CN111625766A - Generalized continuation approximation filtering method, storage medium and processor - Google Patents

Generalized continuation approximation filtering method, storage medium and processor Download PDF

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CN111625766A
CN111625766A CN202010347835.XA CN202010347835A CN111625766A CN 111625766 A CN111625766 A CN 111625766A CN 202010347835 A CN202010347835 A CN 202010347835A CN 111625766 A CN111625766 A CN 111625766A
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刘成
李芳�
高为广
黄晨
王威
宿晨庚
苏牡丹
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63921 Troops of PLA
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Abstract

The embodiment of the invention provides a generalized continuation approximation filtering method, which comprises the following steps: collecting discrete signals, and selecting the optimal estimation value of the prior state quantity of a section of sliding window from the discrete signals
Figure DSA0000207440820000011
The length of the window is L, L is more than or equal to 3, and n is the current signal moment; using the optimal estimated value of the prior state quantity
Figure DSA0000207440820000012
Constructing a generalized continuation approximation equation with interpolation constraint conditions, and solving to obtain a generalized continuation approximation equation coefficient; according to the generalized continuation approximation equation coefficient, constructing a state quantity transfer matrix A based on a state transfer hypothesis model, and calculating to obtain a state quantity predicted value of the next moment n +1
Figure DSA0000207440820000013
Corresponding covariance prediction matrix
Figure DSA0000207440820000014
Predicting value of state quantity according to next time n +1
Figure DSA0000207440820000015
Corresponding covariance prediction matrix
Figure DSA0000207440820000016
Calculating to obtain the optimal state quantity estimated value of the next moment n +1
Figure DSA0000207440820000017
The method can avoid large signal noise influence and has a good filtering effect.

Description

Generalized continuation approximation filtering method, storage medium and processor
Technical Field
The invention relates to the field of data processing, in particular to a generalized continuation approximation filtering method, a storage medium and a processor.
Background
At present, when filtering signals such as communication signals, navigation signals, astronomical radiation signals and the like, a Kalman filtering (KF for short) method is generally adopted, and KFs are widely applied to various engineering and technical fields. Based on a certain motion hypothesis model, the KF associates system state quantities at adjacent moments, so that the original error of an isolated and disordered least square solution is reduced, and the result of data processing is smoother and more accurate.
The nature of KF is based on one-step state transition of Markov chain, always using the state quantity of the latest epoch n to predict the state quantity of the next epoch n + 1. The method has the advantages of greatly reducing the calculation amount, but also causing the method to depend too much on the precision of the current epoch state quantity. In other words, even if we already know that the optimal estimation value of the current epoch state quantity may have a large error, only one-step prediction can be continued by using the state quantity estimation value. In this regard, many algorithms propose artificial intervention or adaptive amplification of the filter error covariance matrix P to suppress the weight of the state quantity pre-measurement in subsequent measurement update processes. However, they also fail to avoid error amplification of the state quantities during the prediction of the branch.
Disclosure of Invention
The embodiment of the invention aims to provide a generalized continuation approximation filtering method, which improves the prediction processing process of signal state quantity by constructing a sliding window with fitting and interpolation functions, and avoids error amplification of the state quantity in the prediction transfer process.
In order to achieve the above object, an embodiment of the present invention provides a generalized continuation approximation filtering method, including: step 1, collecting discrete signals, and selecting a section of optimal estimation value of prior state quantity of a sliding window from the discrete signals
Figure BSA0000207440840000021
The length of the window is L, L is more than or equal to 3, and n is the current signal moment; step 2, utilizing the optimal estimated value of the prior state quantity
Figure BSA0000207440840000022
Constructing a generalized continuation approximation equation with interpolation constraint conditions, and solving to obtain a generalized continuation approximation equation coefficient; step 3, constructing a state quantity transfer matrix A based on a state transfer hypothesis model according to the generalized continuation approximation equation coefficients, and calculating to obtain a state quantity predicted value of the next moment n +1
Figure BSA0000207440840000023
Corresponding covariance prediction matrix
Figure BSA0000207440840000024
Step 4, predicting the state quantity according to the state quantity of the next time n +1
Figure BSA0000207440840000025
Corresponding covariance prediction matrix
Figure BSA0000207440840000026
Calculating to obtain the optimal state quantity estimated value of the next moment n +1
Figure BSA0000207440840000027
Preferably, the step 2 further comprises dividing a time j (j ∈ [ n-L +1, n ] within the length range of the window]) Optimum estimated value of state quantity of
Figure BSA0000207440840000028
And as an interpolation point, the optimal estimated value of the state quantity at other moments in the length range of the window is used as a fitting point, and a generalized continuation approximation equation with an interpolation constraint condition is established:
Figure BSA0000207440840000029
wherein, a0，a1，a2Respectively, generalized prolongation polynomial coefficient, tiIs the value at time i, tjThe value at time j.
Preferably, the step 2 further comprises: the optimal estimation value of the signal state quantity of the current moment n is obtained
Figure BSA00002074408400000210
Corresponding covariance error matrix PnOptimal state quantity estimation value with smaller value
Figure BSA00002074408400000211
As interpolation points.
Preferably, the step 3 further comprises: step 3a, according to the formula
Figure BSA00002074408400000212
The transition calculation of the state quantity is completed, wherein,
Figure BSA00002074408400000213
is the predicted value of the state quantity, t, at the next time n +1n+1Is the value of the next time n + 1; step 3b, obtaining a state transition matrix A based on the state transition hypothesis model, and calculating to obtain the state quantity predicted value of the next moment n +1
Figure BSA00002074408400000214
Corresponding covariance prediction matrix
Figure BSA0000207440840000031
Figure BSA0000207440840000032
Wherein, PnThe optimal estimated value of the signal state quantity of the current moment n
Figure BSA0000207440840000033
The corresponding covariance error matrix.
Preferably, the step 3b further comprises: obtaining a signal state transition matrix A shown as the following formula according to the uniform speed change model:
Figure BSA0000207440840000034
or, obtaining a signal state transition matrix A as shown in the following formula according to the uniform acceleration change model:
Figure BSA0000207440840000035
where Δ t is the time interval between two moments.
Preferably, the step 4 further comprises:
according to the formula
Figure BSA0000207440840000036
Calculating to obtain the optimal state quantity estimated value of the next moment n +1
Figure BSA0000207440840000041
Wherein, Kn+1Is a gain weight matrix, Pn+1For optimal estimation of state quantities
Figure BSA0000207440840000042
The corresponding covariance error matrix is then used,
Figure BSA0000207440840000043
is the predicted value of the state quantity at the time n +1, I is an identity matrix, C is a measurement relation matrix, R is a measurement noise covariance matrix, yn+1Is the measured value at time n + 1.
Preferably, wherein the method further comprises: and step 5, obtaining the optimal estimated value of the state quantity at the next time n +1 by n-n +1
Figure BSA0000207440840000044
And adding the sliding window, and repeatedly executing the steps 2-4 until the filtering operation is stopped.
In another aspect, the present invention also provides a machine-readable storage medium having stored thereon instructions for causing a machine to perform any one of the generalized continuation approximation filtering methods described above.
In yet another aspect, the present invention further provides a processor for executing a program, where the program is executed to perform: a method of generalized continuation approximation filtering as claimed in any one of the preceding claims.
According to the generalized continuation approximation filtering method, a section of sliding window is used for prediction, and the smoothing effect similar to other windowing filters can be achieved. Secondly, the method can flexibly select interpolation constraint points to realize tolerance, one or more interpolation points can be clamped by the method for fitting, and the interpolation points can be flexibly selected. Therefore, when the signal noise at the latest moment n is large, the signal noise can be degraded to be used as a fitting point, and a more accurate signal state quantity estimated value is additionally selected from the recent prior information to be used as an interpolation constraint point, so that the influence of large signal noise is avoided, a better filtering effect is achieved, and the precision of signal filtering processing can be improved. The method has the advantages of interpolation and fitting, can lock the latest data, flexibly perform segmentation or weighting processing on the observation data with different accuracies, and obtain higher accuracy; and the Runge effect is avoided by the thought of domain division processing. The method does not need to increase the degree of freedom and scale, is convenient to use and is easy to realize.
Additional features and advantages of embodiments of the invention will be set forth in the detailed description which follows.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the embodiments of the invention without limiting the embodiments of the invention. In the drawings:
FIG. 1 is a flow diagram of a generalized continuation-approximation filtering method for reducing signal noise according to the present invention;
FIG. 2 is a comparison of filter simulation results in white noise;
FIG. 3 is a comparison of filter error probability statistics in white noise;
FIG. 4 is a comparison of the results of filtering simulations after colored noise is superimposed;
fig. 5 is a statistical comparison of filtering error probabilities after the addition of colored noise.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating embodiments of the invention, are given by way of illustration and explanation only, not limitation.
Referring to fig. 1, the present invention provides a generalized continuation approximation filtering method, including:
step 1, collecting discrete signals, and selecting a section of optimal estimation value of prior state quantity of a sliding window from the discrete signals
Figure BSA0000207440840000051
The length of the window is L, L is more than or equal to 3, and n is the current signal moment;
step 2, utilizing the optimal estimated value of the prior state quantity
Figure BSA0000207440840000052
Constructing a generalized continuation approximation equation with interpolation constraint conditions, and solving to obtain a generalized continuation approximation equation coefficient;
step 3, constructing a state quantity transfer matrix A based on a state transfer model according to the generalized continuation approximation equation coefficient, and calculating to obtain a state quantity predicted value of the next moment n +1
Figure BSA0000207440840000053
Corresponding covariance prediction matrix
Figure BSA0000207440840000054
Step 4, predicting the state quantity according to the state quantity of the next time n +1
Figure BSA0000207440840000061
Corresponding covariance prediction matrix
Figure BSA0000207440840000062
Calculating to obtain the optimal state quantity estimated value of the next moment n +1
Figure BSA0000207440840000063
Specifically, according to the generalized continuation approximation filtering method of the present invention, first, discrete signals are collected, where the discrete signals may be communication signals, navigation signals, astronomical radiation signals, etc., then a smooth window with a certain data length L is selected, and L data in the window are used as the optimal estimation value of the prior state quantity. And constructing a generalized continuation approximation equation with interpolation constraint conditions and solving to obtain a generalized continuation approximation equation coefficient. After the generalized continuation approximation equation coefficient is obtained, the state quantity predicted value of the next moment n +1 can be obtained through extrapolation
Figure BSA0000207440840000064
Then according to the state quantity transfer matrix A, the state quantity predicted value of the next moment n +1 is obtained through calculation
Figure BSA0000207440840000065
Corresponding covariance prediction matrix
Figure BSA0000207440840000066
The predicted value of the state quantity at the next time n +1
Figure BSA0000207440840000067
Corresponding covariance prediction matrix
Figure BSA0000207440840000068
For characterizing the state quantity x for the next momentn+1According to the prediction accuracy and error magnitude
Figure BSA0000207440840000069
The optimal state quantity estimated value of the next moment n +1 can be obtained by calculation
Figure BSA00002074408400000610
According to a preferred embodiment, said step 2 further comprises assigning a time j (j ∈ [ n-L +1, n ] within the length of said window]) Optimum estimated value of state quantity of
Figure BSA00002074408400000611
And as an interpolation point, the optimal estimated value of the state quantity at other moments in the length range of the window is used as a fitting point, and a generalized continuation approximation equation with an interpolation constraint condition is established:
Figure BSA00002074408400000612
wherein, a0，a1，a2Respectively, generalized prolongation polynomial coefficient, tiIs the value at time i, tjThe value at time j.
Preferably, the state quantity at the current time n can be used as the optimal estimation value
Figure BSA00002074408400000613
As interpolation points, or otherwiseAnd taking the data points of the moments (1 to n-1) as fitting points to establish a generalized continuation approximation equation with interpolation constraints. Generally, the optimal state quantity estimated value corresponding to the current time n can be selected as an interpolation point, but when the state quantity estimated value at the current time has a large error (which can be judged by means of a corresponding error covariance matrix value and the like or other auxiliary means), other prior state quantity optimal estimated values in a smooth window can be selected as the interpolation point.
The step 3 further comprises:
step 3a, completing the transfer calculation of the state quantity according to the formula (2),
Figure BSA0000207440840000071
wherein the content of the first and second substances,
Figure BSA0000207440840000072
is the predicted value of the state quantity, t, at the next time n +1n+1Is the value of the next time n + 1;
and 3b, obtaining a state transition matrix A based on the state transition hypothesis model, and calculating according to a formula (3) to obtain the state quantity predicted value of the next moment n +1
Figure BSA0000207440840000073
Corresponding covariance prediction matrix
Figure BSA0000207440840000074
Figure BSA0000207440840000075
Wherein, PnThe optimal estimated value of the signal state quantity of the current moment n
Figure BSA0000207440840000076
The corresponding covariance error matrix.
Further preferably, the step 3b may further include:
obtaining a signal state transition matrix A shown as the following formula according to the uniform speed change model:
Figure BSA0000207440840000077
or, obtaining a signal state transition matrix A as shown in the following formula according to the uniform acceleration change model:
Figure BSA0000207440840000081
where Δ t is the time interval between two moments.
The step 4 further comprises: calculating according to the formula (4) to obtain the optimal state quantity estimated value of the next moment n +1
Figure BSA0000207440840000082
Figure BSA0000207440840000083
Wherein, Kn+1Is a gain weight matrix, Pn+1For optimal estimation of state quantities
Figure BSA0000207440840000084
The corresponding covariance error matrix is then used,
Figure BSA0000207440840000085
is the predicted value of the state quantity at the time n +1, I is an identity matrix, C is a measurement relation matrix, R is a measurement noise covariance matrix, yn+1Is the measured value at time n + 1.
The method may further include a step 5 of optimally estimating the state quantity of the next time n +1 by n-n +1
Figure BSA0000207440840000086
And adding the sliding window, and repeatedly executing the steps 2-4 until the filtering operation is stopped. That is, in step 5, the optimum estimated value of the prior state quantity at the oldest time is discardedAnd adding the state quantity optimal estimation value at the latest moment, forming a new filtering smoothing window and using the new filtering smoothing window for processing at the next moment.
According to the generalized continuation approximation filtering method, a section of sliding window is used for prediction, and the smoothing effect similar to other windowing filters can be achieved. Secondly, the invention can flexibly select interpolation constraint points to realize tolerance. Generalized continuation can "block" one or more interpolation points for fitting, and the interpolation points can be flexibly selected. Therefore, when the signal noise at the latest time n is large, the signal noise can be degraded to be a fitting point, and a more accurate signal state quantity estimated value is additionally selected from the recent prior information to be an interpolation constraint point, so that the influence of the large signal noise is avoided. The method has the advantages of interpolation and fitting, can lock the latest data, flexibly perform segmentation or weighting processing on the observation data with different accuracies, and obtain higher accuracy; and the Runge effect is avoided by the thought of domain division processing. The method does not need to increase the degree of freedom and scale, is convenient to use and is easy to realize.
In the following, a specific embodiment of the generalized continuation approximation filtering method according to the present invention is described in detail, taking the case where L ═ n as an example.
1. Selecting the optimal estimation value of the prior state quantity
Taking the known value of the initial L points in the discrete signal as the optimal estimated value of the prior signal state quantity, and recording the optimal estimated value as the optimal estimated value
Figure BSA0000207440840000091
2. Constructing and solving generalized continuation approximation equation
The data point of the latest time L
Figure BSA0000207440840000092
And establishing a generalized continuation approximation equation with interpolation constraint conditions by taking data points from other moments (1 to L-1) as interpolation points and taking data points from other moments as fitting points:
Figure BSA0000207440840000093
and solving by adopting a linear expansion mode. First, the interpolation constraint equation in equation (5) is rewritten as:
Figure BSA0000207440840000094
substituting the least square formula to obtain:
Figure BSA0000207440840000095
according to differential processing:
Figure BSA0000207440840000101
can be finished to obtain:
Figure BSA0000207440840000102
written in matrix form:
Figure BSA0000207440840000103
wherein the content of the first and second substances,
Figure BSA0000207440840000104
from formula (10):
Figure BSA0000207440840000111
a is obtained by calculation1，a2Then substituting into formula (6) to obtain a0。
3. State transition
Obtaining generalized continuation polynomial coefficient a0，a1，a2Then, the state quantity x of the next time L +1 can be obtained by extrapolationL+1Predicted value of (2)
Figure BSA0000207440840000112
Thereby completing the predicted branch of state quantities:
Figure BSA0000207440840000113
calculating according to the state transition matrix A to obtain the predicted value of the state quantity
Figure BSA0000207440840000114
Corresponding covariance prediction matrix
Figure BSA0000207440840000115
Figure BSA0000207440840000116
Wherein, PLFor the optimum estimation of the state quantity at the time L
Figure BSA0000207440840000117
The corresponding covariance error matrix.
4. Measurement update
The measurement update at time L +1 is completed according to equation (15):
Figure BSA0000207440840000118
wherein, KL+1In order to obtain a matrix of gain weights,
Figure BSA0000207440840000119
for an optimal estimate of the state quantity at the time L +1,
Figure BSA00002074408400001110
is a predicted estimate of the state quantity at time L +1, yL+1Is a measured value at time L +1, PL+1For optimal estimation of state quantities
Figure BSA00002074408400001111
The corresponding covariance error matrix. Thus, the optimal state quantity estimated value at the next time L +1 can be calculated
Figure BSA00002074408400001112
5. Circulation of
Moving the sliding window to the nearest moment by one moment, using the data of the moment L +1 as prior information, and obtaining the data of the sliding window
Figure BSA0000207440840000121
The above steps are repeatedly performed as interpolation points, thereby obtaining the state quantity optimum estimation value at the next time (time L + 2).
Based on the steps, the filtering performance of the sinusoidal signal under the influence of white noise and colored noise is simulated respectively. The simulation time T is 0-30 s, the step length delta T is 0.1s, and the calculation is repeated 1000 times. The accuracy results were counted using monte carlo simulations and the performance of the filters of the method of the invention was analyzed and evaluated by comparison with a widely used kalman filter, see fig. 2-5.
(1) White noise filtering performance
Firstly, Gaussian white noise satisfying r-N (0, 0.1) distribution is added for numerical simulation, and basic characteristics of a filtering method are inspected and analyzed. The initial state quantities of the two filters are X0＝[0 0]Initial covariance of P0＝diag([0.1 2]) Initial process noise Q0＝[0.0 0.0005；0.0005 0.01]Initial measurement noise of R00.01; the window length L of the generalized continuation approximation filtering is 20, and the interpolation constraint point is the current epoch observation point. The effect of the two filtering methods is shown in fig. 2, and the error probability statistics are shown in fig. 3. The Kalman filtering root mean square error (RMS) is about 0.083, the generalized continuation approaches about 0.069, and the improvement is about 17%.
(2) Colored noise filtering performance
On the basis of the white Gaussian noise, colored noise is added, filter error parameters and window data length are kept unchanged, and performance of the method is investigated and analyzed under the colored noise. The effect of the two filtering methods is shown in fig. 4, and the error probability statistics are shown in fig. 5. The Kalman filtering root mean square error (RMS) is about 0.113, the generalized continuation approximation filtering RMS is about 0.102, and the improvement is about 10%.
According to another aspect of the present invention, there is also provided a machine-readable storage medium having stored thereon instructions for causing a machine to perform the generalized continuation approximation filtering method described above.
According to yet another aspect of the present invention, there is also provided a processor for executing a program, wherein the program is executed to perform the generalized continuation approximation filtering method described above.
The present application further provides a computer program product adapted to perform a program for initializing the following method steps when executed on a data processing device:
step 1, collecting discrete signals, and selecting a section of optimal estimation value of prior state quantity of a sliding window from the discrete signals
Figure BSA0000207440840000131
The length of the window is L, L is more than or equal to 3, and n is the current signal moment;
step 2, utilizing the optimal estimated value of the prior state quantity
Figure BSA0000207440840000132
Constructing a generalized continuation approximation equation with interpolation constraint conditions, and solving to obtain a generalized continuation approximation equation coefficient;
step 3, constructing a state quantity transfer matrix A based on a state transfer model according to the generalized continuation approximation equation coefficient, and calculating to obtain a state quantity predicted value of the next moment n +1
Figure BSA0000207440840000133
Corresponding covariance prediction matrix
Figure BSA0000207440840000134
Step 4, predicting the state quantity according to the state quantity of the next time n +1
Figure BSA0000207440840000135
Corresponding covariance prediction matrix
Figure BSA0000207440840000136
Calculating to obtain the optimal state quantity estimated value of the next moment n +1
Figure BSA0000207440840000137
The present application is described with reference to flowchart illustrations and/or block diagrams of methods and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In a typical configuration, a device includes one or more processors (CPUs), memory, and a bus. The device may also include input/output interfaces, network interfaces, and the like.
The memory may include volatile memory in a computer readable medium, Random Access Memory (RAM) and/or nonvolatile memory such as Read Only Memory (ROM) or flash memory (flash RAM), and the memory includes at least one memory chip. The memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. The use of the phrase "including an" as used herein does not exclude the presence of other, identical elements, components, methods, articles, or apparatus that may include the same, unless expressly stated otherwise.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The above are merely examples of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims (9)

1. A generalized continuation approximation filtering method, the method comprising:
step 1, collecting discrete signals, and selecting a section of optimal estimation value of prior state quantity of a sliding window from the discrete signals
Figure FSA0000207440830000011
The length of the window is L, L is more than or equal to 3, and n is the current signal moment;
step 2, utilizing the optimal estimated value of the prior state quantity
Figure FSA0000207440830000012
Constructing a generalized continuation approximation equation with interpolation constraint conditions, and solving to obtain a generalized continuation approximation equation coefficient;
step 3, constructing a state quantity transfer matrix A based on a state transfer hypothesis model according to the generalized continuation approximation equation coefficients, and calculating to obtain a state quantity predicted value of the next moment n +1
Figure FSA0000207440830000013
Corresponding covariance prediction matrix
Figure FSA0000207440830000014
Step 4, predicting the state quantity according to the state quantity of the next time n +1
Figure FSA0000207440830000015
Corresponding covariance prediction matrix
Figure FSA0000207440830000016
Calculating to obtain the optimal state quantity estimated value of the next moment n +1
Figure FSA0000207440830000017
2. The method of claim 1, wherein the step 2 further comprises:
the time j (j ∈ [ n-L +1, n) within the length range of the window]) Optimum estimated value of state quantity of
Figure FSA0000207440830000018
And as an interpolation point, the optimal estimated value of the state quantity at other moments in the length range of the window is used as a fitting point, and a generalized continuation approximation equation with an interpolation constraint condition is established:
Figure FSA0000207440830000019
wherein, a0，a1，a2Respectively, generalized prolongation polynomial coefficient, tiIs the value at time i, tjThe value at time j.
3. The method of claim 2, wherein the step 2 further comprises:
the optimal estimation value of the signal state quantity of the current moment n is obtained
Figure FSA0000207440830000021
Corresponding covariance error matrix PnOptimal state quantity estimation value with smaller value
Figure FSA0000207440830000022
As interpolation points.
4. The method of claim 1, wherein the step 3 further comprises:
step 3a, according to the formula
Figure FSA0000207440830000023
The transition calculation of the state quantity is completed, wherein,
Figure FSA0000207440830000024
is the predicted value of the state quantity, t, at the next time n +1n+1Is the value of the next time n + 1;
step 3b, obtaining a state transition matrix A based on the state transition hypothesis model, and calculating to obtain the state quantity predicted value of the next moment n +1
Figure FSA0000207440830000025
Corresponding covariance prediction matrix
Figure FSA0000207440830000026
Figure FSA0000207440830000027
Wherein, PnThe optimal estimated value of the signal state quantity of the current moment n
Figure FSA0000207440830000028
The corresponding covariance error matrix.
5. The method of claim 4, wherein the step 3b further comprises:
obtaining a signal state transition matrix A shown as the following formula according to the uniform speed change model:
Figure FSA0000207440830000029
or, obtaining a signal state transition matrix A as shown in the following formula according to the uniform acceleration change model:
Figure FSA0000207440830000031
where Δ t is the time interval between two moments.
6. The method of claim 4 or 5, wherein the step 4 further comprises:
according to the formula
Figure FSA0000207440830000032
Calculating to obtain the optimal state quantity estimated value of the next moment n +1
Figure FSA0000207440830000033
Wherein, Kn+1Is a gain weight matrix, Pn+1For optimal estimation of state quantities
Figure FSA0000207440830000034
The corresponding covariance error matrix is then used,
Figure FSA0000207440830000035
is the predicted value of the state quantity at the time n +1, I is an identity matrix, C is a measurement relation matrix, R is a measurement noise covariance matrix, yn+1Is the measured value at time n + 1.
7. The method of any of claims 1-6, wherein the method further comprises:
and step 5, obtaining the optimal estimated value of the state quantity at the next time n +1 by n-n +1
Figure FSA0000207440830000036
And adding the sliding window, and repeatedly executing the steps 2-4 until the filtering operation is stopped.
8. A machine-readable storage medium having stored thereon instructions for causing a machine to perform the generalized continuation approximation filtering method of any one of claims 1-7.
9. A processor configured to execute a program, wherein the program is configured to perform: the generalized continuation approximation filtering method of any one of claims 1-7.
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