CN115711622A - Underwater unmanned vehicle positioning method based on generalized minimum error entropy Kalman - Google Patents

Underwater unmanned vehicle positioning method based on generalized minimum error entropy Kalman Download PDF

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CN115711622A
CN115711622A CN202211455385.1A CN202211455385A CN115711622A CN 115711622 A CN115711622 A CN 115711622A CN 202211455385 A CN202211455385 A CN 202211455385A CN 115711622 A CN115711622 A CN 115711622A
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data sample
matrix
kth
positioning data
positioning
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王洁
何嘉诚
张堃
彭倍
王刚
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University of Electronic Science and Technology of China
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Abstract

The invention provides an underwater unmanned vehicle positioning method based on generalized minimum error entropy Kalman, which comprises the following steps: s1, collecting position and speed data of an underwater unmanned vehicle to construct a positioning data sample set; s2, filtering the positioning data samples in the positioning data sample set by adopting generalized minimum error entropy Kalman filtering to obtain corrected positioning data; the invention solves the problem that the existing filtering method aiming at non-Gaussian noise can only process certain specific types of noise, and the non-Gaussian noise can not be completely filtered, so that the estimation precision of underwater sound positioning is low.

Description

Underwater unmanned vehicle positioning method based on generalized minimum error entropy Kalman
Technical Field
The invention relates to the technical field of unmanned vehicle positioning, in particular to an underwater unmanned vehicle positioning method based on generalized minimum error entropy Kalman.
Background
With the development of marine exploration, the application of the underwater unmanned vehicle is also increasingly wide, and meanwhile, the high-precision underwater acoustic positioning technology of the underwater unmanned vehicle attracts more attention. In an actual marine environment, an underwater acoustic positioning system of an underwater unmanned vehicle usually uses an acoustic signal for measurement and positioning, but due to a complex underwater environment and noise interference generated by ships going to and going to the underwater acoustic positioning system, abnormal measurement is usually generated in the underwater acoustic positioning system of the underwater unmanned vehicle. The noise generated by the marine environment and the passing ships generally belongs to non-Gaussian noise, and the unknown non-Gaussian noise can seriously affect the precision of an underwater acoustic positioning system of the unmanned vehicle and cause great negative influence on the positioning of the underwater unmanned vehicle.
The existing original Kalman filtering algorithm (KF) commonly used for underwater sound positioning is only suitable for Gaussian noise conditions. To understand the effect of non-gaussian noise on state estimation (underwater sound localization): (1) Recently, the maximum correlation entropy criterion (MCC) in Information Theory Learning (ITL) considers high-order statistics, is a good non-gaussian noise state estimation (underwater localization) method, and proposes a new KF algorithm based on MCC, called maximum correlation entropy KF (MCKF), which also extends to state estimation (underwater localization) of nonlinear systems. In addition, some KFs based on modified correlation entropy criteria were also developed. (2) The Minimum Error Entropy (MEE) criterion in ITL outperforms MCC in dealing with complex non-gaussian noise with multimodal distributions. In order to further improve the capability of the KF algorithm to process non-Gaussian noise, a plurality of novel Kalman filtering algorithms based on the MEE criterion are provided. However, neither MCC nor MEE can its shape of error entropy be freely changed because its kernel function is a gaussian function, which makes algorithms based on maximum correlation entropy and error entropy capable of handling only certain specific types of noise. These non-gaussian noise with unknown distribution will inevitably reduce the estimation accuracy of the system underwater sound localization.
Disclosure of Invention
Aiming at the defects in the prior art, the underwater unmanned vehicle positioning method based on the generalized minimum error entropy Kalman solves the problem that the existing filtering method aiming at non-Gaussian noise can only process certain specific types of noise, and the non-Gaussian noise cannot be completely filtered, so that the estimation accuracy of underwater sound positioning is low.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: an underwater unmanned vehicle positioning method based on generalized minimum error entropy Kalman comprises the following steps:
s1, collecting position and speed data of an underwater unmanned vehicle to construct a positioning data sample set;
and S2, filtering the positioning data samples in the positioning data sample set by adopting generalized minimum error entropy Kalman filtering to obtain corrected positioning data.
Further, the step S2 includes the following sub-steps:
s21, substituting the initial value of the positioning data sample into a prediction equation to obtain a predicted value of the positioning data sample;
s22, calculating a positioning data sample error value according to the positioning data sample predicted value and the positioning data sample set;
s23, calculating a component of a covariance matrix of an augmented noise matrix according to the error value of the positioning data sample and the augmented noise matrix;
s24, constructing a generalized minimum error entropy Kalman filtering model according to the components of the covariance matrix of the augmented noise matrix and the predicted values of the positioning data samples;
s25, updating the estimated positioning data samples according to the generalized minimum error entropy Kalman filtering model to obtain updated estimated positioning data samples;
and S26, judging whether the updated estimated positioning data sample meets an error condition, if so, updating the estimated positioning data sample into corrected positioning data, and if not, directly jumping to the step S25.
Further, the prediction equation in step S21 is:
Figure BDA0003953345130000031
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003953345130000032
for the prediction of the kth positioning data sample, A k-1 The state transition matrix for the k-1 th,
Figure BDA0003953345130000033
for the predicted value of the k-1 th positioning data sample, at k =0,
Figure BDA0003953345130000034
an initial value of data samples is located.
Further, the formula for calculating the error value of the positioning data sample in step S22 is:
Figure BDA0003953345130000035
wherein epsilon k|k-1 For the kth positioning of the data sample error value, x k For the kth positioning data sample in the positioning data sample set,
Figure BDA0003953345130000041
the prediction value of the kth position data sample is located.
Further, the step S23 includes the following sub-steps:
s231, calculating an augmented noise matrix of the positioning data samples according to the error values of the positioning data samples;
s232, calculating the components of the covariance matrix of the augmented noise matrix according to the augmented noise matrix of the positioning data samples.
Further, the formula for calculating the augmented noise matrix of the positioning data samples in step S231 is:
Figure BDA0003953345130000042
wherein, mu k An augmented noise matrix, ε, for the kth position data sample k|k-1 For the kth error value of the positioning data sample, v k The observed noise for the kth data sample is located.
Further, the formula for calculating the components of the covariance matrix of the augmented noise matrix in step S232 is:
Figure BDA0003953345130000043
wherein, theta k The components of the covariance matrix of the augmented noise matrix for the kth located data sample,
Figure BDA0003953345130000044
the covariance matrix of the augmented noise matrix for the kth position data sample, T is the transposition operation, μ k An augmented noise matrix for the kth located data sample.
Further, the generalized minimum error entropy kalman filtering model in step S24 is:
Figure BDA0003953345130000045
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003953345130000051
Figure BDA0003953345130000052
Figure BDA0003953345130000053
Figure BDA0003953345130000054
to D k 、W k And e k And solving to obtain:
Figure BDA0003953345130000055
L＝m+n
will be provided with
Figure BDA0003953345130000056
The method comprises the following steps:
Figure BDA0003953345130000057
will theta k Decomposing into:
Figure BDA0003953345130000058
then:
Figure BDA0003953345130000061
Figure BDA0003953345130000062
wherein the content of the first and second substances,
Figure BDA0003953345130000063
for the estimated position data samples updated at the t-th iteration,
Figure BDA0003953345130000064
for the predicted value of the kth positioning data sample,
Figure BDA0003953345130000065
kalman gain, y, of predicted values for the kth positioning data sample k A true measurement vector for the kth positioning of a data sample, C k For the observed transfer matrix of the kth located data sample,
Figure BDA0003953345130000066
W k a transformation matrix for a covariance matrix of predicted values of the kth located data sample,
Figure BDA0003953345130000067
the sum of the squares of the generalized gaussian probability density function values for the predicted values of the kth located data sample,
Figure BDA0003953345130000068
is a weighted sum of the values of the generalized gaussian probability density functions of the predictors of the kth positioned data sample,
Figure BDA0003953345130000069
a generalized gaussian probability density function value for the predictor of the kth positioning data sample,
Figure BDA00039533451300000610
is composed of
Figure BDA00039533451300000611
Element of row i and column j, G α,β () Is a Parzen window function, e j；k Error matrix e for the prediction value of the kth located data sample k J element of (e) i；k Error matrix e for the prediction value of the kth positioning data sample k Is the absolute value, | is the shape parameter, sign () is the sign function,
Figure BDA00039533451300000612
is composed of
Figure BDA00039533451300000613
The ith row and the jth column of (g),
Figure BDA00039533451300000614
is a real number field, m is the column number of the matrix, n is the row number of the matrix, L is the number of the elements in the statistical matrix,
Figure BDA00039533451300000615
is an error matrixe k The (i) th element of (2),
Figure BDA00039533451300000616
is an error matrix e k G element of (2), d i；k Transformation matrix D for prediction value of kth positioning data sample k The ith element of (1) i；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k The matrix of the ith row of (a),
Figure BDA00039533451300000617
for the estimated positioning data samples updated at the t-1 st iteration, D k Transformation matrix for the prediction value of the kth positioning data sample, x k For locating the kth location data sample in the data sample set, e k Error matrix for prediction value of kth positioning data sample, Θ k Component of the covariance matrix of the augmented noise matrix for the kth located data sample, I m Is a vector in the unit of a unit,
Figure BDA00039533451300000715
is a real number field, v k For the observed noise of the kth positioning data sample, T is the transposition operation, d 1；k Transformation matrix D for prediction value of kth positioning data sample k Middle 1 element, d 2；k Transformation matrix D for prediction value of kth positioning data sample k 2 nd element of (A), d L；k Transformation matrix D for prediction value of kth positioning data sample k Middle Lth element, w 1；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k 1 st row matrix of 2；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k Row 2 matrix of (a), w i；k Transformation matrix W of covariance matrix for predicted value of kth positioning data sample k Ith row matrix of L；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k The L-th row of the matrix (c),
Figure BDA0003953345130000071
error matrix e for the prediction value of the kth positioning data sample k The number 1 element of (a) is,
Figure BDA0003953345130000072
error matrix e for the prediction value of the kth positioning data sample k The number 2 element of (a) is,
Figure BDA0003953345130000073
error matrix e for the prediction value of the kth positioning data sample k The L-th element of (a),
Figure BDA0003953345130000074
Figure BDA0003953345130000075
a sum of squares matrix of m-th order gaussian probability density function values for the predicted values of the kth positioning data sample,
Figure BDA0003953345130000076
Figure BDA0003953345130000077
a sum of squares matrix of the n-th order gaussian probability density function values for the predicted value of the kth located data sample,
Figure BDA0003953345130000078
Figure BDA0003953345130000079
a sum of squares matrix of n x m dimensional generalized gaussian probability density function values for the k-th predicted value of the positioning data sample,
Figure BDA00039533451300000710
Figure BDA00039533451300000711
a sum of squares matrix of m x n dimensional generalized gaussian probability density function values for the k-th predicted value of the positioning data sample,
Figure BDA00039533451300000712
is a matrix
Figure BDA00039533451300000713
The positive definite matrix of (a) is,
Figure BDA00039533451300000714
is a matrix
Figure BDA0003953345130000081
Positive definite matrix of (theta) q；k Is theta k Is divided into blocks, Θ v；k Is theta k Is partitioned into blocks.
Further, the error condition in step S26 is:
Figure BDA0003953345130000082
wherein the content of the first and second substances,
Figure BDA0003953345130000083
for the estimated position data samples updated at the t-th iteration,
Figure BDA0003953345130000084
the estimated positioning data sample updated in the t-1 th iteration, | | | is two-norm operation, and τ is a positive threshold.
The invention has the beneficial effects that: according to the method, the generalized minimum error entropy Kalman filtering model is constructed, and the shape of the kernel function of the model is variable, so that the generalized minimum error entropy Kalman filtering model can flexibly process non-Gaussian noises with different distribution types, the underwater navigation positioning precision is improved, and the precision of an inertial navigation system is improved.
Drawings
FIG. 1 is a flow chart of an underwater unmanned vehicle positioning method of generalized minimum error entropy Kalman;
FIG. 2 is a comparative experimental plot.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
As shown in fig. 1, an underwater unmanned vehicle positioning method based on generalized minimum error entropy kalman includes the following steps:
s1, collecting position and speed data of an underwater unmanned vehicle to construct a positioning data sample set;
and S2, filtering the positioning data samples in the positioning data sample set by adopting generalized minimum error entropy Kalman filtering to obtain corrected positioning data.
The step S2 comprises the following sub-steps:
s21, substituting the initial value of the positioning data sample into a prediction equation to obtain a predicted value of the positioning data sample;
the prediction equation in step S21 is:
Figure BDA0003953345130000091
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003953345130000092
for the prediction of the kth positioning data sample, A k-1 The state transition matrix for the k-1 th,
Figure BDA0003953345130000093
for the predicted value of the (k-1) th positioning data sample, at k =0,
Figure BDA0003953345130000094
an initial value of data samples is located.
S22, calculating a positioning data sample error value according to the positioning data sample predicted value and the positioning data sample set;
the formula for calculating the error value of the positioning data sample in step S22 is:
Figure BDA0003953345130000095
wherein epsilon k|k-1 For the kth location data sample error value, x k For the kth positioning data sample in the positioning data sample set,
Figure BDA0003953345130000101
a prediction value for the kth position data sample is located.
S23, calculating a component of a covariance matrix of an augmented noise matrix according to the error value of the positioning data sample and the augmented noise matrix;
the step S23 includes the following sub-steps:
s231, calculating an augmented noise matrix of the positioning data samples according to the error values of the positioning data samples;
the formula for calculating the augmented noise matrix of the positioning data samples in step S231 is:
Figure BDA0003953345130000102
wherein, mu k An augmented noise matrix, ε, for the kth location data sample k|k-1 For the kth error value of the positioning data sample, v k The observed noise for the kth data sample is located.
S232, calculating the covariance matrix component of the augmented noise matrix according to the augmented noise matrix of the positioning data samples.
The formula for calculating the components of the covariance matrix of the augmented noise matrix in step S232 is:
Figure BDA0003953345130000103
wherein, theta k The components of the covariance matrix of the augmented noise matrix for the kth located data sample,
Figure BDA0003953345130000104
the covariance matrix of the augmented noise matrix for the kth position data sample, T is the transposition operation, μ k An augmented noise matrix for the kth located data sample.
S24, constructing a generalized minimum error entropy Kalman filtering model according to the components of the covariance matrix of the augmented noise matrix and the predicted values of the positioning data samples;
the generalized minimum error entropy kalman filtering model in the step S24 is:
Figure BDA0003953345130000111
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003953345130000112
Figure BDA0003953345130000113
Figure BDA0003953345130000114
Figure BDA0003953345130000115
to D k 、W k And e k And solving to obtain:
Figure BDA0003953345130000116
L＝m+n (11)
will be provided with
Figure BDA0003953345130000117
The writing is as follows:
Figure BDA0003953345130000118
will theta k Decomposing into:
Figure BDA0003953345130000121
then:
Figure BDA0003953345130000122
Figure BDA0003953345130000123
wherein the content of the first and second substances,
Figure BDA0003953345130000124
for the estimated position data samples updated at the t-th iteration,
Figure BDA0003953345130000125
for the predicted value of the kth positioning data sample,
Figure BDA0003953345130000126
kalman gain, y, of predicted values for the kth positioning data sample k A true measurement vector for the kth positioning of a data sample, C k For the observed transfer matrix of the kth located data sample,
Figure BDA0003953345130000127
W k for locating data sample kA transformation matrix of a covariance matrix of the predicted values,
Figure BDA0003953345130000128
is the sum of the squares of the generalized gaussian probability density function values of the predicted values of the kth located data sample,
Figure BDA0003953345130000129
is a weighted sum of the values of the generalized gaussian probability density functions of the predictors of the kth positioned data sample,
Figure BDA00039533451300001210
a generalized gaussian probability density function value for the predictor of the kth positioning data sample,
Figure BDA00039533451300001211
is composed of
Figure BDA00039533451300001212
Element of row i and column j, G α,β () As a Parzen window function, e j；k Error matrix e for the prediction value of the kth positioning data sample k J element of (e) i；k Error matrix e for the prediction value of the kth located data sample k Is the absolute value, | is the shape parameter, sign () is the sign function,
Figure BDA00039533451300001213
is composed of
Figure BDA00039533451300001214
The ith row and the jth column of (g),
Figure BDA00039533451300001215
is a real number field, m is the column number of the matrix, n is the row number of the matrix, L is the number of the elements in the statistical matrix,
Figure BDA00039533451300001216
is an error matrix e k The (i) th element of (a),
Figure BDA00039533451300001217
is an error matrix e k The g element of (a), d i；k Transformation matrix D for prediction value of kth positioning data sample k The ith element of (1) i；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k The matrix of the ith row of (a),
Figure BDA0003953345130000131
for the estimated positioning data samples updated at the t-1 st iteration, D k Transformation matrix for the prediction value of the kth positioning data sample, x k For locating the kth location data sample in the data sample set, e k Error matrix for prediction value of kth positioning data sample, Θ k Component of the covariance matrix of the augmented noise matrix for the kth located data sample, I m Is a vector of the unit,
Figure BDA0003953345130000132
is a real number field, v k For the observed noise of the kth positioning data sample, T is the transposition operation, d 1；k Transformation matrix D for prediction value of kth positioning data sample k 1 st element of (C), d 2；k Transformation matrix D for prediction value of kth positioning data sample k 2 nd element of (C), d L；k Transformation matrix D for prediction value of kth positioning data sample k Middle Lth element, w 1；k Transformation matrix W of covariance matrix for predicted value of kth positioning data sample k 1 st row matrix of 2；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k Row 2 matrix of i；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k Ith row matrix of L；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k The L-th row of the matrix (c),
Figure BDA0003953345130000133
error matrix e for the prediction value of the kth located data sample k The number 1 element of (a) is,
Figure BDA0003953345130000134
error matrix e for the prediction value of the kth positioning data sample k The (2) th element of (2),
Figure BDA0003953345130000135
error matrix e for the prediction value of the kth positioning data sample k The L-th element of (a) is,
Figure BDA0003953345130000136
Figure BDA0003953345130000137
a sum of squares matrix of m-th order gaussian probability density function values for the predicted values of the kth positioning data sample,
Figure BDA0003953345130000138
Figure BDA0003953345130000139
a matrix of sums of squares of n-th order gaussian probability density function values for the predicted values of the kth located data sample,
Figure BDA00039533451300001310
Figure BDA00039533451300001311
a sum of squares matrix of n x m dimensional generalized gaussian probability density function values for the k-th predicted value of the positioning data sample,
Figure BDA0003953345130000141
Figure BDA0003953345130000142
a sum of squares matrix of m x n dimensional generalized gaussian probability density function values for the k-th predicted value of the positioning data sample,
Figure BDA0003953345130000143
is a matrix
Figure BDA0003953345130000144
The positive definite matrix of (a) is,
Figure BDA0003953345130000145
is a matrix
Figure BDA0003953345130000146
Positive definite matrix of (theta) q；k Is theta k Is divided into blocks, Θ v；k Is theta k Is partitioned into blocks.
S25, updating the estimated positioning data samples according to the generalized minimum error entropy Kalman filtering model to obtain updated estimated positioning data samples;
and S26, judging whether the updated estimated positioning data sample meets an error condition, if so, updating the estimated positioning data sample into corrected positioning data, and if not, directly jumping to the step S25.
The error condition in step S26 is:
Figure BDA0003953345130000147
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003953345130000148
for the estimated position data samples updated at the t-th iteration,
Figure BDA0003953345130000149
the estimated positioning data sample updated in the t-1 th iteration, | | | is two-norm operation, and τ is a positive threshold.
The generalized Gaussian kernel function of the generalized minimum error entropy Kalman filtering model provided by the invention is a formula (18):
Figure BDA00039533451300001410
Figure BDA00039533451300001411
wherein, G σ (e) Is a common Gaussian kernel function, sigma is kernel bandwidth, exp () is an exponential function, e is a natural constant, gamma () is a gamma function, alpha is a shape parameter, beta is a bandwidth range parameter, G α，β (e) Is a generalized Gaussian kernel function, alpha is more than 0, and beta is more than 0.
According to the formula (18), when the value of the shape parameter alpha is changed, the shape of the generalized Gaussian kernel function is obviously changed, so that the generalized minimum error entropy Kalman filtering model can flexibly process different non-Gaussian distributed noises, and the accuracy of underwater navigation positioning estimation is improved. When the shape parameter is set to 1 or 2, the distribution of the generalized gaussian kernel function becomes a laplacian distribution or a gaussian distribution.
In the generalized minimum error entropy criterion, the error e is measured by Renyi's entropy:
Figure BDA0003953345130000151
wherein mu is the order of Renyi entropy; v μ (e) The specific form is as follows:
V μ (e)＝∫p μ (x)dx＝E[p μ-1 (e)], (20)
wherein p is μ () As a function of probability density, p μ-1 (e) Is the probability density of the function, x is the variable, E is the error, E]Representing the mathematical expectation, the probability density function can be roughly estimated in practical applications using the method of Parzen window:
Figure BDA0003953345130000152
wherein the content of the first and second substances,
Figure BDA0003953345130000153
for the probability density function of the rough estimate, L is the number of error data, G α,β () Is a Parzen window function, e i Is the ith error data.
When the order of the information potential energy is 2, the following can be obtained:
Figure BDA0003953345130000154
wherein the content of the first and second substances,
Figure BDA0003953345130000155
an information potential value of order 2, L an error data amount,
Figure BDA0003953345130000156
is e i Of the coarse estimate of e i For the ith error data, e j Is the ith error data.
Experiment:
under the condition of mixed Gaussian noise, comparing a generalized minimum error entropy Kalman filtering model (GMEEKF) constructed in the invention with a Kalman filtering algorithm (KF), a maximum correlation entropy Kalman filtering algorithm (MCKF), a MEEKF algorithm and a robust student's t-based Kalman filtering algorithm (RSTKF) respectively:
the Gaussian mixture noise model is as follows:
Figure BDA0003953345130000161
wherein r is Gaussian mixture noise, λ is a weighting coefficient,
Figure BDA0003953345130000162
mean a, variance μ 1 The distribution of the gaussian component of (a) is,
Figure BDA0003953345130000163
mean a, variance μ 2 A gaussian distribution of (a).
If the distribution follows equation (23), the distribution is said to follow a Gaussian mixture noise distribution, i.e., r to M (λ, a, μ) 1 ,μ 2 )。
In the following experiment, considering a uniform velocity trajectory tracking model, the equation of the positioning data sample and the equation of the trajectory are as follows:
Figure BDA0003953345130000164
Figure BDA0003953345130000165
wherein x is k ＝[x 1；k x 2；k x 3；k x 4；k ] T ，x 1；k ，x 2；k Representing displacement information in the x-axis and y-axis directions, respectively, x 3；k ，x 4；k Respectively representing speed information in the directions of an x axis and a y axis; time interval Δ T =0.1second; q. q of 1；k-1 Being the first row element of the state noise matrix, q 2；k-1 Being the second row element of the state noise matrix, q 3；k-1 Is the third row element, q, of the state noise matrix 4；k-1 Is the fourth row element of the state noise matrix; covariance matrix of state noise
Figure BDA0003953345130000171
Initial value x 0 ～N(0，I m )，
Figure BDA0003953345130000172
P 0|0 ～N(x 0 ，I m ) Positive threshold τ =10 -6 ，(I m An identity matrix of order m), x 0 Is x k Initial value of (a), x k For locating the kth location data sample, x, in the data sample set 0 ～N(0，I m ) Denotes x 0 Obedience mean 0, covariance matrix I m The gaussian process (normal process) of (a),
Figure BDA0003953345130000173
is composed of
Figure BDA0003953345130000174
Initial value of (1), P 0|0 Is P k|k Is set to the initial value of (a),
Figure BDA0003953345130000175
represent
Figure BDA0003953345130000176
Obedience mean 0, covariance matrix I m Gaussian process (normal process), P 0|0 ～N(x 0 ，I m ) Represents P 0|0 From a mean of 0 and a covariance matrix of I m Gaussian process (normal process).
Considering process noise as a Gaussian distribution q k N (0, 0.01), the observed noise is: v. of k M (0.9, 0,0.01, 100), wherein sigma, chi, eta and N are state parameters of the RSTKF algorithm; obtaining a true value x and an estimated value of the state variable
Figure BDA0003953345130000177
The results of the simulation of the mean square error of (a) are shown in fig. 2.
As can be seen from fig. 2: the generalized minimum error entropy Kalman filtering model GMEEKF is best in mixed Gaussian noise performance, and the positioning precision of the underwater unmanned vehicle is highest.
In summary, the embodiment of the invention has the following effects: according to the formula (18), the values of alpha and beta in the method can be changed, so that the shape of the generalized Gaussian kernel function can be flexibly changed, the generalized minimum error entropy Kalman filtering model can flexibly process non-Gaussian noises with different distribution types, and the accuracy of underwater navigation positioning is improved.
The present invention has been described in terms of the preferred embodiment, and it is not intended to be limited to the embodiment. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. An underwater unmanned vehicle positioning method based on generalized minimum error entropy Kalman is characterized by comprising the following steps:
s1, collecting position and speed data of an underwater unmanned vehicle to construct a positioning data sample set;
and S2, filtering the positioning data samples in the positioning data sample set by adopting generalized minimum error entropy Kalman filtering to obtain corrected positioning data.
2. The method for positioning an underwater unmanned vehicle based on generalized minimum error entropy kalman as claimed in claim 1, wherein the step S2 comprises the sub-steps of:
s21, substituting the initial value of the positioning data sample into a prediction equation to obtain a predicted value of the positioning data sample;
s22, calculating a positioning data sample error value according to the positioning data sample predicted value and the positioning data sample set;
s23, calculating a component of a covariance matrix of an augmented noise matrix according to the error value of the positioning data sample and the augmented noise matrix;
s24, constructing a generalized minimum error entropy Kalman filtering model according to the components of the covariance matrix of the augmented noise matrix and the predicted values of the positioning data samples;
s25, updating the estimated positioning data sample according to the generalized minimum error entropy Kalman filtering model to obtain an updated estimated positioning data sample;
and S26, judging whether the updated estimated positioning data sample meets an error condition, if so, updating the estimated positioning data sample into corrected positioning data, and if not, directly jumping to the step S25.
3. The method for positioning the unmanned underwater vehicle based on the generalized minimum error entropy kalman recited in claim 2, wherein the prediction equation in the step S21 is as follows:
Figure FDA0003953345120000021
wherein the content of the first and second substances,
Figure FDA0003953345120000022
for the prediction of the kth positioning data sample, A k-1 The state transition matrix for the k-1 th,
Figure FDA0003953345120000023
for the predicted value of the (k-1) th positioning data sample, at k =0,
Figure FDA0003953345120000024
an initial value of data samples is located.
4. The generalized minimum error entropy kalman underwater unmanned vehicle positioning method according to claim 2, wherein the formula for calculating the error value of the positioning data sample in step S22 is:
Figure FDA0003953345120000025
wherein epsilon k|k-1 For the kth location data sample error value, x k For the kth positioning data sample in the positioning data sample set,
Figure FDA0003953345120000026
a prediction value for the kth position data sample is located.
5. The method for the generalized minimum error entropy kalman underwater unmanned vehicle positioning according to claim 2, characterized in that the step S23 comprises the sub-steps of:
s231, calculating an augmented noise matrix of the positioning data samples according to the error values of the positioning data samples;
s232, calculating the components of the covariance matrix of the augmented noise matrix according to the augmented noise matrix of the positioning data samples.
6. The method for positioning an underwater unmanned vehicle based on generalized minimum error entropy kalman as claimed in claim 5, wherein the formula for calculating the augmented noise matrix of the positioning data samples in step S231 is:
Figure FDA0003953345120000031
wherein, mu k An augmented noise matrix, ε, for the kth location data sample k|k-1 For the kth positioning of a data sample error value, v k The observed noise for the kth data sample is located.
7. The method for positioning an underwater unmanned vehicle based on generalized minimum error entropy kalman as claimed in claim 5, wherein the formula for calculating the components of the covariance matrix of the augmented noise matrix in step S232 is:
Figure FDA0003953345120000032
wherein, theta k The components of the covariance matrix of the augmented noise matrix for the kth position data sample,
Figure FDA0003953345120000033
covariance matrix of the augmented noise matrix for the kth positioning data sample, T is the transposition operation, μ k An augmented noise matrix for the kth located data sample.
8. The method for positioning the unmanned underwater vehicle with the generalized minimum error entropy kalman according to claim 2, wherein the generalized minimum error entropy kalman filtering model in step S24 is as follows:
Figure FDA0003953345120000034
wherein the content of the first and second substances,
Figure FDA0003953345120000041
Figure FDA0003953345120000042
Figure FDA0003953345120000043
Figure FDA0003953345120000044
to D k 、W k And e k And solving to obtain:
Figure FDA0003953345120000045
L＝m+n
will be provided with
Figure FDA0003953345120000046
The writing is as follows:
Figure FDA0003953345120000047
will theta k Decomposing into:
Figure FDA0003953345120000048
then:
Figure FDA0003953345120000051
Figure FDA0003953345120000052
wherein the content of the first and second substances,
Figure FDA0003953345120000053
for the estimated position data samples updated at the t-th iteration,
Figure FDA0003953345120000054
for the predicted value of the kth positioning data sample,
Figure FDA0003953345120000055
kalman gain, y, of predicted values for the kth positioning data sample k For the k-th actual measurement vector of the data sample, C k For the observed transfer matrix of the kth located data sample,
Figure FDA0003953345120000056
W k a transformation matrix for a covariance matrix of predicted values for the kth positioned data sample,
Figure FDA0003953345120000057
is the sum of the squares of the generalized gaussian probability density function values of the predicted values of the kth located data sample,
Figure FDA0003953345120000058
is a weighted sum of the values of the generalized gaussian probability density functions of the predictors of the kth positioned data sample,
Figure FDA0003953345120000059
a generalized gaussian probability density function value for the predictor of the kth positioning data sample,
Figure FDA00039533451200000510
is composed of
Figure FDA00039533451200000511
Element of row i and column j, G α,β () As a Parzen window function, e j；k Error matrix e for the prediction value of the kth positioning data sample k J element of (e) i；k Error matrix e for the prediction value of the kth located data sample k The ith element of (1), where | is the absolute value, α is the shape parameter, sign () is the sign function,
Figure FDA00039533451200000512
is composed of
Figure FDA00039533451200000513
The ith row and the jth column of (g),
Figure FDA00039533451200000514
is a real number field, m is the column number of the matrix, n is the row number of the matrix, L is the number of the elements in the statistical matrix,
Figure FDA00039533451200000515
is an error matrix e k The (i) th element of (a),
Figure FDA00039533451200000516
is an error matrix e k The g element of (a), d i；k Transformation matrix D for prediction value of kth positioning data sample k The ith element of (1) i；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k The matrix of the ith row of (a),
Figure FDA00039533451200000517
for the estimated positioning data samples updated at the t-1 st iteration, D k Transformation matrix for prediction value of kth positioning data sample, x k For locating the kth location data sample in the data sample set, e k Error matrix for prediction value of kth positioning data sample, Θ k Component of the covariance matrix of the augmented noise matrix for the kth located data sample, I m Is a vector of the unit,
Figure FDA0003953345120000061
is a real number field, v k For the observed noise of the kth positioning data sample, T is the transposition operation, d 1；k Transformation matrix D for prediction value of kth positioning data sample k Middle 1 element, d 2；k Transformation matrix D for prediction value of kth positioning data sample k 2 nd element of (A), d L；k Transformation matrix D for prediction value of kth positioning data sample k Middle Lth element, w 1；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k 1 st row matrix of w 2；k Transformation matrix W of covariance matrix for predicted value of kth positioning data sample k Row 2 matrix of i；k Transformation matrix W of covariance matrix for predicted value of kth positioning data sample k Ith row matrix of (2), w L；k Transformation matrix W of covariance matrix for predicted values of kth positioned data sample k The L-th row of the matrix (c),
Figure FDA0003953345120000062
error matrix e for the prediction value of the kth positioning data sample k The number 1 element of (a) is,
Figure FDA0003953345120000063
error matrix e for the prediction value of the kth positioning data sample k The (2) th element of (2),
Figure FDA0003953345120000064
error matrix e for the prediction value of the kth located data sample k The L-th element of (a),
Figure FDA0003953345120000065
Figure FDA0003953345120000066
a sum of squares matrix of m-th order gaussian probability density function values for the predicted values of the kth positioning data sample,
Figure FDA0003953345120000067
Figure FDA0003953345120000068
a sum of squares matrix of the n-th order gaussian probability density function values for the predicted value of the kth located data sample,
Figure FDA0003953345120000069
Figure FDA00039533451200000610
a sum of squares matrix of n x m dimensional generalized gaussian probability density function values for the k-th predicted value of the positioning data sample,
Figure FDA00039533451200000611
Figure FDA00039533451200000612
a sum of squares matrix of m x n dimensional generalized gaussian probability density function values for the k-th predicted value of the positioning data sample,
Figure FDA00039533451200000613
is a matrix
Figure FDA00039533451200000614
The positive definite matrix of (a) is,
Figure FDA00039533451200000615
is a matrix
Figure FDA00039533451200000616
Positive definite matrix of (theta) q；k Is theta k Is divided into blocks, Θ v；k Is theta k Is partitioned into blocks.
9. The method for positioning the unmanned underwater vehicle with the generalized minimum error entropy kalman as claimed in claim 2, wherein the error condition in step S26 is:
Figure FDA0003953345120000071
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003953345120000072
for the estimated position data samples updated at the t-th iteration,
Figure FDA0003953345120000073
the estimated positioning data sample updated in the t-1 th iteration, | | | is two-norm operation, and τ is a positive threshold.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116680500A (en) * 2023-06-12 2023-09-01 哈尔滨工程大学 Position estimation method and system of underwater vehicle under non-Gaussian noise interference

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116680500A (en) * 2023-06-12 2023-09-01 哈尔滨工程大学 Position estimation method and system of underwater vehicle under non-Gaussian noise interference
CN116680500B (en) * 2023-06-12 2024-03-22 哈尔滨工程大学 Position estimation method and system of underwater vehicle under non-Gaussian noise interference

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