CN109596018B - High-precision estimation method for flight attitude of spinning projectile based on magnetic roll angle rate information - Google Patents

High-precision estimation method for flight attitude of spinning projectile based on magnetic roll angle rate information Download PDF

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CN109596018B
CN109596018B CN201811493891.3A CN201811493891A CN109596018B CN 109596018 B CN109596018 B CN 109596018B CN 201811493891 A CN201811493891 A CN 201811493891A CN 109596018 B CN109596018 B CN 109596018B
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error
equation
attitude
filtering
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CN109596018A (en
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龙达峰
曹建忠
魏晓慧
罗中良
徐瑜
徐德明
孙俊丽
谢珩
蔡远创
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Huizhou University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F42—AMMUNITION; BLASTING
    • F42B—EXPLOSIVE CHARGES, e.g. FOR BLASTING, FIREWORKS, AMMUNITION
    • F42B35/00—Testing or checking of ammunition
    • F42B35/02—Gauging, sorting, trimming or shortening cartridges or missiles

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Abstract

The invention aims at the problem that the existing mature missile-borne attitude measurement system cannot be directly transplanted and applied to the rotating missile due to the three high conditions of high overload, high self-rotation and high dynamic of the launching of the rotating missile. A spinning projectile flight attitude measurement scheme is formed by a triaxial geomagnetic sensor, two uniaxial gyroscopes and a satellite receiver, and a high-precision filtering estimation method suitable for the spinning projectile flight attitude is provided for the measurement scheme, and comprises the following steps: (1) the combined measurement of the flight attitude of the spinning projectile comprises 1.1 of a projectile loading sensor and an installation mode, 1.2 of a projectile body flight attitude high-precision combined filtering structure; (2) the rotating projectile high-precision error model comprises a rotating projectile attitude error model 2.1, a rotating projectile speed error model 2.2 and a position error equation 2.3; (3) a projectile attitude high-order nonlinear filtering model; (4) and performing a filtering updating process by using a projectile attitude high-precision real-time filtering algorithm.

Description

High-precision estimation method for flight attitude of spinning projectile based on magnetic roll angle rate information
Technical Field
The invention relates to a method for measuring the space three-dimensional attitude of an aircraft or a projectile body, in particular to a method for measuring the flight attitude of a spinning projectile with high precision.
Background
Due to the special missile-borne application environment of high overload, high autogyration and high dynamic shooting of the rotating missile, the existing mature missile-borne attitude measurement system cannot be directly transplanted and applied to the rotating ammunition, and the problems of poor reliability, incomplete flight three-dimensional attitude parameter test, low measurement precision and the like exist. In order to solve the problems, currently, a combination measurement scheme of INS + GPS, geomagnetic + GPS or geomagnetic + INS + GPS is usually adopted, and a corresponding filtering algorithm is adopted to complete estimation of the projectile flight attitude parameters, but the adopted filter structure, filtering model or filtering algorithm and the like have certain limitations, and the designed filter has unsatisfactory convergence, instantaneity and estimation accuracy. For example, the existing attitude filtering model based on the assumption of a small misalignment error angle is adopted, and the filtering model neglecting high-order terms cannot accurately describe the strong nonlinear characteristics of the rotating projectile system, so that the problems of convergence speed and filtering precision of the designed projectile attitude filter, even filtering divergence and the like are directly influenced, and the large error parameter estimation result of the filter is also caused.
Therefore, a high-precision measurement method suitable for the flight attitude of the spinning projectile is found, and the method has important theoretical value and practical significance for solving the problem of flight attitude measurement in guidance and transformation of the spinning projectile.
Disclosure of Invention
The invention provides a high-precision filtering estimation method suitable for a spinning projectile flight attitude, which aims at solving the problem that the existing mature projectile-borne attitude measurement system cannot be directly transplanted and applied to spinning projectiles due to the 'three-high' of high overload, high autogyration and high dynamic of the launching of the spinning projectiles.
The invention is realized by adopting the following technical scheme:
a spinning projectile flight attitude high-precision estimation method based on magnetic roll angle rate information comprises the following steps:
(1) combined measurement of flight attitude of spinning projectile
1.1 missile-borne sensor and installation mode
The missile-borne sensor adopts a three-axis geomagnetic sensor, two single-axis gyroscopes and a satellite receiver, wherein the three-axis geomagnetic sensor is used for measuring geomagnetic field vector information in the missile body, and the three-axis geomagnetic sensor is used for measuring the geomagnetic field vector information in the missile bodyDirections of all sensitive axes Mx, My and Mz and a projectile coordinate system OXbYbZbAll the shaft directions are completely consistent; two single-axis gyroscopes Gy and Gz are respectively mounted on Y in a strapdown mannerbAnd ZbOn the axis, the gyroscope is used for measuring Y-axis and Z-axis angular rate information of the projectile body, and the X-axis angular rate information is obtained by filtering and estimating information measured by the geomagnetic sensor; the satellite receiver is used for measuring the speed and the position information of the projectile body, and the antenna of the receiver is annularly arranged on the surface of the projectile body.
1.2 high-precision combined filtering structure for projectile flight attitude
The combined filter consists of a roll angle rate estimation filter and a projectile flight attitude high-precision filter, and is respectively used for finishing the estimation of the projectile roll rate and the high-precision estimation of projectile flight attitude parameters.
(2) High-precision error model of spinning projectile
2.1 rotating missile attitude error model
According to the strapdown inertial navigation theory, the posture quaternion from the missile coordinate system to the navigation coordinate system
Figure GDA0003046335590000031
The differential equation of (a) is expressed as:
Figure GDA0003046335590000032
in the above formula, the first and second carbon atoms are,
Figure GDA0003046335590000033
is a quaternion matrix, is an inverse matrix form:
Figure GDA0003046335590000034
wherein the content of the first and second substances,
Figure GDA0003046335590000035
is the projection of the angular velocity of the projectile coordinate system relative to the inertial coordinate system on the projectile coordinate systemComponent(s) of
Figure GDA0003046335590000036
Namely the projection component of the angular velocity of the navigation coordinate system relative to the inertial coordinate system on the navigation coordinate system
Figure GDA0003046335590000037
Is the projection component of the navigation coordinate system on the carrier coordinate system relative to the angular velocity of the inertial coordinate system.
Figure GDA0003046335590000038
And
Figure GDA0003046335590000039
respectively expressed as:
Figure GDA00030463355900000310
due to angular rate component
Figure GDA00030463355900000311
Is measured by a sensor, the measured value of which
Figure GDA00030463355900000312
There must be a measurement error
Figure GDA00030463355900000313
It is expressed as:
Figure GDA00030463355900000314
angular velocity obtained by strapdown solution
Figure GDA00030463355900000315
There is also a solution error, which is expressed as:
Figure GDA00030463355900000316
substituting the above equations (3) and (4) into the attitude quaternion differential equation (1) to obtain a more differential equation of the attitude quaternion during actual resolving, wherein the more differential equation of the attitude quaternion is as follows:
Figure GDA0003046335590000041
thus, subtracting formula (1) from formula (5) yields the following form:
Figure GDA0003046335590000042
order to
Figure GDA0003046335590000043
Then the error equation of the attitude quaternion is obtained as follows:
Figure GDA0003046335590000044
the last two expressions in equation (7) above satisfy the following relationship:
Figure GDA0003046335590000045
wherein the content of the first and second substances,
Figure GDA0003046335590000046
and
Figure GDA0003046335590000047
are respectively defined as:
Figure GDA0003046335590000048
Figure GDA0003046335590000049
the upper type
Figure GDA00030463355900000410
And
Figure GDA00030463355900000411
in (b), the following relationship is satisfied:
Figure GDA00030463355900000412
and (7) substituting the relation of the formula into the equation to obtain an attitude quaternion error equation:
Figure GDA0003046335590000051
2.2 rotating projectile velocity error model
The projectile velocity error equation is derived from the specific force equation as follows:
Figure GDA0003046335590000052
in the above formula, the first and second carbon atoms are,
Figure GDA0003046335590000053
is a calculation error of the attitude transformation matrix due to
Figure GDA0003046335590000054
Is about quaternion error
Figure GDA0003046335590000055
Is a non-linear function of, therefore
Figure GDA0003046335590000056
Also relates to
Figure GDA0003046335590000057
Of (2) is non-linearA function;
Figure GDA0003046335590000058
the equivalent zero offset of the accelerometer under the navigation system is satisfied
Figure GDA0003046335590000059
δKAAnd delta A are a scale coefficient error matrix and an installation error matrix of the accelerometer respectively; vnIs the navigation down velocity component; delta VnIs the speed error;
Figure GDA00030463355900000510
the rotational angular velocity of the earth;
Figure GDA00030463355900000511
earth rotation angular velocity error;
Figure GDA00030463355900000512
the angular velocity of the navigation coordinate system relative to the earth;
Figure GDA00030463355900000513
the angular velocity error of the navigation coordinate system relative to the earth; f. ofbIs the specific force of the accelerometer.
If the accelerometer is calibrated in advance, δ K may not be consideredAAnd δ A, the projectile velocity error equation is:
Figure GDA00030463355900000514
according to the conversion relation of the above equation (11), the projectile attitude transformation matrix has:
Figure GDA00030463355900000515
therefore, the calculation error of the attitude transformation matrix
Figure GDA00030463355900000516
Comprises the following steps:
Figure GDA00030463355900000517
as has been described in the foregoing, the present invention,
Figure GDA00030463355900000518
substituting into the above formula (16) to obtain
Figure GDA00030463355900000519
Figure GDA00030463355900000520
And due to
Figure GDA00030463355900000521
Then
Figure GDA00030463355900000522
The method is simplified as follows:
Figure GDA0003046335590000061
when the attitude angle error is large,
Figure GDA0003046335590000062
to pair
Figure GDA0003046335590000063
Is non-linear, wherein
Figure GDA0003046335590000064
The calculation formula of (2) is as follows:
Figure GDA0003046335590000065
from the above derivation, the velocity error equation is a non-linear equationLinear error equation of which
Figure GDA0003046335590000066
The term is its nonlinear part, if the nonlinear part in the velocity error equation (14) is assumed to be f1(x,t)：
Figure GDA0003046335590000067
When the nonlinear velocity error equation is linearized1(x, t) pairs
Figure GDA0003046335590000068
The Jacobian matrix formula is as follows:
Figure GDA0003046335590000069
above formula delta ui(i-1, 2,3,4) represents
Figure GDA00030463355900000610
The ith row of (a), wherein,
Figure GDA00030463355900000611
and
Figure GDA00030463355900000612
are respectively defined as:
Figure GDA00030463355900000613
therefore, the comprehensive equations (14) and (18) are used for accurately describing the projectile velocity error propagation law of the projectile under the condition of a large misalignment error angle, and are a projectile velocity error model suitable for the large error angle state.
2.3 equation of position error
The projectile position error equation is:
Figure GDA0003046335590000071
in the formula (24), VE、VN、VUThe speed of the projectile body along the east, north and sky directions respectively; rMAnd RNRespectively the curvature radius of the meridian circle and the unitary mortise circle of the elastomer; l is the latitude of the point of the projectile, lambda is the longitude of the point of the projectile, and h is the height of the point of the projectile; delta VE,δVN,δVUAnd delta h, delta lambda and delta L are position error parameters.
(3) High-order nonlinear filtering model for missile attitude
Selecting a quaternion error delta Q, a speed error delta v, a position error delta p and a gyro drift epsilonbTaking the zero offset of the accelerometer as a state variable of the system
Figure GDA0003046335590000072
Which can be represented as
Figure GDA0003046335590000073
Selecting the projectile flight attitude error equation (12), the velocity error equation (14) and the position error equation (24) obtained by derivation to jointly form a filter state equation set, and simplifying the filter state equation set into the following general form:
Figure GDA0003046335590000074
in the above formula f [ X (t), t]Is a non-linear function of an independent variable X (t), and system process white noise w (t) satisfies E [ w (t)]0 and E [ w (t), wT(τ)]＝Q(t)δ(t-τ)；
Selecting a subtraction result of the position and the speed which are output by the measurement of the satellite navigation system and the position and the speed which are correspondingly solved by the inertial navigation as an observation variable Z (t) of the combined filtering system, wherein the subtraction result is expressed as:
Figure GDA0003046335590000081
in the above formula LGPS,λGPS,hGPSAnd vi,GPS(i ═ N, E, U) respectively represent position and velocity information output by the satellite navigation system measurement, and subscripts represent INS variables representing position and velocity information resolved by inertial navigation; measuring the noise v (t) to satisfy E [ v (t)]0 and E [ v (t), vT(τ)]＝R(t)δ(t-τ)；
Therefore, combining the above equation of state (25) and the measurement equation (26) together forms a high-order nonlinear filtering model suitable for the projectile attitude in the large error angle state.
(4) High-precision real-time filtering algorithm for projectile body posture
The SRUKF filtering algorithm flow based on the correction coefficient is as follows:
4.1, filter initialization:
Figure GDA0003046335590000082
the specific steps of calculating a cycle for any period of UKF filtering algorithm are as follows:
4.2 for given
Figure GDA0003046335590000083
And Pk-1(k ═ 0,2,. n), state one-step prediction is first calculated
Figure GDA0003046335590000084
And a one-step prediction error covariance matrix Pk,k-1The method comprises the following steps of sigma point calculation and propagation process:
4.2.1, calculating sigma point
Figure GDA0003046335590000085
i is 0,2,. 2n, i is:
Figure GDA0003046335590000086
4.2.2, meterCalculating out
Figure GDA0003046335590000087
The sigma point at which i is 0,2,. 2n propagates through the equation of state f (·), is:
Figure GDA0003046335590000091
in the above formula qr {. cndot.) represents orthogonal triangular decomposition of the matrix, and
Figure GDA0003046335590000092
the table is the return value R after QR decomposition; the formula S' choleupdate { S, u, +/-v } is equivalent to SST＝P，S′＝chol{P±vuuT}；
4.3, utilizing UT conversion to solve sigma point
Figure GDA0003046335590000093
And Pk,k-1Propagation through the measurement equation includes the following two update calculation processes:
4.3.1 first, sigma Point is calculated
Figure GDA0003046335590000094
And Pk,k-1By measuring the pair X of the equation h (-) tokPropagation of (2):
Figure GDA0003046335590000095
4.3.2, then, calculate the output one-step advance prediction:
Figure GDA0003046335590000096
4.4, finally, carrying out a filtering updating process by using the obtained new measurement value:
Figure GDA0003046335590000097
the scheme of the invention has the following advantages:
1. the invention adopts a high-precision combined filtering structure of the projectile flight attitude based on magnetic roll angle information, which is suitable for the attitude measurement scheme, wherein the combined filter consists of an EKF (extended Kalman Filter) and a SRUKF (simplified Kalman Filter) which are respectively used for finishing the estimation of the projectile roll rate and the high-precision estimation of the projectile flight attitude.
2. The invention adopts a high-precision projectile attitude high-order nonlinear filtering model suitable for the rotating projectile in a large error angle state. The filtering state equation mainly comprises an additive quaternion error model for describing a spinning projectile attitude error model in a large error angle state, and a spinning projectile velocity error model and a position error model based on the large error angle. And selecting a subtraction result of the position and the speed which are measured and output by the satellite navigation system and the position and the speed which are calculated by inertial navigation as observed quantity of the combined filtering system, and forming a high-precision projectile attitude high-order filtering model by the state equation and the observation equation together. The method adopts the projectile attitude high-order filtering model to more accurately describe the characteristics of the nonlinear system of the projectile attitude high-order filtering model, and can improve the estimation precision of the projectile three-dimensional attitude parameters.
3. The invention adopts a SRUKF projectile body attitude filtering estimation algorithm based on correction coefficients and is used for finishing the high-precision filtering estimation of the flying attitude of the spinning projectile. The SRUKF filtering estimation algorithm based on the correction coefficient is different from the conventional SRUKF filtering method in that a correction coefficient mu is added in sigma point calculation, the size of the correction coefficient mu is determined by selection through priori knowledge, the problem of convergence and divergence of the improved SRUKF filtering algorithm is well restrained, and meanwhile the real-time performance and the filtering estimation precision of the estimation algorithm are considered.
Drawings
Fig. 1 shows a schematic view of a mounting manner of a missile-borne sensor.
FIG. 2 is a schematic diagram of an attitude combination filtering structure of magnetic roll angle information.
Detailed Description
The following detailed description of specific embodiments of the invention refers to the accompanying drawings.
A spinning projectile flight attitude high-precision estimation method based on magnetic roll angle rate information comprises the following steps:
1. combined measuring scheme for flight attitude of spinning projectile
1.1 missile-borne sensor and installation mode
The rotating missile attitude measurement system adopts a geomagnetic/inertia/satellite combination scheme, the missile-borne sensors mainly comprise three-axis geomagnetic sensors, two single-axis gyroscopes and a satellite receiver, and the strapdown installation mode of each sensor is shown in figure 1. Geomagnetic sensor for measuring geomagnetic field vector information in bomb, and its sensitive axis directions (Mx, My and Mz) and bomb coordinate system (OX)bYbZb) All the shaft directions are completely consistent; two single-axis gyroscopes (Gy and Gz) are respectively mounted on Y in a strapdown mannerbAnd ZbOn the axis, the gyroscope is used for measuring Y-axis and Z-axis angular rate information of the projectile body, and the X-axis angular rate information needs to be obtained by filtering and estimating information measured by the geomagnetic sensor; the satellite receiver is used for measuring the speed and the position information of the projectile body, and the antenna of the receiver is annularly arranged on the surface of the projectile body.
1.2 high-precision combined filtering structure for projectile flight attitude
The missile body flight attitude high-precision combined filtering structure based on magnetic roll angle measurement information is shown in fig. 2, and the combined filter consists of two filters, namely a roll angle rate estimation filter (EKF) and a missile body flight attitude high-precision filter (SRUKF), which are respectively used for finishing the estimation of the missile body roll rate and the high-precision estimation of missile body flight attitude parameters. Designing a high-precision filter for the flying attitude of the projectile body: 1) selecting a projectile attitude angle error, velocity error and position error model and an inertial device error model to construct a state equation of the combined filtering system, wherein an additive quaternion error model is used for describing a rotating projectile attitude error model; and describing a rotating bullet speed error model and a position error model based on a large error angle model. 2) And subtracting the speed and the position output by the satellite navigation system measurement and the corresponding strapdown inertial calculation result to be used as the observed quantity of the combined filtering system. 3) The missile body flight attitude high-precision filter adopts a correction coefficient SRUKF-based filtering algorithm to complete real-time high-precision estimation of missile body flight attitude parameters, and the algorithm takes the problems of state parameter convergence speed and estimation precision into account.
2. High-precision error model of rotating bomb
2.1 rotating missile attitude error model
Considering that the inertial navigation system is nonlinear, particularly a gyroscope is not mounted on the X axis of the missile axis, the X axis angular rate is estimated by using geomagnetic information, but the estimation accuracy of the angular rate is not high, if a combined measurement scheme of inertial devices with lower accuracy is adopted, the nonlinearity degree of the system is more obvious, if the existing error model based on the small misalignment angle assumption is adopted, the nonlinear characteristics of the rotating missile system cannot be accurately described by neglecting a filter model of a high-order term, and the nonlinearity directly influences the convergence speed and the filter accuracy of the designed missile attitude filter, even the filter divergence. Therefore, the method adopts the additive quaternion error model to describe the rotating projectile flight attitude error model, can more accurately describe the characteristics of the nonlinear system of the rotating projectile flight attitude error model, and improves the estimation precision of the projectile three-dimensional attitude parameters. According to the strapdown inertial navigation theory, the posture quaternion from the missile coordinate system to the navigation coordinate system
Figure GDA0003046335590000122
The differential equation of (a) can be expressed as:
Figure GDA0003046335590000121
in the above formula, the first and second carbon atoms are,
Figure GDA0003046335590000131
is a quaternion matrix, is an inverse matrix form:
Figure GDA0003046335590000132
wherein the content of the first and second substances,
Figure GDA0003046335590000133
is the projection component of the angular velocity of the missile coordinate system (system b) relative to the inertial coordinate system (system i) on the system b
Figure GDA0003046335590000134
I.e. the projection component of the angular velocity of the navigation coordinate system (n system) relative to the inertial coordinate system (i system) on the n system
Figure GDA0003046335590000135
The projection component of the angular velocity of the navigation coordinate system relative to the inertial coordinate system on the carrier coordinate system is shown;
Figure GDA0003046335590000136
and
Figure GDA0003046335590000137
respectively expressed as:
Figure GDA0003046335590000138
the above equation (1) is a differential equation suitable for updating the attitude quaternion under any angle condition.
Due to angular rate component
Figure GDA0003046335590000139
Is measured by a sensor, the measured value of which
Figure GDA00030463355900001310
There must be a measurement error
Figure GDA00030463355900001311
It can be expressed as:
Figure GDA00030463355900001312
angular velocity obtained by strapdown solution
Figure GDA00030463355900001313
There is also a solution error, which can also be expressed as:
Figure GDA00030463355900001314
substituting the above equations (3) and (4) into the attitude quaternion differential equation (1) can obtain a more differential equation of the attitude quaternion during actual resolving, which is:
Figure GDA0003046335590000141
thus, subtracting formula (1) from formula (5) yields the following form:
Figure GDA0003046335590000142
order to
Figure GDA0003046335590000143
Then the attitude quaternion error equation can be obtained as:
Figure GDA0003046335590000144
the last two expressions in equation (7) above satisfy the following relationship:
Figure GDA0003046335590000145
wherein the content of the first and second substances,
Figure GDA0003046335590000146
and
Figure GDA0003046335590000147
are defined separatelyComprises the following steps:
Figure GDA0003046335590000148
Figure GDA0003046335590000149
the upper type
Figure GDA00030463355900001410
And
Figure GDA00030463355900001411
in (b), the following relationship is satisfied:
Figure GDA00030463355900001412
substituting the relation of the formula into (7) to obtain an attitude quaternion error equation:
Figure GDA00030463355900001413
it should be noted that the derivation process of the attitude quaternion error equation (12) of the present invention does not assume the case of a small misalignment angle, and therefore, it can be used to describe the propagation characteristics of the attitude error of the projectile under a large misalignment angle error, and is a model suitable for the attitude error of the projectile under a large misalignment angle state.
2.2 rotating projectile velocity error model
The projectile velocity error equation can be derived from the specific force equation as follows:
Figure GDA0003046335590000151
in the above formula, the first and second carbon atoms are,
Figure GDA0003046335590000152
is a calculation error of the attitude transformation matrix due to
Figure GDA0003046335590000153
Is about quaternion error
Figure GDA0003046335590000154
Is a non-linear function of, therefore
Figure GDA0003046335590000155
Also relates to
Figure GDA0003046335590000156
A non-linear function of (d);
Figure GDA0003046335590000157
the equivalent zero offset of the accelerometer under the navigation system is satisfied
Figure GDA0003046335590000158
δKAAnd delta A are a scale coefficient error matrix and an installation error matrix of the accelerometer respectively; vnThe velocity component is navigated down. Delta VnIs the speed error;
Figure GDA0003046335590000159
the rotational angular velocity of the earth;
Figure GDA00030463355900001510
earth rotation angular velocity error;
Figure GDA00030463355900001511
the angular velocity of the navigation coordinate system relative to the earth;
Figure GDA00030463355900001512
the angular velocity error of the navigation coordinate system relative to the earth; f. ofbIs the specific force of the accelerometer.
If the accelerometer is calibrated before, delta K can not be consideredAAnd δ A, the projectile velocity error equation is:
Figure GDA00030463355900001513
according to the transformation relationship described in the above equation (11), the projectile attitude transformation matrix can be obtained as follows:
Figure GDA00030463355900001514
therefore, the calculation error of the attitude transformation matrix
Figure GDA00030463355900001515
Can be written as:
Figure GDA00030463355900001516
as has been described in the foregoing, the present invention,
Figure GDA00030463355900001517
can be obtained by substituting into the above formula (16)
Figure GDA00030463355900001518
Figure GDA0003046335590000161
And due to
Figure GDA0003046335590000162
Then
Figure GDA0003046335590000163
Can be abbreviated as:
Figure GDA0003046335590000164
when the attitude angle error is large,
Figure GDA0003046335590000165
to pair
Figure GDA0003046335590000166
Is non-linear, wherein
Figure GDA0003046335590000167
The calculation formula of (2) is as follows:
Figure GDA0003046335590000168
from the above derivation, the velocity error equation is a nonlinear error equation
Figure GDA0003046335590000169
The term is its nonlinear part, if the nonlinear part in the velocity error equation (14) is assumed to be f1(x,t)：
Figure GDA00030463355900001610
When the nonlinear velocity error equation is linearized1(x, t) pairs
Figure GDA00030463355900001611
The Jacobian matrix formula is as follows:
Figure GDA00030463355900001612
above formula delta ui(i-1, 2,3,4) represents
Figure GDA00030463355900001613
The ith row of (a), wherein,
Figure GDA00030463355900001614
and
Figure GDA00030463355900001615
are respectively defined as:
Figure GDA00030463355900001616
therefore, the comprehensive equations (14) and (18) can be used for accurately describing the projectile velocity error propagation law of the projectile under the condition of a large misalignment error angle, and are a projectile velocity error model suitable for the large error angle state.
2.3 equation of position error
The projectile position error equation is:
Figure GDA0003046335590000171
in the formula (24), VE、VN、VUThe speed of the projectile body along the east, north and sky directions respectively; rMAnd RNRespectively the curvature radius of the meridian circle and the unitary mortise circle of the elastomer; l is the latitude of the point of the projectile, lambda is the longitude of the point of the projectile, and h is the height of the point of the projectile; delta VE,δVN,δVUAnd delta h, delta lambda and delta L are position error parameters.
3. High-order nonlinear filtering model for projectile attitude
Selecting a quaternion error delta Q, a speed error delta v, a position error delta p and a gyro drift epsilonbTaking the zero offset of the accelerometer as a state variable of the system
Figure GDA0003046335590000172
Which can be represented as
Figure GDA0003046335590000173
Selecting the projectile flight attitude error equation (12), the velocity error equation (14) and the position error equation (24) obtained by derivation to jointly form a filter state equation set, and simplifying the filter state equation set into the following general form:
Figure GDA0003046335590000174
in the above formula f [ X (t), t]Is a non-linear function of an independent variable X (t), and system process white noise w (t) satisfies E [ w (t)]0 and E [ w (t), wT(τ)]＝Q(t)δ(t-τ)。
The subtraction result of the position and velocity output by the satellite navigation system measurement and the position and velocity calculated correspondingly by the inertial navigation is selected as an observation variable Z (t) of the combined filtering system, which can be expressed as:
Figure GDA0003046335590000181
in the above formula LGPS,λGPS,hGPSAnd vi,GPSAnd (i ═ N, E, U) respectively represent position and velocity information output by the satellite navigation system, and subscripts represent INS variables representing position and velocity information resolved by inertial navigation. Measuring the noise v (t) to satisfy E [ v (t)]0 and E [ v (t), vT(τ)]R (t) δ (t- τ). Therefore, combining the above equation of state (25) and the measurement equation (26) together forms a high-order nonlinear filtering model suitable for the projectile attitude in the large error angle state.
4. High-precision real-time filtering algorithm for projectile attitude
The rotating missile attitude high-precision filtering model is a strong nonlinear equation set, and filtering methods such as UKF and SRUKF based on nonlinear function probability density distribution approximation methods can effectively avoid the problem that filtering precision is influenced by overlarge model error generated by nonlinear equation approximation. However, the filter divergence phenomenon caused by the loss of the state covariance matrix P is easy to occur in some cases in the SRUKF and the conventional UKF filtering method. Aiming at the problems, the SRUKF missile body attitude filtering algorithm based on the correction coefficient is adopted in the invention, so that the convergence speed and the parameter estimation precision of the filtering algorithm are improved.
The SRUKF filtering algorithm flow based on the correction coefficient is as follows:
4.1, filter initialization:
Figure GDA0003046335590000182
the specific steps of calculating a cycle for any period of UKF filtering algorithm are as follows:
4.2 for given
Figure GDA0003046335590000191
And Pk-1(k ═ 0,2,. n), state one-step prediction is first calculated
Figure GDA0003046335590000192
And a one-step prediction error covariance matrix Pk,k-1The method comprises the following steps of sigma point calculation and propagation process:
4.2.1, calculating sigma point
Figure GDA0003046335590000193
i is 0,2,. 2n, i is:
Figure GDA0003046335590000194
4.2.2, calculation
Figure GDA0003046335590000195
The sigma point at which i is 0,2,. 2n propagates through the equation of state f (·), is:
Figure GDA0003046335590000196
wherein QR {. denotes orthogonal triangular decomposition (QR decomposition) of a matrix thereof, and
Figure GDA0003046335590000197
the table is the return value R after QR decomposition; the formula S' choleupdate { S, u, +/-v } is equivalent to SST＝P，S′＝chol{P±vuuT}。
4.3, utilizing UT conversion to solve sigma point
Figure GDA0003046335590000198
And Pk,k-1Propagation through the measurement equation includes the following two update calculation processes:
4.3.1 first, sigma Point is calculated
Figure GDA0003046335590000199
And Pk,k-1By measuring the pair X of the equation h (-) tokPropagation of (2):
Figure GDA00030463355900001910
4.3.2, then, calculate the output one-step advance prediction:
Figure GDA0003046335590000201
4.4, finally, carrying out a filtering updating process by using the obtained new measurement value:
Figure GDA0003046335590000202
the above-mentioned modified coefficient SRUKF filtering estimation algorithm differs from the conventional SRUKF filtering method in sigma point calculation, where one more modification coefficient μ is added in the sigma point calculation formula (28), and its size must be selected by a priori knowledge. Since the correction coefficient satisfies μ > 1, sigma point after time update
Figure GDA0003046335590000203
Error variance S ofk,k-1And advance forecast
Figure GDA0003046335590000204
Error variance S ofzkWill increase, but its observed noise variance matrix RkThe change is not changed, and therefore,gain K of measurement correctionkThe weight of the new measurement value is increased, that is, the influence of old measurement information on the estimation value is reduced, so that the problem of convergence and divergence of the improved correction coefficient SRUKF filtering algorithm is better suppressed. And finally realizing high-precision estimation of the spinning projectile flight parameters through the SRUKF filtering algorithm flow based on the correction coefficient.
It should be noted that modifications and applications may occur to those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A spinning projectile flight attitude high-precision estimation method based on magnetic roll angle rate information is characterized by comprising the following steps: the method comprises the following steps:
(1) combined measurement of flight attitude of spinning projectile
1.1 missile-borne sensor and installation mode
The missile-borne sensor adopts a three-axis geomagnetic sensor, two single-axis gyroscopes and a satellite receiver, wherein the three-axis geomagnetic sensor is used for measuring geomagnetic field vector information in the missile body, and sensitive axis directions Mx, My and Mz of the three-axis geomagnetic sensor and a missile body OX coordinate systembYbZbAll the shaft directions are completely consistent; two single-axis gyroscopes Gy and Gz are respectively mounted on Y in a strapdown mannerbAnd ZbOn the axis, the gyroscope is used for measuring Y-axis and Z-axis angular rate information of the projectile body, and the X-axis angular rate information is obtained by filtering and estimating information measured by the geomagnetic sensor; the satellite receiver is used for measuring the speed and the position information of the projectile body, and the receiver antenna is annularly arranged on the surface of the projectile body;
1.2 high-precision combined filtering structure for projectile flight attitude
The combined filter consists of a roll angle rate estimation filter and a projectile flight attitude high-precision filter and is respectively used for finishing the estimation of the roll rate of the projectile and the high-precision estimation of the parameters of the projectile flight attitude;
(2) high-precision error model of spinning projectile
2.1 rotating missile attitude error model
According to the strapdown inertial navigation theory, the posture quaternion from the missile coordinate system to the navigation coordinate system
Figure FDA0003046335580000011
The differential equation of (a) is expressed as:
Figure FDA0003046335580000021
in the above formula, the first and second carbon atoms are,
Figure FDA0003046335580000022
is a quaternion matrix, is an inverse matrix form:
Figure FDA0003046335580000023
wherein the content of the first and second substances,
Figure FDA0003046335580000024
the projection component of the angular velocity of the projectile coordinate system relative to the inertial coordinate system on the projectile coordinate system
Figure FDA0003046335580000025
Figure FDA0003046335580000026
Namely the projection component of the angular velocity of the navigation coordinate system relative to the inertial coordinate system on the navigation coordinate system
Figure FDA0003046335580000027
Figure FDA0003046335580000028
And
Figure FDA0003046335580000029
respectively expressed as:
Figure FDA00030463355800000210
due to angular rate component
Figure FDA00030463355800000211
Is measured by a sensor, the measured value of which
Figure FDA00030463355800000212
There must be a measurement error
Figure FDA00030463355800000213
It is expressed as:
Figure FDA00030463355800000214
angular velocity obtained by strapdown solution
Figure FDA00030463355800000215
There is also a solution error, which is expressed as:
Figure FDA00030463355800000216
substituting the above equations (3) and (4) into the attitude quaternion differential equation (1) to obtain a more differential equation of the attitude quaternion during actual resolving, wherein the more differential equation of the attitude quaternion is as follows:
Figure FDA0003046335580000031
thus, subtracting formula (1) from formula (5) yields the following form:
Figure FDA0003046335580000032
order to
Figure FDA0003046335580000033
Then the error equation of the attitude quaternion is obtained as follows:
Figure FDA0003046335580000034
the last two expressions in equation (7) above satisfy the following relationship:
Figure FDA0003046335580000035
wherein the content of the first and second substances,
Figure FDA0003046335580000036
and
Figure FDA0003046335580000037
are respectively defined as:
Figure FDA0003046335580000038
Figure FDA0003046335580000039
the upper type
Figure FDA00030463355800000310
And
Figure FDA00030463355800000311
in (b), the following relationship is satisfied:
Figure FDA00030463355800000312
and (7) substituting the relation of the formula into the equation to obtain an attitude quaternion error equation:
Figure FDA00030463355800000313
2.2 rotating projectile velocity error model
The projectile velocity error equation is derived from the specific force equation as follows:
Figure FDA0003046335580000041
in the above formula, the first and second carbon atoms are,
Figure FDA0003046335580000042
is a calculation error of the attitude transformation matrix due to
Figure FDA0003046335580000043
Is about quaternion error
Figure FDA0003046335580000044
Is a non-linear function of, therefore
Figure FDA0003046335580000045
Also relates to
Figure FDA0003046335580000046
A non-linear function of (d);
Figure FDA0003046335580000047
the equivalent zero offset of the accelerometer under the navigation system is satisfied
Figure FDA0003046335580000048
δKAAnd δ A are eachA scale coefficient error matrix and a mounting error matrix of the accelerometer are provided; vnIs the navigation down velocity component; delta VnIs the speed error;
Figure FDA0003046335580000049
the rotational angular velocity of the earth;
Figure FDA00030463355800000410
earth rotation angular velocity error;
Figure FDA00030463355800000411
the angular velocity of the navigation coordinate system relative to the earth;
Figure FDA00030463355800000412
the angular velocity error of the navigation coordinate system relative to the earth; f. ofbIs the specific force of the accelerometer;
if the accelerometer is calibrated in advance, δ K is not consideredAAnd δ A, the projectile velocity error equation is:
Figure FDA00030463355800000413
according to the conversion relation of the above equation (11), the projectile attitude transformation matrix has:
Figure FDA00030463355800000414
therefore, the calculation error of the attitude transformation matrix
Figure FDA00030463355800000415
Comprises the following steps:
Figure FDA00030463355800000416
as has been described in the foregoing, the present invention,
Figure FDA00030463355800000417
substituting into the above formula (16) to obtain
Figure FDA00030463355800000418
Figure FDA00030463355800000419
And due to
Figure FDA00030463355800000420
Then
Figure FDA00030463355800000421
The method is simplified as follows:
Figure FDA00030463355800000422
Figure FDA00030463355800000423
to pair
Figure FDA00030463355800000424
Is non-linear, wherein
Figure FDA00030463355800000425
The calculation formula of (2) is as follows:
Figure FDA0003046335580000051
from the above derivation, the velocity error equation is a nonlinear error equation
Figure FDA0003046335580000052
The term is its nonlinear part, if the nonlinear part in the velocity error equation (14) is assumed to be f1(x,t)：
Figure FDA0003046335580000053
When the nonlinear velocity error equation is linearized1(x, t) pairs
Figure FDA0003046335580000054
The Jacobian matrix formula is as follows:
Figure FDA0003046335580000055
above formula delta ui(i-1, 2,3,4) represents
Figure FDA0003046335580000056
The ith row of (a), wherein,
Figure FDA0003046335580000057
and
Figure FDA0003046335580000058
are respectively defined as:
Figure FDA0003046335580000059
the comprehensive equations (14) and (18) are projectile velocity error models suitable for the large error angle state;
2.3 equation of position error
The projectile position error equation is:
Figure FDA0003046335580000061
in the formula (24), VE、VN、VUThe speed of the projectile body along the east, north and sky directions respectively; rMAnd RNRespectively the curvature radius of the meridian circle and the unitary mortise circle of the elastomer; l is the latitude of the point of the projectile, lambda is the longitude of the point of the projectile, and h is the height of the point of the projectile; delta VE,δVN,δVUThe position error parameters are delta h, delta lambda and delta L;
(3) high-order nonlinear filtering model for missile attitude
Selecting a quaternion error delta Q, a speed error delta v, a position error delta p and a gyro drift epsilonbTaking the zero offset of the accelerometer as a state variable of the system
Figure FDA0003046335580000062
Which is represented as
Figure FDA0003046335580000063
Selecting the projectile flight attitude error equation (12), the velocity error equation (14) and the position error equation (24) obtained by derivation to jointly form a filter state equation set, and simplifying the filter state equation set into the following general form:
Figure FDA0003046335580000064
in the above formula f [ X (t), t]Is a non-linear function of an independent variable X (t), and system process white noise w (t) satisfies E [ w (t)]0 and E [ w (t), wT(τ)]＝Q(t)δ(t-τ)；
Selecting a subtraction result of the position and the speed which are output by the measurement of the satellite navigation system and the position and the speed which are correspondingly solved by the inertial navigation as an observation variable Z (t) of the combined filtering system, wherein the subtraction result is expressed as:
Figure FDA0003046335580000071
in the above formula LGPS,λGPS,hGPSAnd vi,GPS(i ═ N, E, U) respectively represent position and velocity information output by the satellite navigation system measurement, and subscripts represent INS variables representing position and velocity information resolved by inertial navigation; measuring the noise v (t) to satisfy E [ v (t)]0 and E [ v (t), vT(τ)]＝R(t)δ(t-τ)；
Synthesizing the state equation (25) and the measurement equation (26) to jointly form a projectile attitude high-order nonlinear filtering model suitable for the large-error angular state;
(4) high-precision real-time filtering algorithm for projectile body posture
The SRUKF filtering algorithm flow based on the correction coefficient is as follows:
4.1, filter initialization:
Figure FDA0003046335580000072
the specific steps of calculating a cycle for any period of UKF filtering algorithm are as follows:
4.2 for given
Figure FDA0003046335580000073
And Pk-1(k ═ 0,2,. n), state one-step prediction is first calculated
Figure FDA0003046335580000074
And a one-step prediction error covariance matrix Pk,k-1The method comprises the following steps of sigma point calculation and propagation process:
4.2.1, calculating sigma point
Figure FDA0003046335580000075
Namely:
Figure FDA0003046335580000076
4.2.2, calculation
Figure FDA0003046335580000077
The sigma point propagated through the equation of state f (·) is:
Figure FDA0003046335580000081
in the above formula qr {. cndot.) represents orthogonal triangular decomposition of the matrix, and
Figure FDA0003046335580000082
the table is the return value R after QR decomposition; the formula S' choleupdate { S, u, +/-v } is equivalent to SST＝P，S′＝chol{P±vuuT}；
4.3, utilizing UT conversion to solve sigma point
Figure FDA0003046335580000083
And Pk,k-1Propagation through the measurement equation includes the following two update calculation processes:
4.3.1 first, sigma Point is calculated
Figure FDA0003046335580000084
And Pk,k-1By measuring the pair X of the equation h (-) tokPropagation of (2):
Figure FDA0003046335580000085
4.3.2, then, calculate the output one-step advance prediction:
Figure FDA0003046335580000086
4.4, finally, carrying out a filtering updating process by using the obtained new measurement value:
Figure FDA0003046335580000091
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