CN112798016A - SINS and DVL combination-based AUV traveling quick initial alignment method - Google Patents

SINS and DVL combination-based AUV traveling quick initial alignment method Download PDF

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CN112798016A
CN112798016A CN202011543200.3A CN202011543200A CN112798016A CN 112798016 A CN112798016 A CN 112798016A CN 202011543200 A CN202011543200 A CN 202011543200A CN 112798016 A CN112798016 A CN 112798016A
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dvl
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董权威
岳才谦
王奥博
王亭亭
田锋
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China Academy of Aerospace Aerodynamics CAAA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
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Abstract

An AUV traveling-time rapid initial alignment method based on the combination of SINS and DVL meets the technical requirement of rapid initial alignment of the AUV in the traveling process, can further improve the alignment precision in a short time, and improves the robustness of the AUV. The navigation information output by the SINS is corrected through the speed information obtained by the DVL, and the corrected information is repeatedly and alternately processed in the forward direction and the reverse direction by combining the idea of reverse navigation calculation, so that the navigation system makes full use of the navigation information generated in the alignment process, the utilization rate of the information is improved, and the alignment precision is improved. From simulation results, the forward and reverse processing times of the alignment stage are increased within a certain time, the misalignment angle error can be estimated more quickly, and the estimation precision is improved by two times. Under the condition of large angular misalignment angle of the AUV, the method still has higher estimation precision and better universality. The method can be used in the fields of multi-AUV navigation formation control, cooperative operation, submarine topography detection, sea map surveying and mapping and the like, and has guidance and application values in the aspects of theoretical research and engineering practice.

Description

SINS and DVL combination-based AUV traveling quick initial alignment method
Technical Field
The invention belongs to an initial alignment method of an Autonomous Underwater Vehicle (AUV), and relates to an AUV inter-travelling rapid initial alignment method based on a combination of a strapdown inertial navigation system and a Doppler velocimeter.
Background
In the field of underwater navigation, a Strapdown Inertial Navigation System (SINS) and Doppler Velocimeter (DVL) combined navigation system is more mature in application. The high-precision speed information provided by DVL in real time inhibits the divergence of SINS position error, and has the characteristics of high autonomy and positioning precision, so that the method is widely applied to AUV underwater navigation. Before formally entering a navigation task, an inertial navigation system needs to complete initial alignment, two important indexes of the initial alignment are accuracy and rapidity, the alignment accuracy of the inertial navigation system directly influences the navigation accuracy of an AUV, the rapidity of the alignment determines whether the AUV can be quickly put into use, and the two indexes are often contradictory.
Although the conventional onshore static base initial alignment does not need to provide motion information of an aircraft externally, compensation and correction of an inertial navigation system can be directly realized, long alignment time is needed, the maneuverability of the AUV can be reduced to a great extent, and the application range of the AUV is limited. Therefore, in some task scenarios, it is no longer applicable when the AUV is required to be able to respond quickly and aggregate quickly for use. Therefore, the research on the alignment method capable of rapidly estimating the misalignment angle error has great significance in the field of AUV engineering application. Unlike alignment with an onshore static base, the alignment between advances in the course of AUV navigation requires the introduction of external measurement information to assist in completing the initial alignment. Because the DVL is an autonomous speed measuring device, the speed information of the AUV in the process of sailing can be directly measured, and the method has strong autonomy and high precision, and meets the use requirements under water and in a certain speed range.
Generally, the initial alignment of the AUV is processed by a forward navigation solution method, which requires more navigation data to perform error estimation, and has a long estimation time and low estimation accuracy. Therefore, in order to solve the above problem, a processing method combining forward and reverse directions is proposed. By storing navigation information generated by a gyroscope and an accelerometer in the AUV navigation system at the alignment stage and then repeatedly performing forward and reverse navigation calculation on the information, the navigation data generated at the alignment stage can be fully utilized, so that the system can perform initial alignment in a short time by using less navigation data and obtain higher estimation accuracy. Finally, a navigation track simulating AUV underwater to execute submarine topography mapping task is designed by simulation, alignment angle error estimation is carried out for a period of time before navigation starts, and compared analysis is carried out on a conventional alignment method and the alignment method provided by the invention through estimation errors at different alignment time, so that the feasibility and the effectiveness of the method are verified. In addition, simulation also verifies that the misalignment angle error of the system can be rapidly and accurately estimated by adopting the method under the condition of a large-angle misalignment angle, thereby proving the universality of the method.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, provides a pilot AUV navigation data post-processing method based on reverse resolving, and solves the problem of contradiction between the dynamic performance of a carrier tracking loop and low noise.
The technical solution of the invention is as follows:
an AUV inter-travelling rapid initial alignment method based on combination of a strapdown inertial navigation system and a Doppler velocimeter comprises the following steps:
step 1: establishing a mathematical model of SINS and DVL, comprising:
(1.1) establishing a state equation of the SINS;
(1.2) establishing an error differential equation of the SINS;
(1.3) establishing an error model of the DVL;
(1.4) establishing a measurement equation of SINS/DVL;
step 2: establishing a differential update equation of the SINS/DVL according to the mathematical model of the SINS and the DVL established in the step 1, wherein the differential update equation comprises the following steps:
(2.1) establishing an attitude differential updating equation;
(2.2) establishing a speed differential update equation;
(2.3) establishing a position differential updating equation;
and step 3: discretizing the attitude, speed and position updating differential equation to obtain a discretized updating equation;
and 4, step 4: establishing a reverse-resolving discretization updating equation according to the discretization updating equation obtained in the step (3);
and 5: performing Kalman filtering estimation on the discretization updating equation obtained in the step 3 and the step 4;
step 6: and forward navigation data and reverse navigation data are alternately resolved, so that fast initial alignment between AUV advances based on the combination of the strapdown inertial navigation system and the Doppler velocimeter is realized.
Further, the establishing of the SINS state equation specifically includes:
Figure BDA0002852786880000031
wherein X is the state vector of the SINS system,
Figure BDA0002852786880000032
in the differential form of X, F is the state matrix of SINS, and the system noise W is zero-mean white Gaussian noise. Selecting a geographic coordinate system as a reference system, and selecting position error, speed error, attitude error, gyroscope drift and accelerometer zero offset as state quantities, wherein the state vector X is as follows:
Figure BDA0002852786880000033
wherein,
Figure BDA0002852786880000034
north, sky and east misalignment angles, respectively; delta VN、δVU、δVENorth, sky and east speed errors, respectively; δ L, δ λ are latitude and longitude errors, respectively; epsilonN、εU、εERespectively a gyroscope in the north east directionDrifting;
Figure BDA0002852786880000035
the accelerometer biases in the northeast direction of the accelerometer, respectively, and the state matrix F is represented as follows:
Figure BDA0002852786880000036
wherein, each variable in the state matrix F is represented as follows:
Figure BDA0002852786880000037
Figure BDA0002852786880000041
Figure BDA0002852786880000042
Figure BDA0002852786880000043
Figure BDA0002852786880000044
in the above formula, RM,RNThe curvature radiuses of the earth meridian and the prime unit circle at the position of the carrier are respectively, and the approximate calculation formula is as follows: rM≈Re(1-2e+3esin2L) and RN≈Re(1+esin2L); re is the long semi-axis of the earth reference ellipsoid, and e is the ellipticity of the reference ellipsoid; vN、VU、VEThe velocity of the AUV in the north-east direction, L and h respectively represent the longitude and depth of the carrier; omegaieIs the earth rotation rate; f. ofN、fU、fERespectively the carrier is in the northSpecific force in the east direction;
Figure BDA0002852786880000045
state transition matrix from AUV coordinate system b to geographic coordinate system n
Figure BDA0002852786880000046
Wherein phi, psi and theta respectively represent the roll angle, the course angle and the yaw angle of the AUV.
Further, the established error differential equation of the SINS is specifically as follows:
Figure BDA0002852786880000051
further, the established DVL error model specifically includes:
δVb＝ΔC·Vb+u；
wherein, δ VbAnd VbRespectively representing the speed measurement error and the navigation speed of the AUV under the AUV coordinate system; u is measurement noise; Δ C is the scale coefficient error;
in the SINS/DVL combined navigation mode, the speed relationship between the DVL coordinate system and the AUV coordinate system is expressed as
Figure BDA0002852786880000052
Wherein,
Figure BDA0002852786880000053
a transformation matrix from a DVL coordinate system d system to an AUV coordinate system b system; vdRepresenting the measured velocity in the DVL coordinate system.
Further, the established measurement equation of SINS/DVL is specifically:
first, the velocity equation of SINS in the geographic coordinate system is
VE＝VE0+δVE
VN＝VN0+δVN
VU＝VU0+δVU
Wherein, VN0、VU0、VE0Respectively representing the ideal speed of the SINS measured in the north east direction of the north; delta VN、δVU、δVERespectively, the velocity error of the SINS in the north-east direction.
The velocity of the DVL in the northeast direction under the geographic coordinate system n is
Figure BDA0002852786880000061
Figure BDA0002852786880000062
Figure BDA0002852786880000063
Wherein,
Figure BDA0002852786880000064
respectively representing the velocity of the DVL measured in the north-east direction under a geographic coordinate system n;
Figure BDA0002852786880000065
respectively representing the projections of the measurement errors in the east direction, the north direction and the sky direction,
Figure BDA0002852786880000066
Figure BDA0002852786880000067
respectively representing the projections of random interference errors of the measured values in the east direction, the north direction and the sky direction;
the calculated velocity of the SINS is subtracted from the projection of the measured velocity of the DVL in the geographic coordinate system to obtain
Figure BDA0002852786880000068
Therefore, the measurement equation Z (t) is
Figure BDA0002852786880000069
Further, the established SINS attitude differential update equation specifically comprises:
Figure BDA00028527868800000610
each variable is represented as follows
Figure BDA00028527868800000611
Figure BDA00028527868800000612
Figure BDA00028527868800000613
Wherein,
Figure BDA00028527868800000614
for state transition matrix
Figure BDA00028527868800000615
In the form of a differential of (a),
Figure BDA00028527868800000616
is the measured angular rate of the AUV;
Figure BDA00028527868800000617
AUV angular velocity measured for a gyroscope;
Figure BDA00028527868800000618
is the earth rotation rate;
Figure BDA00028527868800000619
is the position velocity;
Figure BDA00028527868800000620
representing the transition matrix from the navigation coordinate system n to the AUV coordinate system b.
Further, the established SINS velocity differential update equation specifically includes:
Figure BDA00028527868800000621
Figure BDA00028527868800000622
gn＝[0 -g 0]T
wherein f isnLinear acceleration under a navigation coordinate system; f. ofbLinear acceleration measured by an accelerometer under an AUV coordinate system; gnAcceleration in a spatial direction; g is the acceleration of gravity.
Further, the established SINS position differential update equation specifically includes:
Figure BDA0002852786880000071
wherein,
Figure BDA0002852786880000072
in differential form, L, λ, h, respectively.
Further, the discretization update equation of the posture, the speed and the position established in the step 3 specifically includes:
Figure BDA0002852786880000073
Figure BDA0002852786880000074
Figure BDA0002852786880000075
Figure BDA0002852786880000076
Figure BDA0002852786880000077
wherein,
Figure BDA0002852786880000078
Figure BDA0002852786880000079
Figure BDA00028527868800000710
and,
Figure BDA00028527868800000711
respectively representing state transition matrixes at k and k-1;
Figure BDA00028527868800000712
respectively representing the speed of the AUV at the k and k-1 moments; l isk、Lk-1Respectively showing the latitude of the AUV at the k and k-1 times; lambda [ alpha ]k、λk-1Respectively indicates the longitude of AUV at the k and k-1 time; h isk、hk-1Respectively showing the navigation depth of the AUV at the k and k-1 moments; t issTo get awayScattering period;
Figure BDA00028527868800000713
acceleration of the AUV measured by the accelerometer at the k moment;
Figure BDA00028527868800000714
angular rate of AUV at time k;
Figure BDA00028527868800000715
the angular velocity of the AUV measured by the gyroscope at the kth moment;
Figure BDA00028527868800000716
the earth rotation rate at the k and k-1 moments;
Figure BDA00028527868800000717
the position rate of the kth and k-1 time;
Figure BDA00028527868800000718
respectively represents the velocity components of the AUV measured in three directions in the northeast on the k and k-1 moments.
Further, the discrete update equation of the reverse navigation solution established in step 4 specifically includes:
suppose AUV is at TmSailing to T at any momentnAt the moment, the navigation point navigates from the M point to the N point, and the forward navigation resolving process is performed by TmResolving to TnI.e. resolving from point M to point N; the reverse navigation solution takes the ending time of the forward solution process as the starting time, and then the reverse solution is carried out to the initial time of the forward solution process, namely from TnBackward recursion of time to TmThe time of day. Therefore, converting the forward solving discrete update equation in claim 8 yields:
Figure BDA0002852786880000081
Figure BDA0002852786880000082
Figure BDA0002852786880000083
Figure BDA0002852786880000084
Figure BDA0002852786880000085
let p-k-1, p-1-k, and replace and simplify the above formula variables to get
Figure BDA0002852786880000086
Figure BDA0002852786880000087
Figure BDA0002852786880000088
Figure BDA0002852786880000089
Figure BDA00028527868800000810
Wherein,
Figure BDA00028527868800000811
Figure BDA00028527868800000812
are respectively as
Figure BDA00028527868800000813
Figure BDA00028527868800000814
Lk-1、Lk、hk-1、hk、λk-1、λk、
Figure BDA00028527868800000815
And (3) represents the same meaning.
Further, Kalman filtering estimation is carried out on the equations obtained in the step 3 and the step 4.
Figure BDA0002852786880000091
Figure BDA0002852786880000092
Figure BDA0002852786880000093
Figure BDA0002852786880000094
Figure BDA0002852786880000095
In the above formula, the first and second carbon atoms are,
Figure BDA0002852786880000096
is a state estimation;
Figure BDA0002852786880000097
predicting for one step; kkIs a filter gain array; zkIs a measured value; hkIs a measuring array; phik,k-1Is k-a one-step transfer matrix from time 1 to k;
Figure BDA0002852786880000098
estimating the state of the previous moment; pk\k-1To estimate the mean square error; pk-1To estimate the mean square error; gamma-shapedk-1A noise driving array; rkTo measure the noise variance matrix.
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention provides an AUV (autonomous underwater vehicle) traveling initial alignment method based on combination of a strapdown inertial navigation system and a Doppler velocimeter, which aims at solving the problem that the alignment speed and the alignment precision of the AUV in the traveling process cannot be met simultaneously and carries out related research and simulation. By establishing an SINS and DVL error model, forward and reverse repeated alternative solution is carried out on the acquired navigation information, and the utilization rate of the information is further increased.
(2) Simulation tests are carried out under the conditions of different resolving times and different resolving times, and the method is comprehensively compared with the traditional alignment method. The final result shows that the method can be used for further improving the estimation precision of the system in shorter alignment time, thereby improving the overall navigation performance of the system and effectively verifying the method through simulation.
(3) Simulation shows that the method is still suitable for the condition of the large misalignment angle of the AUV, and rapid estimation can be carried out on the premise of ensuring the estimation precision. The alignment method can be applied to the fields of AUV formation rapid aggregation, AUV terrain detection, chart surveying and mapping and the like, and has good guidance and application values in the aspects of theoretical research and engineering practice.
Drawings
FIG. 1: working schematic diagram of inertial navigation system;
FIG. 2: a SINS/DVL integrated navigation system resolving schematic diagram;
FIG. 3: AUV navigation track schematic diagram;
FIG. 4: a misalignment angle estimation error curve of forward solution within 100 s;
FIG. 5: alternately resolving a misalignment angle estimation error curve for 3 times in a forward and reverse direction within 100 s;
FIG. 6: alternately resolving misalignment angle estimation error curves for 6 times in a forward and reverse direction within 100 s;
FIG. 7: a misalignment angle estimation error curve calculated in the forward direction within 300 s;
FIG. 8: alternately resolving a misalignment angle estimation error curve for 3 times in a forward and reverse direction within 300 s;
FIG. 9: alternately resolving misalignment angle estimation error curves for 6 times in a forward and reverse direction within 300 s;
FIG. 10: a misalignment angle estimation error curve of forward calculation within 300s under a large misalignment angle;
FIG. 11: under a large misalignment angle, a misalignment angle estimation error curve is calculated for 3 times in a forward and reverse alternating mode within 300 s;
FIG. 12: and under a large misalignment angle, the misalignment angle estimation error curve is solved for 6 times in a forward and reverse alternating mode within 300 s.
Detailed Description
The features of the invention will now be further described with reference to the examples, the accompanying drawings and the attached tables:
the invention provides an AUV (autonomous underwater vehicle) traveling fast initial alignment method based on combination of a strapdown inertial navigation system and a Doppler velocimeter, which comprises the following steps of:
step 1: establishing a mathematical model of SINS and DVL, comprising:
(1) establishing a state equation of SINS;
specifically, according to the working principle of SINS, as shown in fig. 1, an SINS state equation is established, specifically:
Figure BDA0002852786880000101
wherein X is the state vector of the SINS system,
Figure BDA0002852786880000102
in the differential form of X, F is the state matrix of SINS, and the system noise W is zero-mean white Gaussian noise. Selecting a geographic coordinate system as a reference system, and selecting position error, speed error, attitude error, gyroscope drift and accelerometer zero offset as state quantities, and then state directionThe amount X is:
Figure BDA0002852786880000103
wherein,
Figure BDA0002852786880000104
north, sky and east misalignment angles, respectively; delta VN、δVU、δVENorth, sky and east speed errors, respectively; δ L, δ λ are latitude and longitude errors, respectively; epsilonN、εU、εEGyroscope drift in the north east direction;
Figure BDA0002852786880000105
the accelerometer biases in the northeast direction of the accelerometer, respectively, and the state matrix F is represented as follows:
Figure BDA0002852786880000111
wherein, each variable in the state matrix F is represented as follows:
Figure BDA0002852786880000112
Figure BDA0002852786880000113
Figure BDA0002852786880000114
Figure BDA0002852786880000115
Figure BDA0002852786880000116
in the above formula, RM,RNThe curvature radiuses of the earth meridian and the prime unit circle at the position of the carrier are respectively, and the approximate calculation formula is as follows: rM≈Re(1-2e+3esin2L) and RN≈Re(1+esin2L); re is the long semi-axis of the earth reference ellipsoid, and e is the ellipticity of the reference ellipsoid; vN、VU、VEThe velocity of the AUV in the north-east direction, L and h respectively represent the longitude and depth of the carrier; omegaieIs the earth rotation rate; f. ofN、fU、fERespectively the specific force of the carrier in the north-east direction;
Figure BDA0002852786880000125
state transition matrix from AUV coordinate system b to geographic coordinate system n
Figure BDA0002852786880000121
Wherein phi, psi and theta respectively represent the roll angle, the course angle and the yaw angle of the AUV.
(2) Establishing an SINS error differential equation;
the established SINS error differential equation specifically comprises the following steps:
Figure BDA0002852786880000122
(3) establishing an error model of the DVL;
the established DVL error model specifically comprises the following steps:
δVb＝ΔC·Vb+u；
wherein, δ VbAnd VbRespectively representing the speed measurement error and the navigation speed of the AUV under the AUV coordinate system; u is measurement noise; Δ C is the scale coefficient error;
in the SINS/DVL combined navigation mode, the speed relationship between the DVL coordinate system and the AUV coordinate system is expressed as
Figure BDA0002852786880000123
Wherein,
Figure BDA0002852786880000124
a transformation matrix from a DVL coordinate system d system to an AUV coordinate system b system; vdRepresenting the measured velocity in the DVL coordinate system.
(4) Establishing a measurement equation of SINS/DVL;
the established SINS/DVL measurement equation specifically comprises the following steps:
first, the velocity equation of SINS in the geographic coordinate system is
VE＝VE0+δVE
VN＝VN0+δVN
VU＝VU0+δVU
Wherein, VN0、VU0、VE0Respectively representing the ideal speed of the SINS measured in the north east direction of the north; delta VN、δVU、δVERespectively, the velocity error of the SINS in the north-east direction.
The velocity of the DVL in the northeast direction under the geographic coordinate system n is
Figure BDA0002852786880000131
Wherein,
Figure BDA0002852786880000132
respectively representing the velocity of the DVL measured in the north-east direction under a geographic coordinate system n;
Figure BDA0002852786880000133
respectively representing the projections of the measurement errors in the east direction, the north direction and the sky direction,
Figure BDA0002852786880000134
Figure BDA0002852786880000135
respectively representing the projections of random interference errors of the measured values in the east direction, the north direction and the sky direction;
the calculated velocity of the SINS is subtracted from the projection of the measured velocity of the DVL in the geographic coordinate system to obtain
Figure BDA0002852786880000136
Therefore, the measurement equation Z (t) is
Figure BDA0002852786880000137
Step 2: based on the mathematical models of SINS and DVL established in step 1, a differential update equation for SINS/DVL is established as shown in FIG. 2.
(1) Establishing an attitude differential updating equation;
the established SINS attitude differential update equation specifically comprises the following steps:
Figure BDA0002852786880000141
each variable is represented as follows
Figure BDA0002852786880000142
Figure BDA0002852786880000143
Figure BDA0002852786880000144
Wherein,
Figure BDA0002852786880000145
for state transition matrix
Figure BDA0002852786880000146
In the form of a differential of (a),
Figure BDA0002852786880000147
is the measured angular rate of the AUV;
Figure BDA0002852786880000148
AUV angular velocity measured for a gyroscope;
Figure BDA0002852786880000149
is the earth rotation rate;
Figure BDA00028527868800001410
is the position velocity;
Figure BDA00028527868800001411
representing the transition matrix from the navigation coordinate system n to the AUV coordinate system b.
(2) Establishing a speed differential updating equation;
the established SINS velocity differential update equation specifically comprises the following steps:
Figure BDA00028527868800001412
Figure BDA00028527868800001413
gn＝[0 -g 0]T
wherein f isnLinear acceleration under a navigation coordinate system; f. ofbLinear acceleration measured by an accelerometer under an AUV coordinate system; gnAcceleration in a spatial direction; g is the acceleration of gravity.
(3) Establishing a position differential updating equation;
the established SINS position differential update equation specifically comprises the following steps:
Figure BDA00028527868800001414
wherein,
Figure BDA00028527868800001415
in differential form, L, λ, h, respectively.
And step 3: discretizing the attitude, speed and position updating differential equation to obtain a discretized updating equation;
establishing a discretization updating equation of the attitude, the speed and the position, which specifically comprises the following steps:
Figure BDA0002852786880000151
Figure BDA0002852786880000152
Figure BDA0002852786880000153
Figure BDA0002852786880000154
Figure BDA0002852786880000155
wherein,
Figure BDA0002852786880000156
Figure BDA0002852786880000157
Figure BDA0002852786880000158
and,
Figure BDA0002852786880000159
respectively representing state transition matrixes at k and k-1;
Figure BDA00028527868800001510
respectively representing the speed of the AUV at the k and k-1 moments; l isk、Lk-1Respectively showing the latitude of the AUV at the k and k-1 times; lambda [ alpha ]k、λk-1Respectively indicates the longitude of AUV at the k and k-1 time; h isk、hk-1Respectively showing the navigation depth of the AUV at the k and k-1 moments; t issIs a discrete period;
Figure BDA00028527868800001511
acceleration of the AUV measured by the accelerometer at the k moment;
Figure BDA00028527868800001512
angular rate of AUV at time k;
Figure BDA00028527868800001513
the angular velocity of the AUV measured by the gyroscope at the kth moment;
Figure BDA00028527868800001514
the earth rotation rate at the k and k-1 moments;
Figure BDA00028527868800001515
the position rate of the kth and k-1 time;
Figure BDA00028527868800001516
respectively represents the velocity components of the AUV measured in three directions in the northeast on the k and k-1 moments.
And 4, step 4: according to the step 3, establishing a discretization updating equation based on reverse resolving;
suppose AUV is at TmSailing to T at any momentnAt the moment, the navigation point navigates from the M point to the N point, and the forward navigation resolving process is performed by TmResolving to TnI.e. resolving from point M to point N; the reverse navigation solution takes the ending time of the forward solution process as the starting time, and then the reverse solution is carried out to the initial time of the forward solution process, namely from TnBackward recursion of time to TmThe time of day. Thus, converting the forward solving discrete update equation yields:
Figure BDA00028527868800001517
Figure BDA0002852786880000161
Figure BDA0002852786880000162
Figure BDA0002852786880000163
Figure BDA0002852786880000164
let p-k-1, p-1-k, and replace and simplify the above formula variables to get
Figure BDA0002852786880000165
Figure BDA0002852786880000166
Figure BDA0002852786880000167
Figure BDA0002852786880000168
Figure BDA0002852786880000169
Wherein,
Figure BDA00028527868800001610
Figure BDA00028527868800001611
are respectively as
Figure BDA00028527868800001612
Figure BDA00028527868800001613
Lk-1、Lk、hk-1、hk、λk-1、λk、
Figure BDA00028527868800001614
And (3) represents the same meaning.
And 5: according to the step 4, performing Kalman filtering estimation on the obtained discretization equation;
and performing Kalman filtering estimation on the equations obtained in the step 3 and the step 4.
Figure BDA00028527868800001615
Figure BDA00028527868800001616
Figure BDA00028527868800001617
Figure BDA00028527868800001618
Figure BDA00028527868800001619
In the above formula, the first and second carbon atoms are,
Figure BDA00028527868800001620
is a state estimation;
Figure BDA00028527868800001621
predicting for one step; kkIs a filter gain array; zkIs a measured value; hkIs a measuring array; phik,k-1A one-step transfer matrix from k-1 to k;
Figure BDA00028527868800001622
estimating the state of the previous moment; pk\k-1To estimate the mean square error; pk-1To estimate the mean square error; gamma-shapedk-1A noise driving array; rkTo measure the noise variance matrix.
Step 6: forward and reverse navigation data are alternately solved;
according to the steps, a forward-reverse navigation calculation process can be realized, according to an actual calculation result, only one forward-reverse calculation is carried out, although the estimation accuracy of the navigation system can be improved to a certain extent, the estimation accuracy and speed of the misalignment angle of the system can be further improved along with the increase of the forward-reverse alternate calculation times, the problem of calculation amount brought to the navigation system due to the infinite increase of the alternate calculation times is solved, and therefore, the problem needs to be further worked. According to the steps, a complete forward and reverse processing process can be carried out once, when forward and reverse processing is carried out for a plurality of times, only the navigation information needs to be repeatedly stored and loaded, and the simulation time of the system is modified, so that forward and reverse processing results with different resolving times and different resolving times can be realized.
The embodiment of the invention comprises the following steps:
(1) and initializing navigation parameters.
1) The initial longitude and latitude of the AUV are (24 degrees 30',102 degrees 30');
2) the initial sailing speed is 2 m/s;
3) the initial attitude angles are respectively: yaw angle psi is 45 deg., pitch angle theta is 0 deg., and roll angle
Figure BDA0002852786880000171
4) DVL speed measurement error is 2mm +/-1% FS;
5) the initial misalignment angle errors are: error in north misalignment angle
Figure BDA0002852786880000172
Angular error of antenna misalignment
Figure BDA0002852786880000173
Angular error of antenna misalignment
Figure BDA0002852786880000174
6) When large misalignment angle error estimation is performed, the initial misalignment angles of the system are respectively: error in north misalignment angle
Figure BDA0002852786880000175
Angular error of antenna misalignment
Figure BDA0002852786880000176
Angular error of antenna misalignment
Figure BDA0002852786880000177
7) The error parameters of a gyroscope and an accelerometer in the strapdown inertial navigation equipment are respectively as follows: the gyroscope constant drift error is (0.02 degree/h ), and the gyroscope random drift error is (0.02 degree/h ); the accelerometer has zero offset of (100ug,100ug,100ug) and the gyroscope has random offset error of (50ug,50ug,50 ug).
(2) According to the initialization parameters, AUV navigation path planning and simulation are carried out
The navigation path of the AUV is designed to be an underwater dressing scanning route, as shown in FIG. 3. The following table sets the navigation track parameters
TABLE 1 AUV navigation trajectory parameter settings
Figure BDA0002852786880000181
At the beginning, the AUV sails on the water surface at the speed of 2m/s in the north-north direction, and after the sailing time is 105s, the AUV enters a submergence state. The dressing terrain mapping process was started after 100s to a predetermined working depth of 35m, and after 1900s the task was completed and the floating was started. And returning the AUV to the initial origin point according to the designed task flow after the AUV is drained, setting the AUV to reach the origin point at a distance of 50m around the origin point, namely reaching the origin point, and setting the duration of the whole navigation process to 2710 s. And forward calculation and forward and reverse calculation of different times and different alignment times are carried out on the navigation information acquired by the AUV in a certain time before the navigation phase, and comparison analysis is carried out.
Fig. 4 to 6 are alignment results obtained 100s before the AUV sails, where fig. 4 is a misalignment angle estimation error curve obtained after forward solution within 100s, fig. 5 is a misalignment angle estimation error curve obtained after forward and reverse alternate solution for 3 times within 100s, and fig. 6 is a misalignment angle estimation error curve obtained after forward and reverse alternate solution for 6 times within 100 s. The result shows that forward and reverse alternate solution for 3 times has faster estimation speed and higher estimation accuracy than forward solution, but the AUV state information contained in the navigation information within 100s is still insufficient, which causes the misalignment angle estimation error divergence of forward and reverse solution for 6 times, as shown in FIG. 6.
Fig. 7-9 show alignment results in 300s before the AUV sails, where fig. 7 shows misalignment angle estimation error curves obtained by forward calculation in the first 300s, fig. 8 shows misalignment angle estimation error curves obtained by forward and reverse calculation 3 times in the first 300s, and fig. 9 shows misalignment angle estimation error curves obtained by forward and reverse calculation 6 times in the first 300 s. As in the first 100s, alternating forward and reverse 3 times has a faster estimation speed than performing only forward calculation, and at the same time, has a higher estimation accuracy. Different from the first 100s estimation result, because the AUV state information contained in 300s is more sufficient, the estimation accuracy of forward and backward alternate solution 6 times is higher than that of solution 3 times, and the performance of the misalignment angle estimation is obviously improved, as shown in FIG. 9.
To verify that the method is still effective under the condition of large misalignment angle of AUV, the following simulation analysis and comparison are carried out, such as fig. 10-12.
Fig. 10 is a misalignment angle estimation error curve calculated in the forward direction within the first 300s under the large misalignment angle of the AUV, fig. 11 is a misalignment angle error estimation curve calculated in the forward and reverse directions for 3 times within the first 300s under the large misalignment angle of the AUV, and fig. 12 is a misalignment angle error estimation curve calculated in the forward and reverse directions for 6 times within the first 300s under the large misalignment angle of the AUV. Simulation results show that when the AUV is in a large misalignment angle, the misalignment angle error estimated by the method still has good estimation precision, so that the method is verified to have a wide application range, and the method has important engineering guidance and application values in the fields of rapid aggregation of AUV formation, long-time underwater navigation, surveying and mapping and the like.
Those skilled in the art will appreciate that the details of the invention not described in detail in this specification are well within the skill of those in the art.

Claims (10)

1. An AUV inter-traveling rapid initial alignment method based on combination of a strapdown inertial navigation system and a Doppler velocimeter is characterized by comprising the following steps:
step 1: establishing a mathematical model of SINS and DVL, comprising:
(1.1) establishing a state equation of the SINS;
(1.2) establishing an error differential equation of the SINS;
(1.3) establishing an error model of the DVL;
(1.4) establishing a measurement equation of SINS/DVL;
step 2: establishing a differential update equation of the SINS/DVL according to the mathematical model of the SINS and the DVL established in the step 1, wherein the differential update equation comprises the following steps:
(2.1) establishing an attitude differential updating equation;
(2.2) establishing a speed differential update equation;
(2.3) establishing a position differential updating equation;
and step 3: discretizing the attitude, speed and position updating differential equation to obtain a discretized updating equation;
and 4, step 4: establishing a reverse-resolving discretization updating equation according to the discretization updating equation obtained in the step (3);
and 5: performing Kalman filtering estimation on the discretization updating equation obtained in the step 3 and the step 4;
step 6: and forward navigation data and reverse navigation data are alternately resolved, so that fast initial alignment between AUV advances based on the combination of the strapdown inertial navigation system and the Doppler velocimeter is realized.
2. The method of claim 1, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the establishing of the SINS state equation specifically comprises the following steps:
Figure RE-FDA0003002297900000011
wherein X is the state vector of the SINS system,
Figure RE-FDA0003002297900000012
the system noise W is zero mean Gaussian white noise, and F is a state matrix of SINS; selecting a geographic coordinate system as a reference system, and selecting position error, speed error, attitude error, gyroscope drift and accelerometer zero offset as state quantities, wherein the state vector X is as follows:
Figure RE-FDA0003002297900000021
wherein,
Figure RE-FDA0003002297900000022
north, sky and east misalignment angles, respectively; delta VN、δVU、δVENorth, sky and east speed errors, respectively; δ L, δ λ are latitude and longitude errors, respectively; epsilonN、εU、εEGyroscope drift in the north east direction;
Figure RE-FDA0003002297900000023
the accelerometer biases in the northeast direction of the accelerometer, respectively, and the state matrix F is represented as follows:
Figure RE-FDA0003002297900000024
wherein, each variable in the state matrix F is represented as follows:
Figure RE-FDA0003002297900000025
Figure RE-FDA0003002297900000026
Figure RE-FDA0003002297900000027
Figure RE-FDA0003002297900000031
Figure RE-FDA0003002297900000032
in the above formula, RM,RNRespectively the curvature radius of the earth meridian and the prime unit circle of the position of the carrier, and approximately calculatingThe calculation formula is as follows: rM≈Re(1-2e+3esin2L) and RN≈Re(1+esin2L)；ReThe semiaxis is the long semiaxis of the earth reference ellipsoid, and e is the ellipticity of the reference ellipsoid; vN、VU、VEThe velocity of the AUV in the north-east direction, L and h respectively represent the longitude and depth of the carrier; omegaieIs the earth rotation rate; f. ofN、fU、fERespectively the specific force of the carrier in the north-east direction;
Figure RE-FDA0003002297900000033
state transition matrix from AUV coordinate system b to geographic coordinate system n
Figure RE-FDA0003002297900000034
Wherein phi, psi and theta respectively represent the roll angle, the course angle and the yaw angle of the AUV.
3. The method of claim 2, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the error differential equation of the SINS established in the step (1.2) specifically includes:
Figure RE-FDA0003002297900000041
4. the method of claim 3, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the DVL error model established in the step (1.3) specifically includes:
δVb＝ΔC·Vb+u；
wherein, δ VbAnd VbRespectively representing the speed measurement error and the navigation speed of the AUV under the AUV coordinate system; u is measurement noise; Δ C is the scale coefficient error;
in the SINS/DVL combined navigation mode, the speed relationship between the DVL coordinate system and the AUV coordinate system is expressed as
Figure RE-FDA0003002297900000042
Wherein,
Figure RE-FDA0003002297900000043
a transformation matrix from a DVL coordinate system d system to an AUV coordinate system b system; vdRepresenting the measured velocity in the DVL coordinate system.
5. The method of claim 4, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the measurement equation of the SINS/DVL established in the step (1.4) specifically includes:
the velocity equation of the SINS on the geographic coordinate system is
VE＝VE0+δVE
VN＝VN0+δVN
VU＝VU0+δVU
Wherein, VN0、VU0、VE0Respectively representing the ideal speed of the SINS measured in the north east direction of the north; delta VN、δVU、δVERespectively representing the velocity error of the SINS in the north-east direction;
the velocity of the DVL in the northeast direction under the geographic coordinate system n is
Figure RE-FDA0003002297900000051
Figure RE-FDA0003002297900000052
Figure RE-FDA0003002297900000053
Wherein,
Figure RE-FDA0003002297900000054
respectively representing the velocity of the DVL measured in the north-east direction under a geographic coordinate system n;
Figure RE-FDA0003002297900000055
respectively representing the projections of the measurement errors in the east direction, the north direction and the sky direction,
Figure RE-FDA0003002297900000056
Figure RE-FDA0003002297900000057
respectively representing the projections of random interference errors of the measured values in the east direction, the north direction and the sky direction;
the calculated velocity of the SINS is subtracted from the projection of the measured velocity of the DVL in the geographic coordinate system to obtain
Figure RE-FDA0003002297900000058
SINS/DVL measurement equation Z (t) is
Figure RE-FDA0003002297900000059
6. The method of claim 5, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the SINS attitude differential update equation established in the step (2.1) specifically comprises:
Figure RE-FDA00030022979000000510
each variable is represented as follows
Figure RE-FDA00030022979000000511
Figure RE-FDA00030022979000000512
Figure RE-FDA00030022979000000513
Wherein,
Figure RE-FDA00030022979000000514
as a pair state transition matrix
Figure RE-FDA00030022979000000515
In the form of a differential of (a),
Figure RE-FDA00030022979000000516
is the measured angular rate of the AUV;
Figure RE-FDA00030022979000000517
AUV angular velocity measured for a gyroscope;
Figure RE-FDA0003002297900000061
is the earth rotation rate;
Figure RE-FDA0003002297900000062
is the position velocity;
Figure RE-FDA0003002297900000063
representing a navigation coordinate system n toTransfer matrix of AUV coordinate system b.
7. The method of claim 6, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the SINS velocity differential update equation established in the step (2.2) specifically comprises:
Figure RE-FDA0003002297900000064
Figure RE-FDA0003002297900000065
gn＝[0 -g 0]T
wherein f isnLinear acceleration under a navigation coordinate system; f. ofbLinear acceleration measured by an accelerometer under an AUV coordinate system; gnAcceleration in a spatial direction; g is the acceleration of gravity;
the SINS position differential update equation established in the step (2.3) specifically includes:
Figure RE-FDA0003002297900000066
wherein,
Figure RE-FDA0003002297900000067
in differential form, L, λ, h, respectively.
8. The method of claim 7, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the discretization updating equation of the attitude, the speed and the position established in the step 3 specifically comprises the following steps:
Figure RE-FDA0003002297900000068
Figure RE-FDA0003002297900000069
Figure RE-FDA00030022979000000610
Figure RE-FDA00030022979000000611
Figure RE-FDA00030022979000000612
wherein,
Figure RE-FDA00030022979000000613
Figure RE-FDA00030022979000000614
Figure RE-FDA00030022979000000615
and,
Figure RE-FDA0003002297900000071
respectively representing state transition matrixes at k and k-1;
Figure RE-FDA0003002297900000072
respectively representing the speed of the AUV at the k and k-1 moments; l isk、Lk-1Respectively showing the latitude of the AUV at the k and k-1 times; lambda [ alpha ]k、λk-1Respectively indicates the longitude of AUV at the k and k-1 time; h isk、hk-1Respectively showing the navigation depth of the AUV at the k and k-1 moments; t issIs a discrete period;
Figure RE-FDA0003002297900000073
acceleration of the AUV measured by the accelerometer at the k moment;
Figure RE-FDA0003002297900000074
angular rate of AUV at time k;
Figure RE-FDA0003002297900000075
the angular velocity of the AUV measured by the gyroscope at the kth moment;
Figure RE-FDA0003002297900000076
the earth rotation rate at the k and k-1 moments;
Figure RE-FDA0003002297900000077
the position rate of the kth and k-1 time;
Figure RE-FDA0003002297900000078
respectively represents the velocity components of the AUV measured in three directions in the northeast on the k and k-1 moments.
9. The method of claim 8, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: the discrete update equation for the reverse navigation solution established in the step 4 specifically includes:
suppose AUV is at TmSailing to T at any momentnAt the moment, the navigation point navigates from the M point to the N point, and the forward navigation resolving process is performed by TmResolving to TnI.e. resolving from point M to point N; the reverse navigation solution takes the end time of the forward solution process as the starting time, and then the reverse solution is carried outTo the initial moment of the forward solution process, i.e. from TnBackward recursion of time to TmTime of day;
converting the forward solving discrete updating equation to obtain:
Figure RE-FDA0003002297900000079
Figure RE-FDA00030022979000000710
Figure RE-FDA00030022979000000711
Figure RE-FDA00030022979000000712
Figure RE-FDA00030022979000000713
let p-k-1, p-1-k, and replace and simplify the above formula variables to get
Figure RE-FDA00030022979000000714
Figure RE-FDA00030022979000000715
Figure RE-FDA0003002297900000081
Figure RE-FDA0003002297900000082
Figure RE-FDA0003002297900000083
Wherein,
Figure RE-FDA0003002297900000084
Figure RE-FDA0003002297900000085
are respectively as
Figure RE-FDA0003002297900000086
Figure RE-FDA0003002297900000087
Lk-1、Lk、hk-1、hk、λk-1、λk、
Figure RE-FDA0003002297900000088
And (3) represents the same meaning.
10. The method of claim 9, wherein the method for fast initial alignment between AUV travels based on a combination of a strapdown inertial navigation system and a Doppler velocimeter, comprises: performing kalman filtering estimation on the equations obtained in the step 3 and the step 4, specifically:
Figure RE-FDA0003002297900000089
Figure RE-FDA00030022979000000810
Figure RE-FDA00030022979000000811
Pk\k-1＝Φk,k-1Pk-1ΦT k,k-1+Γk-1Qk-1ΓT k-1
Pk＝(I-KkHk)Pk|k-1(I-KkHk)T+KkRkKT k
in the above formula, the first and second carbon atoms are,
Figure RE-FDA00030022979000000812
is a state estimation;
Figure RE-FDA00030022979000000813
predicting for one step; kkIs a filter gain array; zkIs a measured value; hkIs a measuring array; phik,k-1A one-step transfer matrix from k-1 to k;
Figure RE-FDA00030022979000000814
estimating the state of the previous moment; pk\k-1To estimate the mean square error; pk-1To estimate the mean square error; gamma-shapedk-1A noise driving array; rkTo measure the noise variance matrix.
CN202011543200.3A 2020-12-22 2020-12-22 SINS and DVL combination-based AUV traveling quick initial alignment method Pending CN112798016A (en)

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