CN110487276B - Sampling vector matching positioning method based on correlation analysis - Google Patents

Sampling vector matching positioning method based on correlation analysis Download PDF

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CN110487276B
CN110487276B CN201910770081.6A CN201910770081A CN110487276B CN 110487276 B CN110487276 B CN 110487276B CN 201910770081 A CN201910770081 A CN 201910770081A CN 110487276 B CN110487276 B CN 110487276B
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王博
马子玄
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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
    • 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
    • G01C21/20—Instruments for performing navigational calculations
    • G01C21/203—Specially adapted for sailing ships

Abstract

The invention discloses a sampling vector matching positioning method based on correlation analysis, relates to the technical field of navigation, guidance and control, and can improve the matching precision of a gravity vector matching algorithm. The method specifically comprises the following steps: and acquiring output points of the inertial navigation system at all times and a matching point set based on particle filtering. The vector A is formed by the current time matching point and the last time matching point, and the vector B is formed by the current time output point and the last time output point. And if the difference value between the Euclidean distances of A and B exceeds a distance threshold value, performing distance correction. And if the differences of the phase information, the distance information and the gravity abnormal value information between the sampling particle points and the inertial navigation track points in the particle filtering process exceed the threshold, performing correlation analysis on the phase relationship between the sampling particle points to recalculate the particle weight, then performing particle weight normalization and residual resampling of the particle set, and obtaining a final matching result after weighting summation.

Description

Sampling vector matching positioning method based on correlation analysis
Technical Field
The invention relates to the technical field of navigation, guidance and control, in particular to a sampling vector matching positioning method based on correlation analysis.
Background
The inertial navigation system adopts a completely autonomous working mode and is highly concealed, but because the error of the inertial navigation system is accumulated along with time, the navigation requirement of the underwater vehicle during long-term navigation cannot be met, and therefore the error needs to be corrected. In the passive navigation auxiliary means, the information of the marine geophysical field is rich and the characteristics are obvious, so that the auxiliary correction of inertial navigation by utilizing a gravity field, a geomagnetic field, terrain and the like becomes a classical means. The seafloor topography is obtained by multi-beam measurements, and the implementation of topography assistance methods becomes difficult in some complex terrain areas. The gravity field generally does not change along with time, has good space-time distribution characteristics, navigation positioning information obtained by matching the characteristics and the information has autonomy, and the precision does not diverge along with time, so that the requirement of underwater navigation positioning is met.
The gravity-assisted inertial navigation system comprises four parts: the system comprises an inertial navigation system, an ocean gravity field background image, an ocean gravity sensor and a gravity matching algorithm. Wherein the gravity matching algorithm is a key technology of gravity-assisted navigation. Conventional gravity matching algorithms fall into two categories: sequence matching and single point matching. Representative algorithms of the sequence matching algorithm are the ICCP algorithm and the related extremum algorithm. The sequence matching algorithm needs to collect a series of matching points as a whole for matching, so that the real-time performance is poor. The representative algorithm of the single-point matching mainly comprises a Sangyo terrain aided navigation method based on the extended Kalman filtering, the SITAN algorithm can carry out real-time measurement and estimation, but an accurate initial position is required, the anti-jamming capability is poor, and Kalman filtering divergence is possibly caused by linearization errors.
The sampling points of the matching algorithms are independent from each other, and the gravity vector matching algorithm takes the position correlation between the sampling points into consideration, so that the matching precision is improved compared with the traditional method. However, the navigation trajectory of the aircraft varies from navigation mission to mission, so the accuracy of the method can be further improved.
Therefore, how to further improve the matching precision of the gravity vector matching algorithm and make the matching track closer to the real track is a problem to be solved urgently at present
Disclosure of Invention
In view of this, the invention provides a sampling vector matching positioning method based on correlation analysis, which can further improve the matching precision of the gravity vector matching algorithm, so that the matching track is closer to the real track.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
in the navigation process of the underwater carrier, output points of the inertial navigation system at all times are obtained to form an inertial navigation track point set, and a particle filter-based matching point set is obtained according to a gravity-assisted inertial navigation matching model.
And obtaining a vector A formed by the current time matching point and the last time matching point in the matching point set and a vector B formed by the current time output point and the last time output point in the inertial navigation track point set.
And taking initial matching points in the matching point set to form a matched point set, and carrying out rigid transformation on the matched point set to obtain an error-free inertial navigation track.
Judging whether the difference value between the direction angle of the vector A and the direction angle of the vector B exceeds a set angle threshold value, if so, correcting the azimuth angle of the vector A formed by the current moment matching point and the last moment matching point according to the error-free inertial navigation track, and recalculating the central position and the state transition probability of the particles sprayed in the particle filter; otherwise no correction is required.
Judging whether the difference value between the Euclidean distance of the vector A and the Euclidean distance of the vector B exceeds a set distance threshold value, if so, correcting the Euclidean distance of the vector A formed by the matching point at the current moment and the matching point at the previous moment according to the error-free inertial navigation track, and recalculating the central position and the state transition probability of the particles sprayed in the particle filtering; otherwise no correction is required.
And judging whether the difference between the phase information, the distance information and the gravity abnormal value information between the sampling particle points and the inertial navigation track points in the particle filtering process exceeds a threshold value, and if so, performing correlation analysis on the phase relationship between the sampling particle points to recalculate the particle weight.
And carrying out normalization processing on the particle weight, then carrying out residual resampling on the particle set, and carrying out weighted summation to obtain a final matching result.
Furthermore, during the navigation process of the underwater vehicle, a gravimeter is adopted to obtain a gravity anomaly measurement value.
The sampling point set is { P'k,P′k+1,P′k+2,P′k+3,…,P′k+nN +1 sampling points, k-k + n being time, wherein the vector information between the sampling points satisfies
Figure BDA0002173280020000031
i is a positive integer, 1-n is taken, epsilon is an error value set according to the precision of the gravimeter, dist (. +) is an Euclidean distance function.
Further, when the current time is the (k + 1) th time and the previous time is the (k) th time, the vector a is
Figure BDA0002173280020000032
The vector B is
Figure BDA0002173280020000033
Judging whether the difference value between the direction angle of the vector A and the direction angle of the vector B exceeds a set angle threshold value, namely judging
Figure BDA0002173280020000034
Whether or not this is true.
Wherein
Figure BDA0002173280020000035
ζ is an angle threshold set according to an empirical value for a unit vector in the horizontal direction.
Further, determining whether a difference between the euclidean distance of the vector a and the euclidean distance of the vector B exceeds a set distance threshold specifically includes:
Figure BDA0002173280020000036
epsilon is the set distance threshold.
And further, judging whether the difference between the phase information, the distance information and the gravity abnormal value information between the sampling particle point and the inertial navigation track point exceeds a threshold value.
Namely, whether the following three discriminants are satisfied simultaneously is judged:
Figure BDA0002173280020000037
Figure BDA0002173280020000041
Figure BDA0002173280020000042
the angle information and length information of the vector formed by the ith particle at the k +1 th time and the ith particle at the k +1 th time are respectively
Figure BDA0002173280020000043
The angle information of the vector formed by the k-th time matching point and the k + 1-th time matching point is
Figure BDA0002173280020000044
The length information is
Figure BDA0002173280020000045
Figure BDA0002173280020000046
G (y) is the gravity anomaly value of the ith particle at the time of the (k + 1) < th > timek+1) And sampling the gravity anomaly measured value of the particle point at the k +1 th moment.
Performing correlation analysis on the phase relationship among the sampling particle points to recalculate the particle weight, specifically:
the weight of the ith particle at the (k + 1) th moment is recalculated into
Figure BDA0002173280020000047
Where σ is the set variance.
Has the advantages that:
according to the method, the vector matching algorithm is improved, the characteristic of high short-time precision of inertial navigation is utilized, the phase correction and the distance correction are carried out on the inertial navigation track in sequence, and the longitude and latitude errors of the gravity matching track are effectively reduced. Meanwhile, relevance analysis is carried out on the position vector information between the inertial navigation track points and the matching track by introducing a relevance analysis algorithm, and the particle weight is considered, so that the matching precision is improved. The matching precision of the gravity matching algorithm is further improved through the improvement of the two aspects, and the matching track is closer to the real track.
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Fig. 1 is a schematic flow chart of a sampling vector matching positioning method based on correlation analysis according to the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a gravity sampling vector matching positioning method, as shown in figure 1, comprising the following steps:
acquiring output points of an inertial navigation system at each moment in the navigation process of an underwater carrier to form an inertial navigation track point set; and obtaining a matching point set based on particle filtering according to the gravity-assisted inertial navigation matching model.
In the navigation process of the underwater carrier, acquiring a gravity anomaly measured value by adopting a gravimeter;
the sampling point set is { P'k,P′k+1,P′k+2,P′k+3,…,P′k+nN +1 sampling points, k-k + n being time, wherein the vector information between the sampling points satisfies
Figure BDA0002173280020000051
i is a positive integer, 1-n is taken, epsilon is an error value set according to the precision of the gravimeter, dist (. +) is an Euclidean distance function. (wherein sampling point P'kExpressed in longitude and latitude information, i.e. P'k(L′k,λ′k)，L′kIs P'kLongitude of λ'kIs P'kThe latitude of (a) is determined,
Figure BDA0002173280020000052
in the embodiment of the invention, the phase and distance information of the vector formed by the matching point of the current sampling moment and the last moment is considered into the discriminant by utilizing the characteristic of high short-time precision of inertial navigation. Mainly comprises the steps of step two, step three and step four.
Step two, the vector A formed by the current matching point and the last matching point of the particle filter is
Figure BDA0002173280020000053
The vector B formed by the output point of the inertial navigation track point set at the current moment and the output point at the last moment is
Figure BDA0002173280020000054
And taking initial matching points in the matching point set to form a matched point set, and carrying out rigid transformation on the matched point set to obtain an error-free inertial navigation track.
Judging whether the difference value between the direction angle of the vector A and the direction angle of the vector B exceeds a set angle threshold value, if so, correcting the azimuth angle of the vector A formed by the current moment matching point and the last moment matching point according to the error-free inertial navigation track, and recalculating the central position and the state transition probability of the particles sprayed in the particle filter; otherwise no correction is required.
The step is phase correction, and in order to better represent angle information, a polar coordinate representation method is adopted, and a sampling point P is adoptedkWhen the polar coordinates of (c) are (l, θ), the coordinates of the sampling point in the rectangular coordinate system are (l · cos θ, l · sin θ).
In the embodiment of the invention, the current time is the (k + 1) th time, the last time is the kth time, and the vector A is
Figure BDA0002173280020000061
The vector B is
Figure BDA0002173280020000062
Judging whether the difference value between the direction angle of the vector A and the direction angle of the vector B exceeds a set angle threshold value, namely judging
Figure BDA0002173280020000063
Whether or not this is true.
Wherein
Figure BDA0002173280020000064
ζ is an angle threshold set according to an empirical value for a unit vector in the horizontal direction.
In the embodiment of the invention, a sine function is taken into consideration as a differential operator
Figure BDA0002173280020000065
When the deviation position is small, the eigen function of (2) can be approximated as
Figure BDA0002173280020000066
The eigenfunction problem of (2). And considering the taylor expansion:
Figure BDA0002173280020000067
and
Figure BDA0002173280020000068
the navigation track changes due to different navigation tasks in the navigation process, and the sine function discrimination precision is high when the small angle range of the heading angle changes, and the method is also suitable for turning tracks.
If the above discriminant expression is not satisfied, the expression is P'kIs an origin, has an angle theta with the horizontal direction and has a distance of an inertial navigation sampling point as a vector
Figure BDA0002173280020000069
Then P ″)k+1Is the central position of the particles sprinkled in the particle filter
Figure BDA00021732800200000610
And recalculating the state transition probability in the particle filter matching, wherein theta is the error-free inertial navigation track angle.
Step three, judging whether the difference value between the Euclidean distance of the vector A and the Euclidean distance of the vector B exceeds a set distance threshold value, if so, correcting the Euclidean distance of the vector A formed by the matching point at the current moment and the matching point at the previous moment according to the error-free inertial navigation track, and recalculating the central position and the state transition probability of the particles sprayed in the particle filter; otherwise no correction is required.
This step is distance correction. In the embodiment of the present invention, determining whether a difference between the euclidean distance of the vector a and the euclidean distance of the vector B exceeds a set distance threshold specifically includes:
Figure BDA00021732800200000611
epsilon is the set distance threshold. (specific method for recalculating the center position of the particles sprinkled in the particle filter is P'kAs a center of circle, in
Figure BDA0002173280020000071
Make a circle for the radius, and vector
Figure BDA0002173280020000072
Is C'2. Then is formed by
Figure BDA0002173280020000073
And recalculating the center position of the sprinkled particles in the particle filter.
And step four, adding the phase relation among the sampling points into a correlation analysis link according to the characteristic of high short-time precision of inertial navigation. And judging whether the difference between the phase information, the distance information and the gravity abnormal value information between the sampling particle points and the inertial navigation track points in the particle filtering process exceeds a threshold value, and if so, performing correlation analysis on the phase relationship between the sampling particle points to recalculate the particle weight.
In the embodiment of the invention, considering that INS has high short-time precision, the relative position relation between sampling points is added into a correlation analysis link, in each sampling time, a path section formed by the optimal sampling points is parallel to a corresponding inertial navigation path section as much as possible, and the angle and the length of a vector formed by the sampling points are selected to express the parallel relation. Defining the angle:
Figure BDA0002173280020000074
defining the length:
Figure BDA0002173280020000075
wherein the content of the first and second substances,
Figure BDA0002173280020000076
the angle information of the vector is formed for the i-1 th and i-th sample points,
Figure BDA0002173280020000077
length information of the vector formed for the i-1 th and i-th sample points, λiAnd LiRespectively, the longitude and latitude information of the ith particle. In the invention, the particle filtering based on Bayesian estimation is introduced to carry out the sampling of the sampling points and the inertial navigation track pointsAnd carrying out correlation analysis on the phase information and considering the phase information into the particle weight.
In the embodiment of the invention, whether the phase information, the distance information and the difference between the gravity abnormal value information of the sampling particle point and the inertial navigation track point exceed the threshold value or not is judged, namely whether the following three discriminants are simultaneously satisfied is judged:
Figure BDA0002173280020000078
Figure BDA0002173280020000079
Figure BDA00021732800200000710
the angle information and length information of the vector formed by the ith particle at the k +1 th time and the ith particle at the k +1 th time are respectively
Figure BDA00021732800200000711
The angle information of the vector formed by the k-th time matching point and the k + 1-th time matching point is
Figure BDA00021732800200000712
The length information is
Figure BDA00021732800200000713
Figure BDA00021732800200000714
G (y) is the gravity anomaly value of the ith particle at the time of the (k + 1) < th > timek+1) Sampling the gravity anomaly measured value of the particle point at the (k + 1) th moment;
the phase relation between the sampling particle points is subjected to correlation analysis to recalculate the particle weight, the correlation analysis is a performance index, and the most common algorithms comprise three algorithms: cross correlation algorithm (COR), mean absolute difference algorithm (MAD) and mean square error algorithm (MSD), where the mean square error algorithm is chosen to take the vector position information of the particle points into account in the particle weights.
Mean square error algorithm (MSD):
Figure BDA0002173280020000081
wherein, gr(i) Is the measured gravity anomaly value, gm(i) The number of particle points sprinkled for each match is n for the gravity anomaly value stored in the digital gravity map.
The weight of the ith particle at the (k + 1) th moment is recalculated into
Figure BDA0002173280020000082
Wherein σ is a set variance, and is specifically set according to an empirical value.
And 5, carrying out normalization processing on the particle weight, then carrying out residual error resampling on the particle set, and obtaining a final matching result after weighting summation.
Compared with the traditional method, the method effectively reduces the longitude and latitude errors of the gravity matching track, and enables the algorithm to have better robustness when the track has a curve.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. 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 (4)

1. A sampling vector matching positioning method based on correlation analysis is characterized by comprising the following steps:
in the navigation process of the underwater carrier, acquiring output points of the inertial navigation system at each moment to form an inertial navigation track point set, and acquiring a particle filter-based matching point set according to a gravity-assisted inertial navigation matching model;
obtaining a vector A formed by the matching points at the current moment in the matching point set and the matching points at the previous moment, and a vector B formed by the output points at the current moment in the inertial navigation track point set and the output points at the previous moment;
taking initial matching points in the matching point set to form a matched point set, and carrying out rigid transformation on the matched point set to obtain an error-free inertial navigation track;
judging whether the difference value between the direction angle of the vector A and the direction angle of the vector B exceeds a set angle threshold value, if so, correcting the azimuth angle of the vector A formed by the current moment matching point and the last moment matching point according to the error-free inertial navigation track, and recalculating the central position and the state transition probability of the particles sprayed in the particle filter; otherwise, no correction is needed;
judging whether the difference value between the Euclidean distance of the vector A and the Euclidean distance of the vector B exceeds a set distance threshold value, if so, correcting the Euclidean distance of the vector A formed by the matching point at the current moment and the matching point at the previous moment according to the error-free inertial navigation track, and recalculating the central position and the state transition probability of the particles sprayed in the particle filtering; otherwise, no correction is needed;
judging whether the difference between phase information, distance information and gravity abnormal value information between sampling particle points and inertial navigation track points in the particle filtering process exceeds a threshold value, and if so, performing correlation analysis on the phase relationship between the sampling particle points to recalculate the particle weight;
carrying out normalization processing on the particle weight, then carrying out residual resampling on the particle set, and carrying out weighted summation to obtain a final matching result;
the specific method for judging whether the difference between the phase information, the distance information and the gravity abnormal value information between the sampling particle point and the inertial navigation track point in the particle filtering process exceeds the threshold value is as follows: judging whether the following three discriminants are satisfied simultaneously:
Figure FDA0002755739610000021
Figure FDA0002755739610000022
Figure FDA0002755739610000023
the angle information and length information of the vector formed by the ith particle at the k +1 th time and the ith particle at the k +1 th time are respectively
Figure FDA0002755739610000024
The angle information of the vector formed by the k-th time matching point and the k + 1-th time matching point is
Figure FDA0002755739610000025
The length information is
Figure FDA0002755739610000026
Figure FDA0002755739610000027
G (y) is the gravity anomaly value of the ith particle at the time of the (k + 1) < th > timek+1) Sampling the gravity anomaly measured value of the particle point at the (k + 1) th moment;
the correlation analysis of the phase relationship between the sampling particle points is performed to recalculate the particle weight, which specifically comprises the following steps:
the weight of the ith particle at the (k + 1) th moment is recalculated into
Figure FDA0002755739610000028
Where σ is the set variance.
2. The method of claim 1, further comprising, during the navigation of the underwater vehicle, obtaining a gravity anomaly measurement using a gravimeter;
the sampling point set is { Pk',P′k+1,P′k+2,P′k+3,…,P′k+nN +1 sampling points, k-k + n being time, where the sampling points are located betweenIs satisfied with
Figure FDA0002755739610000029
i is a positive integer, 1 to n are taken, epsilon is an error value set according to the precision of the gravimeter, dist (phi) is an Euclidean distance function.
3. The method of claim 2, wherein the current time is the (k + 1) th time, and the previous time is the (k) th time, then the vector a is
Figure FDA00027557396100000210
The vector B is
Figure FDA00027557396100000211
Judging whether the difference value between the direction angle of the vector A and the direction angle of the vector B exceeds a set angle threshold value, namely judging
Figure FDA0002755739610000031
Whether the result is true or not;
wherein
Figure FDA0002755739610000032
ζ is an angle threshold set according to an empirical value for a unit vector in the horizontal direction.
4. The method according to claim 3, wherein said determining whether the difference between the euclidean distance of the vector a and the euclidean distance of the vector B exceeds a predetermined distance threshold is:
Figure FDA0002755739610000033
epsilon is the set distance threshold.
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