CN117268376A - Combined navigation system data fusion method suitable for measuring noise uncertainty - Google Patents
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- 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
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Abstract
The invention discloses a data fusion method of an integrated navigation system suitable for measuring uncertain noise, which is characterized by comprising the following steps of: s1: constructing an inertial/astronomical combined navigation system model; s2: the measurement noise sequence is obtained by predicting multi-step measurement through CKF to expand the measurement sequence, and then combining an empirical mode decomposition method and a filtering operation mean method to decompose the expanded measurement sequence. The invention relates to a data fusion method, in particular to a data fusion method of a combined navigation system suitable for measuring noise uncertainty. The invention aims to solve the technical problem of providing the data fusion method of the integrated navigation system suitable for measuring the uncertainty of the noise, which not only has the advantage of low calculation complexity, but also shows better robustness to the uncertainty of the noise, thereby improving the navigation data fusion precision of the inertial/astronomical integrated navigation system.
Description
Technical Field
The invention relates to a data fusion method, in particular to a data fusion method of a combined navigation system suitable for measuring noise uncertainty.
Background
In integrated navigation systems, kalman Filters (KF), extended Kalman Filters (EKF), unscented Kalman Filters (UKF) and volumetric kalman filters (CKF) are widely used for fusion of navigation data. When the prior information of the integrated navigation system is given and the model parameters are known, the EKF, UKF and CKF can obtain better data fusion performance. However, the inertial/astronomical integrated navigation system is generally applied to navigation of satellites, high altitude reconnaissance aircraft, strategic missiles and other spacecrafts, the space environment of the operation of the navigation system is complex and changeable, and the spacecrafts are inevitably affected by various random interferences in the flight process. Thus, inertial/astronomical integrated navigation systems may suffer from slow variation or uncertainty in measurement noise. Since EKF, UKF and CKF cannot accommodate the variation of measurement noise, their data fusion accuracy may be degraded or even diverged. Aiming at the problem, a plurality of self-adaptive filtering methods based on multiple models and a plurality of self-adaptive filtering methods based on innovation are provided, but the methods have the problems of high calculation complexity, excessive adjustment of measurement noise and low fusion precision of navigation data.
In order to realize that the inertial/astronomical integrated navigation system can still obtain high-precision navigation data fusion information under the condition of uncertain measurement noise, the invention provides a data fusion method of the integrated navigation system suitable for uncertain measurement noise.
Disclosure of Invention
The invention aims to solve the technical problem of providing the data fusion method of the integrated navigation system suitable for measuring the uncertainty of the noise, which not only has the advantage of low calculation complexity, but also shows better robustness to the uncertainty of the noise, thereby improving the navigation data fusion precision of the inertial/astronomical integrated navigation system.
The invention adopts the following technical scheme to realize the aim of the invention:
the integrated navigation system data fusion method suitable for measuring the uncertainty of noise is characterized by comprising the following steps of:
s1: constructing an inertial/astronomical combined navigation system model;
s2: predicting multi-step measurement by CKF to expand the measurement sequence, and then combining an empirical mode decomposition method and a filtering operation mean method to decompose the measurement sequence to obtain a measurement noise sequence;
s3: and estimating measurement noise covariance based on the measurement noise sequence obtained by decomposition and an exponential decay weighting method, and updating parameters based on the CKF data fusion process in real time.
As a further limitation of the present technical solution, the step S1 includes the following steps:
s11: setting a state vector of an inertial/astronomical combined navigation system as follows:
x＝[φ x ,φ y ,φ z ,δv x ,δv y ,δv z ,P x ,P y ,P z ,ε x ,ε y ,ε z ,Δ x ,Δ y ,Δ z ,Θ x ,Θ y ,Θ z ] T
wherein: phi (phi) x ,φ y ,φ z Representing an attitude misalignment angle;
δv x ,δv y ,δv z representing a speed error;
P x ,P y ,P z representing a position error;
ε x ,ε y ,ε z indicating gyro constant drift;
Δ x ,Δ y ,Δ z representing accelerometer constant bias;
Θ x ,Θ y ,Θ z representing a low frequency error of the astronomical navigation system;
s12: establishing a state equation of the system according to an 18-dimensional state vector x of the inertial/astronomical combined navigation system:
x k ＝f(x k-1 )+w k-1 (1)
wherein: f (·) represents a nonlinear system function;
x k and x k-1 State vectors respectively representing the k time and the k-1 time;
w k-1 representing process noise, w k-1 Covariance Q of (2) k-1 Is that
S13: taking the difference between the attitude angle output by the inertial navigation system and the attitude angle output by the astronomical navigation system, the difference between the position vector output by the inertial navigation system and the position vector output by the astronomical navigation system, the refractive apparent height error caused by the atmospheric density error and the refractive measurement error and the kinematic constraint as measurement information, and establishing a measurement equation of the inertial/astronomical combined navigation system:
z k ＝h(x k )+v k (2)
wherein: z k A measurement vector representing moment k of the inertial/astronomical combined navigation system;
h (·) represents a metrology function;
v k measurement noise v representing moment k of inertial/astronomical integrated navigation system k Covariance R of (2) k The method comprises the following steps:
as a further limitation of the present technical solution, the S2 includes:
s21: state estimation value x at moment k-1 of given inertial/astronomical combined navigation system k-1|k-1 Covariance matrix P of state estimation value k-1|k-1 Calculating a volume point by the formulas (3) and (4);
S k-1|k-1 ＝chol(P k-1|k-1 ) (3)
X i,k-1|k-1 ＝S k-1|k-1 ξ i +x k-1k-1 ,i＝1,...,2n (4)
wherein: chol (·) represents Cholesky decomposition;
e i an ith column representing an n×n-dimensional identity matrix, n representing the dimension of the state quantity;
generating transfer volume points by state functions
Calculating a state prediction value x by equations (6) and (7), respectively k|k-1 Covariance matrix P of state prediction value k|k-1 ；
Wherein: omega i Weights representing volume points and
updated volume points can be obtained based on the predicted state and covariance matrix:
S k|k-1 ＝chol(P k|k-1 ) (8)
X i,k|k-1 ＝S k|k-1 ξ i +x k|k-1 (9)
the volume points are transmitted through a measurement equation, so that the volume points can be obtained:
Z i,k|k-1 ＝h(X i,k|k-1 ) (10)
based on the transfer volume point, we can get a predicted amount of measurement:
the measurement sequence accumulated at time k-1 is expressed asz k-1 (t) represents the measurement at time t, N represents a positive integer;
when the inertial/astronomical integrated navigation system is not updated, CKF is only in the predicted state of state quantity, and let x k|k ＝x k|k-1 ；
Thus, the extended amount measurement at time k can be expressed as: z k-1 (k)＝z k|k-1 ，
S22: by performing the above procedure in S21L times, L measured extension values can be obtained:
thus, the measurement sequence after expansion at time k-1 can be expressed as:
s23: the extended measurement sequence is subjected to empirical mode decompositionPerforming self-adaptive decomposition to obtain M modal components: ->
Because the measurement noise has high frequency characteristics, the measurement noise is mainly distributed in the modal components of the first two ordersAnd->In (a) and (b);
measuring noise by wavelet denoising methodAnd->The separated measurement noise sequence can be expressed as v k-1 ；
For measuring noise sequence v k-1 G times of arbitrary changes to the position distribution of (b) to obtain G new measurement noise distribution sequences:then obtaining a reconstructed measurement noise sequence by a mean value solving method of the formula (12):
as a further limitation of the present technical solution, the S3 includes:
based on the reconstructed measurement noise sequenceAnd estimating a covariance matrix of the measurement noise at the k moment by an exponential decay weighting method:
wherein:b has a value of [0.99,0.999 ]]；
Calculating a covariance matrix of the measurement quantity and a cross covariance matrix between the state quantity and the measurement quantity according to the transmission volume point and the estimated measurement noise covariance matrix:
through P zz,k|k-1 And P xz,k|k-1 Calculating Kalman filtering gain:
updating the state quantity and covariance matrix of the inertial/astronomical combined navigation system by equations (17) and (18):
x k|k ＝x k|k-1 +K k (z k -z k|k-1 ) (17)
according to the obtained x k|k Correcting the navigation information independently output by the inertial navigation system, so as to obtain fusion data of the inertial/astronomical combined navigation system at the moment k;
let k=k+1, return to execute the S1, S2 and S3 and then the inertial/astronomical integrated navigation system enters the next data fusion process;
and (3) iteratively executing the S1, the S2 and the S3 until the inertial/astronomical integrated navigation system stops working, so as to obtain navigation fusion data of the inertial/astronomical integrated navigation system in the running period.
Compared with the prior art, the invention has the advantages and positive effects that:
1. the method has the advantage of low calculation complexity, and also shows stronger robustness on measurement noise uncertainty, so that the navigation data fusion precision of the inertial/astronomical combined navigation system is improved.
2. The invention can eliminate the influence of the noise position on the navigation data fusion result in the measurement noise covariance estimation process.
3. The method provided by the invention is applied to the low-cost integrated navigation system, so that the navigation precision of the high-cost high-precision integrated navigation system can be achieved.
Drawings
FIG. 1 is a flow chart of a data fusion method according to the present invention.
Detailed Description
One embodiment of the present invention will be described in detail below with reference to the attached drawings, but it should be understood that the scope of the present invention is not limited by the embodiment.
The invention comprises the following steps:
s1: an inertial/astronomical combined navigation system model is constructed.
The step S1 comprises the following steps:
s11: setting a state vector of an inertial/astronomical combined navigation system as follows:
x＝[φ x ,φ y ,φ z ,δv x ,δv y ,δv z ,P x ,P y ,P z ,ε x ,ε y ,ε z ,Δ x ,Δ y ,Δ z ,Θ x ,Θ y ,Θ z ] T
wherein: phi (phi) x ,φ y ,φ z Representing an attitude misalignment angle;
δv x ,δv y ,δv z representing a speed error;
P x ,P y ,P z representing a position error;
ε x ,ε y ,ε z indicating gyro constant drift;
Δ x ,Δ y ,Δ z representing accelerometer constant bias;
Θ x ,Θ y ,Θ z representing a low frequency error of the astronomical navigation system;
s12: establishing a state equation of the system according to an 18-dimensional state vector x of the inertial/astronomical combined navigation system:
x k ＝f(x k-1 )+w k-1 (1)
wherein: f (·) represents a nonlinear system function;
x k and x k-1 State vectors respectively representing the k time and the k-1 time;
w k-1 representing process noise, w k-1 Covariance Q of (2) k-1 Is that
S13: taking the difference between the attitude angle output by the inertial navigation system and the attitude angle output by the astronomical navigation system, the difference between the position vector output by the inertial navigation system and the position vector output by the astronomical navigation system, the refractive apparent height error caused by the atmospheric density error and the refractive measurement error and the kinematic constraint as measurement information, and establishing a measurement equation of the inertial/astronomical combined navigation system:
z k ＝h(x k )+v k (2)
wherein: z k A measurement vector representing moment k of the inertial/astronomical combined navigation system;
h (·) represents a metrology function;
v k measurement noise v representing moment k of inertial/astronomical integrated navigation system k Covariance R of (2) k The method comprises the following steps:
s2: the measurement noise sequence is obtained by predicting multi-step measurement through CKF to expand the measurement sequence, and then combining an empirical mode decomposition method and a filtering operation mean method to decompose the expanded measurement sequence.
The step S2 comprises the following steps:
s21: state estimation value x at moment k-1 of given inertial/astronomical combined navigation system k-1|k-1 Covariance matrix P of state estimation value k-1|k-1 Calculating a volume point by the formulas (3) and (4);
S k-1|k-1 ＝chol(P k-1|k-1 ) (3)
X i,k-1|k-1 ＝S k-1|k-1 ξ i +x k-1|k-1 ,i＝1,...,2n (4)
wherein: chol (·) represents Cholesky decomposition;
e i an ith column representing an n×n-dimensional identity matrix, n representing the dimension of the state quantity;
generating transfer volume points by state functions
Calculating a state prediction value x by equations (6) and (7), respectively k|k-1 Covariance matrix P of state prediction value k|k-1 ；
Wherein: omega i Weights representing volume points and
updated volume points can be obtained based on the predicted state and covariance matrix:
S k|k-1 ＝chol(P k|k-1 ) (8)
X i,k|k-1 ＝S k|k-1 ξ i +x k|k-1 (9)
the volume points are transmitted through a measurement equation, so that the volume points can be obtained:
Z i,k|k-1 ＝h(X i,k|k-1 ) (10)
based on the transfer volume point, we can get a predicted amount of measurement:
the measurement sequence accumulated at time k-1 is expressed asz k-1 (t) represents the measurement at time t, N represents a positive integer;
when the inertial/astronomical integrated navigation system is not updated, CKF is only in the predicted state of state quantity, and let x k|k ＝x k|k-1 ；
Thus, the extended amount measurement at time k can be expressed as: z k-1 (k)＝z k|k-1 ，
S22: by performing the above procedure in S21L times, L measured extension values can be obtained:
thus, the measurement sequence after expansion at time k-1 can be expressed as:
s23: the extended measurement sequence is subjected to empirical mode decompositionPerforming self-adaptive decomposition to obtain M modal components: ->
Because the measurement noise has high frequency characteristics, the measurement noise is mainly distributed in the modal components of the first two ordersAnd->In (a) and (b);
measuring noise by wavelet denoising methodAnd->The separated measurement noise sequence can be expressed as v k-1 ；
For measuring noise sequence v k-1 G times of arbitrary changes to the position distribution of (b) to obtain G new measurement noise distribution sequences:then obtaining a reconstructed measurement noise sequence by a mean value solving method of the formula (12):
s3: and estimating measurement noise covariance based on the measurement noise sequence obtained by decomposition and an exponential decay weighting method, and updating parameters based on the CKF data fusion process in real time.
The step S3 comprises the following steps:
based on the reconstructed measurement noise sequenceAnd estimating a covariance matrix of the measurement noise at the k moment by an exponential decay weighting method:
wherein:b has a value of [0.99,0.999 ]]；
Calculating a covariance matrix of the measurement quantity and a cross covariance matrix between the state quantity and the measurement quantity according to the transmission volume point and the estimated measurement noise covariance matrix:
through P zz,k|k-1 And P xz,k|k-1 Calculating Kalman filtering gain:
updating the state quantity and covariance matrix of the inertial/astronomical combined navigation system by equations (17) and (18):
x k|k ＝x k|k-1 +K k (z k -z k|k-1 ) (17)
according to the obtained x k|k Correcting the navigation information independently output by the inertial navigation system to obtain the k moment inertial/astronomical combined navigationFusion data of the system;
let k=k+1, return to execute the S1, S2 and S3 and then the inertial/astronomical integrated navigation system enters the next data fusion process;
and (3) iteratively executing the S1, the S2 and the S3 until the inertial/astronomical integrated navigation system stops working, so as to obtain navigation fusion data of the inertial/astronomical integrated navigation system in the running period.
And the implementation of S1 is to construct an inertial/astronomical combined navigation system model.
And realizing the construction of the measurement noise sequence through the S2. And S2, calculating volume points, calculating the transfer volume points of an inertial/astronomical combined navigation system equation, calculating a state predicted value and a state error covariance matrix, and expanding a predicted quantity measurement sequence. And (3) constructing the measurement noise sequence by performing empirical mode decomposition and filtering operation mean on the extended measurement sequence of the S2.
And realizing navigation data fusion through the S3. And (3) carrying out exponential decay weighting on the measurement noise sequence constructed in the step (S2) to obtain measurement noise covariance estimation and system state and covariance update, and correcting navigation information output by the inertial navigation system to realize data fusion of the integrated navigation system.
The above disclosure is merely illustrative of specific embodiments of the present invention, but the present invention is not limited thereto, and any variations that can be considered by those skilled in the art should fall within the scope of the present invention.
Claims (4)
1. The integrated navigation system data fusion method suitable for measuring the uncertainty of noise is characterized by comprising the following steps of:
s1: constructing an inertial/astronomical combined navigation system model;
s2: predicting multi-step measurement by CKF to expand the measurement sequence, and then combining an empirical mode decomposition method and a filtering operation mean method to decompose the measurement sequence to obtain a measurement noise sequence;
s3: and estimating measurement noise covariance based on the measurement noise sequence obtained by decomposition and an exponential decay weighting method, and updating parameters based on the CKF data fusion process in real time.
2. The integrated navigation system data fusion method applicable to measurement noise uncertainty of claim 1, wherein: the step S1 comprises the following steps:
s11: setting a state vector of an inertial/astronomical combined navigation system as follows:
x＝[φ x ,φ y ,φ z ,δv x ,δv y ,δv z ,P x ,P y ,P z ,ε x ,ε y ,ε z ,Δ x ,Δ y ,Δ z ,Θ x ,Θ y ,Θ z ] T
wherein: phi (phi) x ,φ y ,φ z Representing an attitude misalignment angle;
δv x ,δv y ,δv z representing a speed error;
P x ,P y ,P z representing a position error;
ε x ,ε y ,ε z indicating gyro constant drift;
Δ x ,Δ y ,Δ z representing accelerometer constant bias;
Θ x ,Θ y ,Θ z representing a low frequency error of the astronomical navigation system;
s12: establishing a state equation of the system according to an 18-dimensional state vector x of the inertial/astronomical combined navigation system:
x k ＝f(x k-1 )+w k-1 (1)
wherein: f (·) represents a nonlinear system function;
x k and x k-1 State vectors respectively representing the k time and the k-1 time;
w k-1 representing process noise, w k-1 Covariance Q of (2) k-1 Is that
S13: taking the difference between the attitude angle output by the inertial navigation system and the attitude angle output by the astronomical navigation system, the difference between the position vector output by the inertial navigation system and the position vector output by the astronomical navigation system, the refractive apparent height error caused by the atmospheric density error and the refractive measurement error and the kinematic constraint as measurement information, and establishing a measurement equation of the inertial/astronomical combined navigation system:
z k ＝h(x k )+v k (2)
wherein: z k A measurement vector representing moment k of the inertial/astronomical combined navigation system;
h (·) represents a metrology function;
v k measurement noise v representing moment k of inertial/astronomical integrated navigation system k Covariance R of (2) k The method comprises the following steps:
3. the integrated navigation system data fusion method applicable to measurement noise uncertainty of claim 2, wherein: the step S2 comprises the following steps:
s21: state estimation value x at moment k-1 of given inertial/astronomical combined navigation system k-1|k-1 Covariance matrix P of state estimation value k-1|k-1 Calculating a volume point by the formulas (3) and (4);
S k-1|k-1 ＝chol(P k-1|k-1 ) (3)
X i,k-1|k-1 ＝S k-1|k-1 ξ i +x k-1|k-1 ,i＝1,...,2n (4)
wherein: chol (·) represents Cholesky decomposition;
e i an ith column representing an n×n-dimensional identity matrix, n representing the dimension of the state quantity;
generating transfer volume points by state functions
Calculating a state prediction value x by equations (6) and (7), respectively k|k-1 Covariance matrix P of state prediction value k|k-1 ；
Wherein: omega i Weights representing volume points and
updated volume points can be obtained based on the predicted state and covariance matrix:
S k|k-1 ＝chol(P k|k-1 ) (8)
the volume points are transmitted through a measurement equation, so that the volume points can be obtained:
Z i,k|k-1 ＝h(X i,k|k-1 ) (10)
based on the transfer volume point, we can get a predicted amount of measurement:
the measurement sequence accumulated at time k-1 is expressed asz k-1 (t) represents the measurement at time t, N represents a positive integer;
when the inertial/astronomical integrated navigation system is not updated, CKF is only in the predicted state of state quantity, and let x k|k ＝x k|k-1 ；
Thus, the extended amount measurement at time k can be expressed as: z k-1 (k)＝z k|k-1 ，
S22: by performing the above procedure in S21L times, L measured extension values can be obtained:
thus, the measurement sequence after expansion at time k-1 can be expressed as:
s23: the extended measurement sequence is subjected to empirical mode decompositionPerforming self-adaptive decomposition to obtain M modal components: ->
Because the measurement noise has high frequency characteristics, the measurement noise is mainly distributed in the modal components of the first two ordersAndin (a) and (b);
measuring noise by wavelet denoising methodAnd->The separated measurement noise sequence can be expressed as v k-1 ；
For measuring noise sequence v k-1 G times of arbitrary changes to the position distribution of (b) to obtain G new measurement noise distribution sequences:then obtaining a reconstructed measurement noise sequence by a mean value solving method of the formula (12):
4. the integrated navigation system data fusion method for measuring noise uncertainty of claim 3, wherein: the step S3 comprises the following steps:
based on the reconstructed measurement noise sequenceAnd estimating a covariance matrix of the measurement noise at the k moment by an exponential decay weighting method:
wherein:b has a value of [0.99,0.999 ]]；
Calculating a covariance matrix of the measurement quantity and a cross covariance matrix between the state quantity and the measurement quantity according to the transmission volume point and the estimated measurement noise covariance matrix:
through P zz,k|k-1 And P xz,k|k-1 Calculating Kalman filtering gain:
updating the state quantity and covariance matrix of the inertial/astronomical combined navigation system by equations (17) and (18):
x k|k ＝x k|k-1 +K k (z k -z k|k-1 ) (17)
according to the obtained x k|k Correcting the navigation information independently output by the inertial navigation system, so as to obtain fusion data of the inertial/astronomical combined navigation system at the moment k;
let k=k+1, return to execute the S1, S2 and S3 and then the inertial/astronomical integrated navigation system enters the next data fusion process;
and (3) iteratively executing the S1, the S2 and the S3 until the inertial/astronomical integrated navigation system stops working, so as to obtain navigation fusion data of the inertial/astronomical integrated navigation system in the running period.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN118392190A (en) * | 2024-06-25 | 2024-07-26 | 齐鲁工业大学(山东省科学院) | Combined navigation data fusion method based on hypothesis constraint |
| CN118424290A (en) * | 2024-05-13 | 2024-08-02 | 齐鲁工业大学(山东省科学院) | Combined navigation data fusion method suitable for time-varying measurement noise |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN118424290A (en) * | 2024-05-13 | 2024-08-02 | 齐鲁工业大学(山东省科学院) | Combined navigation data fusion method suitable for time-varying measurement noise |
| CN118424290B (en) * | 2024-05-13 | 2024-10-22 | 齐鲁工业大学(山东省科学院) | Combined navigation data fusion method suitable for time-varying measurement noise |
| CN118392190A (en) * | 2024-06-25 | 2024-07-26 | 齐鲁工业大学(山东省科学院) | Combined navigation data fusion method based on hypothesis constraint |
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