CN106441291B - A kind of integrated navigation system and air navigation aid based on strong tracking SDRE filtering - Google Patents

A kind of integrated navigation system and air navigation aid based on strong tracking SDRE filtering Download PDF

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CN106441291B
CN106441291B CN201610855565.7A CN201610855565A CN106441291B CN 106441291 B CN106441291 B CN 106441291B CN 201610855565 A CN201610855565 A CN 201610855565A CN 106441291 B CN106441291 B CN 106441291B
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CN106441291A (en
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赵良玉
任珊珊
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Beijing Institute of Technology BIT
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    • 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
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
    • G01S19/49—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)
  • Navigation (AREA)

Abstract

The invention discloses a kind of integrated navigation systems and air navigation aid based on strong tracking SDRE filtering, wherein, the system comprises GPS receiver, inertial navigation subsystem and filters, wherein, the filter includes space module, SDRE decomposing module, sliding-model control module and Strong tracking filter module, also, the Strong tracking filter module includes initialization module again, one-step prediction submodule, gain matrix obtains submodule, virtual condition estimates submodule and error covariance matrix updates submodule.It the described method comprises the following steps: first carrying out SDRE decomposition, then carry out sliding-model control, finally carry out Strong tracking filter, obtain integrated navigation data, and carry out data output.System and method of the present invention introduce adaptive fading factor, are able to carry out accurate filtering, obtain accurate navigation data.

Description

Combined navigation system and navigation method based on strong tracking SDRE filtering
Technical Field
The invention relates to the field of navigation, in particular to an integrated navigation system and a navigation method, and particularly relates to an integrated navigation system and a navigation method based on strong tracking SDRE filtering.
Background
The combined navigation based on the GPS technology and the inertial navigation is widely applied to various fields of military and civilian, and the technology carries out estimation, correction and fusion on the GPS positioning data and the inertial navigation positioning data, so that the purpose of improving the navigation positioning precision of a carrier by complementing advantages is achieved. In the GPS and inertial navigation combined navigation, the navigation parameters are used as estimation objects, the dynamic change process of the navigation parameters can be visually described, and the evolution condition of the real state can be accurately reflected.
In a combined navigation system, there are always different degrees of non-linearity in a real system. Meanwhile, the actual system also has Gaussian or non-Gaussian random noise interference. In this case, it is important to perform efficient and even optimal state estimation for nonlinear systems, and nonlinear filtering techniques need to be employed. In the case of non-linear systems, Extended Kalman Filtering (EKF) is typically used for processing.
However, the method has high-order truncation errors, and a Jacobian matrix of the system must be solved, and meanwhile, the possibility of losing filtering stability under a strong nonlinear system exists. The filtering technology is based on establishing an accurate model, and if the system model is not accurate, the filtering precision is influenced.
Disclosure of Invention
In order to overcome the problems, the inventor of the present invention has made a keen study, and uses a GPS receiver and an Inertial Navigation (INS) subsystem (an inertial navigation system for short) to form a combined navigation system, then uses an SDRE technique to process a filtering model, designs a filter by using a principle that a residual sequence is orthogonal everywhere, and designs a combined navigation system and a navigation method based on a strong tracking SDRE filtering, so that high-precision position and speed information can be obtained, and precise combined navigation is realized, thereby completing the present invention.
In one aspect, the present invention provides a combined navigation system based on strong tracking SDRE filtering, wherein the system includes a GPS receiver 1, an inertial navigation subsystem 2, and a filter 3, wherein the filter 3 includes a space module 31, an SDRE decomposition module 32, a discretization processing module 33, and a strong tracking filtering module 34, and the strong tracking filtering module 34 includes an initialization module 340, a one-step prediction sub-module 341, a gain matrix obtaining sub-module 342, an actual state estimation sub-module 343, and an error variance matrix updating sub-module 344.
In another aspect, the present invention provides a navigation method based on strong tracking SDRE filtering, which is preferably performed by the system of the first aspect of the present invention, wherein the method includes the following steps:
step 1, performing state-related decomposition on a state space and a measurement space in a space module 31 by using an SDRE decomposition module 32 to obtain a state decomposition space and a measurement decomposition space respectively;
step 2, discretizing the state decomposition space and the measurement decomposition space in the SDRE decomposition module 32 by using a discretization processing module 33 to obtain a state discrete space and a measurement discrete space respectively;
and 3, performing strong tracking filtering processing on the state discrete space and the measurement discrete space in the discretization processing module 33 by using a strong tracking filtering module 34 to obtain combined navigation data, and outputting the data.
Drawings
FIG. 1 is a schematic diagram of a combined navigation system according to the present invention;
FIG. 2 is a flow chart of the integrated navigation method of the present invention;
FIG. 3 shows the trajectory of the motion made by the aircraft in the experimental example;
FIG. 4a shows the position error in the east direction obtained using the methods described in the examples and comparative examples;
FIG. 4b shows the position error in the north direction obtained using the method described in the examples and comparative examples;
FIG. 4c shows the position error in the sky obtained using the methods described in the examples and comparative examples;
FIG. 5a shows the velocity error in the east direction obtained using the methods described in the examples and comparative examples;
FIG. 5b shows the velocity error in the north direction obtained using the methods described in the examples and comparative examples;
figure 5c shows the velocity error in the direction of the day obtained using the methods described in the examples and comparative examples.
Reference numerals
1-a GPS receiver; 2-an inertial navigation subsystem; 21-an accelerometer; 22-a gyroscope; 3-a filter; 31-a space module; 32-an SDRE decomposition module; 33-a discretization processing module; 34-a strong tracking filtering module; 340-an initialization module; 341-one-step predictor module; 342-gain matrix obtaining submodule; 343-an actual state estimation sub-module; 344-error variance matrix update submodule.
Detailed Description
The invention is explained in further detail below with reference to the drawing. The features and advantages of the present invention will become more apparent from the description.
The invention provides a combined navigation system based on strong tracking SDRE filtering, which comprises a GPS receiver 1, an inertial navigation subsystem 2 and a filter 3. The GPS receiver 1 is used for outputting current geographic position and current speed information obtained by a GPS technology; the inertial navigation subsystem 2 comprises an accelerometer 21 and a gyroscope 22 and is used for detecting and outputting current geographic position, current speed and current attitude angle information obtained by an inertial navigation technology; and the filter 3 is used for carrying out data processing on the data output by the GPS receiver 1 and the inertial navigation subsystem 2 to obtain and output combined navigation information.
According to a preferred embodiment of the present invention, the filter 3 comprises a spatial module 31, an SDRE decomposition module 32, a discretization processing module 33 and a strong tracking filtering module 34.
In a further preferred embodiment, a state space and a measurement space are integrated in the space module 31.
In a further preferred embodiment, the state space and the measurement space are represented by equations (31-1) and (31-2), respectively:
z ═ h (x) + V formula (31-2)
Wherein, in formula (31-1):
wherein phi ise、φnAnd phiuRespectively as mathematical platform error angles, and updating in real time; v. ofe、vnAnd vuThe speed of the carrier in the east direction, the north direction and the sky direction respectively;λ and h are respectively latitude, longitude and height of the carrier; epsilone、εnAnd εuRespectively, gyro constant drift, Deltae、ΔnAnd ΔuRespectively, accelerometer constant drift;
wherein,andrespectively representing random errors of the gyroscope in the east direction, the north direction and the sky direction,andrespectively representing random errors of the accelerometer in east, north and sky directions; wherein the random error is system noise;
g is a system noise transfer matrix, wherein,
wherein I represents an identity matrix.
According to a preferred embodiment of the present invention, the state space as shown in equation (31-2) is established as follows: taking a geographic system (east, north and sky) as a basic coordinate system for navigation calculation, considering the flight altitude h, and assuming that the earth is an ellipsoid, an Inertial Navigation (INS) state equation is as follows:
(1) attitude error angle equation of the north-seeking inertial navigation system:
wherein, in the formulae (31-1-1) to (31-1-3), RMIs the principal radius of curvature in the local meridian plane; rNIs the major curvature radius in the prime plane; omegaieIs the earth rotation angular rate;λ and h are respectively latitude, longitude and altitude of the carrier measured by an Inertial Navigation System (INS); phi is ae、φnAnd phieIs a mathematical platform error angle; v. ofe、vnAnd vuThe speed of the carrier measured by an Inertial Navigation System (INS) in the east direction, the north direction and the sky direction respectively; epsilone、εnAnd εuThe constant drift of the gyroscope in the east direction, the north direction and the sky direction respectively; delta veIs the difference, δ v, between the east velocity measured by an Inertial Navigation System (INS) and the east velocity measured by a GPS receivernIs used toA difference between an east velocity measured by a navigation system (INS) and a north velocity measured by a GPS receiver;is the difference between the latitude measured by the Inertial Navigation System (INS) and the latitude measured by the GPS receiver, and δ h is the difference between the altitude measured by the Inertial Navigation System (INS) and the altitude measured by the GPS receiver. Wherein,long radius of the earth Re6378245, global oblateness e 1/298.257.
(2) The velocity equation is:
wherein, in the formulae (31-1-4) to (31-1-6), fe、fnAnd fuAcceleration components of the measurement value of the accelerometer in the east direction, the north direction and the sky direction are respectively; deltae、ΔnAnd ΔuIs the constant drift of the accelerometer in the east, north and sky directions.
(3) Position equation:
(4) inertial element error equation: assuming that the error of the inertial element is a constant noise, the error equation is:
in a further preferred embodiment, the attitude error angle equation of the north-pointing inertial navigation system according to (1) above, the velocity equation according to (2) above, the position equation according to (3) above, and the inertial element error equation according to (4) above are combined to obtain a state variable of order 15:the state space shown in the formula (31-1) can be obtained, wherein f (x) is 9 basic navigation parameter equations shown in the corresponding formulas (31-1-1) to (31-1-9) and an inertial element error equation shown in the formulas (31-1-10) and (31-1-11).
According to a preferred embodiment of the present invention, in formula (31-2):
measurement information z ═ vge,vgn,vgu,pge,pgn,pgu]TWherein v isgeIndicating the speed, v, of the carrier in the east direction as measured by the GPS receivergnIndicating the velocity, v, of the carrier in the north direction as measured by the GPS receiverguIndicating the speed, p, of the carrier in the direction of the day as measured by the GPS receivergeRepresenting measured carriers of a GPS receiverBody in east position, pgnIndicating the position of the carrier in the north direction, p, measured by the GPS receiverguRepresenting the position of the carrier measured by the GPS receiver in the direction of the day;
v is measurement noise, V ═ Vvge,Vvgn,Vvgu,Vpge,Vpgn,Vpgu]TWherein V isvgeIndicating random errors, V, in east velocity of the carrier measured by the GPS receivervgnIndicating the random error, V, of the speed of the carrier measured by the GPS receiver in the north directionvguRepresenting random errors in the speed of the carrier measured by the GPS receiver in the direction of the sky, PpgeIndicating random errors, P, of the east position of the carrier measured by the GPS receiverpgnIndicating random errors in the north position of the carrier measured by the GPS receiver, PpguRepresenting the random error of the vehicle position in the sky as measured by the GPS receiver.
In a further preferred embodiment, H (x) is a linear equation, which can be written as H (x) Hx, where H is a measurement matrix, where:
according to a preferred embodiment of the present invention, the SDRE decomposition module 32 is configured to perform state-dependent decomposition on a state space and a measurement space in the space module 31 as shown in equations (31-1) and (31-2) to obtain a state decomposition space and a measurement decomposition space, respectively.
In a further preferred embodiment, the state decomposition space and the measurement decomposition space are represented by formulas (32-1) and (32-2), respectively:
z is Hx + V formula (32-2).
Where SDRE is a form in which a nonlinear state space (equation (31-1)) is decomposed into states multiplied by a transition matrix by a state-dependent decomposition method, that is, f (x) x. In the measurement space shown in the formula (31-2), h (x) is a linear equation, so that the SDRE decomposition is not needed, and therefore, the SDRE decomposition is performed on the state space shown in the formula (31-1) to obtain the formula (32-1). In the present invention, although the formula (32-2) is not obtained by the decomposition of the formula (31-2) SDRE, the formula (32-2) is expressed as a measurement decomposition space for the sake of uniform expression.
In the present invention, the state transition matrix f (x) is:
wherein, FNIs a 9-dimensional matrix in which the non-zero elements are:
F(4,2)＝-fu F(4,3)＝fn
F(5,1)＝fu F(5,3)＝-fe
F(6,1)＝-fn F(6,2)＝fe
F(9,6)＝1；
Fscomprises the following steps:
according to a preferred embodiment of the present invention, the discretization processing module 33 is configured to perform discretization on the state decomposition space and the measurement decomposition space in the SDRE decomposition module 32 to obtain a state discrete space and a measurement discrete space.
In a further preferred embodiment, the state discrete space and the measurement discrete space are represented by formulas (33-1) and (33-2), respectively:
xk+1＝Φk+1/kxk+Γkwkformula (33-1);
zk+1＝Θk+1xk+1+Vk+1formula (33-2).
Wherein phik+1/kIs a discrete state transition matrix, ГkIs a discrete noise transfer matrix, Θk+1Is a discretized measurement matrix, wherein, after discretization:
according to Taylor expansion,. phik+1/k＝I+f(xk)Δt+f(xk)Δt2/2！+f(xk)Δt2/3！+…，
Γk＝GΔt+GΔt2/2！+GΔt2/3！+…。
In a further preferred embodiment, the system noise vector wkAnd measure the noise vector VkAre respectively QkAnd RkAnd w iskAnd VkSatisfies the following conditions:
E[wk]0 denotes wkThe mean value of (a) is 0;
wherein, Cov [ w ]k,wj]Denotes wkAnd wjFor measuring wkAnd wjThe overall error of (2);
E[Vk]0 denotes VkThe mean value of (a) is 0;
Cov[Vk,Vj]represents VkAnd VjCovariance of (2) for measuring VkAnd VjThe overall error of (2);
Cov[wk,Vj]denotes wkAnd VjFor measuring wkAnd VjThe overall error of (2).
Wherein, wkRepresenting the system noise vector at time k, wjRepresenting the system noise vector, V, at time jkA measurement noise vector, V, representing time kjRepresenting the measurement noise vector, delta, at time jkjIs a Kronecker-delta function and shows that noises at different moments are independent of each other.
According to a preferred embodiment of the present invention, the strong tracking filtering module 34 is configured to perform strong tracking filtering processing on the state discrete space shown as the formula (33-1) and the measurement discrete space shown as the formula (33-2) in the discretization processing module 33 to obtain the combined navigation information.
In a further preferred embodiment, the strong tracking filtering module 34 includes a further prediction sub-module 341, a gain matrix obtaining sub-module 342, an actual state estimation sub-module 343, and an error variance matrix updating sub-module 344.
According to a preferred embodiment of the present invention, the one-step prediction sub-module is configured to perform one-step prediction of the state and one-step prediction of the error variance matrix.
The one-step prediction of the state refers to predicting the state information of the next time (k +1 time) according to the state information of the current time (k time), and the one-step prediction of the error variance matrix refers to predicting the error variance matrix of the next time according to the error square matrix of the current time.
In a further preferred embodiment, the further prediction of the state is as shown in equation (341-1):
wherein, in the formula (341-1),indicates the predicted value of the state at the time k +1 from the state at the time k, xkIndicating the state at time k and deltat the filter period.
In a further preferred embodiment, the one-step prediction of the error variance matrix is as shown in equation (341-2):
wherein, in the formula (341-2), Pk+1/kβ shows the predicted value of the error variance matrix at the time k +1 obtained by the prediction of the error variance matrix at the time kkFor adaptive fading factor, PkError variance matrix, phi, representing time kk+1/kRepresenting the state transition matrix after the discretization,represents phik+1/kTransposed matrix of (2), QkDenotes wkK denotes the current time, k +1 denotes the next time, where k is 0,1,2,3, …, L, where L is determined by the filtering time and the filtering period, and L is the filtering time/filtering period.
In the invention, in order to enhance the robustness of the filter to model uncertainty, an adaptive fading factor β is introduced when one-step prediction of an error variance matrix is carried outkThe uncertainty of the one-step prediction state is improved. It is mainly based on the principle of information residual orthogonalization, i.e.Wherein the innovation is a difference between the actual measurement and the one-step predicted measurementIf the predicted value of one step is accurate, the information at each moment is orthogonal, namely the information is Gaussian white noise with the average value of 0, and once the information is inaccurate, the information is not orthogonal any more.
According to a preferred embodiment of the present invention, the adaptive fading factor is adjusted by the following equations (a) to (e), (see: Zhoudowanhua, Matyu Zhang clock. extended Kalman filtering with sub-optimal fading factor [ J ] control and decision, 1990(05): 1-6.):
wherein, in the formula (a),the sequence of the new message is represented,to representWhere ρ represents a forgetting factor, is set artificially, and is 0 to 1, and V isk-1Representing the measurement noise at time k-1;
wherein, in the formula (b), NkIt has no practical meaning and is used to representWherein the first and second substrates are selected from the group consisting of,Θk+1the measurement matrix after the dispersion is shown,denotes Θk+1Transposed matrix of (2), QkDenotes wkOf variance matrix of Rk+1Representing a metrology noise vector Vk+1The variance matrix of (2);
wherein, in formula (c), MkIt has no practical meaning and is intended to representΘk+1The measurement matrix after the dispersion is shown,denotes Θk+1Transposed matrix of phik+1/kRepresenting the state transition matrix after the discretization,represents phik+1/kTransposed matrix of (1), PkAn error variance matrix representing the k time;
wherein, in formula (d), tr (N)k) Represents NkTrace of (d), tr (M)k) Represents MkThe trace is the trace of the matrix, namely the sum of each element on the diagonal of the matrix;
wherein, the reaction is carried out by the above formulaAdjusting the derived adaptive fading factor can improve the accuracy of the filtering and result in an accurate state value, specifically, the adaptive fading factor β is obtainedkThe final purpose of the method is to increase the filter gain matrix under the condition that the difference between the one-step prediction state value and the actual state value is larger, so that the trust of measurement on the quantity is increased, and a more accurate state estimation value is obtained.
According to a preferred embodiment of the present invention, the gain matrix obtaining sub-module 342 is configured to obtain the gain matrix at the time k +1, as shown in equation (342-1):
wherein, in the formula (342-1), Pk+1/kRepresents an error variance matrix at time k +1 predicted from the error variance matrix at time kk+1Is a measurement matrix after the dispersion of the measured data,is thetak+1Transposed matrix of (2), Rk+1For measuring noise vector Vk+1The variance matrix of (2).
According to a preferred embodiment of the present invention, the actual state estimation sub-module 343 is configured to estimate an actual state value at a time k +1, that is, to obtain an actual state estimation value at a time k +1, as shown in equation (343-1):
wherein,a predicted state value at time K +1, K, representing a state prediction from time Kk+1The gain matrix representing the time instant k +1, zk+1Measured data for time k +1 (given by GPS)The information at the time k +1 is obtained),representing one-step predicted state valuesThe measured value of (a).
According to a preferred embodiment of the present invention, the error variance matrix updating sub-module 344 is configured to update the error variance matrix at the time K +1, wherein the gain matrix K at the time K +1 is utilizedk+1And an error variance matrix P at the k +1 moment obtained by prediction according to the error variance matrix at the k momentk+1/kObtaining an error variance matrix P at the k +1 momentk+1。
In a further preferred embodiment, the update of the error variance matrix at time k +1 is performed as equation (344-1):
Pk+1＝(I-Kk+1Θk+1)Pk+1/kformula (344-1)
In order to make the filter continuously run until the system process is finished, the error variance matrix at the next time (k +1 time) must be updated.
According to a preferred embodiment of the present invention, the filter further comprises an initialization module 340 for initializing the state and error variance matrix and updating the time.
In a further preferred embodiment, the initialization module 340 assigns an initial value x to the state0I.e., the initial value provided by the inertial navigation system.
In a further preferred embodiment, the initialization module 340 assigns an initial error variance matrix P0Which represents the uncertainty of the inertial navigation system. Wherein, according to the error statistic, the initial error variance matrix is estimated, and in order to make the filtering reach the accurate position faster, P can be used0Setting to 10 times of error statistic value, wherein the error statistic valueThe value is the error value of the sensor which is counted.
The invention also provides a combined navigation method based on the strong tracking SDRE filtering.
According to a preferred embodiment of the present invention, as shown in fig. 2, the navigation method includes the steps of:
step 1, the SDRE decomposition module 32 is used to perform state-related decomposition on the state space and the measurement space in the space module 31, so as to obtain a state decomposition space and a measurement decomposition space, respectively.
According to a preferred embodiment of the present invention, in step 1, the state space and the measurement space are respectively represented by the following formulas (31-1) and (31-2):
z ═ h (x) + V formula (31-2).
According to a preferred embodiment of the present invention, in step 1, the state decomposition space and the measurement decomposition space obtained after the SDRE decomposition module 32 performs the state-related decomposition are respectively represented by the following formulas (32-1) and (32-2):
z is Hx + V formula (32-2).
The SDRE decomposition is a linear system form in which a nonlinear state space (equation (31-1)) is decomposed into states multiplied by a transition matrix by a state-dependent decomposition method, that is, f (x) x. In the measurement space shown in the formula (31-2), h (x) is a linear equation, so that the SDRE decomposition is not needed, and therefore, the SDRE decomposition is performed on the state space shown in the formula (31-1) to obtain the formula (32-1). In the present invention, although the formula (32-2) is not obtained by the decomposition of the formula (31-2) SDRE, the formula (32-2) is expressed as a measurement decomposition space for the sake of uniform expression.
According to a preferred embodiment of the invention, step 1' is carried out before step 1:
step 1', the state and error variance matrix is initialized and time updated using the initialization block 340.
In a further preferred embodiment, the initialization module 340 initializes the state to obtain an initial value x of the state0And initial error variance matrix P0Namely, an initial value provided for the inertial navigation system and uncertainty of the inertial navigation system.
Step 2, the discretization processing module 33 is used to perform discretization processing on the state decomposition space and the measurement decomposition space in the SDRE decomposition module 32, so as to obtain a state discrete space and a measurement discrete space respectively.
According to a preferred embodiment of the present invention, the state discrete space and the measurement discrete space obtained by the discretization module 33 are respectively represented by the following formulas (33-1) and (33-2):
xk+1＝Φk+1/kxk+Γkwkformula (33-1);
zk+1＝Θk+1xk+1+Vk+1formula (33-2).
Wherein phik+1/kIs a discrete state transition matrix, ГkIs a discrete noise transfer matrix, Θk+1Is a discrete measurement matrix.
In a further preferred embodiment, the system noise vector wkAnd measure the noise vector VkAre respectively QkAnd RkAnd w iskAnd VkSatisfies the following conditions:
E[wk]＝0，E[Vk]＝0，
wherein, wkRepresenting the system noise vector at time k, wjRepresenting the system noise vector, V, at time jkA measurement noise vector, V, representing time kjRepresenting the measurement noise vector, delta, at time jkjIs a Kronecker-delta function and shows that noises at different moments are independent of each other.
And 3, performing strong tracking filtering processing on the state discrete space and the measurement discrete space in the discretization processing module 33 by using a strong tracking filtering module 34 to obtain combined navigation data, and outputting the data.
According to a preferred embodiment of the present invention, in step 3, the combined navigation data includes: phi is ae(k+1)、φn(k+1)、φe(k+1)、Δe(k+1)、Δn(k+1)、Δu(k+1)、ve(k+1)、vn(k+1)、vu(k+1)、λ (k +1) and h (k + 1).
In a further preferred embodiment, as shown in fig. 2, said step 3 comprises the following sub-steps:
step 3-1, the one-step prediction submodule 341 performs one-step prediction on the state and error square matrix at the next time (k +1 time) to obtain a state prediction value and an error square matrix prediction value at the next time, which are respectively calculated according to the state prediction value and the error square matrix prediction valueAndand (4) showing.
Step 3-2, utilizingP obtained in step 3-1k+1/kProcessed by the gain matrix obtaining sub-module 342 to obtain the gain matrix at the next time, which is represented by Kk+1Represents;
step 3-3 of utilizing the product obtained in step 3-1And K obtained in step 3-2k+1The actual state value at the next time is obtained by the actual state estimation submodule 343, and is expressed by xk+1And representing, namely combining the navigation information and outputting the information.
According to a preferred embodiment of the present invention, in step 3-1, the one-step prediction of the state refers to predicting the state information of the next time (k +1 time) according to the state information of the current time (k time), which is performed according to equation (341-1):
wherein, in the formula (341-1),a state prediction value at time k +1, x, representing a state prediction from time kkIndicating the state at time k and deltat the filter period.
In a further preferred embodiment, the further prediction of the error variance matrix refers to predicting the error variance matrix at the next time according to the error variance matrix at the current time, which is performed according to equation (341-2):
wherein, in the formula (341-2), Pk+1/kβ shows the predicted value of the error variance matrix at the time k +1 obtained by the prediction of the error variance matrix at the time kkIs self-adaptiveThe fading factor, PkError variance matrix, phi, representing time kk+1/kRepresenting the state transition matrix after the discretization,represents phik+1/kTransposed matrix of (2), QkDenotes wkK denotes the current time, k +1 denotes the next time, where k is 0,1,2,3, …, L, where L is determined by the filtering time and the filtering period, and L is the filtering time/filtering period.
According to a preferred embodiment of the present invention, in step 3-2, P obtained in step 3-1 is utilizedk+1/kThe gain matrix obtaining submodule 342 performs the processing as shown in formula (342-1) to obtain the gain matrix at the time k + 1:
wherein, in the formula (342-1), Pk+1/kRepresents an error variance matrix at time k +1 predicted from the error variance matrix at time kk+1Is a measurement matrix after the dispersion of the measured data,is thetak+1Transposed matrix of (2), Rk+1For measuring noise vector Vk+1The variance matrix of (2).
According to a preferred embodiment of the present invention, in step 3-3, the product obtained in step 3-1 is usedAnd P obtained in step 3-2k+1/kThe actual state estimation submodule 343 performs processing as shown in formula (343-1) to obtain the actual state estimation value x at the time of k +1k+1。
Wherein,indicating the predicted state at time K +1 predicted from the state at time K, Kk+1The gain matrix representing the time instant k +1, zk+1Measured data at the time k +1 (obtained according to the information of the time k +1 given by the GPS),representing one-step predicted state valuesThe measured value of (a).
According to a preferred embodiment of the present invention, in order to make the filter run continuously until the system process is finished, the update of the error variance matrix at the next time (time k +1) must be performed while performing step 3-3, that is, step 3-4 is performed simultaneously with step 3-3:
step 3-4 of utilizing P obtained in step 3-1k+1/kAnd K obtained in step 3-2k+1The error variance matrix updating sub-module 344 performs processing as shown in formula (344-1):
Pk+1＝(I-Kk+1Θk+1)Pk+1/kformula (344-1)
The error variance matrix updating sub-module 344 is configured to update the error variance matrix at the time K +1, where the gain matrix K at the time K +1 is usedk+1And an error variance matrix P at the k +1 moment obtained by prediction according to the error variance matrix at the k momentk+1/kObtaining an error variance matrix P at the k +1 momentk+1。
The invention has the beneficial effects that:
(1) the system of the invention has simple structure and high running speed;
(2) the system of the invention introduces the self-adaptive fading factor, and the high-precision state value can be obtained through the system processing;
(3) the method adopts SDRE decomposition, does not need linear treatment and solves a Jacobian matrix, reduces the processing amount and has practical significance for final engineering application;
(4) the method improves the robustness under the condition of system uncertainty and the tracking capability under the condition of sudden change of the flight state, improves the navigation precision and improves the reliability of the navigation system;
(5) the method is simple and easy to implement, and the result is accurate.
Examples
In this embodiment, the aircraft is set to maneuver as shown in FIG. 3, with the flight path including climb, descent, turn, and shift motions. The sampling period of an Inertial Navigation System (INS) is 0.01s, the sampling period and the filtering period of a GPS receiver are 1s, and the simulation time is 1932 s.
Sequentially performing SDRE decomposition and discretization processing according to the state space and the measurement space in the space module 31, and then performing strong filtering tracking, wherein the specific process is as follows:
(1) at the zero moment, x is obtained by measuring through an inertial navigation system0Simultaneously, an initial error variance matrix P is obtained through processing0。
Wherein, according to the error statistic, the initial error variance matrix is estimated, and in order to make the filtering reach the accurate position faster, P can be used0The error value is set to 10 times of the error statistic value, wherein the error statistic value is the error value of the counted sensor.
(2) The one-step prediction submodule 341 performs one-step prediction on the state and the error square matrix at the first time to respectively obtain predicted values of the state at the first timeSum error variance matrix prediction value P1/0。
Wherein:
wherein: x is the number of0Obtained by the step (1); Δ t is a set value, set to 0.01s in the present embodiment; f (x)0)＝F(x0)x0Wherein x is0Obtained in step (1), F (x)0) Inputting a parameter value output by the inertial navigation system at the zero moment into a state transfer matrix F (x) to obtain the parameter value;
wherein, β0For adaptive fading factor, phi1/0＝I+F(x0) T, wherein, in F (x)0) Internally inputting inertial navigation information at zero time, Q0Is set manually.
(3) Utilizing P obtained in step (2)1/0The gain matrix K at the first time is obtained after being processed by the gain matrix obtaining submodule 3421。
Wherein,wherein, P1/0Obtained by the above (2) to1＝H，R1Is set manually.
(4) Using the product obtained in step (2)And K obtained in step (3)1The actual state value x at the next time is obtained by the actual state estimation submodule 3431。
Wherein,wherein,obtained by step (2), K1Obtained by step (3), z1Indicating GPS detection data at a first time,
(5) using K obtained in step (3)1P obtained in step (2)1/0Processed by the error variance matrix updating submodule 344 to obtain the error variance matrix P at the first time1。
Wherein, P1＝(I-K1Θ1)P1/0Wherein, the purpose of step (5) is to make the filter continuously run, and step (5) and step (4) are carried out simultaneously.
X to be obtained1And P1And inputting the information of the inertial navigation at the first moment after the inertial navigation is solved into a filter, updating data, and repeating the processes of the steps (2) to (5).
Comparative example
Unlike the embodiment where the processing is done with SDRE filtering, rather than strong tracking SDRE filtering, the adaptive fading factor β in step 3 is 1.
Examples of the experiments
Respectively adopting the method described in the embodiment and the method described in the comparative example to simulate the aircraft, meanwhile, assuming that the existing space model is an accurate space model, keeping the filter model unchanged within 500 s-800 s, and introducing a state break variable delta x of [0 ] into flight data1×3,1,1,1,10/Re,10/Re,10,01×6]TLet the real space of this time be:
xk+1＝f(xk)+Δx
the results of the position errors between the positions of east, north, and day and the real position of the comparative example and the real space are shown in fig. 4a to 4c, respectively, and the results of the velocity errors between the velocities of east, north, and day and the real velocity are shown in fig. 5a to 5c, respectively.
Wherein: as can be seen in fig. 4a to 4c, in the period of 500s to 800s, the position error of the embodiment after filtering in the period is obviously smaller than that of the comparative example, and remains within 5m, and the filtering result of the embodiment is closer to the real state; as can be seen in fig. 5a to 5c, the errors of the embodiments are smaller than the comparative examples and smaller than 1m/s in the error time period, and the filtering results of the embodiments are proved to be closer to the real state again;
therefore, in the stable flight time, the speed error is less than 1m/s and the position error is less than 5m by adopting the method.
The present invention has been described above in connection with preferred embodiments, but these embodiments are merely exemplary and merely illustrative. On the basis of the above, the invention can be subjected to various substitutions and modifications, and the substitutions and the modifications are all within the protection scope of the invention.

Claims (7)

1. A combined navigation system based on strong tracking SDRE filtering, the system comprising:
a GPS receiver (1) for outputting the current geographical position and current speed information obtained by GPS technology;
an inertial navigation subsystem (2) comprising an accelerometer (21) and a gyroscope (22) for detecting and outputting current geographic position, current velocity and current attitude angle information obtained by inertial navigation techniques; and
the filter (3) is used for carrying out data processing on data output by the GPS receiver (1) and the inertial navigation subsystem (2) to obtain and output combined navigation information;
the filter (3) comprises
A space module (31) in which a state space and a measurement space are integrated;
the SDRE decomposition module (32) is used for carrying out state correlation decomposition on the state space and the measurement space in the space module (31) to respectively obtain a state decomposition space and a measurement decomposition space;
the discretization processing module (33) is used for discretizing the state decomposition space and the measurement decomposition space in the SDRE decomposition module (32) to respectively obtain a state discrete space and a measurement discrete space; and
the strong tracking filtering module (34) is used for carrying out strong tracking filtering processing on the state discrete space and the measurement discrete space in the discretization processing module (33) to obtain combined navigation information;
the state space and the measurement space are respectively expressed by the formulas (31-1) and (31-2):
z ═ h (x) + V formula (31-2);
wherein, in formula (31-1):
wherein phi ise、φnAnd phiuRespectively as mathematical platform error angles, and updating in real time; v. ofe、vnAnd vuThe speed of the carrier in the east direction, the north direction and the sky direction respectively;λ and h are respectively latitude, longitude and height of the carrier; epsilone、εnAnd εuRespectively, gyro constant drift, Deltae、ΔnAnd ΔuRespectively, accelerometer constant drift;
wherein,andrespectively representing random errors of the gyroscope in the east direction, the north direction and the sky direction,andrespectively representing random errors of the accelerometer in east, north and sky directions; wherein the random error is system noise;
g is a system noise transfer matrix and G is a system noise transfer matrix,wherein I represents an identity matrix;
in formula (31-2):
measurement information z ═ vge,vgn,vgu,pge,pgn,pgu]TWherein v isgeIndicating the speed, v, of the carrier in the east direction as measured by the GPS receivergnIndicating the velocity, v, of the carrier in the north direction as measured by the GPS receiverguIndicating the speed, p, of the carrier in the direction of the day as measured by the GPS receivergeIndicating the east position, p, of the carrier as measured by the GPS receivergnIndicating the position of the carrier in the north direction, p, measured by the GPS receiverguRepresenting the position of the carrier measured by the GPS receiver in the direction of the day;
v is measurement noise, V ═ Vvge,Vvgn,Vvgu,Vpge,Vpgn,Vpgu]TWherein V isvgeIndicating random errors in east speed of a carrier measured by a GPS receiverDifference, VvgnIndicating the random error, V, of the speed of the carrier measured by the GPS receiver in the north directionvguRepresenting random errors in the speed of the carrier measured by the GPS receiver in the direction of the sky, PpgeIndicating random errors, P, of the east position of the carrier measured by the GPS receiverpgnIndicating random errors in the north position of the carrier measured by the GPS receiver, PpguRepresenting the random error of the position of the carrier measured by the GPS receiver in the direction of the sky;
h (x) is a linear equation, H (x) Hx, where H is a measurement matrix, where:
the state decomposition space and the measurement decomposition space are respectively shown as a formula (32-1) and a formula (32-2):
z ═ Hx + V formula (32-2);
wherein, in the formula (32-1), F (x) is a state transition matrix,wherein, FNIs a 9-dimensional matrix in which the non-zero elements are:
F(4,2)＝-fu F(4,3)＝fn
F(5,1)＝fu F(5,3)＝-fe
F(6,1)＝-fn F(6,2)＝fe
F(9,6)＝1；
wherein, ω isieIs the earth rotation angular rate;and h is respectively the carrier measured by the inertial navigation systemLatitude and altitude; v. ofe、vnRespectively measuring the east and north speeds of the carrier by the inertial navigation system; delta veIs the difference, δ v, between the east velocity measured by the inertial navigation system and the east velocity measured by the GPS receivernThe difference between the east speed measured by the inertial navigation system and the north speed measured by the GPS receiver;the difference between the latitude measured by the inertial navigation system and the latitude measured by the GPS receiver is delta h, and the difference between the height measured by the inertial navigation system and the height measured by the GPS receiver is delta h; f. ofe、fnAnd fuAcceleration components of the measurement value of the accelerometer in the east direction, the north direction and the sky direction are respectively; rMIs the principal radius of curvature in the local meridian plane; rNIs the major curvature radius in the prime plane; wherein,long radius of the earth Re6378245, global oblateness e 1/298.257;
Fscomprises the following steps:
h is a measurement matrix, wherein:
the state discrete space and the measurement discrete space are respectively expressed by the formulas (33-1) and (33-2):
xk+1＝Φk+1/kxk+Γkwka compound of the formula (33-1),
zk+1＝Θk+1xk+1+Vk+1formula (33-2);
wherein phik+1/kIs a discrete state transition matrix, ГkIs a discrete noise transfer matrix，Θk+1Is a discrete measurement matrix; w is akRepresenting the system noise vector at time k; x is the number ofkIndicating the state at time k; x is the number ofk+1Representing the actual state estimate at time k + 1; z is a radical ofk+1Measured data at the moment k + 1;
the strong tracking filtering module (34) comprises a one-step prediction sub-module (341), a gain matrix obtaining sub-module (342), an actual state estimation sub-module (343) and an error variance matrix updating sub-module (344);
the one-step prediction of the state is processed as shown in equation (341-1):
wherein, in the formula (341-1),indicates the predicted value of the state at the time k +1 from the state at the time k, xkRepresents the state at time k, Δ t represents the filtering period;
the one-step prediction of the error variance matrix is processed as shown in equation (341-2):
wherein, in the formula (341-2), Pk+1/kβ shows the predicted value of the error variance matrix at the time k +1 obtained by prediction from the error variance matrix at the time kkFor adaptive fading factor, PkError variance matrix, phi, representing time kk+1/kRepresenting the state transition matrix after the discretization,represents phik+1/kTransposed matrix of (2), QkDenotes wkK denotes the current time, k +1 denotes the next time, where k is 0,1,2,3, …, L, where L is determined by the filtering time and the filtering periodL ═ filter time/filter period;
the actual state estimate xk+1Is obtained as shown in formula (343-1):
wherein,a predicted state value at time K +1, K, representing a state prediction from time Kk+1The gain matrix representing the time instant k +1, zk+1The measured data of the time k +1 is obtained according to the information of the time k +1 given by the GPS,indicating the prediction of state values from one stepThe measured value of (a).
2. The system according to claim 1, wherein the strong tracking filter module (34) comprises
A one-step prediction submodule (341) for performing one-step prediction of the state and one-step prediction of the error variance matrix to obtainAnd Pk+1/k；
A gain matrix obtaining submodule (342) for utilizing Pk+1/kGain matrix at time K +1 is obtained, in Kk+1Represents;
an actual state estimation sub-module (343) for utilizingAnd Kk+1Obtaining an actual state estimation value at the k +1 moment by xk+1Represents;
the error variance matrix updates the sub-module (344) with Kk+1And Pk+1/kUpdating the error variance matrix at the k +1 moment to obtain Pk+1。
3. The system of claim 1,
the gain matrix Kk+1Is obtained as shown in formula (342-1):
wherein, in the formula (342-1), Pk+1/kRepresents an error variance matrix at time k +1 obtained by prediction of the error variance matrix at time kk+1Is a measurement matrix after the dispersion of the measured data,is thetak+1Transposed matrix of (2), Rk+1For measuring noise vector Vk+1Measuring a noise variance matrix;
and/or
The update of the error variance matrix at time k +1 is performed as shown in equation (344-1):
Pk+1＝(I-Kk+1Θk+1)Pk+1/kformula (344-1).
4. The system of claim 1, wherein the filter further comprises an initialization module (340) configured to initialize the state and the error variance matrix to obtain an initial state value and an initial error variance matrix, respectively, each x0And P0And (4) showing.
5. A combined navigation method based on strong tracking SDRE filtering, the method being performed with the combined navigation system of claims 1 to 4, wherein the method comprises the steps of:
step 1, performing state correlation decomposition on a state space and a measurement space in a space module (31) by using an SDRE decomposition module (32) to respectively obtain a state decomposition space and a measurement decomposition space;
step 2, a discretization processing module (33) is used for discretizing the state decomposition space and the measurement decomposition space in the SDRE decomposition module (32) to respectively obtain a state discrete space and a measurement discrete space;
and 3, carrying out strong tracking filtering processing on the state discrete space and the measurement discrete space in the discretization processing module (33) by using a strong tracking filtering module (34) to obtain combined navigation data, and outputting the data.
6. The method of claim 5, wherein,
the step 3 comprises the following substeps:
step 3-1, the state and the error square matrix at the next moment and the k +1 moment are predicted in one step by utilizing a one-step prediction submodule (341) to obtain a state prediction value and an error square matrix prediction value at the next moment respectivelyAnd Pk+1/kRepresents;
step 3-2 of Using P obtained in step 3-1k+1/kProcessed by a gain matrix acquisition submodule (342) to obtain a gain matrix for the next time instant, denoted by Kk+1Represents;
step 3-3 of utilizing the product obtained in step 3-1And K obtained in step 3-2k+1The actual state value at the next time is obtained by the actual state estimation submodule (343) as xk+1And representing, namely combining the navigation information and outputting the information.
7. The method according to claim 6, wherein the updating of the error variance matrix at the next time instant, time k +1, must be performed while step 3-3 is performed, i.e. step 3-4 is performed simultaneously with step 3-3:
step 3-4 of utilizing P obtained in step 3-1k+1/kAnd K obtained in step 3-2k+1And processing the data by an error variance matrix updating sub-module (344) as shown in a formula (344-1):
Pk+1＝(I-Kk+1Θk+1)Pk+1/kthe compound of the formula (344-1),
wherein the error variance matrix updating submodule (344) is configured to update the error variance matrix at the time K +1, wherein the gain matrix K at the time K +1 is usedk+1And an error variance matrix P at the k +1 moment obtained by prediction according to the error variance matrix at the k momentk+1/kObtaining an error variance matrix P at the k +1 momentk+1。
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