CN112014811A - Method for finely estimating radar carrier frequency - Google Patents

Method for finely estimating radar carrier frequency Download PDF

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CN112014811A
CN112014811A CN202010829967.6A CN202010829967A CN112014811A CN 112014811 A CN112014811 A CN 112014811A CN 202010829967 A CN202010829967 A CN 202010829967A CN 112014811 A CN112014811 A CN 112014811A
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fft
carrier frequency
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frequency
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CN112014811B (en
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邱文旗
曾庆化
刘建业
史进恒
许睿
张玲
王融
赖际舟
李荣冰
吕品
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis

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Abstract

The invention discloses a fine estimation method of radar carrier frequency, which belongs to the field of fine estimation of carrier frequency, and comprises the following steps of firstly, extracting a maximum value in a radar carrier signal FFT output amplitude spectrum sequence and a maximum value in a value adjacent to the maximum value; then, obtaining an estimation threshold value according to the statistical characteristics of the FFT output sequence, and judging whether the two values exceed the estimation threshold value so as to judge whether the radar carrier wave is successfully captured; finally, according to the constructed discrimination function linearly related to the carrier frequency, the compensation quantity of the FFT process for carrier frequency estimation is calculated, so that the estimation precision of the radar carrier frequency is improved; the invention has simple structure and small calculation amount, can greatly improve the estimation precision of the carrier frequency by adding the carrier frequency fine estimation module after the carrier frequency estimation structure in the original FFT process, and has higher engineering use value.

Description

Method for finely estimating radar carrier frequency
Technical Field
The invention belongs to the field of fine estimation of radar carrier frequency, and particularly relates to a fine estimation method of radar carrier frequency.
Background
The carrier frequency of radar is an important parameter in radar frequency domain parameters, and the existing radar carrier frequency estimation generally adopts an FFT frequency estimator, but the frequency estimation precision of FFT is related to the data length.
Increasing the frequency estimation accuracy by increasing the length of the FFT processing sequence can lead to the counting of the system
Computational resources are consumed exponentially.
Disclosure of Invention
In order to solve the technical problems of the background art, the invention aims to improve the estimation precision of the radar carrier frequency according to the FFT output amplitude spectrum characteristic, and provides a fine estimation method of the radar carrier frequency on the basis of not increasing the calculated amount and not changing the original structure of the FFT estimated carrier frequency.
In order to achieve the purpose, the invention provides the technical scheme that: radar carrier frequency essence
A fine estimation method comprising the steps of:
step one, extracting a maximum value M in an FFT output amplitude spectrum sequence S (k) of a radar carrier signalFFTAnd the maximum value S of the values adjacent theretoubm；
Step two, respectively judging the maximum value MFFTAnd the most adjacent value to itLarge value SubmAnd an estimated threshold value YtIf both are larger than the estimated threshold value YtIf yes, continuing to estimate, otherwise, ending;
step three, obtaining the compensation value of the FFT process to the carrier frequency estimation according to the formula (1),
Figure BDA0002637584400000011
wherein, Deltaf' is the compensation value of the FFT process to the carrier frequency estimation, Deltaf is the carrier frequency after frequency reduction, TLIs the size of the rectangular window;
and step four, obtaining a radar carrier frequency fine estimation value according to the compensation value.
Further, the first step includes:
the structure of the radar carrier signal s (t) after frequency reduction is shown in formula (2),
Figure BDA0002637584400000021
where A is the amplitude of the carrier signal, i is the imaginary unit, Δ f is the down-converted carrier frequency,
Figure BDA0002637584400000022
is the carrier initial phase;
after the radar carrier signal s (t) subjected to frequency reduction is dispersed and cut, as shown in formula (3),
Figure BDA0002637584400000023
where (·) is a Dirac Delta function, TsIs the sampling period, rect () is a rectangular window function, TLIs the size of the rectangular window;
the formula (3) is abbreviated as:
Figure BDA0002637584400000024
wherein d (t) is a sampling pulse signal; w (t) is a rectangular window signal;
the spectrum of S (n) is obtained according to the time domain multiplication frequency domain convolution principle as shown in the following formula,
Figure BDA0002637584400000025
wherein, is a convolution symbol;
Figure BDA0002637584400000026
is the frequency spectrum of a discrete finite long time domain signal s (n); (f) is the frequency spectrum of the continuous infinite time domain signal S (t); d (f) is the frequency spectrum of the continuous infinite time domain signal d (t); w (f) is the frequency spectrum of a continuous infinite time domain signal w (t);
each term in the formula (5) is developed, the amplitude spectrum sequence of the DTFT output is shown as the following formula,
Figure BDA0002637584400000027
where sinc (·) is a sinc function;
according to FFT principle, continuous infinite length frequency spectrum obtained by DTFT
Figure BDA0002637584400000036
Performing dispersion and truncation to obtain an amplitude spectrum sequence output by the FFT:
Figure BDA0002637584400000031
as can be seen from equation (7), the maximum value of the FFT output magnitude spectrum sequence can be represented by equation (8),
Figure BDA0002637584400000032
in the FFT output amplitude spectrum sequence, one value among the points adjacent to the maximum value point of the FFT output is only smaller than the maximum value, as shown in equation (9),
Figure BDA0002637584400000033
where round (. cndot.) is an integer function, MFFTRepresenting the maximum value, S, of the FFT output amplitude spectrum sequenceubmRepresents and MFFTThe larger of the neighboring points.
The estimated threshold value Y in the second steptThe method comprises the following steps:
noise mixed in the FFT amplitude spectrum belongs to Rayleigh (Rayleigh) distribution, and FFT amplitude output belongs to Rice (Rice) distribution, so that a calculation formula (11) for estimating a threshold value can be deduced according to a formula (10);
Figure BDA0002637584400000034
Figure BDA0002637584400000035
in the formula (f)n(. is a probability density function of the Rayleigh distribution, PfaIs the false alarm rate, Yt is the estimated threshold, and σ is the noise statistical standard deviation.
In the third step, a compensation value of the FFT process for carrier frequency estimation is obtained according to formula (1), further comprising:
a linear discrimination function D related to the down-converted carrier frequency Deltaf is constructed according to the formula (9)isc(. cndot.) represented by formula (12).
Figure BDA0002637584400000041
In the formula, | · | is an absolute value symbol.
If SubmAnd MFFTAdjacent positions in the FFT output amplitude sequence, the FFT estimation compensation formula can be obtained by formula (1),
Figure BDA0002637584400000042
where Δ f' is a compensation value for the carrier frequency estimation in the FFT process.
Optionally, the step four further includes:
if the maximum value S among the adjacent valuesubmAt a maximum M at the position of the FFT output amplitude sequenceFFTTo the left of the position, the estimated carrier frequency estimate
Figure BDA0002637584400000043
Can be expressed by formula (13); if on the right, it can be expressed by equation (14),
Figure BDA0002637584400000044
Figure BDA0002637584400000045
in the formula (f)FFTFor the FFT process to estimate the carrier frequency,
Figure BDA0002637584400000046
a fine estimate of the compensated carrier frequency.
Compared with the prior art, the invention has the beneficial effects that: the fine estimation method comprises the steps of firstly, constructing an identification function linearly related to carrier frequency according to two values (the maximum value and the maximum value in the adjacent values) in an FFT output amplitude spectrum sequence; then, designing an estimation threshold value according to the statistical characteristics of the FFT output sequence, and judging whether the radar carrier is captured or not by judging whether the two values exceed the estimation threshold value or not; and finally, calculating to obtain the compensation quantity of the FFT process to the carrier frequency estimation according to the constructed linear correlation discrimination function, thereby improving the estimation precision of the radar carrier frequency. The invention has simple structure and small calculation amount, can greatly improve the estimation precision of the carrier frequency by adding the carrier frequency fine estimation module after the carrier frequency estimation structure in the original FFT process, and has higher engineering use value.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As used in this application and the appended claims, the terms "a," "an," "the," and/or "the" are not intended to be inclusive in the singular, but rather are intended to be inclusive in the plural unless the context clearly dictates otherwise. In general, the terms "comprises" and "comprising" merely indicate that steps and elements are included which are explicitly identified, that the steps and elements do not form an exclusive list, and that a method or apparatus may include other steps or elements.
The relative arrangement of the components and steps, the numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present application unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
Referring to fig. 1, the present embodiment provides a method for fine estimation of a radar carrier frequency, including the following steps:
step 1: two values (maximum value M) in an FFT (Fast Fourier Transform) output amplitude spectrum sequence S (k) of a radar carrier signal are extractedFFTAnd the maximum value S of the values adjacent theretoubm)；
Specifically, the structure of the radar carrier signal s (t) after frequency reduction is shown in formula (1),
Figure BDA0002637584400000061
where A is the amplitude of the carrier signal, i is the imaginary unit, Δ f is the down-converted carrier frequency,
Figure BDA0002637584400000062
is the carrier initial phase.
After the radar carrier signal s (t) subjected to frequency reduction is dispersed and cut, as shown in formula (2),
Figure BDA0002637584400000063
where (·) is a Dirac Delta function, TsIs the sampling period, rect () is a rectangular window function, TLIs the size of a rectangular window.
The formula (2) is abbreviated as:
Figure BDA0002637584400000064
wherein d (t) is a sampling pulse signal; w (t) is a rectangular window signal;
the spectrum of S (n) is obtained according to the time domain multiplication frequency domain convolution principle as shown in the following formula,
Figure BDA0002637584400000065
in the formula, denotes a convolution symbol.
The amplitude spectrum sequence of the DTFT (Discrete-time Fourier Transform) output by expanding each term in the formula (4) is shown as the following formula,
Figure BDA0002637584400000071
wherein, is a convolution symbol;
Figure BDA0002637584400000075
is the frequency spectrum of a discrete finite long time domain signal s (n); (f) is the frequency spectrum of the continuous infinite time domain signal S (t); d (f) is the frequency spectrum of the continuous infinite time domain signal d (t); w (f) is the frequency spectrum of a continuous infinite time domain signal w (t);
according to FFT principle, continuous infinite length frequency spectrum obtained by DTFT
Figure BDA0002637584400000076
Performing dispersion and truncation to obtain an amplitude spectrum sequence output by the FFT:
Figure BDA0002637584400000072
as can be seen from equation (6), the maximum value of the FFT output magnitude spectrum sequence can be represented by equation (7),
Figure BDA0002637584400000073
in the FFT output magnitude spectrum sequence, one of the points (or left point, or right point) adjacent to the FFT output maximum value point is only smaller than the maximum value, which can be expressed by equation (8),
Figure BDA0002637584400000074
where round (. cndot.) is an integer function, MFFTRepresenting the maximum value, S, of the FFT output amplitude spectrum sequenceubmRepresents and MFFTThe larger of the neighboring points.
Step 2: for the two values (M)FFTAnd Subm) Performing an analysis by comparison with an estimated threshold value YtComparing and judging MFFTAnd SubmWhether a condition that can be used to improve the estimation accuracy of the FFT on the frequency is satisfied or not is used to attenuate the influence of noise on the method;
wherein the threshold value Y is estimatedtThe calculation formula (10) for estimating the threshold value can be derived from the following calculation, in which the noise mixed in the FFT magnitude spectrum belongs to the rayleigh distribution and the FFT magnitude output belongs to the rice distribution, according to the formula (9).
Figure BDA0002637584400000081
Figure BDA0002637584400000082
In the formula (f)n(. is a probability density function of the Rayleigh distribution, PfaIs the false alarm rate, Yt is the estimated threshold, and σ is the noise statistical standard deviation.
Will be obtained by outputting the maximum M in the amplitude spectrum sequence S (k) by FFTFFTAnd the maximum value S of the values adjacent theretoubmRespectively comparing with the estimated threshold value Yt, if both are greater than Yt, then M is indicatedFFTAnd SubmCan be used to improve the estimation accuracy of FFT to frequency, and then proceed the subsequent steps, if M isFFTIf the value is less than or equal to Yt, the carrier wave is not detected, the calculation is finished, and if S is less than or equal to Yt, the calculation is finishedubmIf it is less than or equal to Yt, then S is indicatedubmCan not be used for improving the frequency estimation precision of FFT, and the calculation is finished。
And step 3: if M is as aboveFFTAnd SubmBoth values are greater than the threshold value Yt, then the two values (M) are usedFFTAnd Subm) And calculating to obtain the compensation quantity of the FFT process to the carrier frequency estimation, thereby improving the estimation precision of the radar carrier frequency.
Specifically, a linear discrimination function D associated with the down-converted carrier frequency Δ f can be constructed according to equation (8)isc(. cndot.) represented by formula (9).
Figure BDA0002637584400000083
In the formula, | · | is an absolute value symbol.
If S isubmAnd MFFTAdjacent positions in the FFT output amplitude sequence, the FFT estimation compensation formula can be obtained by formula (11),
Figure BDA0002637584400000091
where Δ f' is a compensation value for the carrier frequency estimation in the FFT process.
And 4, step 4: judgment SubmWhether or not at M at the position of the FFT output amplitude sequenceFFTOn the left-hand side of the position,
if on the left, the estimated carrier frequency estimate
Figure BDA0002637584400000095
Can be expressed by formula (13);
if on the right, it can be expressed by equation (14),
Figure BDA0002637584400000092
Figure BDA0002637584400000093
in the formula (f)FFTFor the FFT process to estimate the carrier frequency,
Figure BDA0002637584400000094
a fine estimate of the compensated carrier frequency.
The invention has simple structure and small calculation amount, can greatly improve the estimation precision of the carrier frequency by adding the carrier frequency fine estimation module after the carrier frequency estimation structure in the original FFT process, and has higher engineering use value.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (5)

1. A method for fine estimation of a radar carrier frequency, comprising:
extracting maximum value M in FFT output amplitude spectrum sequence S (k) of radar carrier signalFFTAnd the maximum value S of the values adjacent theretoubm；
Respectively judging the maximum values MFFTAnd the maximum value S of the values adjacent to itubmAnd an estimated threshold value YtIf both are larger than the estimated threshold value YtIf yes, continuing to estimate, otherwise, ending;
the compensation value of the FFT process for the carrier frequency estimation is obtained according to the formula (1),
Figure FDA0002637584390000011
wherein, Deltaf' is the compensation value of the FFT process to the carrier frequency estimation, Deltaf is the carrier frequency after frequency reduction, TLIs the size of the rectangular window; mFFTOutputting a maximum value in the amplitude spectrum sequence for the FFT; submIs the maximum value among the adjacent values of the maximum values;
and obtaining a carrier frequency fine estimation value of the radar carrier according to the compensation value.
2. The fine estimation method according to claim 1, wherein the maximum value M in the extracted radar carrier signal FFT output magnitude spectrum sequence s (k)FFTAnd the maximum value S of the values adjacent theretoubmFurther comprising:
the structure of the radar carrier signal s (t) after frequency reduction is shown in formula (2),
Figure FDA0002637584390000012
where A is the amplitude of the carrier signal, i is the imaginary unit, Δ f is the down-converted carrier frequency,
Figure FDA0002637584390000014
is the carrier initial phase;
after the radar carrier signal s (t) subjected to frequency reduction is dispersed and cut, as shown in formula (3),
Figure FDA0002637584390000013
where (·) is a Dirac Delta function, TsIs the sampling period, rect () is a rectangular window function, TLIs the size of the rectangular window;
the formula (3) is abbreviated as:
Figure FDA0002637584390000021
wherein d (t) is a sampling pulse signal; w (t) is a rectangular window signal;
according to the principle of time-domain multiplied frequency-domain convolution, s (n) is transformed into the frequency domain by a discrete-time fourier transform, as shown in equation (5):
Figure FDA0002637584390000022
wherein, is a convolution symbol;
Figure FDA0002637584390000023
is the frequency spectrum of a discrete finite long time domain signal s (n); (f) is the frequency spectrum of the continuous infinite time domain signal S (t); d (f) is the frequency spectrum of the continuous infinite time domain signal d (t); w (f) is the frequency spectrum of a continuous infinite time domain signal w (t);
each term in the formula (5) is expanded to obtain, the amplitude spectrum sequence of the DTFT output is shown as the following formula,
Figure FDA0002637584390000024
where sinc (·) is a sinc function;
according to FFT principle, continuous infinite length frequency spectrum obtained by DTFT
Figure FDA0002637584390000026
Performing dispersion and truncation to obtain an amplitude spectrum sequence output by the FFT:
Figure FDA0002637584390000025
as can be seen from equation (7), the maximum value of the FFT output magnitude spectrum sequence can be represented by equation (8),
Figure FDA0002637584390000031
in the FFT output amplitude spectrum sequence, one value among the points adjacent to the maximum value point of the FFT output is only smaller than the maximum value, as shown in equation (9),
Figure FDA0002637584390000035
Figure FDA0002637584390000032
where round (. cndot.) is an integer function, MFFTRepresenting the maximum value, S, of the FFT output amplitude spectrum sequenceubmRepresents and MFFTThe larger of the neighboring points.
3. The fine estimation method according to claim 1, characterized in that the estimation threshold value YtThe method comprises the following steps:
the noise mixed in the FFT amplitude spectrum belongs to Rayleigh distribution, and the FFT amplitude output belongs to Rice distribution, so that a calculation formula (11) for estimating the threshold value can be deduced according to a formula (10);
Figure FDA0002637584390000033
Figure FDA0002637584390000034
in the formula (f)n(. is a probability density function of the Rayleigh distribution, PfaIs the false alarm rate, Yt is the estimated threshold, and σ is the noise statistical standard deviation.
4. The fine estimation method according to claim 2, wherein the deriving the compensation value for the carrier frequency estimation by the FFT process according to equation (1) further comprises:
a linear discrimination function D related to the down-converted carrier frequency Deltaf is constructed according to the formula (9)isc(. cndot.) represented by formula (12).
Figure FDA0002637584390000041
In the formula, | · | is an absolute value symbol.
If SubmAnd MFFTAdjacent positions in the FFT output amplitude sequence, the FFT estimation compensation formula can be obtained by formula (1),
Figure FDA0002637584390000042
where Δ f' is a compensation value for the carrier frequency estimation in the FFT process.
5. The fine estimation method of claim 4, wherein the deriving a radar carrier frequency fine estimate from the compensation value further comprises:
if the maximum value S among the adjacent valuesubmAt a maximum M at the position of the FFT output amplitude sequenceFFTTo the left of the position, the estimated carrier frequency estimate
Figure FDA0002637584390000045
Can be expressed by formula (13); if on the right, it can be expressed by equation (14),
Figure FDA0002637584390000043
Figure FDA0002637584390000044
in the formula (f)FFTFor the FFT process to estimate the carrier frequency,
Figure FDA0002637584390000046
a fine estimate of the compensated carrier frequency.
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