CN112924761B - Method and controller for evaluating uncertainty of pulse waveform - Google Patents

Method and controller for evaluating uncertainty of pulse waveform Download PDF

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CN112924761B
CN112924761B CN202011576606.1A CN202011576606A CN112924761B CN 112924761 B CN112924761 B CN 112924761B CN 202011576606 A CN202011576606 A CN 202011576606A CN 112924761 B CN112924761 B CN 112924761B
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frequency domain
covariance matrix
pulse waveform
matrix
measurement result
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CN112924761A (en
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龚鹏伟
刘爽
谢文
姜河
谌贝
马红梅
杨春涛
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Beijing Institute of Radio Metrology and Measurement
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/02—Measuring characteristics of individual pulses, e.g. deviation from pulse flatness, rise time or duration
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/08—Measuring electromagnetic field characteristics
    • G01R29/0864—Measuring electromagnetic field characteristics characterised by constructional or functional features
    • G01R29/0892—Details related to signal analysis or treatment; presenting results, e.g. displays; measuring specific signal features other than field strength, e.g. polarisation, field modes, phase, envelope, maximum value

Abstract

The invention relates to a method and a controller for pulse waveform uncertainty assessment, the method comprising: measuring the pulse waveform to obtain a pulse waveform measurement result with N sampling points; obtaining a corresponding frequency domain vector signal according to the pulse waveform measurement result; obtaining a frequency domain covariance matrix corresponding to the frequency domain vector signal according to the frequency domain vector signal
Figure DDA0002864046260000011
For the frequency domain covariance matrix
Figure DDA0002864046260000012
Rearranging to obtain a frequency domain covariance matrix
Figure DDA0002864046260000013
For frequency domain covariance matrix
Figure DDA0002864046260000014
Performing dimension reduction to obtain a frequency domain covariance matrix after dimension reduction
Figure DDA0002864046260000015
Calculating the frequency domain covariance matrix after dimension reduction
Figure DDA0002864046260000016
Uncertainty information meeting tolerance requirements is obtained. By the invention is described inThe method of (3) no longer requires calculation
Figure DDA0002864046260000017
Only need to calculate
Figure DDA0002864046260000018
The frequency domain covariance matrix containing the uncertainty information which can be accepted by people can be obtained with less operation amount, so that the operation amount of the frequency domain covariance matrix is greatly reduced, and the operation efficiency is improved.

Description

Method and controller for evaluating uncertainty of pulse waveform
Technical Field
The invention relates to the technical field of uncertainty evaluation, in particular to a method and a controller for evaluating pulse waveform uncertainty.
Background
The pulse technique is widely applied in the military and civil fields, the measurement of pulse waveforms is a basic and important measurement requirement in the technical field of electronic instrument measurement, and in order to promote the rapid development and application of high-speed pulses, the requirement on the measurement precision of pulse parameters is higher and higher. It is therefore a very important task to determine the pulse parameters and to analyze them for uncertainty.
The conventional uncertainty evaluation method is to directly transmit the uncertainty source to specific pulse waveform parameters, for example, to specific pulse waveform parameters such as half-amplitude pulse width, rise time, amplitude and the like according to the uncertainty source, however, the uncertainty evaluation method of single pulse waveform parameters has certain limitations, and cannot transmit the uncertainty of the time domain measurement result to the frequency domain or transmit the uncertainty of the frequency domain measurement result to the time domain.
Currently, in order toThe problem is solved by adopting a pulse waveform uncertainty assessment technology based on a covariance matrix. If the pulse waveform measurement result has N sampling points, the corresponding covariance matrix is N, and the calculated quantity is equal to N 2 Proportional to the ratio. However, for pulse waveforms, N is generally larger, resulting in huge computation of covariance matrix, so that the uncertainty evaluation technology of pulse waveform measurement results based on covariance matrix is difficult to apply in engineering. In addition, in the field of radio pulse parameter calibration, most of the cases are measurement in the time domain and the frequency domain, calculation in the frequency domain, obtaining a frequency domain calibration result, and then reconverting the frequency domain calibration result to the time domain, thus obtaining a time domain calibration result. In the whole process, firstly, a covariance matrix of the uncertainty of the frequency domain is obtained, and then, the covariance matrix of the uncertainty of the time domain is obtained, so that the operation amount is large.
Disclosure of Invention
In view of the above, the present invention aims to overcome the shortcomings of the prior art, provide a method and a controller for evaluating uncertainty of pulse waveforms, and solve the problem of excessive operand of the current method for evaluating uncertainty of pulse waveforms based on covariance matrix.
In order to achieve the above purpose, the invention adopts the following technical scheme: a method for pulse waveform uncertainty assessment, comprising:
measuring the pulse waveform to obtain a pulse waveform measurement result with N sampling points;
obtaining a corresponding frequency domain vector signal according to the pulse waveform measurement result;
obtaining a frequency domain covariance matrix corresponding to the frequency domain vector signal according to the frequency domain vector signal
Figure BDA0002864046240000021
For the frequency domain covariance matrix
Figure BDA0002864046240000022
Rearranging to obtain a frequency domain covariance matrix +.>
Figure BDA0002864046240000023
For frequency domain covariance matrix
Figure BDA0002864046240000024
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure BDA0002864046240000025
Calculating the frequency domain covariance matrix after dimension reduction
Figure BDA0002864046240000026
Uncertainty information meeting tolerance requirements is obtained.
Optionally, the obtaining a corresponding frequency domain vector signal according to the pulse waveform measurement result includes:
assume that the pulse waveform measurement result with N sampling points is [ y ] 0 ,y 1 ,…,y N-1 ] T Then its corresponding Fourier transform is [ Y ] 0 ,Y 1 ,…,Y N-1 ] T ，
The relationship between them is expressed as:
Figure BDA0002864046240000027
wherein ,
Figure BDA0002864046240000028
the [ Y ] 0 ,Y 1 ,…,Y N-1 ] T Is a frequency domain vector signal.
Optionally, the frequency domain covariance matrix corresponding to the frequency domain vector signal is obtained according to the frequency domain vector signal
Figure BDA0002864046240000031
Comprising the following steps:
obtaining the frequency domain measurement result of the pulse waveform according to the frequency domain vector signal
Figure BDA0002864046240000032
The frequency domain measurement result
Figure BDA0002864046240000033
Contains n frequency components, does not contain a direct current component f=0 Hz, where k=1, 2,3, … m, represents m independent uncorrelated calibrations;
frequency domain covariance matrix corresponding to the frequency domain measurement result
Figure BDA0002864046240000034
Expressed as:
Figure BDA0002864046240000035
wherein ,E(ai ) Representation a i Is the mathematical expectation of E (b) i ) Representation b i I=1, 2, …, n.
Alternatively, the frequency domain covariance matrix
Figure BDA0002864046240000036
The simplified representation is:
Figure BDA0002864046240000037
wherein ,u(ai ,a j ) Representation a i and aj Covariance of u (a) i ,b j ) Representation a i and bj Covariance of u (b) i ,a j ) Representation b i and aj Covariance of u (b) i ,b j ) Representation b i and bj J=1, 2, …, n.
Optionally, the pair of frequency domain covariance matrices
Figure BDA0002864046240000038
Rearrangement is performedObtaining a frequency domain covariance matrix->
Figure BDA0002864046240000039
Comprising the following steps:
the simplified frequency domain covariance matrix
Figure BDA00028640462400000310
Dividing n complex data of the frequency domain measurement result arranged in columns into a real part corresponding to the n complex data arranged in columns and an imaginary part corresponding to the n complex data;
rearranged frequency domain covariance matrix
Figure BDA00028640462400000311
Expressed as: />
Figure BDA0002864046240000041
Optionally, the
Figure BDA0002864046240000042
Is a real symmetric positive definite matrix, can diagonalize, meets the condition of matrix characteristic decomposition, and performs characteristic decomposition on the matrix>
Figure BDA0002864046240000043
Wherein q=eΛ 1/2 E is a 2n x 2 n-dimensional matrix, each column vector being
Figure BDA0002864046240000044
A feature vector corresponding to the feature value; Λ is 2n×2n-dimensional real diagonal matrix with diagonal elements +.>
Figure BDA0002864046240000045
Is a characteristic value of (a).
Optionally, the pair of frequency domain covariance matrices
Figure BDA0002864046240000046
Performing dimension reduction to obtain a frequency domain covariance matrix after dimension reduction
Figure BDA0002864046240000047
Comprising the following steps:
with p maximum eigenvalue pairs
Figure BDA0002864046240000048
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure BDA0002864046240000049
The frequency domain covariance matrix
Figure BDA00028640462400000410
Denoted as->
Figure BDA00028640462400000411
wherein ,Q0 Is a 2n x p dimensional matrix, comprising the first p columns in the Q matrix,
Figure BDA00028640462400000412
d 1 、d 2 and d3 Are n x 1 dimensional row vectors.
Alternatively, the principle of determining p is: when k > p, Λ k,k ≈0。
Optionally, D is determined such that
Figure BDA00028640462400000413
and />
Figure BDA00028640462400000414
The invention also provides a controller for performing the method for pulse waveform uncertainty assessment of any of the preceding claims.
The invention adopts the above technologyIn one embodiment, the method for pulse waveform uncertainty assessment comprises: measuring the pulse waveform to obtain a pulse waveform measurement result with N sampling points; obtaining a corresponding frequency domain vector signal according to the pulse waveform measurement result; obtaining a frequency domain covariance matrix corresponding to the frequency domain vector signal according to the frequency domain vector signal
Figure BDA0002864046240000051
For the frequency domain covariance matrix->
Figure BDA0002864046240000052
Rearranging to obtain a frequency domain covariance matrix +.>
Figure BDA0002864046240000053
For the frequency domain covariance matrix->
Figure BDA0002864046240000054
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure BDA0002864046240000055
Calculating the frequency domain covariance matrix after dimension reduction
Figure BDA0002864046240000056
Uncertainty information meeting tolerance requirements is obtained. By the method according to the invention no calculation of +.>
Figure BDA0002864046240000057
Only calculate +.>
Figure BDA0002864046240000058
The frequency domain covariance matrix containing the uncertainty information which can be accepted by people can be obtained with less operation amount, so that the operation amount of the frequency domain covariance matrix is greatly reduced, and the operation efficiency is improved. />
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart illustrating a method for pulse waveform uncertainty assessment according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, based on the examples herein, which are within the scope of the invention as defined by the claims, will be within the scope of the invention as defined by the claims.
FIG. 1 is a flow chart illustrating a method for pulse waveform uncertainty assessment according to the present invention.
As shown in fig. 1, a method for pulse waveform uncertainty assessment according to the present invention includes:
s11: measuring the pulse waveform to obtain a pulse waveform measurement result with N sampling points;
s12: obtaining a corresponding frequency domain vector signal according to the pulse waveform measurement result;
further, the obtaining the corresponding frequency domain vector signal according to the pulse waveform measurement result includes:
assume that the pulse waveform measurement result with N sampling points is [ y ] 0 ,y 1 ,…,y N-1 ] T Then its corresponding Fourier transform is [ Y ] 0 ,Y 1 ,…,Y N-1 ] T ，
The relationship between them is expressed as:
Figure BDA0002864046240000061
wherein ,
Figure BDA0002864046240000062
the [ Y ] 0 ,Y 1 ,…,Y N-1 ] T Is a frequency domain vector signal.
S13: obtaining a frequency domain covariance matrix corresponding to the frequency domain vector signal according to the frequency domain vector signal
Figure BDA0002864046240000063
Further, the frequency domain covariance matrix corresponding to the frequency domain vector signal is obtained according to the frequency domain vector signal
Figure BDA0002864046240000064
Comprising the following steps:
the frequency domain measurement result of the pulse waveform can be obtained according to the frequency domain vector signal of step S12
Figure DEST_PATH_GDA0003059743660000065
The frequency domain measurement result
Figure BDA0002864046240000066
Contains n frequency components, does not contain a direct current component f=0 Hz, where k=1, 2,3, … m, represents m independent uncorrelated calibrations;
frequency domain covariance matrix corresponding to the frequency domain measurement result
Figure BDA0002864046240000067
Expressed as: />
Figure BDA0002864046240000068
wherein ,E(ai ) Representation a i Is the mathematical expectation of E (b) i ) Representation b i I=1,2,…,n。
For more convenient analysis of the frequency domain covariance matrix
Figure BDA0002864046240000069
Is constructed by (1) frequency domain covariance matrix +.>
Figure BDA00028640462400000610
The simplified representation is:
Figure BDA0002864046240000071
wherein ,u(ai ,a j ) Representation a i and aj Covariance of u (a) i ,b j ) Representation a i and bj Covariance of u (b) i ,a j ) Representation b i and aj Covariance of u (b) i ,b j ) Representation b i and bj J=1, 2, …, n.
S14: for the frequency domain covariance matrix
Figure BDA0002864046240000072
Rearranging to obtain a frequency domain covariance matrix +.>
Figure BDA0002864046240000073
Further, the pair of frequency domain covariance matrices
Figure BDA0002864046240000074
Rearranging to obtain a frequency domain covariance matrix +.>
Figure BDA0002864046240000075
Comprising the following steps:
the simplified frequency domain covariance matrix
Figure BDA0002864046240000076
The n complex data of the frequency domain measurement results arranged in columns are split into the data in columnsReal parts corresponding to n complex data arranged in columns and imaginary parts corresponding to n complex data;
rearranged frequency domain covariance matrix
Figure BDA0002864046240000077
Expressed as:
Figure BDA0002864046240000078
the following are described in step S14
Figure BDA0002864046240000079
Is a real symmetric positive definite matrix, can diagonalize and meet the condition of matrix characteristic decomposition, so that the characteristic decomposition can be carried out on the matrix>
Figure BDA00028640462400000710
Wherein q=eΛ 1/2 E is a 2n x 2 n-dimensional matrix, each column vector being
Figure BDA00028640462400000711
A feature vector corresponding to the feature value; Λ is 2n×2n-dimensional real diagonal matrix with diagonal elements +.>
Figure BDA00028640462400000712
Is a characteristic value of (a).
S15: to reduce the computation of the frequency domain covariance matrix, the frequency domain covariance matrix is obtained
Figure BDA00028640462400000713
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure BDA00028640462400000714
Further, the pair of frequency domain covariance matrices
Figure BDA00028640462400000715
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure BDA00028640462400000716
Comprising the following steps:
with p maximum eigenvalue pairs
Figure BDA00028640462400000717
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure BDA00028640462400000718
The frequency domain covariance matrix
Figure BDA0002864046240000081
Denoted as->
Figure BDA0002864046240000082
wherein ,Q0 Is a 2n x p dimensional matrix, comprising the first p columns in the Q matrix,
Figure BDA0002864046240000083
d 1 、d 2 and d3 Are n x 1 dimensional row vectors.
In order to ensure that uncertainty information contained in the frequency domain covariance matrix after dimension reduction can meet tolerance requirements, the principle of determining p is as follows: when k > p, Λ k,k ≈0。
The purpose of the matrix D is to enable the variances and covariances associated with the real and imaginary parts of each frequency component complex data in the rearranged frequency domain covariance matrix to be accurately preserved in the reduced-dimension frequency domain covariance matrix. Determining D, making
Figure BDA0002864046240000084
and />
Figure BDA0002864046240000085
S16: calculating the frequency domain covariance matrix after dimension reduction
Figure BDA0002864046240000086
Uncertainty information meeting tolerance requirements is obtained.
The invention uses p maximum eigenvalue pairs
Figure BDA0002864046240000087
Performing dimension reduction to obtain a frequency domain covariance matrix after dimension reduction
Figure BDA0002864046240000088
Uncertainty information contained in the dimensionality-reduced frequency domain covariance matrix meets tolerance requirements, and at the moment, we do not need to calculate +.>
Figure BDA0002864046240000089
Only calculate +.>
Figure BDA00028640462400000810
The frequency domain covariance matrix containing the uncertainty information which can be accepted by us can be obtained with less calculation amount, so that the calculation amount of the frequency domain covariance matrix is greatly reduced.
For rearranged frequency domain covariance matrix
Figure BDA00028640462400000811
Need to store N full ＝2n 2 +n elements, and for the reduced-dimension frequency domain covariance matrix +.>
Figure BDA00028640462400000812
Only N needs to be stored compact =2np+3n elements.
Defining the dimension reduction ratio as S, the dimension reduction ratio is expressed as:
Figure BDA00028640462400000813
because of N compact /N full The method is approximately equal to p/n, so that when p is approximately equal to n, the operation amount of the frequency domain covariance matrix can be greatly reduced, and the operation efficiency is improved.
The invention also provides a controller for performing the method for pulse waveform uncertainty assessment described in fig. 1.
It is to be understood that the same or similar parts in the above embodiments may be referred to each other, and that in some embodiments, the same or similar parts in other embodiments may be referred to.
It should be noted that in the description of the present invention, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Furthermore, in the description of the present invention, unless otherwise indicated, the meaning of "plurality" means at least two.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and further implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present invention.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product.
The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.

Claims (2)

1. A method for pulse waveform uncertainty assessment, comprising:
measuring the pulse waveform to obtain a pulse waveform measurement result with N sampling points;
obtaining a corresponding frequency domain vector signal according to the pulse waveform measurement result, wherein the obtaining the corresponding frequency domain vector signal according to the pulse waveform measurement result comprises the following steps: assume that the pulse waveform measurement result with N sampling points is [ y ] 0 ,y 1 …,y N-1 ] T Then its corresponding Fourier transform is [ Y ] 0 ,Y 1 …,Y N-1 ] T ，
The relationship between them is expressed as:
Figure FDA0004141454990000011
wherein ,
Figure FDA0004141454990000012
the [ Y ] 0 ,Y 1 …,Y N-1 ] T Is a frequency domain vector signal;
obtaining a frequency domain covariance matrix corresponding to the frequency domain vector signal according to the frequency domain vector signal
Figure FDA0004141454990000013
Wherein, the frequency domain covariance matrix corresponding to the frequency domain vector signal is obtained according to the frequency domain vector signal>
Figure FDA0004141454990000014
Comprising the following steps:
obtaining the frequency domain measurement result of the pulse waveform according to the frequency domain vector signal
Figure FDA0004141454990000015
The frequency domain measurement result
Figure FDA0004141454990000016
Contains n frequency components, does not contain a direct current component f=0 Hz, where k=1, 2,3, … m, represents m independent uncorrelated calibrations;
frequency domain covariance matrix corresponding to the frequency domain measurement result
Figure FDA0004141454990000017
Expressed as:
Figure FDA0004141454990000021
wherein ,E(ai ) Representation a i Is the mathematical expectation of E (b) i ) Representation b i I=1, 2, …, n;
covariance matrix of frequency domain
Figure FDA0004141454990000022
The simplified representation is:
Figure FDA0004141454990000023
wherein ,u(ai ,a j ) Representation a i and aj Covariance of u (a) i ,b j ) Representation a i and bj Covariance of u (b) i ,a j ) Representation b i and aj Covariance of u (b) i ,b j ) Representation b i and bj J=1, 2, …, n;
for the frequency domain covariance matrix
Figure FDA0004141454990000024
Rearranging to obtain a frequency domain covariance matrix +.>
Figure FDA0004141454990000025
Wherein the pair ofThe frequency domain covariance matrix->
Figure FDA0004141454990000026
Rearranging to obtain a frequency domain covariance matrix +.>
Figure FDA0004141454990000027
Comprising the following steps:
the simplified frequency domain covariance matrix
Figure FDA0004141454990000028
Dividing n complex data of the frequency domain measurement result arranged in columns into a real part corresponding to the n complex data arranged in columns and an imaginary part corresponding to the n complex data;
rearranged frequency domain covariance matrix
Figure FDA0004141454990000029
Expressed as:
Figure FDA00041414549900000210
the said
Figure FDA0004141454990000031
Is a real symmetric positive definite matrix, can diagonalize, meets the condition of matrix characteristic decomposition, and performs characteristic decomposition on the matrix
Figure FDA0004141454990000032
Wherein q=eΛ 1/2 E is a 2n x 2 n-dimensional matrix, each column vector being
Figure FDA0004141454990000033
A feature vector corresponding to the feature value; Λ is 2n×2n-dimensional real diagonal matrix with diagonal elements +.>
Figure FDA0004141454990000034
Is a characteristic value of (2);
for frequency domain covariance matrix
Figure FDA0004141454990000035
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure FDA0004141454990000036
Wherein the pair of frequency domain covariance matrices +.>
Figure FDA0004141454990000037
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure FDA0004141454990000038
Comprising the following steps:
with p maximum eigenvalue pairs
Figure FDA0004141454990000039
Performing dimension reduction to obtain a frequency domain covariance matrix +.>
Figure FDA00041414549900000310
The frequency domain covariance matrix
Figure FDA00041414549900000311
Denoted as->
Figure FDA00041414549900000312
wherein ,Q0 Is a 2n x p dimensional matrix, comprising the first p columns in the Q matrix,
Figure FDA00041414549900000313
d 1 、d 2 and d3 Du Shin x 1-dimensional row vectors;
the principle of determining p is: when k > p, Λ k,k ≈0；
Determining D, making
Figure FDA00041414549900000314
and />
Figure FDA00041414549900000315
Calculating the frequency domain covariance matrix after dimension reduction
Figure FDA00041414549900000316
Uncertainty information meeting tolerance requirements is obtained.
2. A controller for performing the method for pulse waveform uncertainty assessment of claim 1.
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