CN111193496A - Sub-pixel target tracking method applied to precision guide star measurement system - Google Patents
Sub-pixel target tracking method applied to precision guide star measurement system Download PDFInfo
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Abstract
The invention belongs to the technical field of space optical remote sensing, and relates to a sub-pixel target tracking method applied to a precision guide star measurement system. The invention provides a sub-pixel target tracking method based on a phase correlation algorithm and Kalman filtering, and the phase correlation algorithm achieves sub-pixel precision by adding two-dimensional up-sampling processing; single-step prediction of the position of the moving target is realized through Kalman filtering; only the related peak and the adjacent area thereof are transformed through ROI-IDFT matrix multiplication selection, so that the calculation of redundant parts is avoided, and the operation efficiency is improved.
Description
Technical Field
The invention relates to a sub-pixel target tracking method applied to a precision guide star measurement system, and belongs to the technical field of space optical remote sensors.
Background
The space astronomical observation can completely get rid of the influence of the atmosphere, the observation wavelength range is wide, the sky background noise is low, the angular resolution of the diffraction limit of the telescope can be approached, and the space astronomical telescope is promoted to become a research hotspot in the field of astronomical observation under the favorable conditions. However, attitude changes of the spacecraft, orbital precession, and slight vibrations of moving parts can all affect space detection. In order to achieve the detection accuracy expected by the spatial astronomical telescope, measures must be taken to suppress image blurring caused by platform vibration and the like. Representative space astronomical telescopes in foreign countries such as Hubble and James Weber utilize the edge field of view of an optical system to image, so as to provide feedback information for a precise image stabilizing system, further realize image stabilizing closed-loop control and realize precise observation of astronomical targets.
The precise guide star measuring system is an important component of a precise image stabilizing control system of a large-caliber space astronomical telescope, obtains optical axis pointing deviation by utilizing an ultralong focal length of an optical system and a relevant algorithm, and provides feedback information for the precise image stabilizing control system in an image mode. Under the condition that the focal length of an optical system of the space astronomical telescope is determined, the sub-pixel subdivision positioning precision directly determines the measurement precision of the precision guide star measurement system.
In the prior art, the star point centroid location is calculated based on a Gaussian surface fitting method, a gray level centroid and an improved algorithm thereof, and the calculation complexity and the subdivision location precision cannot simultaneously meet the requirement of real-time subpixel level target tracking. The invention relates to a sub-pixel target tracking method giving consideration to both precision and efficiency.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, provides a sub-pixel level target tracking method suitable for a precise guide star measurement system, and realizes closed-loop control of a precise image stabilization control system while considering both precision and efficiency.
The technical solution of the invention is as follows: a sub-pixel target tracking method applied to a precision guide star measurement system comprises the following steps
(1) Setting a state equation, a measurement equation and a state transition matrix of a discrete time linear system, and giving initial conditions; (initial conditions: initial value of observed quantity and error correlation matrix set)
(2) Calculating a Kalman gain matrix and an innovation vector of a discrete time linear system based on a Kalman filter of single-step prediction;
(3) calculating the state quantity of the state equation according to the state transition matrix set in the step (1) and the Kalman gain matrix and the innovation vector obtained in the step (2), and updating an error correlation matrix;
(4) according to the reference frame and current frame images acquired by the precision leading star measuring system and the state quantity in the step (3), performing two-dimensional cross-correlation operation on the two images to obtain a correlation function, performing ROI-IDFT matrix multiplication operation on the correlation function, realizing that only the correlation peak value and the area nearby the correlation peak value are transformed to obtain a subdivided correlation peak value, namely an updated observed quantity;
(5) judging whether a tracking stopping instruction is received or not, if not, feeding back the updated observed quantity obtained in the step (4) to the Kalman filter in the step (2), and re-executing the steps (2) to (4); and if so, stopping tracking the target.
Preferably, the step (2) and the step (3) adopt a Kalman filter based on single-step prediction, the optimal state estimation of the next moment can be calculated by processing the updated observed quantity at each moment, and the prediction can be continuously corrected by using actual motion parameters, so that the estimation accuracy is improved;
preferably, the step (4) calculates the correlation coefficient matrix by using a phase correlation method. Only the peak value in the correlation coefficient matrix and the data near the peak value are calculated, the redundant part is prevented from being operated, and the operation efficiency is high;
preferably, the step (2) to the step (4) are realized by the following steps:
predicting the position of the moving target in the current frame image by using a Kalman filter in a single step according to the position of the moving target in the reference frame image; searching in the neighborhood of the region of interest by utilizing motion prediction and inter-frame similarity to perform sub-pixel subdivision positioning of the target, and further determining the accurate position of the target of the current frame to be fed back to a Kalman filter as an observation vector;
preferably, the sub-pixel target tracking method is suitable for a precise image stabilization control system;
preferably, the sub-pixel target tracking method calculates two-dimensional inverse discrete fourier transform for the region of interest, and is suitable for solving the problem that image motion of two frames of images observed in space astronomical observation is small or image motion is concentrated in a fixed range.
Compared with the prior art, the invention has the advantages that:
(1) the image motion algorithm based on phase correlation can only reach the detection precision of the whole pixel, and the sub-pixel precision is reached through the interpolation or fitting of the correlation coefficient;
(2) the method utilizes Kalman filtering to continuously correct actual motion parameters, reduces the search range of the target and accurately positions the position of the target which possibly appears;
(3) the ROI-IDFT is selected, and only the relevant peak value and the area nearby the relevant peak value are selected to be transformed through two-dimensional IDFT matrix multiplication operation, so that the calculation of a redundant part is avoided, and the operation efficiency is improved;
(4) the invention provides a sub-pixel target tracking method based on a phase correlation algorithm and Kalman filtering, and the sub-pixel precision of the phase correlation algorithm is skillfully achieved by adding two-dimensional up-sampling treatment; single-step prediction of the position of the moving target is realized through Kalman filtering; only the related peak value and the area nearby the related peak value are transformed through ROI-IDFT matrix multiplication selection, so that the calculation of a redundant part is avoided, and the operation efficiency is improved. And calculating two-dimensional inverse discrete Fourier transform aiming at the region of interest, and suitably solving the problem that the image motion of two frames of images observed by space astronomy is small or the image motion is concentrated in a fixed range.
Drawings
FIG. 1 is a logic diagram of a target tracking method combining a phase correlation method and Kalman filtering according to the present invention;
FIG. 2a is a schematic diagram of the original correlation peak;
FIG. 2b is a schematic representation of the subdivided correlation peak;
FIG. 3 is a flow chart of the method of the present invention.
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
The invention belongs to the technical field of space optical remote sensing, and relates to a sub-pixel target tracking method applied to a precision guide star measurement system. The invention provides a sub-pixel target tracking method based on a phase correlation algorithm and Kalman filtering, and the phase correlation algorithm achieves sub-pixel precision by adding two-dimensional up-sampling processing; single-step prediction of the position of the moving target is realized through Kalman filtering; only the related peak and the adjacent area thereof are transformed through ROI-IDFT matrix multiplication selection, so that the calculation of redundant parts is avoided, and the operation efficiency is improved.
The precise navigation measurement system is widely applied to a space infrared astronomical telescope, obtains high-precision image motion by using a long focal length and a related algorithm, and provides compensation information for a precise image stabilization control system in real time. Under the condition that the focal length of the optical system of the space astronomical telescope is determined, the sub-pixel subdivision positioning precision directly determines the measurement precision of the precise navigation measurement system. The invention mainly relates to a sub-pixel level target tracking and positioning method for a precision guide star measurement system, which improves the measurement precision and the real-time property from the perspective of a software algorithm and realizes the closed-loop control of a precision image stabilization control system.
The invention designs a sub-pixel level target tracking method suitable for a precision guide star measurement system, wherein the target tracking process is divided into two stages, as shown in figure 1. Firstly, predicting the position of a moving target in a current frame image by a Kalman filter in a single step according to the position of the moving target in a previous frame image; and then, the motion prediction and the inter-frame similarity are fully utilized to search in the neighborhood of the region of interest to carry out subdivision positioning on the target, so that the accurate position of the target of the current frame is determined and then is fed back to the Kalman filter as an observation vector. The tracking process for each frame is as described above.
In order to narrow the target search range, it is necessary to estimate various motion parameters of the target at the next time, and further accurately locate the position where the target may appear. The Kalman filtering can calculate the optimal state estimation only by processing the updated observed quantity at each moment, and can continuously correct the prediction by utilizing the actual motion parameters, thereby improving the estimation accuracy. The two-dimensional discrete inverse Fourier transform is calculated aiming at the region of interest, and the method is suitable for solving the problem that the image motion of two frames of images observed in space astronomy is small or the image motion is concentrated in a fixed range.
As shown in fig. 3, the sub-pixel target tracking method applied to the precision guide star measurement system of the present invention preferably includes:
(1) the state equation and observation equation of the discrete-time linear system are set, preferably as follows:
x(n+1)＝F(n+1,n)x(n)+v1(n) (1)
y(n)＝C(n)x(n)+v2(n) (2)
wherein v is1(n) is process noise, v2(n) is the measurement noise and can be regarded as a normal distribution with a mean value of 0, and the correlation matrices are defined as
The motion characteristics of the target can be described by position and speed information, and (c (n), r (n)) is the position of the target centroid at the moment n, and (u (n), v (n)) is the speed of the target centroid at the moment n in the x direction and the y direction, so that the characteristic vector of the target at the moment n, namely the state quantity is x (n) ═ c (n), r (n), u (n), v (n))TThe state equation of the system can be expressed as formula (1).
Assuming that the image motion of the target between two consecutive frames of images is small, and the time interval between two frames is set to Δ t, which can be regarded as a uniform linear motion, the state transition matrix of the transition matrix from n time to n +1 time can be expressed as:
the observed quantity is the position of the centroid of the object at time n, i.e. the observed quantity y (mn)＝(c(n),r(n))TThe observation equation of the system can be expressed as formula (2).
Since y (n) is only position dependent, the measurement matrix C (n) can be expressed as:
initial conditions were given as:
K(1,0)＝E[(x(1)-E[x(1)])(x(1)-E[x(1)])H]＝Π0(4)
wherein the content of the first and second substances,
for a given initial position, K (1,0) is the error correlation matrix under the initial conditions.
(2) Based on the kalman filter of the single-step prediction, the kalman gain matrix and the innovation vector of the discrete-time linear system are calculated, preferably as follows:
G(n)＝F(n+1,n)K(n,n-1)CH(n)[C(n)K(n,n-1)CH(n)+Q2(n)]-1(5)
wherein G (n) is n +1 moment Kalman gain matrix, and K (n, n-1) is
Correlation matrix of the error.
Wherein a (n) is the calculated innovation vector,
the predicted estimates of the states at time n for a given observation y (1), y (2), …, y (n-1).
(3) Calculating the state quantity of the step (1) according to the state transition matrix set in the step (1) and the Kalman gain matrix and the innovation vector obtained in the step (2), and updating the error correlation matrix, preferably as follows:
wherein the content of the first and second substances,
for a given observation y (1), y (2), …, y (n), the predicted estimate of the state at time n +1, i.e. the state quantity.
K(n)＝K(n,n-1)-F(n,n+1)G(n)C(n)K(n,n-1) (8)
Wherein K (n) is
Correlation matrix of the error.
K(n+1,n)＝F(n+1,n)K(n)FH(n+1,n)+Q1(n) (9)
Wherein K (n +1, n) is
Correlation matrix of the error.
(4) According to the reference frame and current frame images acquired by the precision leading star measurement system and the state quantity in the step (3), performing two-dimensional cross-correlation operation on the two images to obtain a correlation function, performing ROI-IDFT matrix multiplication operation on the correlation function, selecting to only transform a correlation peak value and a region near the correlation peak value to obtain a subdivided correlation peak value, namely an updated observed quantity, preferably as follows:
assuming that the reference frame and current frame images can be g (x, y) and f (x, y), respectively, the relative image shift of the two images is (x)0,y0) I.e. g (x, y) ═ f (x-x)0,y-y0). The traditional phase correlation algorithm directly performs phase correlation on two images, and can be expressed as
The preferred scheme is as follows: performing two-dimensional inverse discrete Fourier transform on the correlation function C (u, v) to obtain C (u, v) ═ delta (x)0,y0) That is, the result of the phase correlation method is a unit impulse function, the whole pixel image shift between two images can be obtained from the position information of the peak, as shown in fig. 2a, the zero padding in the frequency domain actually realizes the interpolation in the time domain, and further realizes the subdivision of the spatial correlation coefficient curved surface, as shown in fig. 2 b. The spatial correlation coefficient matrix of the phase correlation method can be obtained by two-dimensional inverse discrete fourier transform of the calculation formula (10). For the spatial correlation coefficient matrix, only the data of the peak value and the data near the peak value in the matrix are valuable, other data belong to redundant data, whether the data processing process can be optimized or not is judged, and only the data of the peak value and the data near the peak value in the correlation coefficient matrix are calculated. In fact, ROI-IDFT can be selected, only the peak value and the area nearby the peak value are transformed, the operation of redundant parts is avoided, and the calculation efficiency is improved.
Preferably, the specific principle and flow of ROI-IDFT are introduced by taking one-dimensional kappa-time up-sampling IDFT as an example, and the computational complexity of one-time kappa-time up-sampling IFFT is O [ (kappa N) log2(κN)]Where N is the length of the one-dimensional sampling sequence, if the input sequence is too long or the up-sampling multiple is too high, even IFFT will occupy a large amount of storage resources and computation time. In order to improve the algorithm execution efficiency without sacrificing the sampling precision, the inverse discrete Fourier transform upsampling is only calculated for the region of interest, so that the calculation amount is greatly reduced. The one-dimensional κ -times upsampled IDFT may preferably be expressed as:
wherein, WκN＝exp(-2πi/κN)。
Rewritten into matrix multiplication form
Where D is an IDFT relationship matrix, preferably expressed as
Since X 'u is the spectrum of X u after zero-filling expansion, it is noted that zero-filling expansion is required in the high-frequency part of X' u, and since zero-filling part does not participate in operation, the multiplication form of one-dimensional inverse discrete Fourier transform of up-sampling can be obtained by simplification, preferably
Wherein the content of the first and second substances,
assuming the original correlation sequence x [ n ]]The maximum value of (N is 0,1, …, N-1) is obtained at k (k is more than or equal to 0 and less than or equal to N), and an interval [ k-1, k +1 ] is selected]For the region of interest, up-sampling by k times, the interval length is 2 k, and then only the output interval [ k-1, k +1 ] is needed]Up-sampling results with an internal length of 2 k are sufficient. Memory [ k ]1,k2](0≤k1<k2κ N-1) is the output interval of the up-sampling, preferably the equation (14) is further simplified to
Wherein U is an IDFT relationship matrix expressed as
The computational complexity in the formula (17) is O (kappa N), which is superior to the computational complexity O [ (kappa N) log of the traditional IFFT2(κN)]. Extending equation (17) to perform an inverse two-dimensional discrete fourier transform on the region of interest, then
Meter of formula (18)The computational complexity is O (kappa MN), and the 1/kappa upsampling precision is kept, and the computational complexity is superior to the computational complexity O [ kappa MN (log) of the traditional IFFT2(κN)+log2(κM))]Therefore, the up-sampling efficiency is improved, and the storage space required by the operation is reduced.
It should be noted that this method must know the region of interest in advance, and for target tracking, it is very effective to know the approximate position of the relevant peak, especially for the case of small image motion or image motion concentrated in a fixed range in spatial astronomical observation. According to the method, the reference frame and current frame images acquired by a precise guide star measurement system and the state estimator (approximate position of a related peak) in the step (3) are required, and the upsampling precision of 1/kappa can be kept only for a bounded region [ k ] by calculating a formula (17) and a formula (18)1,k2]And performing two-dimensional discrete Fourier transform to obtain a correlation peak value after subdivision, namely the updated observed quantity. The calculation of redundant parts is avoided, and the operation efficiency is improved.
(5) Judging whether a tracking stopping instruction is received or not, if not, feeding the observation quantity obtained in the step (4) back to the Kalman filter in the step (2), updating the parameters of the Kalman filter in the step (2), and returning to the step (2); and if so, stopping tracking the target.
The image motion algorithm based on phase correlation can only achieve the detection precision of the whole pixel, and the sub-pixel precision is achieved through interpolation or fitting of the correlation coefficient; continuously correcting actual motion parameters by using Kalman filtering, reducing the target search range, and accurately positioning the position of a target which may appear;
the ROI-IDFT is optimized, only the related peak value and the area nearby the related peak value are selected to be transformed through two-dimensional IDFT matrix multiplication, the calculation of a redundant part is avoided, and the operation efficiency is improved; the invention provides a sub-pixel target tracking method based on a phase correlation algorithm and Kalman filtering, and the phase correlation algorithm is skillfully enabled to reach sub-pixel precision by increasing the processing of two-dimensional up-sampling; single-step prediction of the position of the moving target is realized through Kalman filtering; only the related peak value and the area nearby the related peak value are transformed through ROI-IDFT matrix multiplication selection, so that the calculation of a redundant part is avoided, and the operation efficiency is improved. The two-dimensional inverse discrete Fourier transform is calculated aiming at the region of interest, and the method is suitable for solving the problem that the image motion of two frames of images observed by space astronomy is small or the image motion is concentrated in a fixed range.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (6)
1. A sub-pixel target tracking method applied to a precision guide star measurement system is characterized by comprising the following steps:
(1) setting a state equation, a measurement equation and a state transition matrix of a discrete time linear system, and giving initial conditions;
(2) calculating a Kalman gain matrix and an innovation vector of a discrete time linear system based on a Kalman filter of single-step prediction;
(3) calculating the state quantity of the state equation according to the state transition matrix set in the step (1) and the Kalman gain matrix and the innovation vector obtained in the step (2), and updating an error correlation matrix;
(4) according to the reference frame and current frame images acquired by the precision leading star measuring system and the state quantity in the step (3), performing two-dimensional cross-correlation operation on the two images to obtain a correlation function, performing ROI-IDFT matrix multiplication operation on the correlation function, realizing that only the correlation peak value and the area nearby the correlation peak value are transformed to obtain a subdivided correlation peak value, namely an updated observed quantity;
(5) judging whether a tracking stopping instruction is received or not, if not, feeding back the updated observed quantity obtained in the step (4) to the Kalman filter in the step (2), and re-executing the steps (2) to (4); and if so, stopping tracking the target.
2. The sub-pixel target tracking method applied to the precision guide star measurement system according to claim 1, wherein the sub-pixel target tracking method comprises the following steps: and (3) adopting a Kalman filter based on single-step prediction to process the observation quantity updated at each moment, so that the optimal state estimation at the next moment can be calculated, and the prediction can be continuously corrected by using actual motion parameters, thereby improving the estimation accuracy.
3. The sub-pixel target tracking method applied to the precision guide star measurement system according to claim 1, wherein the sub-pixel target tracking method comprises the following steps: and (4) calculating a correlation coefficient matrix by using a phase correlation method. And only the peak value in the correlation coefficient matrix and the data near the peak value are calculated, so that the redundant part is prevented from being operated, and the operation efficiency is high.
4. The sub-pixel target tracking method applied to the precision guide star measurement system according to claim 1, wherein the sub-pixel target tracking method comprises the following steps: the implementation of the steps (2) to (4) comprises the following steps:
predicting the position of the moving target in the current frame image by using a Kalman filter in a single step according to the position of the moving target in the reference frame image; and searching in the neighborhood of the region of interest by utilizing motion prediction and inter-frame similarity to perform sub-pixel subdivision positioning of the target, further determining the accurate position of the target of the current frame, and feeding back the accurate position as an observation vector to the Kalman filter.
5. The sub-pixel target tracking method applied to the precision guide star measurement system according to claim 1, wherein the sub-pixel target tracking method comprises the following steps: the sub-pixel target tracking method is suitable for a precise image stabilization control system.
6. The sub-pixel target tracking method applied to the precision guide star measurement system according to claim 1, wherein the sub-pixel target tracking method comprises the following steps: the sub-pixel target tracking method calculates two-dimensional inverse discrete Fourier transform aiming at the region of interest, and is suitable for solving the problem that the image motion of two frames of images observed by space astronomical observation is small or the image motion is concentrated in a fixed range.
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Application publication date: 20200522 |
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