measurement unitsEquation (8) directly yields the matrix
In the formula, due to ib0Is a reaction of with i0The systems are stationary with respect to the inertial frame, i.e. the system i, so that the angular velocity of the inertial measurement unit is used to sample the dataDirect substitutionIn addition, at the initial alignment start time, ib0Is coincident with b, so that the matrixThe integral calculation initial value is a unit matrix I3×3；
Matrix arrayThe calculation of the method needs to use the slow drift property of the earth gravity acceleration in an inertial system; the calculation method is as follows:
ib0a series of and i0The systems are stationary with respect to the inertial space and thus, it is easy to know the matrixIs a constant value matrix; for carrier velocityTwo sides are derived:
wherein,is the component of the carrier acceleration in the n system;is the component of the carrier acceleration in the b system;
substituting the inertial navigation basic equation into the inertial navigation basic equation, wherein the inertial navigation basic equation can be rewritten into a form shown in a formula (10);
wherein, gnIs the component of the earth gravity acceleration in the n system;is the component of the rotational angular velocity of the earth in the n system;is the angular velocity of rotation of n relative to i; f. ofnSampling the component of the data in the n system for the specific force of the inertia measuring element;
differential equation of known attitude matrixWhereinB is a rotational angular velocity relative to n, and the following is obtained by substituting (10):
in the formula,neglect not toThe above formula is further rewritten as formula (12);
wherein, gbIs the component of the earth gravity acceleration in the b system; f. ofbSampling data for the specific force of the inertial measurement unit; v. ofbData sampling with odometer speedConstructed velocity measurement vectorReplacing; whileVector differentiation with odometer speed measurementReplacing; it should be noted that, since the odometer speed sampling data contains noise and direct differentiation amplifies the noise to cause a decrease in alignment accuracy, it is necessary to use a tracking differentiator pairDifferential processing to obtain a signal with less noise interference
To obtain a matrixIt is necessary to pass through gbAnd gn(ii) an important relation (13);
in the formula, gn＝[0 0 -g]TIs a known amount; matrix arrayAll can be derived from previous calculations, hence the matrixThe solution of (2) is only needed to construct three vectors which are not in the same plane according to the formula (13);
in order to construct a vector and weaken noise at the same time, the two sides of equation (13) are integrated to obtain:
in the formula,
take two moments t1And t2Integral value ofAndthenCalculated by formula (15);
to this end, during the movement of the carrier, the initial alignment end time t is calculated by using equations (6), (8) and (15)endCoarse attitude matrix ofHowever, the attitude matrix is not accurate and cannot be obtained at this timeCarrier position is taken, so sensor sample data needs to be saved for further processing;
step three: the tracking differentiator processes the speedometer differentiation;
order toThere is the following non-linear tracking differentiator
wherein r is a tracking differentiator parameter, v (t) is a signal to be tracked containing noise, and the signal is odometer speed sampling data;
obtaining an odometer speed differential with small degree of pollution caused by interference noise;
step four: utilizing the stored sampling data of the sensor subsystem to perform reverse attitude tracking calculation on an attitude matrix at the initial alignment starting moment;
the inverse attitude tracking algorithm is to obtain the attitude matrix by coarse alignmentReversely calculating to the initial alignment starting moment to obtain an attitude matrixTo lay the foundation for subsequent fine alignment and position determination;
the carrier attitude is expressed by a quaternion q, and the resolution of the attitude is obtained by a quaternion differential equation (18);
wherein,
in the formula,is the component of the angular velocity of b in b relative to n;is the component of the rotational angular velocity of the earth in the n system;is the component of the angular velocity of the system n relative to the terrestrial coordinate system, i.e. the system e in the system n;
in the forward solution of the attitude, the attitude quaternion q (k) at the last moment k and the inertial measurement element sampling data at the moment k +1 are usedSolving an attitude quaternion q (k +1) at the moment of k + 1; the calculation process adopts a Picard solution method; the Picard solution is a common method for solving attitude quaternion by using angle increment, and the three-order approximate calculation formula is as follows:
in the formula, TsAn attitude update period;
Δθ(k+1)＝||Δθ(k+1)|| (23)
in addition, theIn the backward attitude tracking calculation, the attitude quaternion q (k +1) at the moment of k +1 and the angular velocity sampling data of the inertial measurement element at the moment of k are knownSolving an attitude quaternion q (k) at the moment k; therefore, formula (21) is rewritten to formula (24);
wherein,
considering that after coarse alignment the position information of the carrier is not known, thereforeIs approximately taken asMeanwhile, in order to improve the calculation precision of delta theta (k), the speed sampling data of the odometer is used for calculationThe calculation process is as follows:
wherein,
to this end, the attitude matrix is expressed by equations (24), (25) and (26)Tracking back to the initial alignment start time to obtainThereby laying a foundation for the next fine alignment;
step five: carrying out inertial navigation resolving by using the stored sampling data of the sensor subsystem, establishing a Kalman filter for fine alignment, and acquiring accurate attitude matrix and carrier position information;
a. inertial navigation solution and odometer position estimation
At the latitude L of the initial alignment start time0Longitude λ, longitude0Height h0And reverse attitude tracking resultsIn order to solve the initial value, the stored sensor sampling data is used for carrying out attitude, speed and position calculation to obtain an inertial navigation calculation position p ═ L lambda h at each sampling point]TInertial navigation resolving speedInertial navigation resolving attitude matrixAnd the estimated position p of the odometerD＝[LDλDhD]TAnd estimate the speed
b. Constructing a model of the filtering state
Taking the n system as a reference coordinate system of inertial navigation, the filtering state model is as follows:
in the formula, is the inertial navigation platform misalignment angle; delta vnInertial navigation speed error; δ p is the inertial navigation position error; epsilon is the null shift of the navigation inertial measurement unit;zero bias for inertial navigation accelerometers;
δpDcalculating a position error for the odometer; delta KDScale factor error for odometer; known equatorial radius R of the eartheMatrix M1To M6Respectively as follows:
M2＝M′+M″ (30)
M4＝(vn×)·(2M′+M″) (32)
filter state model is abbreviated as
Wherein the system state transition matrix F∈R19×19The matrix is specifically shown as a formula (36); g is a system noise transfer array; w is system noise;
c. building a metrology model
Calculating the inertial navigation calculated position p and the odometer calculated position pDThe difference is used as a measurement vector Z, and the error of the calculated position caused by the noise measured by the odometer is established as the measurement noise of the measurement model;
Z＝p-pD＝δp-δpD+V＝H·X+V (37)
wherein H is a measurement transfer matrix, and H is [0 ]3×6I3×303×6-I3×303×1](ii) a V is position measurement noise;
the measurement vector Z is [ L-L ═ LDλ-λDh-hD]T；
Finally, the inertial navigation attitude matrix which is estimated by the filter and is corrected and solved by the inertial navigation errorObtaining an accurate inertial navigation attitude matrixMeanwhile, the accurate estimated position p of the odometer is obtainedD(ii) a And the accurate attitude alignment and position navigation of inertial navigation are realized.
2. The method for autonomous inertial navigation inter-travel initial alignment based on backward attitude tracking according to claim 1, wherein: the sensor subsystem recited in step two, comprising an inertial measurement unit and an odometer; the inertial measurement element measures the angular velocity and specific force of the carrier relative to an inertial space to obtain angular velocity and specific force sampling data; the odometer measures the speed of the carrier to obtain carrier speed sampling data.
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