CN111896031B - Error compensation method and system for inertia base combined navigation system under black-out condition - Google Patents

Error compensation method and system for inertia base combined navigation system under black-out condition Download PDF

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CN111896031B
CN111896031B CN202010781187.9A CN202010781187A CN111896031B CN 111896031 B CN111896031 B CN 111896031B CN 202010781187 A CN202010781187 A CN 202010781187A CN 111896031 B CN111896031 B CN 111896031B
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杨波
杨剑
齐鑫
单斌
樊红东
高久安
薛亮
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Rocket Force University of Engineering of PLA
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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

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Abstract

The invention relates to an error compensation method and system for an inertia base combined navigation system under the condition of black obstacles, which comprises the following steps: establishing a system state equation of error compensation based on an error model of the inertial navigation system; acquiring measurement data of the inertia base combined navigation system at each moment before the current moment to serve as an actual measurement data set; determining a system state estimation value at the last moment by adopting a Kalman filtering method according to the actually measured data set and a system state equation of error compensation; when the current moment is the occurrence of the black barrier, determining the system state estimation value of the current moment by adopting a linear minimum variance estimation method according to the system state estimation value of the previous moment; and correcting the error of the inertial navigation system by using the system state estimated value at the current moment. By the method, error online compensation is carried out on the inertial navigation system in the black-obstacle environment, so that the integrated navigation system keeps high navigation positioning precision, and the adaptability of the inertial-based integrated navigation system to the black-obstacle and other complex environments is enhanced.

Description

Error compensation method and system for inertia base combined navigation system under black-out condition
Technical Field
The invention relates to the technical field of navigation system error compensation, in particular to an error compensation method and system for an inertia base combined navigation system under the condition of black fault.
Background
In order to realize high-precision and high-reliability navigation and positioning of various modern aircrafts, the aircrafts are generally provided with navigation and positioning equipment which takes an inertial navigation system (inertial navigation for short) as a main part and takes a satellite navigation system, a radar navigation system, an astronomical navigation system and the like as an auxiliary part, and the navigation and positioning equipment are organically combined through modern information fusion technologies such as Kalman filtering and the like to form an inertial-based combined navigation system, so that the navigation and positioning equipment not only can make up for the deficiencies of each other, but also can realize the performance superior to that of any navigation system, and is the most ideal aircraft navigation mode recognized by various countries in the world at present.
When the aircraft flies at high supersonic speed in the atmosphere, high-temperature plasma is generated after the surface of the aircraft is in violent friction combustion with air, and the high-temperature plasma can shield or interfere electromagnetic waves and electronic instruments, namely, a phenomenon of so-called 'black barrier' is generated. At the moment, modern navigation means such as satellite navigation, astronomical navigation, radar navigation and the like can not work normally, only an inertial navigation system can still work normally, and the inertial navigation system has a prominent problem: the navigation error is continuously accumulated along with the working time, so that the long-time high-precision navigation can not be realized by only the inertial navigation system. In addition, during long-time high-speed navigation, the aircraft is inevitably affected by various external severe natural environments or artificial interference, especially complex electromagnetic interference, and at this time, the satellite navigation system, the radar navigation system and the like are very likely to be completely shielded or interfered and cannot normally work, and the situation can also be regarded as a 'black barrier' phenomenon in a broad sense.
With the continuous and deep research of China on the relevant technology of the hypersonic flight vehicle, the problem of poor navigation accuracy of the combined navigation system caused by the problem of black barrier needs to be solved urgently in the hypersonic flight process of the flight vehicle.
Disclosure of Invention
The invention aims to provide an error compensation method and system for an inertia base combined navigation system under the condition of black obstacles, which can perform error online compensation on the inertia navigation system in the combined navigation system under the complex severe environments such as the black obstacles, so that the combined navigation system can always keep higher navigation positioning accuracy, and the adaptability of the inertia base combined navigation system to the complex severe environments such as the black obstacles is enhanced.
In order to achieve the purpose, the invention provides the following scheme:
an error compensation method for an inertia base combined navigation system under the condition of black fault comprises the following steps:
establishing a system state equation of error compensation based on an error model of the inertial navigation system;
acquiring measurement data of the inertia base combined navigation system at each moment before the current moment to serve as a measured data set; the measured data set comprises measured data of each moment before the current moment; the current moment is the moment when the black barrier appears;
determining a system state estimation value at the last moment by adopting a Kalman filtering method according to the actually measured data set and the system state equation of error compensation;
determining the system state estimation value at the current moment by adopting a linear minimum variance estimation method according to the system state estimation value at the previous moment;
and correcting the error of the inertial navigation system by using the estimated value of the system state at the current moment.
Optionally, the correcting the error of the inertial navigation system by using the estimated value of the system state at the current time further includes:
and updating the current time to the last time, updating the system state estimation value of the current time to the system state estimation value of the last time, and returning to the step of determining the system state estimation value of the current time by adopting a linear minimum variance estimation method according to the system state estimation value of the last time.
Optionally, the determining the system state estimation value at the current time by using a linear minimum variance estimation method according to the system state estimation value at the previous time specifically includes:
according to the formula
Figure BDA0002620272010000021
Determining a system state estimation value at the current moment;
wherein the content of the first and second substances,
Figure BDA0002620272010000022
is the estimated value of the system state at the kth moment, namely the estimated value of the system state at the current moment,
Figure BDA0002620272010000023
is the system state estimate at time k-1, i.e., the last time, phik,k-1Is the state transition matrix from the k-1 th time to the k-th time.
Alternatively, the formula
Figure BDA0002620272010000024
The acquisition process specifically comprises:
discretizing the system state equation of the error compensation to obtain a discretized error compensation system state equation;
estimating the system state at the kth moment by adopting a linear minimum variance estimation method according to the actually measured data set to obtain a linear minimum variance estimation equation of the system state at the kth moment;
substituting the discrete error compensation system state equation into the linear minimum variance estimation equation of the system state at the kth moment to obtain a system state estimation formula
Figure BDA0002620272010000031
An error compensation system of an inertia-based integrated navigation system under the condition of black fault comprises:
the system state equation building module for error compensation is used for building a system state equation for error compensation based on an error model of the inertial navigation system;
the measured data set acquisition module is used for acquiring measured data of the inertia base combined navigation system at each moment before the current moment as a measured data set; the measured data set comprises measured data of each moment before the current moment; the current moment is the moment when the black barrier appears;
the last-time system state estimation value determining module is used for determining the last-time system state estimation value by adopting a Kalman filtering method according to the measured data set and the error compensation system state equation;
a current time system state estimation value determining module, configured to determine a current time system state estimation value by using a linear minimum variance estimation method according to the previous time system state estimation value;
and the error correction module is used for correcting the error of the inertial navigation system by using the system state estimation value at the current moment.
Optionally, the error compensation system for an inertia-based integrated navigation system under the black fault condition further includes:
and the state updating module is used for updating the current time to the last time, updating the system state estimation value of the current time to the system state estimation value of the last time, and returning to the system state estimation value determining module at the current time.
Optionally, the module for determining the estimated value of the system state at the current time specifically includes:
a current time system state estimation value determination unit for determining the current time system state estimation value according to a formula
Figure BDA0002620272010000032
Determining a system state estimation value at the current moment;
wherein the content of the first and second substances,
Figure BDA0002620272010000033
is the estimated value of the system state at the kth moment, namely the estimated value of the system state at the current moment,
Figure BDA0002620272010000034
is the system state estimate at time k-1, i.e., the last time, phik,k-1Is the state transition matrix from the k-1 th time to the k-th time.
Alternatively, the formula
Figure BDA0002620272010000035
The acquisition process specifically comprises:
the discretization unit is used for discretizing the system state equation of the error compensation to obtain a discretized error compensation system state equation;
a linear minimum variance estimation equation obtaining unit of the system state at the kth moment, configured to estimate the system state at the kth moment by using a linear minimum variance estimation method according to the actually measured data set, so as to obtain a linear minimum variance estimation equation of the system state at the kth moment;
a system state estimation equation determination unit for substituting the discrete error compensation system state equation into the system at the k-th timeObtaining a linear minimum variance estimation equation of the system state to obtain a system state estimation formula
Figure BDA0002620272010000041
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides an error compensation method and system for an inertia base combined navigation system under the condition of black obstacles, wherein the method comprises the following steps: establishing a system state equation of error compensation based on an error model of the inertial navigation system; acquiring measurement data of the inertia base combined navigation system at each moment before the current moment to serve as an actual measurement data set; determining a system state estimation value at the last moment by adopting a Kalman filtering method according to the actually measured data set and a system state equation of error compensation; when the current moment is the occurrence of the black barrier, determining the system state estimation value of the current moment by adopting a linear minimum variance estimation method according to the system state estimation value of the previous moment; and correcting the error of the inertial navigation system by using the system state estimated value at the current moment. By the method, the error online compensation can be performed on the inertial navigation system in the combined navigation system under the complex severe environments such as the black obstacle, so that the combined navigation system can always keep higher navigation positioning precision, and the adaptability of the inertial-based combined navigation system to the complex severe environments such as the black obstacle is enhanced.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of an error compensation method for an inertia based integrated navigation system under a black-out condition according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of an error compensation system of an inertia-based integrated navigation system under a black-out condition according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an error compensation method and system for an inertia base combined navigation system under the condition of black obstacles, which can perform error online compensation on the inertia navigation system in the combined navigation system under the complex severe environments such as the black obstacles, so that the combined navigation system can always keep higher navigation positioning accuracy, and the adaptability of the inertia base combined navigation system to the complex severe environments such as the black obstacles is enhanced.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of an error compensation method for an inertia based integrated navigation system under a black-out condition according to an embodiment of the present invention, as shown in fig. 1, the error compensation method for an inertia based integrated navigation system under a black-out condition according to the present invention includes:
s101, establishing a system state equation of error compensation based on an error model of the inertial navigation system.
Specifically, the fact that the error compensation of the inertial-based integrated navigation system is to compensate the error of the inertial navigation system is considered, so that the error of the inertial navigation system needs to be selected as a system state based on an error model of the inertial navigation system, and a system state equation for compensating the system error is established. The inertial navigation system in the embodiment of the invention selects a strapdown inertial navigation system.
Errors of the strapdown inertial navigation system mainly include errors of inertial devices, system errors caused by the errors of the inertial devices, and the like, so that the errors need to be analyzed and modeled respectively, and a corresponding error equation is established. Wherein, the error equation of the inertia device is as follows:
Figure BDA0002620272010000051
Figure BDA0002620272010000052
wherein epsilonbiIs a random constant drift of the gyroscope i,
Figure BDA0002620272010000053
is epsilonbiThe first order differential of the first order of the,
Figure BDA0002620272010000054
for a random constant error of the accelerometer i,
Figure BDA0002620272010000055
is composed of
Figure BDA0002620272010000056
Where i ═ x, y, z denotes gyroscopes or accelerometers mounted along the x, y, z axes of the carrier.
Due to the fact that the inertial device has errors, certain errors exist in the strapdown inertial navigation system and navigation parameters output by the strapdown inertial navigation system, specifically including a mathematical platform attitude error, a speed error and a position error, and the specific error equation is in the form as described below.
The mathematical platform attitude error equation of the strapdown inertial navigation system is as follows:
Figure BDA0002620272010000057
Figure BDA0002620272010000061
Figure BDA0002620272010000062
wherein phi isE、φN、φURespectively representing attitude errors of a mathematical platform of the strapdown inertial navigation system along east, north and sky directions;
Figure BDA0002620272010000063
is phiEThe first order differential of the first order of the,
Figure BDA0002620272010000064
is phiNThe first order differential of the first order of the,
Figure BDA0002620272010000065
is phiUFirst order differentiation of; delta vE、δvN、δvURespectively the east, north and sky speed errors of the strapdown inertial navigation system; delta L, delta lambda and delta h are respectively latitude, longitude and altitude errors of the strapdown inertial navigation system; w is agiWhite noise, w, for the measurement of gyroscope iaiWhite noise for the accelerometer i; omegaieThe rotational angular velocity of the earth, and R is the radius of the earth; v. ofE、vN、vUThe east, north and sky speeds of the carrier respectively; l, lambda and h are respectively the latitude, longitude and altitude of the carrier position; t isij(i, j ═ 1,2,3) is an attitude matrix
Figure BDA0002620272010000066
Row i and column j.
The velocity error equation of the strapdown inertial navigation system is as follows:
Figure BDA0002620272010000067
Figure BDA0002620272010000068
Figure BDA0002620272010000069
wherein f isE、fN、fURespectively, the accelerometer outputs equivalent specific forces along the east, north and sky directions.
The position error equation of the strapdown inertial navigation system is as follows:
Figure BDA0002620272010000071
Figure BDA0002620272010000072
Figure BDA0002620272010000073
therefore, according to the error model of the strapdown inertial navigation system, taking the mathematical platform attitude error, the velocity error, the position error, the gyroscope error and the accelerometer error of the strapdown inertial navigation system as the system state, the method comprises the following steps: attitude error phi of mathematical platform along east, north and sky directionsE,φN,φUVelocity error δ v in east, north and sky directionsE,δvN,δvUConstant drift epsilon of gyroscope on weft, warp and height errors delta L, delta lambda, delta h, x, y and z axesbx,εby,εbzConstant offset of accelerometer in x, y, z axes
Figure BDA0002620272010000074
I.e. the system state X of the error compensation is:
Figure BDA0002620272010000075
obviously, in combination with the above system state X, the various error equations of the previous strapdown inertial navigation system can be written in the form of:
Figure BDA0002620272010000076
the above equation is the system state equation for error compensation. Wherein, F is recorded as a system state matrix; g is recorded as a system noise driving array; w is noted as system white noise. Obviously, the system state equation describes the relationship between the system input and the system state, namely the relationship between various motion parameters of the carrier and various errors of the strapdown inertial navigation system.
Let the above-mentioned continuous system state equation be discretized into the following form:
Xk＝Φk,k-1Xk-1+Γk-1Wk-1
wherein, Xk-1、XkThe system states at the k-1 and k-th time, phik,k-1Is the state transition matrix from time k-1 to time k, Γk-1For discrete system noise-driven arrays, Wk-1A noise sequence is excited for a discrete system.
S102, acquiring measurement data of the inertia base combined navigation system at each moment before the current moment to serve as a measured data set; the measured data set comprises measured data of each moment before the current moment; the current moment is the moment when the black barrier appears.
And S103, determining the system state estimation value at the previous moment by adopting Kalman filtering according to the actually measured data set and the system state equation of error compensation.
Considering that the output of each subsystem of the integrated navigation system is normal before the black-fault phenomenon occurs, namely the measurement of the integrated navigation system is known at the moment, and only the strapdown inertial navigation system can normally output navigation parameters after the black-fault phenomenon occurs, the error of the inertial navigation system during the black-fault period is estimated online in real time by using the known measurement data of the integrated navigation system before the black-fault occurs and the real-time output information of the inertial navigation system during the black-fault period and adopting a linear minimum variance estimation method.
And S104, determining the system state estimation value at the current moment by adopting a linear minimum variance estimation method according to the system state estimation value at the previous moment. In particular, according to the formula
Figure BDA0002620272010000081
Determining a system state estimation value at the current moment; wherein the content of the first and second substances,
Figure BDA0002620272010000082
is the estimated value of the system state at the kth moment, namely the estimated value of the system state at the current moment,
Figure BDA0002620272010000083
is the system state estimate at time k-1, i.e., the last time, phik,k-1Is the state transition matrix from the k-1 th time to the k-th time.
Formula (II)
Figure BDA0002620272010000084
The acquisition process specifically comprises:
step 401, discretizing the system state equation of the error compensation to obtain a discretized error compensation system state equation Xk＝Φk,k-1Xk-1+Γk-1Wk-1。
Step 402, estimating the system state at the kth moment by adopting a linear minimum variance estimation method according to the actually measured data set to obtain a linear minimum variance estimation equation of the system state at the kth moment;
step 403, substituting the discrete error compensation system state equation into the linear minimum variance estimation equation of the system state at the kth moment to obtain a system state estimation formula
Figure BDA0002620272010000085
Specifically, suppose that a black-out condition occurs at the k-th time, that is, the inertial-based integrated navigation filter at the k-th time has no measurement data, and the measurement data at the k-1 previous times exist. In thatIs based on the measured data Z of k-1 previous time points1、Z2…Zk-1For the current k-th system state XkMaking linear minimum variance estimates, i.e.
Figure BDA0002620272010000086
Here, E*[·]Representing a linear minimum variance estimate.
Substituting the discretized form of the previous system state equation into the above equation and estimating the linear property according to the linear minimum variance can obtain:
Figure BDA0002620272010000087
and W is known from the discretization form of the state equation of the systemk-1To X onlykHas an influence on Z1、Z2…Zk-1Not correlation, then E*[Wk-1/Z1,Z2…Zk-1]＝E*[Wk-1]Is equal to 0, thus having
Figure BDA0002620272010000088
Because the combined navigation system has the black fault condition at the kth moment and the measured data of the combined navigation system at the previous k-1 moments exist, the measured data Z at the previous k-1 moments can be obtained1、Z2…Zk-1Performing Kalman filtering calculation of normal integrated navigation to obtain the system state estimation value at the k-1 th moment
Figure BDA0002620272010000091
Since Kalman filtering is also a linear minimum variance estimation, it is obtained by Kalman filtering calculation
Figure BDA0002620272010000092
Can be considered as being based on the measurement data Z of k-1 previous time points1、Z2…Zk-1For the system state at the k-1 th time
Figure BDA0002620272010000093
Linear minimum variance estimation is
Figure BDA0002620272010000094
Thus, the system state X at the k-th time can be obtained from the above relationskIs estimated by the formula
Figure BDA0002620272010000095
And S105, correcting the error of the inertial navigation system by using the system state estimated value at the current moment.
After S105, further comprising:
and updating the current time to the last time, updating the system state estimation value of the current time to the system state estimation value of the last time, and returning to the step S104. Similarly, the estimated value of the system state at the k-th moment is further determined
Figure BDA0002620272010000099
For the system state X at the k +1 th timek+1The system state X at the k +1 th moment can be obtained by linear minimum variance estimationk+1Is estimated by the formula
Figure BDA0002620272010000096
By analogy, the estimated value of the system state at the k +2 th moment can be obtained by calculation
Figure BDA0002620272010000097
Thus, a recursion calculation formula of system state estimation under severe environments such as blackout and the like can be obtained as
Figure BDA0002620272010000098
Therefore, under severe environments such as blackout, the recursive calculation formula of the system state estimation can be used for realizing the system state X (namely the error of the strapdown inertial navigation system)And estimating on line until the black barrier is finished.
The error compensation method of the inertia base combined navigation system under the black-out condition provided by the invention fully utilizes the propagation characteristic of the system error, establishes a system state equation, combines with the previously known external measurement data, carries out linear minimum variance estimation on the system state, namely the inertial navigation system error under the condition that the external measurement data is not updated for a short time, realizes the continuous updating calculation of the system state, further realizes the continuous correction on the error of the inertial navigation system, effectively solves the problems that the navigation systems such as satellites, radars and the like can not work normally under the condition that the black-out condition occurs, the error of the inertial navigation system diverges rapidly along with time, the rapid decline of the precision of the whole combined navigation system can not meet the navigation requirement with higher precision, and obviously enhances the adaptability of the inertia base combined navigation system to various complex and severe environments. The method has the advantages of ingenious design, easy realization of engineering, low cost and strong practicability, and is very suitable for the application fields of spaceflight, aviation, weaponry and the like.
The invention also provides an error compensation system of the inertia-based integrated navigation system under the condition of black fault, as shown in fig. 2, the system comprises:
and the error compensation system state equation building module 1 is used for building an error compensation system state equation based on an error model of the inertial navigation system.
The measured data set acquisition module 2 is used for acquiring measured data of the inertia base combined navigation system at each moment before the current moment as a measured data set; the measured data set includes measured data at each time prior to the current time. The current moment is the moment when the black barrier appears;
and the last-time system state estimation value determining module 3 is used for determining the last-time system state estimation value by adopting a Kalman filtering method according to the actually measured data set and the error compensation system state equation.
And the current-time system state estimation value determining module 4 is used for determining the current-time system state estimation value by adopting a linear minimum variance estimation method according to the previous-time system state estimation value.
And the error correction module 5 is used for correcting the error of the inertial navigation system by using the system state estimation value at the current moment.
Preferably, the error compensation system for the inertia-based integrated navigation system under the black fault condition further includes:
and the state updating module is used for updating the current time to the last time, updating the system state estimation value of the current time to the system state estimation value of the last time, and returning to the current time system state estimation value determining module 4.
Preferably, the module for determining the estimated value of the system state at the current time specifically includes:
a current-time system state estimation value determination unit for determining the current-time system state estimation value according to a formula
Figure BDA0002620272010000101
And determining the system state estimation value at the current moment.
Wherein the content of the first and second substances,
Figure BDA0002620272010000102
is the estimated value of the system state at the kth moment, namely the estimated value of the system state at the current moment,
Figure BDA0002620272010000103
is the system state estimate at time k-1, i.e., the last time, phik,k-1Is the state transition matrix from the k-1 th time to the k-th time.
Preferably, the formula
Figure BDA0002620272010000104
The acquisition process specifically comprises:
the discretization unit is used for discretizing the system state equation of the error compensation to obtain a discretized error compensation system state equation;
a linear minimum variance estimation equation obtaining unit of the system state at the kth moment, configured to estimate the system state at the kth moment by using a linear minimum variance estimation method according to the actually measured data set, so as to obtain a linear minimum variance estimation equation of the system state at the kth moment;
a system state estimation equation determining unit for substituting the discrete error compensation system state equation into the linear minimum variance estimation equation of the system state at the kth moment to obtain a system state estimation formula
Figure BDA0002620272010000111
The system state estimation value of the current moment in the embodiment of the invention
Figure BDA0002620272010000112
The mean square error matrix of (a) is solved,
Figure BDA0002620272010000113
has an error of
Figure BDA0002620272010000114
Then
Figure BDA0002620272010000115
The discretization form of the state equation of the system is substituted into the formula and is sorted to obtain the final product
Figure BDA0002620272010000116
Thus, the system state estimation at the k-th time
Figure BDA0002620272010000117
Of mean square error matrix of
Figure BDA0002620272010000118
Due to Wk-1Influencing only XkWithout affecting Xk-1To do so
Figure BDA0002620272010000119
Thereby Wk-1And
Figure BDA00026202720100001110
is not related, again because of E [ W ]k-1]The system state estimation under the severe environment such as black barrier can be obtained by derivation by the above formula
Figure BDA00026202720100001111
Of mean square error matrix of
Figure BDA00026202720100001112
By the above mean square error matrix PkFor previous system state estimates
Figure BDA00026202720100001113
And judging the quality degree.
The real-time estimation value of the inertial navigation system error is proved to meet the unbiased requirement through mathematical derivation, and then the online estimation and correction compensation of the inertial navigation system error can be realized by utilizing the estimation value.
Before the black fault condition appears at the kth moment, all the parts of the integrated navigation system are normal, at the moment, the integrated navigation system carries out conventional Kalman filtering, and the unbiased cognition of the Kalman filtering is that
Figure BDA00026202720100001114
The recursion calculation formula of the system state estimation obtained by combining the previous derivation is as follows:
Figure BDA00026202720100001115
thus, using the two equations above, one can obtain:
Figure BDA00026202720100001116
the same can be obtained
Figure BDA00026202720100001117
By analogy, the recursion calculation formula of the system state estimation is obtained
Figure BDA00026202720100001118
Is the system state XkUnbiased estimation of (d).
Therefore, when the inertia base combined navigation system faces the complex and severe environment such as the black obstacle, no navigation equipment such as a satellite navigation system, a radar navigation system and the like outputs, but the strapdown inertial navigation system can still normally output, at the moment, the error compensation method of the inertia base combined navigation system under the condition of the black obstacle can calculate the estimated value of the error of the inertial navigation system at the current moment on line in real time, the error of the strapdown inertial navigation system can be corrected and compensated by using the estimated value, and the output of the strapdown inertial navigation system after being corrected and compensated is used as the output of the whole combined navigation system, so that the inertia base combined navigation system can still keep higher navigation precision under the complex and severe environment such as the black obstacle.
The invention has the advantages that:
1. the error compensation method and the error compensation system for the inertia base combined navigation system under the condition of the black obstacle provide a technical method which is feasible in engineering and obvious in effect for solving the problem of maintaining the combined navigation precision under the complicated severe environments such as the black obstacle, and the method has the advantages of high precision, ingenious conception, low cost, easiness in implementation of the engineering and the like.
2. The method not only can be suitable for solving the problem of 'black barrier' caused by high-temperature plasma generated by high-supersonic-speed flight of an aircraft in the atmosphere, but also can be further popularized and applied to generalized 'black barrier' occasions in which satellite navigation, radar navigation and the like cannot work normally due to various complex electromagnetic interferences, effectively ensures the navigation and positioning accuracy of the inertia-based combined navigation system in complex severe environments such as the black barrier and the like, and obviously enhances the adaptability of the system to severe environments.
3. According to the method, the error model of the inertial navigation system is utilized, the inertial navigation system error is selected as the state, and the system state equation of error compensation is established, so that the propagation characteristic of the inertial navigation system error is disclosed, and a necessary model foundation is laid for the subsequent online estimation of the inertial navigation system error.
4. According to the method, the known measurement information of the integrated navigation system before the black barrier appears and the real-time output information of the inertial navigation system during the black barrier appears are fully utilized, and the error of the inertial navigation system during the black barrier appears is estimated on line in real time by adopting the linear minimum variance estimation, so that not only is the estimation result of the error of the inertial navigation system obtained in real time, but also the estimation result is estimated by utilizing a mean square error calculation formula, and therefore the system error compensation is possible to realize.
5. The theoretical derivation proves that the estimated value of the system state of the inertial navigation system error at the current moment meets the unbiased requirement, so that the error compensation technology provided by the invention is fully demonstrated.
6. The invention does not change the original structure of the inertia-based integrated navigation system, does not need to be equipped with additional auxiliary equipment, only needs to embed the corresponding compensation method into the original integrated navigation computer, can solve the problem of maintaining the precision of the integrated navigation system under the complicated and severe environments such as black obstacles and the like by using the technology provided by the invention, and has the advantages of easy realization of engineering, low cost and good practicability.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (6)

1. An error compensation method for an inertia-based combined navigation system under the condition of black fault is characterized by comprising the following steps:
establishing a system state equation of error compensation based on an error model of the inertial navigation system; the errors of the strapdown inertial navigation system mainly comprise inertial device errors and system errors caused by the inertial device errors, wherein an inertial device error equation is as follows:
Figure FDA0003559850770000011
Figure FDA0003559850770000012
wherein epsilonbiIs a random constant drift of the gyroscope i,
Figure FDA0003559850770000013
is epsilonbiThe first order differential of the first order of the,
Figure FDA0003559850770000014
for a random constant error of the accelerometer i,
Figure FDA0003559850770000015
is composed of
Figure FDA0003559850770000016
X, y, z denotes a gyroscope or accelerometer mounted along the x, y, z axes of the carrier;
due to the fact that errors exist in the inertial device, certain errors exist in the strapdown inertial navigation system and navigation parameters output by the strapdown inertial navigation system, specifically including a mathematical platform attitude error, a speed error and a position error, and the specific error equation is in the following form;
Figure FDA0003559850770000017
Figure FDA0003559850770000018
Figure FDA0003559850770000019
wherein phi isE、φN、φURespectively representing attitude errors of a mathematical platform of the strapdown inertial navigation system along east, north and sky directions;
Figure FDA00035598507700000110
is phiEThe first order differential of the first order of the,
Figure FDA00035598507700000111
is phiNThe first order differential of the first order of the,
Figure FDA00035598507700000112
is phiUFirst order differentiation of; delta vE、δvN、δvURespectively the east, north and sky speed errors of the strapdown inertial navigation system; delta L, delta lambda and delta h are respectively latitude, longitude and altitude errors of the strapdown inertial navigation system; w is agiWhite noise, w, for the measurement of gyroscope iaiWhite noise for the accelerometer i; omegaieThe rotational angular velocity of the earth, and R is the radius of the earth; v. ofE、vN、vUThe east, north and sky speeds of the carrier respectively; l, lambda and h are respectively the latitude, longitude and altitude of the carrier position; t isijI, j is 1,2,3, which is the attitude matrix
Figure FDA0003559850770000021
Row i and column j elements of (1);
the velocity error equation of the strapdown inertial navigation system is as follows:
Figure FDA0003559850770000022
Figure FDA0003559850770000023
Figure FDA0003559850770000024
wherein f isE、fN、fURespectively outputting equivalent specific forces along the east, north and sky directions for the accelerometer;
the position error equation of the strapdown inertial navigation system is as follows:
Figure FDA0003559850770000025
Figure FDA0003559850770000026
Figure FDA0003559850770000027
according to the error model of the strapdown inertial navigation system, taking the mathematical platform attitude error, the speed error, the position error, the gyroscope error and the accelerometer error of the strapdown inertial navigation system as the system state, the method comprises the following steps: attitude error phi of mathematical platform along east, north and sky directionsE,φN,φUVelocity error δ v in east, north and sky directionsE,δvN,δvUConstant drift epsilon of gyroscope on weft, warp and height errors delta L, delta lambda, delta h, x, y and z axesbx,εby,εbzConstant offset of accelerometer in x, y, z axes
Figure FDA0003559850770000031
I.e. system for error compensationThe system state X is:
Figure FDA0003559850770000032
obviously, in combination with the above system state X, the various error equations of the prior strapdown inertial navigation system can be written in the following form:
Figure FDA0003559850770000033
the above formula is the system state equation of error compensation; wherein, F is recorded as a system state matrix; g is recorded as a system noise driving array; w is recorded as system white noise, and the system state equation describes the relationship between system input and system state, namely describes the relationship between various motion parameters of a carrier and various errors of a strapdown inertial navigation system; let the continuous system state equation be discretized into the form:
Xk＝Φk,k-1Xk-1+Γk-1Wk-1
wherein, Xk-1、XkThe system states at the k-1 and k-th time, phik,k-1Is the state transition matrix from time k-1 to time k, Γk-1For discrete system noise-driven arrays, Wk-1Exciting a noise sequence for the discrete system;
acquiring measurement data of the inertia base combined navigation system at each moment before the current moment to serve as a measured data set; the current moment is the moment when the black barrier appears;
determining a system state estimation value at the last moment by adopting a Kalman filtering method according to the actually measured data set and the system state equation of error compensation;
determining the system state estimation value at the current moment by adopting a linear minimum variance estimation method according to the system state estimation value at the previous moment;
correcting the error of the inertial navigation system by using the estimated value of the system state at the current moment;
and updating the current time to the last time, updating the system state estimation value of the current time to the system state estimation value of the last time, and returning to the step of determining the system state estimation value of the current time by adopting a linear minimum variance estimation method according to the system state estimation value of the last time.
2. The method for compensating the error of the inertia based integrated navigation system under the black-out condition according to claim 1, wherein the determining the estimated value of the system state at the current time by using a linear minimum variance estimation method according to the estimated value of the system state at the previous time specifically comprises:
according to the formula
Figure FDA0003559850770000041
Determining a system state estimation value at the current moment;
wherein the content of the first and second substances,
Figure FDA0003559850770000042
is the estimated value of the system state at the kth moment, namely the estimated value of the system state at the current moment,
Figure FDA0003559850770000043
is the system state estimate at time k-1, i.e., the last time, phik,k-1Is the state transition matrix from the k-1 th time to the k-th time.
3. The method for compensating the error of the inertia-based integrated navigation system under the black barrier of claim 2, wherein the formula
Figure FDA0003559850770000044
The acquisition process specifically comprises:
discretizing the system state equation of the error compensation to obtain a discretized error compensation system state equation;
estimating the system state at the kth moment by adopting a linear minimum variance estimation method according to the actually measured data set to obtain a linear minimum variance estimation equation of the system state at the kth moment;
substituting the discrete error compensation system state equation into the linear minimum variance estimation equation of the system state at the kth moment to obtain a system state estimation formula
Figure FDA0003559850770000045
4. An error compensation system of an inertia-based integrated navigation system under the condition of black fault is characterized by comprising:
the system state equation building module for error compensation is used for building a system state equation for error compensation based on an error model of the inertial navigation system; the errors of the strapdown inertial navigation system mainly comprise inertial device errors and system errors caused by the inertial device errors, wherein an inertial device error equation is as follows:
Figure FDA0003559850770000051
Figure FDA0003559850770000052
wherein epsilonbiIs a random constant drift of the gyroscope i,
Figure FDA0003559850770000053
is epsilonbiThe first order differential of the first order of the,
Figure FDA0003559850770000054
for a random constant error of the accelerometer i,
Figure FDA0003559850770000055
is composed of
Figure FDA0003559850770000056
X, y, z denotes a gyroscope or accelerometer mounted along the x, y, z axes of the carrier;
due to the fact that errors exist in the inertial device, certain errors exist in the strapdown inertial navigation system and navigation parameters output by the strapdown inertial navigation system, specifically including a mathematical platform attitude error, a speed error and a position error, and the specific error equation is in the following form;
Figure FDA0003559850770000057
Figure FDA0003559850770000058
Figure FDA0003559850770000059
wherein phi isE、φN、φURespectively representing attitude errors of a mathematical platform of the strapdown inertial navigation system along east, north and sky directions;
Figure FDA00035598507700000510
is phiEThe first order differential of the first order of the,
Figure FDA00035598507700000511
is phiNThe first order differential of the first order of the,
Figure FDA00035598507700000512
is phiUFirst order differentiation of; delta vE、δvN、δvURespectively the east, north and sky speed errors of the strapdown inertial navigation system; delta L, delta lambda and delta h are respectively latitude, longitude and altitude errors of the strapdown inertial navigation system; w is agiIs the white noise of the measurement of the gyroscope i,waiwhite noise for the accelerometer i; omegaieThe rotational angular velocity of the earth, and R is the radius of the earth; v. ofE、vN、vUThe east, north and sky speeds of the carrier respectively; l, lambda and h are respectively the latitude, longitude and altitude of the carrier position; t isijI, j is 1,2,3, which is the attitude matrix
Figure FDA0003559850770000061
Row i and column j elements of (1);
the velocity error equation of the strapdown inertial navigation system is as follows:
Figure FDA0003559850770000062
Figure FDA0003559850770000063
Figure FDA0003559850770000064
wherein f isE、fN、fURespectively outputting equivalent specific forces along the east, north and sky directions for the accelerometer;
the position error equation of the strapdown inertial navigation system is as follows:
Figure FDA0003559850770000065
Figure FDA0003559850770000066
Figure FDA0003559850770000067
according to the error model of the strapdown inertial navigation system, taking the mathematical platform attitude error, the speed error, the position error, the gyroscope error and the accelerometer error of the strapdown inertial navigation system as the system state, the method comprises the following steps: attitude error phi of mathematical platform along east, north and sky directionsE,φN,φUVelocity error δ v in east, north and sky directionsE,δvN,δvUConstant drift epsilon of gyroscope on weft, warp and height errors delta L, delta lambda, delta h, x, y and z axesbx,εby,εbzConstant offset of accelerometer in x, y, z axes
Figure FDA0003559850770000071
I.e. the system state X of the error compensation is:
Figure FDA0003559850770000072
obviously, in combination with the above system state X, the various error equations of the prior strapdown inertial navigation system can be written in the following form:
Figure FDA0003559850770000073
the above formula is the system state equation of error compensation; wherein, F is recorded as a system state matrix; g is recorded as a system noise driving array; w is recorded as system white noise, and the system state equation describes the relationship between system input and system state, namely describes the relationship between various motion parameters of a carrier and various errors of a strapdown inertial navigation system; let the continuous system state equation be discretized into the form:
Xk＝Φk,k-1Xk-1+Γk-1Wk-1
wherein, Xk-1、XkThe system states at the k-1 and k-th time, phik,k-1Is the state transition matrix from time k-1 to time k, Γk-1As a discreteSystem noise driving array, Wk-1Exciting a noise sequence for the discrete system;
the measured data set acquisition module is used for acquiring measured data of the inertia base combined navigation system at each moment before the current moment as a measured data set; the current moment is the moment when the black barrier appears;
the last-time system state estimation value determining module is used for determining the last-time system state estimation value by adopting a Kalman filtering method according to the measured data set and the error compensation system state equation;
a current time system state estimation value determining module, configured to determine a current time system state estimation value by using a linear minimum variance estimation method according to the previous time system state estimation value;
the error correction module is used for correcting the error of the inertial navigation system by using the system state estimation value at the current moment;
and the state updating module is used for updating the current time to the last time, updating the system state estimation value of the current time to the system state estimation value of the last time, and returning to the system state estimation value determining module at the current time.
5. The system for compensating error of an inertia based integrated navigation system under the black-out condition of claim 4, wherein the module for determining the estimated value of the system state at the current time specifically comprises:
a current time system state estimation value determination unit for determining the current time system state estimation value according to a formula
Figure FDA0003559850770000081
Determining a system state estimation value at the current moment;
wherein the content of the first and second substances,
Figure FDA0003559850770000082
is the estimated value of the system state at the kth moment, namely the estimated value of the system state at the current moment,
Figure FDA0003559850770000083
is the system state estimate at time k-1, i.e., the last time, phik,k-1Is the state transition matrix from the k-1 th time to the k-th time.
6. The system of claim 5, wherein the formula is a system for compensating for errors in an inertial based integrated navigation system under black barrier
Figure FDA0003559850770000084
The acquisition process specifically comprises:
the discretization unit is used for discretizing the system state equation of the error compensation to obtain a discretized error compensation system state equation;
a linear minimum variance estimation equation obtaining unit of the system state at the kth moment, configured to estimate the system state at the kth moment by using a linear minimum variance estimation method according to the actually measured data set, so as to obtain a linear minimum variance estimation equation of the system state at the kth moment;
a system state estimation equation determining unit for substituting the discrete error compensation system state equation into the linear minimum variance estimation equation of the system state at the kth moment to obtain a system state estimation formula
Figure FDA0003559850770000091
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