CN114264304B - High-precision horizontal attitude measurement method and system for complex dynamic environment - Google Patents
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Abstract
The invention discloses a high-precision horizontal attitude measurement method and a high-precision horizontal attitude measurement system for a complex dynamic environment, which comprise the steps of calculating an initial attitude matrix; respectively filtering feedback compensation is carried out on the output increment information of the accelerometer and the gyroscope; constructing a speed update equation, a posture update equation and a position update equation; constructing a Kalman filtering state equation and a measurement equation; and constructing a Kalman filter equation, carrying out partial feedback correction when the continuous rotation accumulated time exceeds the set time, and carrying out feedback correction of all state quantities when the continuous rotation accumulated time is smaller than the set time. The invention can adapt to the processes of alternating rotation and stop at different rotation speeds, rising and standing of the radar antenna, and the like, ensures the high-precision horizontal attitude measurement of the radar chassis in the processes of leveling, rising and standing of the radar antenna and in the complex working state of the radar antenna, and improves the anti-interference capability of the system.
Description
Technical Field
The invention belongs to the technical field of inertial navigation, and particularly relates to a high-precision horizontal attitude measurement method and system for a complex dynamic environment.
Background
According to the radar error principle, the large-disc levelness is an important component of a radar shafting error source and has an important influence on radar angle measurement accuracy, so that the accurate large-disc levelness is a premise for improving the radar measurement accuracy. The non-level of the large disc refers to the non-parallelism of the plane of the azimuth rotating disc and the reference plane of the inertial navigation coordinate system, and if the reference plane of the inertial navigation coordinate system is not flat, the error of the non-levelness of the large disc is increased.
At present, a domestic antenna radar station adopts an imaging level meter to perform the horizontal calibration of a traditional radar antenna. The image-combining level is a level instrument with a seat measuring surface and a micrometer screw pair which is adjusted relative to a base measuring surface, and the instrument combines image reading by an optical principle, improves the accuracy of aiming reading, and adopts the working principle that a prism is used for amplifying bubble symbols in the level to improve the accuracy of reading, and a set of transmission mechanisms, namely a lever and a micro-screw, is used for improving the sensitivity of reading. So that the measured piece can be accurately read in the image combining instrument when being inclined by 0.01 millimeter/meter. The use method of the image combining level meter is that the image combining level meter is arranged on the working surface of the inspected piece, and the two bubble images are not overlapped due to the inclination of the inspected surface, the dial is rotated until the two bubble images are overlapped, at this time, the reading can be obtained, and the actual inclination of the inspected piece can be calculated through the actual inclination = scale value x fulcrum distance x dial reading.
For example, zhong Dean, titled "calibration and flight calibration technology for measurement and control communication equipment for spaceflight measurement ship" (published by national defense industry press), and qiang qi, ji Hui, "application of electronic level to large-disc levelness test" (value engineering), all disclose the measurement of large-disc levelness by using the level. However, the measurement method cannot record the inclination amount of the large disc in real time when the antenna rotates, and human factor errors are introduced, so that the measurement data precision is low, and the measurement precision of the non-levelness of the large disc is reduced.
Meanwhile, the rotation state of the vehicle-mounted radar system is complex in operation, the same algorithm possibly introduces algorithm errors in the preparation state (leveling and erection) and the working state (complex dynamic state and continuous rotation stop is needed) of the radar system, and the levelness measurement accuracy is greatly reduced.
Disclosure of Invention
The invention aims to provide a high-precision horizontal attitude measurement method and a high-precision horizontal attitude measurement system for a complex dynamic environment, so as to solve the problem of low measurement precision of the existing measurement method.
The invention solves the technical problems by the following technical scheme: a high-precision horizontal attitude measurement method of a complex dynamic environment comprises the following steps:
acquiring gravitational acceleration information and inertial device output information of a geographic position where a strapdown inertial navigation system is located, and calculating an initial attitude matrix C according to the gravitational acceleration information and the inertial device output information b n 0 ；
Respectively carrying out filtering feedback compensation on the output increment information of the accelerometer and the gyroscope to obtain compensated output increment information of the accelerometer and output increment information of the gyroscope;
utilizing the compensated accelerometer output increment information and gyroscope output increment information to construct a speed update equation, a posture update equation and a position update equation according to the strapdown inertial navigation system error equation and the inertial device error equation;
constructing a Kalman filtering state equation according to a strapdown inertial navigation system error equation, an inertial device error equation and an accelerometer size effect error equation, and constructing a measurement equation according to the speed updating equation;
constructing a Kalman filtering equation according to the Kalman filtering state equation and the measurement equation;
and obtaining the continuous rotation accumulated time of the gyroscope, judging whether the continuous rotation accumulated time exceeds a set time, if so, carrying out feedback correction according to the speed error, the attitude error, the position error and the zero offset error of the gyroscope estimated by the Kalman filter equation, otherwise, carrying out feedback correction according to the full state quantity estimated by the Kalman filter equation.
Further, the initial pose matrix
The calculation formula of (2) is as follows:
wherein g is gravity acceleration, omega ie The rotation angular velocity of the earth, L is the latitude of the geographic position,
output increment average value of accelerometer with x axis, y axis and z axis respectively, < >>
Output increment average values of the gyroscopes with x axis, y axis and z axis respectively, n is a navigation coordinate system, b is a carrier coordinate system,/respectively>
The projection of the carrier movement angle of the carrier coordinate system b relative to the geocentric inertial coordinate system i in the carrier coordinate system b; />
The projection of the carrier movement angle of the navigation coordinate system n relative to the geocentric inertial coordinate system i in the navigation coordinate system n; g b Projection of gravitational acceleration on a carrier coordinate system b; g n Projection of gravitational acceleration on a navigation coordinate system n; r is (r) n For the output vector cross multiplication of the accelerometer and the gyroscope in the navigation coordinate system n, r b The accelerometer and the gyroscope are output vector cross multiplied under the carrier coordinate system b.
Further, the specific expression of the filtering feedback compensation is:
the output increment information of the gyroscope after filtering feedback compensation is as follows:
the output increment information of the accelerometer after filtering feedback compensation is as follows:
wherein,,
for the projection of the compensated gyroscope output increment information on the carrier coordinate system b,/for the compensation>
To compensate the projection of the incremental information of the output of the front gyroscope on the carrier coordinate system b, w gj A feedback value obtained by zero offset filtering estimation of the gyroscope; f (f) b For compensating the projection of the accelerometer output increment information in the carrier coordinate system b +.>
Output of incremental information at carrier coordinates for compensation of pre-accelerometerProjection of series b, f gj Feedback value f obtained by zero offset filtering estimation of accelerometer a For accelerometer dimensional effect error, f a ＝[f ax ,f ay ,f az ] T 。
Further, the calculation formula of the accelerometer size effect error is as follows:
wherein f ax 、f ay 、f az The dimension effect errors of the accelerometer are respectively x-axis, y-axis and z-axis,
for the projection of the compensated gyroscope output increment information on the carrier coordinate system b,/for the compensation>
To compensate for the projection of the rear gyroscope angular velocity in the carrier coordinate system b,
the projections of the distances from the x-axis accelerometer, the y-axis accelerometer and the z-axis accelerometer to the rotation center of the carrier in a carrier coordinate system b are respectively shown; a, a bij (i=x, y, z; j=x, y, z) is the projection of the distances of the x-axis, y-axis, z-axis accelerometers from the carrier rotation center in the carrier coordinate system x-axis, y-axis, z-axis, respectively.
Further, the velocity update equation, the gesture matrix update equation and the position update equation are respectively:
the velocity update equation:
wherein,,
for the speed in the navigation coordinate system n at time k, < >>
For the speed in the navigation coordinate system n at time k-1,/v>
Projection of the incremental information of the accelerometer output after compensation for the k time on the carrier coordinate system b, +.>
For the gesture matrix at time k>
For projection of the carrier movement angle in the navigation coordinate system n, < >>
For the projection of the rotational angular velocity of the earth in the navigation coordinate system n, Δt is the data sampling time,/for the navigation coordinate system n>
The projection of the gravity acceleration at the moment k under a navigation coordinate system n;
updating an equation of the attitude matrix:
wherein->
The method comprises the following steps:
wherein,,
for the moment k-1 gesture matrix omega ie The rotation angular velocity of the earth, L is the latitude of the geographic position, and +.>
Initially as a unitary matrix, i.e.)>
Is a unitary matrix->
The updated formula of (2) is:
wherein:
wherein,,
respectively outputting the projection of the incremental information of the gyroscope output on the x axis, the y axis and the z axis after the k moment compensation on a carrier coordinate system b,
respectively outputting projections of incremental information of the gyroscope output of the x-axis, the y-axis and the z-axis on a carrier coordinate system b after k-1 time compensation;
the position update equation:
wherein L is k 、λ k 、h k Latitude, longitude, altitude, L of the geographic location where the system is located at time k (k-1) 、λ (k-1) 、h (k-1) The latitude, longitude and altitude of the geographic position of the system at the moment k-1 are respectively, and R is the earth radius.
Further, the strapdown inertial navigation system error equation is:
the inertial device error equation is:
the accelerometer size effect error equation is:
wherein δv x 、δv y 、δv z Respectively, the system is in the east direction, the north direction and the sky directionA speed error; phi (phi) x 、φ y 、φ z Respectively a pitch angle error, a roll angle error and an azimuth angle error of the system;
zero offset error of the eastern accelerometer and zero offset error of the northbound accelerometer and zero offset error of the heaven accelerometer are respectively; δL, δλ, δh are systematic latitude errors, longitude errors, and altitude errors, respectively; f (f) x 、f y 、f z Outputting incremental information for the compensated accelerometers respectively; f (f) a ＝[f ax ,f ay ,f az ] T ，f ax 、f ay 、f az The dimension effect errors of the accelerometers of the x axis, the y axis and the z axis are respectively; τ a Zero offset correlation time for the accelerometer; epsilon= [ epsilon ] x ,ε y ,ε z ] T ，ε x 、ε y 、ε z The zero offset errors of the east gyro, the north gyro and the sky gyro are respectively; τ g The zero drift related time of the gyroscope; omega ie Is the rotation angular velocity of the earth; r is R M Is the radius of the latitude circle of the earth; v x 、v y 、v z The system east direction, north direction and sky direction speeds are respectively; r is R N Is the radius of the longitude circle of the earth; w (w) a 、w g White noise with zero mean value of accelerometer and gyroscope respectively; δv l ＝[δv lx ,δv ly ,δv lz ] T ，δv l Is the speed error caused by the size effect; c (C) b Is a gesture matrix;
the Kalman filtering state equation is:
X k ＝Φ k,k-1 X k-1 +Γ k,k-1 W k-1
wherein X is k 、X k-1 State quantity of k time and k-1 time respectively, phi k,k-1 Is a discrete state transition matrix Γ k,k- For driving the array by system noise, W k-1 Is a state noise array;
W＝[w vx w vy w vz w φx w φy w φz w δL w δλ 0 1×15 ] T
wherein w is vx Is the noise coefficient of the x-direction speed error, w vy Is the noise coefficient of y-direction speed error, w vz Is the noise coefficient of the z-direction speed error, w φx Is the noise coefficient of the x-direction attitude error, w φy Is the noise coefficient of the Y-direction attitude error, w φz Is the noise coefficient of the z-direction attitude error, w δL Is the latitude error noise coefficient, w δλ Is a longitude error noise figure;
taking the speed error as an observed quantity, the measurement equation is as follows:
Z k ＝H k X k +V k
wherein Z is k For Kalman filtering observance, Z is obtained by updating a speed update equation in real time k ＝[v xk ,v yk ,v zk ] T ，H k To observe the coefficient matrix, H k ＝[I 2×2 0 2×21 ]，V k To observe the noise array.
Further, the kalman filter equation is:
wherein,,
the estimated value is predicted for one step; />
Is X k State estimation values of (2); k (K) k A gain matrix at the moment k; z is Z k The Kalman filtering observance quantity; h k Is an observed quantity coefficient matrix; p (P) k,k-1 Estimation of variance matrix for one-step prediction；P k-1 Estimating a variance matrix for the state; r is R k Measuring a noise variance matrix; q (Q) k-1 Is a system noise variance matrix.
Further, when feedback correction is performed according to the full state quantity estimated by the kalman filter equation, a specific correction formula is as follows:
the accelerometer size effect error correction formula is:
a bxx(k) ＝a bxx(k-1) +X(15)
a bxy(k) ＝a bxy(k-1) +X(16)
a bxz(k) ＝a bxz(k-1) +X(17)
a byx(k) ＝a byx(k-1) +X(18)
a byy(k) ＝a byy(k-1) +X(19)
a byz(k) ＝a byz(k-1) +X(20)
a bzx(k) ＝a bzx(k-1) +X(21)
a bzy(k) ＝a bzy(k-1) +X(22)
a bzz(k) ＝a bzz(k-1) +X(23)
the zero offset error correction formula of the gyroscope is as follows:
w gjx(k) ＝w gjx(k-1) +X(12)
w gjy(k) ＝w gjy(k-1) +X(13)
w gjz(k) ＝w gjz(k-1) +X(14)
the accelerometer zero offset error correction formula is:
f gjx(k) ＝f gjx(k-1) +X(9)
f gjy(k) ＝f gjy(k-1) +X(10)
f gjz(k) ＝f gjz(k-1) +X(11)
wherein X (i) represents a filtered estimate, w gjx(k) 、w gjy(k) 、w gjz(k) Zero offset filtering estimated value, w of gyroscope with k moment x axis, y axis and z axis gjx(k-1) 、w gjy(k-1) 、w gjz(k-1) Is the x-axis, the y-axis at the moment of k-1,zero offset filter estimated value f of z-axis gyroscope gjx(k) 、f gjy(k) 、f gjz(k) Zero offset filtering estimated value of the accelerometer with the x axis, the y axis and the z axis at the moment of k, f gjx(k-1) 、f gjy(k-1) 、f gjz(k-1) The estimated values are zero offset filtered for the x-axis, y-axis and z-axis accelerometers at time k-1.
Further, the set time is 2s.
The invention also provides a high-precision horizontal attitude measurement system of the complex dynamic environment, which comprises:
the acquisition unit is used for acquiring the gravity acceleration information of the geographic position where the strapdown inertial navigation system is located and the output information of the inertial device; a first calculation unit for calculating an initial posture matrix according to the gravitational acceleration information and the inertial device output information
The filtering compensation unit is used for respectively carrying out filtering feedback compensation on the output increment information of the accelerometer and the gyroscope to obtain compensated output increment information of the accelerometer and output increment information of the gyroscope;
the first construction unit is used for constructing a speed update equation, a posture update equation and a position update equation according to the strapdown inertial navigation system error equation and the inertial device error equation by using the compensated accelerometer output increment information and the gyroscope output increment information;
the second construction unit is used for constructing a Kalman filtering state equation according to the strapdown inertial navigation system error equation, the inertial device error equation and the accelerometer size effect error equation and constructing a measurement equation according to the speed updating equation;
the third construction unit is used for constructing a Kalman filtering equation according to the Kalman filtering state equation and the measurement equation;
and the feedback correction unit is used for acquiring the continuous rotation accumulated time of the gyroscope, judging whether the continuous rotation accumulated time exceeds the set time, if so, carrying out feedback correction according to the speed error, the attitude error, the position error and the zero offset error of the gyroscope estimated by the Kalman filter equation, and otherwise, carrying out feedback correction according to the full state quantity estimated by the Kalman filter equation.
Advantageous effects
Compared with the prior art, the invention has the advantages that:
1. only the output data of the gravity acceleration, the accelerometer and the gyroscope are used for realizing the rapid coarse alignment within 10 seconds, and no additional input information is needed;
2. the invention provides a size effect error parameter self-estimation method, which can automatically estimate the distance from the product centroid to the rotation center of a radar large wheel without providing initial information externally;
3. when the external input size effect error parameters exist, the measurement error of the accelerometer caused by the size effect error can be estimated and compensated in real time, so that the measurement accuracy of the accelerometer is improved, and the measurement accuracy of the horizontal posture is further improved;
4. the method and the device take the continuous rotation accumulated time of the gyroscope as the basis to judge and control, can adapt to the processes of alternating rotation and stop of different rotation speeds, erection of the radar antenna and the like, ensure the high-precision horizontal attitude measurement of the radar chassis in the leveling process, the erection process of the radar antenna and the complex working state of the radar antenna, improve the anti-interference capability of the system, and adapt to the high-precision horizontal attitude measurement in the complex dynamic environment.
Drawings
In order to more clearly illustrate the technical solutions of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawing in the description below is only one embodiment of the present invention, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for measuring high-precision horizontal gestures in a complex dynamic environment in an embodiment of the invention;
FIG. 2 is a flow chart of the lever arm self-estimation in an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made more apparent and fully by reference to the accompanying drawings, in which it is shown, however, only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The technical scheme of the present application is described in detail below with specific examples. The following embodiments may be combined with each other, and some embodiments may not be repeated for the same or similar concepts or processes.
As shown in fig. 1, the method for measuring the high-precision horizontal attitude of the complex dynamic environment provided by the embodiment of the invention comprises the following steps:
step 1: acquiring gravitational acceleration information and inertial device output information of the geographic position of the strapdown inertial navigation system, and calculating an initial attitude matrix according to the gravitational acceleration information and the inertial device output information
When the strapdown inertial navigation system is initialized, inputting the gravity acceleration g, and calculating an initial attitude matrix by utilizing the gravity acceleration g and the output information of the inertial device within 10s, wherein a specific calculation formula is as follows:
wherein g is gravity acceleration, omega ie The rotation angular velocity of the earth, L is the locationThe latitude of the physical location is determined,
output increment average value of accelerometer with x axis, y axis and z axis respectively, < >>
Output increment average values of the gyroscopes with x axis, y axis and z axis respectively, n is a navigation coordinate system, b is a carrier coordinate system,/respectively>
The projection of the carrier movement angle of the carrier coordinate system b relative to the geocentric inertial coordinate system i in the carrier coordinate system b; />
The projection of the carrier movement angle of the navigation coordinate system n relative to the geocentric inertial coordinate system i in the navigation coordinate system n; g b Projection of gravitational acceleration on a carrier coordinate system b; g n Projection of gravitational acceleration on a navigation coordinate system n; r is (r) n For the output vector cross multiplication of the accelerometer and the gyroscope in the navigation coordinate system n, r b The accelerometer and the gyroscope are output vector cross multiplied under the carrier coordinate system b.
Step 2: and respectively carrying out filtering feedback compensation on the output increment information of the accelerometer and the gyroscope to obtain compensated output increment information of the accelerometer and output increment information of the gyroscope.
The product will not be mounted at the absolute centre of rotation of the carrier, so the dimensional effect parameters typically are an outer lever arm, which is defined as the vector of the position of the product centroid relative to the centre of rotation of the carrier, and an inner lever arm, which is defined as the vector of the position of the x-axis, y-axis, z-axis accelerometer centroid relative to the origin of the carrier coordinate system b-system. When the external or product internal structure is complex and accurate lever arm parameters are not easy to obtain, accurate estimation and compensation are needed (the specific estimation process is shown in fig. 2) so as to improve the measurement accuracy of the accelerometer and further improve the measurement accuracy of the horizontal attitude.
In this embodiment, the inner and outer lever arms are not distinguished,lever arm with product x-axis, y-axis and z-axis accelerometers to rotation center of carrier where product is installed (such as distance from accelerometer in product installed on radar big disk to rotation center of radar big disk), projection under carrier coordinate system x-axis, y-axis and z-axis
The method comprises the following steps:
wherein a is bij (i=x, y, z; j=x, y, z) is the projection of the distances of the x-axis, y-axis, z-axis accelerometers from the carrier rotation center under the carrier coordinate system x-axis, y-axis, z-axis, respectively; for example a bxx Respectively, projection of distance from the x-axis accelerometer to the rotation center of the carrier under the x-axis of the carrier coordinate system, a byz The projections of the distances of the y-axis accelerometer to the center of rotation of the carrier in the z-axis of the carrier coordinate system are respectively. If no external input initial value exists, a bij If the initial value of (a) is 0, if the initial value is input from outside, a bij Is an input value, and is then updated according to equations (19) and (21).
Accelerometer measurement error f caused by dimensional effects ax 、f ay 、f az The calculation formula of (i.e. the size effect error) is:
therefore, the output increment information of the gyroscope after filtering feedback compensation is as follows:
the output increment information of the accelerometer after filtering feedback compensation is as follows:
wherein,,
for the projection of the compensated gyroscope output increment information on the carrier coordinate system b,/for the compensation>
To compensate the projection of the incremental information of the output of the front gyroscope on the carrier coordinate system b, w gj A feedback value obtained by zero offset filtering estimation of the gyroscope; f (f) b For compensating the projection of the accelerometer output increment information in the carrier coordinate system b +.>
To compensate for the projection of the incremental information of the front accelerometer output on the carrier coordinate system b, f gj Feedback value f obtained by zero offset filtering estimation of accelerometer a For accelerometer dimensional effect error, f a ＝[f ax ,f ay ,f az ] T 。w gj 、f gj The initial value of (2) is 0.
Step 3: and constructing a speed update equation, a posture update equation and a position update equation according to the strapdown inertial navigation system error equation and the inertial device error equation by using the compensated accelerometer output increment information and the gyroscope output increment information.
The velocity update equation:
wherein,,
for the speed in the navigation coordinate system n at time k, < >>
For the speed in the navigation coordinate system n at time k-1,/v>
Projection of the incremental information of the accelerometer output after compensation for the k time on the carrier coordinate system b, +.>
For the gesture matrix at time k>
For projection of the carrier movement angle in the navigation coordinate system n, < >>
For the projection of the rotational angular velocity of the earth in the navigation coordinate system n, Δt is the data sampling time,/for the navigation coordinate system n>
The projection of the gravitational acceleration at time k under the navigation coordinate system n.
Updating an equation of the attitude matrix:
wherein the method comprises the steps of
The method comprises the following steps:
wherein,,
for the moment k-1 gesture matrix omega ie The rotation angular velocity of the earth, L is the latitude of the geographic position, and +.>
Initially as a unitary matrix, i.e.)>
Is a matrix of units which is a matrix of units,/>
the updated formula of (2) is:
wherein:
wherein,,
respectively outputting the projection of the incremental information of the gyroscope output on the x axis, the y axis and the z axis after the k moment compensation on a carrier coordinate system b,
and respectively outputting projections of incremental information of the gyroscope output on the x axis, the y axis and the z axis after k-1 time compensation on a carrier coordinate system b.
The position update equation:
wherein L is k 、λ k 、h k Latitude, longitude, altitude, L of the geographic location where the system is located at time k (k-1) 、λ (k-1) 、h (k-1) Respectively k-1 timeLatitude, longitude, and altitude of the geographic location where the system is located, R is the earth radius.
System speed, position and attitude information can be obtained from equations (6), (7) and (12).
Step 4: and constructing a Kalman filtering state equation according to the error equation of the strapdown inertial navigation system, the error equation of the inertial device and the error equation of the accelerometer size effect, and constructing a measurement equation according to the speed updating equation.
In order to simplify the formula, the superscript n is omitted, and the error equation of the strapdown inertial navigation system is as follows:
the inertial device error equation is:
the accelerometer size effect error equation is:
wherein δv x 、δv y 、δv z The system east direction, north direction and sky direction speed errors are respectively; phi (phi) x 、φ y 、φ z Respectively a pitch angle error, a roll angle error and an azimuth angle error of the system;
zero offset error of the eastern accelerometer and zero offset error of the northbound accelerometer and zero offset error of the heaven accelerometer are respectively; δL, δλ, δh are systematic latitude errors, longitude errors, and altitude errors, respectively; f (f) x 、f y 、f z Outputting incremental information for the compensated accelerometers respectively; f (f) a ＝[f ax ,f ay ,f az ] T ，f ax 、f ay 、f az The dimension effect errors of the accelerometers of the x axis, the y axis and the z axis are respectively; τ a Zero offset correlation time for the accelerometer; epsilon= [ epsilon ] x ,ε y ,ε z ] T ，ε x 、ε y 、ε z The zero offset errors of the east gyro, the north gyro and the sky gyro are respectively; τ g The zero drift related time of the gyroscope; omega ie Is the rotation angular velocity of the earth; r is R M Is the radius of the latitude circle of the earth; v x 、v y 、v z The system east direction, north direction and sky direction speeds are respectively; r is R N Is the radius of the longitude circle of the earth; w (w) a 、w g White noise with zero mean value of accelerometer and gyroscope respectively; δv l ＝[δv lx ,δv ly ,δv lz ] T ，δv l To be due to the size effectA speed error; c (C) b Is a gesture matrix. East, north and sky are the three axes of the system navigation coordinate system.
The Kalman filtering state equation is constructed according to the formulas (13) to (15), and after discretization, the Kalman filtering state equation is as follows:
X k ＝Φ k,k-1 X k-1 +Γ k,k-1 W k-1 (16)
wherein X is k 、X k-1 State quantity of k time and k-1 time respectively, phi k,k-1 Is a discrete state transition matrix Γ k,k-1 For the system noise driving matrix (obtained by formulas (13) - (15)), W k-1 Is a state noise array;
W＝[w vx w vy w vz w φx w φy w φz w δL w δλ 0 1×15 ] T
wherein w is vx Is the noise coefficient of the x-direction speed error, w vy Is the noise coefficient of y-direction speed error, w vz Is the noise coefficient of the z-direction speed error, w φx Is the noise coefficient of the x-direction attitude error, w φy Is the noise coefficient of the Y-direction attitude error, w φz Is the noise coefficient of the z-direction attitude error, w δL Is the latitude error noise coefficient, w δλ Is a longitude error noise figure. The specific values of these error noise coefficients are typically obtained from engineering experience and are typically zero-mean white noise.
Taking the speed error as an observed quantity, the measurement equation is as follows:
Z k ＝H k X k +V k (17)
wherein Z is k For Kalman filtering observance, Z is obtained by updating a speed update equation in real time k ＝[v xk ,v yk ,v zk ] T ，
H k To observe the coefficient matrix, H k ＝[I 2×2 0 2×21 ]，V k To observe the noise array.
Step 5: the Kalman filtering equation is constructed according to the Kalman filtering state equation and the measurement equation, and specifically comprises the following steps:
wherein,,
the estimated value is predicted for one step; />
Is X k State estimation values of (2); k (K) k A gain matrix at the moment k; z is Z k The Kalman filtering observance quantity; h k Is an observed quantity coefficient matrix; p (P) k,k-1 Estimating a variance matrix for the one-step prediction; p (P) k-1 Estimating a variance matrix for the state; r is R k Measuring a noise variance matrix; q (Q) k-1 Is a system noise variance matrix.
Step 6: and obtaining the continuous rotation accumulated time of the gyroscope, judging whether the continuous rotation accumulated time exceeds the set time, if so, carrying out feedback correction according to the speed error, the attitude error, the position error and the zero offset error of the gyroscope estimated by the Kalman filter equation, otherwise, carrying out feedback correction according to the full state quantity estimated by the Kalman filter equation.
When the radar vehicle is in leveling and the radar antenna is in a standing state, instantaneous shaking condition can occur, if a filtering algorithm is adopted, filtering estimation is inaccurate (the time required by navigation filtering convergence estimation is not accurate for instantaneous shaking), so the method takes the continuous rotation accumulated time of the gyroscope as a basis, and when the continuous rotation accumulated time of the gyroscope is smaller than set time, only partial feedback correction is carried out, namely, the dimension effect error and the zero offset error of the accelerometer are not corrected and compensated, and the estimation result of the last moment is used; and when the continuous rotation accumulated time of the gyroscope is greater than or equal to the set time, full-state feedback is carried out.
In this embodiment, the set time is 2s.
If partial feedback is performed, the size effect error estimation value and the accelerometer zero offset error are not corrected, specifically:
if full state feedback is performed, the specific correction formula is:
the accelerometer size effect error correction formula is:
the zero offset error correction formula of the gyroscope is as follows:
the accelerometer zero offset error correction formula is:
wherein X (i) represents a filtered estimate, w gjx(k) 、w gjy(k) 、w gjz(k) Zero offset filtering estimated value, w of gyroscope with k moment x axis, y axis and z axis gjx(k-1) 、w gjy(k-1) 、w gjz(k-1) Zero offset filtering estimated value of the gyroscope with the axis x, the axis y and the axis z at the moment k-1, f gjx(k) 、f gjy(k) 、f gjz(k) Zero offset filtering estimated value of the accelerometer with the x axis, the y axis and the z axis at the moment of k, f gjx(k-1) 、f gjy(k-1) 、f gjz(k-1) The estimated values are zero offset filtered for the x-axis, y-axis and z-axis accelerometers at time k-1.
The embodiment of the invention also provides a high-precision horizontal attitude measurement system of the complex dynamic environment, which comprises the following steps:
the acquisition unit is used for acquiring the gravitational acceleration information of the geographic position where the strapdown inertial navigation system is located and the output information of the inertial device.
A first calculation unit for calculating an initial posture matrix according to the gravity acceleration information and the inertial device output information
As shown in formula (1).
And the filtering compensation unit is used for respectively carrying out filtering feedback compensation on the output increment information of the accelerometer and the gyroscope to obtain compensated output increment information of the accelerometer and output increment information of the gyroscope, and the output increment information of the accelerometer and the output increment information of the gyroscope are shown in formulas (2) to (5).
The first construction unit is used for constructing a speed update equation, a posture update equation and a position update equation according to the strapdown inertial navigation system error equation and the inertial device error equation by using the compensated accelerometer output increment information and the gyroscope output increment information, and the speed update equation, the posture update equation and the position update equation are shown in formulas (6) to (12).
The second construction unit is used for constructing a Kalman filtering state equation (shown as a formula (16)) according to the strapdown inertial navigation system error equation, the inertial device error equation and the accelerometer size effect error equation, and constructing a measurement equation (shown as a formula (17)) according to the speed update equation.
And a third construction unit for constructing a Kalman filter equation according to the Kalman filter state equation and the measurement equation, as shown in formula (18).
And the feedback correction unit is used for acquiring the continuous rotation accumulated time of the gyroscope and judging whether the continuous rotation accumulated time exceeds the set time, if so, carrying out feedback correction according to the speed error, the attitude error, the position error and the zero offset error of the gyroscope estimated by the Kalman filter equation, otherwise, carrying out feedback correction according to the full state quantity estimated by the Kalman filter equation (as shown in formulas (21) - (23)).
The foregoing disclosure is merely illustrative of specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art will readily recognize that changes and modifications are possible within the scope of the present invention.
Claims (10)
1. The high-precision horizontal attitude measurement method for the complex dynamic environment is characterized by comprising the following steps of:
acquiring gravitational acceleration information and inertial device output information of a geographic position where a strapdown inertial navigation system is located, and calculating an initial attitude matrix according to the gravitational acceleration information and the inertial device output information
Respectively carrying out filtering feedback compensation on the output increment information of the accelerometer and the gyroscope to obtain compensated output increment information of the accelerometer and output increment information of the gyroscope;
utilizing the compensated accelerometer output increment information and gyroscope output increment information to construct a speed update equation, a posture update equation and a position update equation according to the strapdown inertial navigation system error equation and the inertial device error equation;
constructing a Kalman filtering state equation according to a strapdown inertial navigation system error equation, an inertial device error equation and an accelerometer size effect error equation, and constructing a measurement equation according to the speed updating equation;
constructing a Kalman filtering equation according to the Kalman filtering state equation and the measurement equation;
and obtaining the continuous rotation accumulated time of the gyroscope, judging whether the continuous rotation accumulated time exceeds a set time, if so, carrying out feedback correction according to the speed error, the attitude error, the position error and the zero offset error of the gyroscope estimated by the Kalman filter equation, otherwise, carrying out feedback correction according to the full state quantity estimated by the Kalman filter equation.
2. The complex dynamic environment high-precision horizontal pose measurement method according to claim 1, wherein the initial pose matrix
The calculation formula of (2) is as follows:
wherein g is gravity acceleration, omega ie The rotation angular velocity of the earth, L is the latitude of the geographic position,
output increment average value of accelerometer with x axis, y axis and z axis respectively, < >>
Output increment average values of the gyroscopes with x axis, y axis and z axis respectively, n is a navigation coordinate system, b is a carrier coordinate system,/respectively>
The projection of the carrier movement angle of the carrier coordinate system b relative to the geocentric inertial coordinate system i in the carrier coordinate system b; />
The projection of the carrier movement angle of the navigation coordinate system n relative to the geocentric inertial coordinate system i in the navigation coordinate system n; g b Projection of gravitational acceleration on a carrier coordinate system b; g n Projection of gravitational acceleration on a navigation coordinate system n; r is (r) n For the output vector cross multiplication of the accelerometer and the gyroscope in the navigation coordinate system n, r b The accelerometer and the gyroscope are output vector cross multiplied under the carrier coordinate system b.
3. The method for measuring the high-precision horizontal attitude of the complex dynamic environment according to claim 1, wherein the specific expression of the filtering feedback compensation is:
the output increment information of the gyroscope after filtering feedback compensation is as follows:
the output increment information of the accelerometer after filtering feedback compensation is as follows:
wherein,,
for the projection of the compensated gyroscope output increment information on the carrier coordinate system b,/for the compensation>
To compensate the projection of the incremental information of the output of the front gyroscope on the carrier coordinate system b, w gj A feedback value obtained by zero offset filtering estimation of the gyroscope; f (f) b For compensating the projection of the accelerometer output increment information in the carrier coordinate system b +.>
To compensate for the projection of the incremental information of the front accelerometer output on the carrier coordinate system b, f gj Feedback value f obtained by zero offset filtering estimation of accelerometer a For accelerometer dimensional effect error, f a ＝[f ax ,f ay ,f az ] T 。
4. The method for measuring the high-precision horizontal attitude of the complex dynamic environment according to claim 3, wherein a calculation formula of the dimension effect error of the accelerometer is as follows:
wherein f ax 、f ay 、f az The dimension effect errors of the accelerometer are respectively x-axis, y-axis and z-axis,
for the projection of the compensated gyroscope output increment information on the carrier coordinate system b,/for the compensation>
To compensate for the projection of the rear gyroscope angular velocity in the carrier coordinate system b,
the projections of the distances from the x-axis accelerometer, the y-axis accelerometer and the z-axis accelerometer to the rotation center of the carrier in a carrier coordinate system b are respectively shown; a, a bij Respectively projecting distances from the x-axis, the y-axis and the z-axis accelerometers to the rotation center of the carrier under the x-axis, the y-axis and the z-axis of the carrier coordinate system, wherein i=x, y and z; j=x, y, z.
5. The method for measuring the high-precision horizontal attitude of the complex dynamic environment according to claim 4, wherein the velocity update equation, the attitude update equation and the position update equation are respectively:
the velocity update equation:
wherein,,
for the speed in the navigation coordinate system n at time k, < >>
For the speed in the navigation coordinate system n at time k-1,/v>
f k b Projection of the incremental information of the accelerometer output after compensation for the k time on the carrier coordinate system b, +.>
For the gesture matrix at time k>
For projection of the carrier movement angle in the navigation coordinate system n, < >>
For the projection of the rotational angular velocity of the earth in the navigation coordinate system n, Δt is the data sampling time,/for the navigation coordinate system n>
The projection of the gravity acceleration at the moment k under a navigation coordinate system n;
attitude update equation:
wherein->
The method comprises the following steps:
wherein,,
for the moment k-1 gesture matrix omega ie The rotation angular velocity of the earth, L is the latitude of the geographic position, and +.>
Initially as a unitary matrix, i.e.)>
Is a unitary matrix->
The updated formula of (2) is:
wherein:
wherein,,
projection of output increment information of the x-axis gyroscope, the y-axis gyroscope and the z-axis gyroscope on a carrier coordinate system b after k time compensation is respectively carried out, < >>
Respectively outputting projections of incremental information of the gyroscopes of the x axis, the y axis and the z axis on a carrier coordinate system b after k-1 time compensation;
the position update equation:
wherein L is k 、λ k 、h k Latitude, longitude, altitude, L of the geographic location where the system is located at time k (k-1) 、λ (k-1) 、h (k-1) The latitude, longitude and altitude of the geographic position of the system at the moment k-1 are respectively, and R is the earth radius.
6. The method for measuring the high-precision horizontal attitude of the complex dynamic environment according to claim 5, wherein the strapdown inertial navigation system error equation is:
the inertial device error equation is:
the accelerometer size effect error equation is:
wherein δv x 、δv y 、δv z The system east direction, north direction and sky direction speed errors are respectively; phi (phi) x 、φ y 、φ z Respectively a pitch angle error, a roll angle error and an azimuth angle error of the system;
respectively are provided withZero offset error of the eastern accelerometer, zero offset error of the northbound accelerometer and zero offset error of the heaven accelerometer; δL, δλ, δh are systematic latitude errors, longitude errors, and altitude errors, respectively; f (f) x 、f y 、f z Outputting incremental information for the compensated accelerometers respectively; f (f) a ＝[f ax ,f ay ,f az ] T ，f ax 、f ay 、f az The dimension effect errors of the accelerometers of the x axis, the y axis and the z axis are respectively; τ a Zero offset correlation time for the accelerometer; epsilon= [ epsilon ] x ,ε y ,ε z ] T ，ε x 、ε y 、ε z The zero offset errors of the east gyro, the north gyro and the sky gyro are respectively; τ g The zero drift related time of the gyroscope; omega ie Is the rotation angular velocity of the earth; r is R M Is the radius of the latitude circle of the earth; v x 、v y 、v z The system east direction, north direction and sky direction speeds are respectively; r is R N Is the radius of the longitude circle of the earth; w (w) a 、w g White noise with zero mean value of accelerometer and gyroscope respectively; δv l ＝[δv lx ,δv ly ,δv lz ] T ，δv l Is the speed error caused by the size effect; c (C) b Is a gesture matrix;
the Kalman filtering state equation is:
X k ＝Φ k,k-1 X k-1 +Γ k,k-1 W k-1
wherein X is k 、X k-1 State quantity of k time and k-1 time respectively, phi k,k-1 Is a discrete state transition matrix Γ k,k-1 For driving the array by system noise, W k-1 Is a state noise array;
W＝[w vx w vy w vz w φx w φy w φz w δL w δλ 0 1×15 ] T
wherein w is vx Is the noise coefficient of the x-direction speed error, w vy Is the noise coefficient of y-direction speed error, w vz Is the noise coefficient of the z-direction speed error, w φx Is the noise coefficient of the x-direction attitude error, w φy Is the noise coefficient of the Y-direction attitude error, w φz Is the noise coefficient of the z-direction attitude error, w δL Is the latitude error noise coefficient, w δλ Is a longitude error noise figure;
taking the speed error as an observed quantity, the measurement equation is as follows:
Z k ＝H k X k +V k
wherein Z is k For Kalman filtering observance, Z is obtained by updating a speed update equation in real time k ＝[v xk ,v yk ,v zk ] T ，H k To observe the coefficient matrix, H k ＝[I 2×2 0 2×21 ]，V k To observe the noise array.
7. The complex dynamic environment high-precision horizontal attitude measurement method according to claim 6, wherein the kalman filter equation is:
wherein,,
the estimated value is predicted for one step; />
Is X k State estimation values of (2); k (K) k A gain matrix at the moment k; z is Z k The Kalman filtering observance quantity; h k Is an observed quantity coefficient matrix; p (P) k,k-1 Estimating a variance matrix for the one-step prediction; p (P) k-1 Estimating a variance matrix for the state; r is R k Measuring a noise variance matrix; q (Q) k-1 Is a system noise variance matrix.
8. The method for measuring the high-precision horizontal attitude of the complex dynamic environment according to claim 7, wherein when the feedback correction is performed according to the full state quantity estimated by the kalman filter equation, a specific correction formula is as follows:
the accelerometer size effect error correction formula is:
a bxx(k) ＝a bxx(k-1) +X(15)
a bxy(k) ＝a bxy(k-1) +X(16)
a bxz(k) ＝a bxz(k-1) +X(17)
a byx(k) ＝a byx(k-1) +X(18)
a byy(k) ＝a byy(k-1) +X(19)
a byz(k) ＝a byz(k-1) +X(20)
a bzx(k) ＝a bzx(k-1) +X(21)
a bzy(k) ＝a bzy(k-1) +X(22)
a bzz(k) ＝a bzz(k-1) +X(23)
the zero offset error correction formula of the gyroscope is as follows:
w gjx(k) ＝w gjx(k-1) +X(12)
w gjy(k) ＝w gjy(k-1) +X(13)
w gjz(k) ＝w gjz(k-1) +X(14)
the accelerometer zero offset error correction formula is:
f gjx(k) ＝f gjx(k-1) +X(9)
f gjy(k) ＝f gjy(k-1) +X(10)
f gjz(k) ＝f gjz(k-1) +X(11)
wherein X (i) represents a filtered estimate, w gjx(k) 、w gjy(k) 、w gjz(k) Zero offset filtering estimated value, w of gyroscope with k moment x axis, y axis and z axis gjx(k-1) 、w gjy(k-1) 、w gjz(k-1) For time x-axis of k-1Zero offset filter estimated value f of y-axis gyroscope and z-axis gyroscope gjx(k) 、f gjy(k) 、f gjz(k) Zero offset filtering estimated value of the accelerometer with the x axis, the y axis and the z axis at the moment of k, f gjx(k-1) 、f gjy(k-1) 、f gjz(k-1) The estimated values are zero offset filtered for the x-axis, y-axis and z-axis accelerometers at time k-1.
9. The method for measuring the high-precision horizontal posture of the complex dynamic environment according to claim 8, wherein the set time is 2s.
10. A complex dynamic environment high precision horizontal attitude measurement system, comprising:
the acquisition unit is used for acquiring the gravity acceleration information of the geographic position where the strapdown inertial navigation system is located and the output information of the inertial device;
a first calculation unit for calculating an initial posture matrix according to the gravitational acceleration information and the inertial device output information
The filtering compensation unit is used for respectively carrying out filtering feedback compensation on the output increment information of the accelerometer and the gyroscope to obtain compensated output increment information of the accelerometer and output increment information of the gyroscope;
the first construction unit is used for constructing a speed update equation, a posture update equation and a position update equation according to the strapdown inertial navigation system error equation and the inertial device error equation by using the compensated accelerometer output increment information and the gyroscope output increment information;
the second construction unit is used for constructing a Kalman filtering state equation according to the strapdown inertial navigation system error equation, the inertial device error equation and the accelerometer size effect error equation and constructing a measurement equation according to the speed updating equation;
the third construction unit is used for constructing a Kalman filtering equation according to the Kalman filtering state equation and the measurement equation;
and the feedback correction unit is used for acquiring the continuous rotation accumulated time of the gyroscope, judging whether the continuous rotation accumulated time exceeds the set time, if so, carrying out feedback correction according to the speed error, the attitude error, the position error and the zero offset error of the gyroscope estimated by the Kalman filter equation, and otherwise, carrying out feedback correction according to the full state quantity estimated by the Kalman filter equation.
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