CN107147392B - TIADC mismatch error calibration method based on adaptive filtering and Taylor series - Google Patents

TIADC mismatch error calibration method based on adaptive filtering and Taylor series Download PDF

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CN107147392B
CN107147392B CN201710311363.0A CN201710311363A CN107147392B CN 107147392 B CN107147392 B CN 107147392B CN 201710311363 A CN201710311363 A CN 201710311363A CN 107147392 B CN107147392 B CN 107147392B
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error
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weighting factor
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白旭
胡辉
李万军
刘澜涛
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North China Institute of Aerospace Engineering
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    • H03—ELECTRONIC CIRCUITRY
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Abstract

The invention discloses a TIADC mismatch error calibration method based on adaptive filtering and Taylor series, which comprises the steps of channel signal acquisition, estimation of bias error of sampling data of a channel 1, correction of bias error of the channel 1, fractional delay filtering, estimation of gain error and time phase error of the channel 1 by using an adaptive filter, and correction of gain error and time phase error of the channel 1. The invention has the characteristics of less sampling points, less calculated amount and the like, and is suitable for portable acquisition equipment such as a handheld oscilloscope and the like.

Description

TIADC mismatch error calibration method based on adaptive filtering and Taylor series
Technical Field
The invention relates to a TIADC mismatch error calibration method, in particular to a TIADC mismatch error calibration method based on adaptive filtering and Taylor series, and belongs to the field of instruments.
Background
Parallel sampling systems (TIADC) can produce offset errors, gain errors, and time phase errors due to non-ideal characteristics of the devices. The two-channel TIADC model is shown in FIG. 1 below, with a sampling rate fsWith a sampling period of Ts. Parameter g0,o0,Δt0Gain error, bias error and time phase error of channel 0, respectively, parameter g1,o1,Δt1Respectively, gain error, bias error, and time phase error for channel 1. In actual operation, channel 0 is used as a reference channel, and gain error, bias error and time phase error g of channel 1 are required1,o1,Δt1Estimate and correct to finally make g1＝g0,o1＝o0And Δ t1＝Δt0Thereby completing the mismatch error correction for the entire system.
As shown in fig. 1, the standard signal source simultaneously inputs channel 0 and channel 1, and with channel 0 as a reference, the data of the two channels after discretization by the ADC is represented as follows:
Figure GDA0002725653530000011
wherein X0(k) Sample data, X, represented as channel 01(k) Represented as sampled data for channel 1. The relationship between data for channel 1 and data for channel 0 can be expressed as
X1(k)＝(1+g1)X0(k+0.5-Δt1/2)+o1 (2)
The correction techniques for the three major errors in the TIADC focus on two large directions, namely the non-blind estimation and correction algorithm and the blind estimation and correction algorithm for mismatch errors. The non-blind estimation and correction algorithm of mismatch errors needs to inject excitation signals into the acquisition system periodically to obtain error parameters of the system, and the non-blind estimation and correction algorithm influences the real-time performance of the operation of the acquisition system. The blind estimation and correction algorithm does not need to inject excitation signals into the acquisition system regularly, and the estimation and correction of system error parameters are completed while the acquisition system measures the measured signals. The existing blind estimation and correction algorithm mostly adopts a closed loop mode to estimate parameters in the estimation process of three main errors. Although the blind estimation and correction algorithm does not need to inject excitation signals into the acquisition system regularly, the sampling point number required by the existing blind estimation and correction algorithm is very large. The number of sampling points needed in the one-time estimation and correction process is mostly more than 10000, and the calculated amount is complex, so that higher requirements are generated on the calculation and storage of an acquisition system, and the method is not suitable for being used in portable instruments such as a handheld oscilloscope. In fact, for a TIADC system with a good hardware design, three mismatch errors of the system do not change drastically in a short time, and system parameters obtained by calculation after one correction of a non-blind estimation correction algorithm can still bring improvement of a signal-to-noise ratio to the whole TIADC system within a certain time.
Disclosure of Invention
The invention aims to provide a TIADC mismatch error calibration method based on adaptive filtering and Taylor series.
In order to solve the technical problems, the invention adopts the technical scheme that:
a TIADC mismatch error calibration method based on adaptive filtering and Taylor series comprises the following steps:
step 1: channel signal acquisition: a standard signal source X (t) sin (w)int) simultaneously inputting a channel 0 and a channel 1; angular frequency w of standard signal sourceinSatisfies the following conditions:
Figure GDA0002725653530000021
Tsfor the sample interval time, channel 0 is the reference channel, and channel 0 and channel 1 are separated by the sample interval time TsInterleaved sampling, channel 1 samples data X1(k) Comprises the following steps:
X1(k)＝(1+g1)X0(k+0.5-Δt1/2)+o1 (2)
wherein X0(k) Is the sampled data of channel 0, g1,o1,Δt1Respectively is the gain error, the offset error and the time phase error of the channel 1, and k is the number of discrete sampling points of the channel 1, the channel 0 and the fractional delay filter;
step 2: estimating offset error of sampled data for channel 1
Figure GDA0002725653530000022
Figure GDA0002725653530000023
Wherein E is an averaging operation;
and step 3: correction of offset error for channel 1:
Figure GDA0002725653530000024
in the formula
Figure GDA0002725653530000025
The data is the sampling data of the channel 1 after the offset error correction;
and 4, step 4: fractional delay filtering: the offset error corrected sampling data of the channel 1
Figure GDA0002725653530000038
Filtering by an input fractional delay filter, wherein the system transfer function of the fractional delay filter is as follows:
Figure GDA0002725653530000031
wherein h isid(k) K is the number of discrete sampling points of the channel 1, the channel 0 and the fractional delay filter, and M is the length of the filter;
the first order Taylor series expansion of the sampled data of the channel 1 after the fractional delay filtering processing is
Figure GDA0002725653530000032
Figure GDA0002725653530000033
In the formula
Figure GDA0002725653530000034
Is a first order Taylor series expansion, X 'of the sampled data of channel 1 after fractional delay filtering processing'0(k) Sampled data X for channel 00(k) The calculation method of the derivative of (2) is:
X'0(k)＝[-X0(k+2)+8X0(k+1)-8X0(k-1)+X0(k-2)]/[(48×π×f0)/fs] (7)
in the formula f0Is the frequency of the input signal to be measured, fsIs the sampling rate of the TIADC system;
and 5: estimation of the gain error of channel 1 with an adaptive filterg1And the time phase error Δ t1。
The adaptive filter includes a weighting coefficient w0Adjusting unit, weighting factor w1Adjusting part, first to second accumulators, sampling data X of channel 00(k) Input weighting factor w0Adjustment component, derivative X 'of sampled data of channel 0'0(k) Input weighting factor w1Adjusting means, weighting factor w0Adjusting unit, weighting factor w1The output of the adjusting component is sent to a first accumulator, and the output of the first accumulator and the first-order Taylor series expansion of the sampling data of the channel 1 after the fractional delay filtering processing
Figure GDA0002725653530000035
Subtracted in a second accumulator, the output of which is used to control the weighting factor w0Adjusting unit, weighting factor w1An adjusting component for adjusting the weighting coefficient w according to a preset adjusting step length0And a weighting factor w1Until the mean square error of the output of the second accumulator is not reduced;
gain error g1The estimated values of (c) are:
Figure GDA0002725653530000036
time phase error Δ t1The estimated values of (c) are:
Figure GDA0002725653530000037
step 6: correction of gain error and time phase error for channel 1:
Figure GDA0002725653530000041
in the formula (I), the compound is shown in the specification,
Figure GDA0002725653530000042
for the corrected sample data of channel 1,
Figure GDA0002725653530000043
for the system transfer function of the time phase error correction filter,
Figure GDA0002725653530000044
in order to obtain the final calibration data,
Figure GDA0002725653530000045
gain error g for channel 11Is determined by the estimated value of (c),
Figure GDA0002725653530000046
is a time phase error Δ t1An estimate of (d).
The TIADC mismatch error calibration method based on the adaptive filtering and the Taylor series comprises 1 reference channel and more than 1 calibration channel, and each calibration channel adopts the same calibration method as the channel 1.
The technical effect obtained by adopting the technical scheme is as follows:
1. the invention has the characteristics of less sampling points, less calculated amount and the like, and is suitable for portable acquisition equipment such as a handheld oscilloscope and the like.
2. The invention is equally applicable to multi-channel TIADC systems.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a TIADC system model;
FIG. 2 is a flow chart of the present invention;
fig. 3 is a schematic block diagram of the adaptive filter of the present invention.
Detailed Description
Example 1:
as shown in fig. 2, a TIADC mismatch error calibration method based on adaptive filtering and taylor series includes the following steps:
step 1: channel signal acquisition: a standard signal source X (t) sin (w)int) simultaneously inputting a channel 0 and a channel 1; angular frequency w of standard signal sourceinSatisfies the following conditions:
Figure GDA0002725653530000047
Tsfor the sample interval time, channel 0 is the reference channel, and channel 0 and channel 1 are separated by the sample interval time TsInterleaved sampling, channel 1 samples data X1(k) Comprises the following steps:
X1(k)＝(1+g1)X0(k+0.5-Δt1/2)+o1 (2)
wherein X0(k) Is the sampled data of channel 0, g1,o1,Δt1Respectively is the gain error, the offset error and the time phase error of the channel 1, and k is the number of discrete sampling points of the channel 1, the channel 0 and the fractional delay filter;
step 2: estimating offset error of sampled data for channel 1
Figure GDA0002725653530000051
Figure GDA0002725653530000052
Wherein E is an averaging operation;
and step 3: correction of offset error for channel 1:
Figure GDA0002725653530000053
in the formula
Figure GDA0002725653530000054
The data is the sampling data of the channel 1 after the offset error correction;
and 4, step 4: fractional delay filtering: the offset error corrected sampling data of the channel 1
Figure GDA0002725653530000055
Filtering by an input fractional delay filter, wherein the system transfer function of the fractional delay filter is as follows:
Figure GDA0002725653530000056
wherein h isid(k) K is the number of discrete sampling points of the channel 1, the channel 0 and the fractional delay filter, and M is the length of the filter;
ignoring ripples in the passband of the fractional delay filter, the sampled data of the channel 1 after being processed by the fractional delay filtering is:
Figure GDA0002725653530000057
due to Δ t1Per 2 itself is a term much smaller than 1, and for a hardware well-designed TIADC system, Δ t is usually the case1The/2 is less than or equal to 0.05. So that the Taylor series expansion is performed on the formula (6) and terms with more than two orders are ignored to obtain
The first order Taylor series expansion of the sampled data of the channel 1 after the fractional delay filtering processing is
Figure GDA00027256535300000511
Figure GDA0002725653530000059
In the formula
Figure GDA00027256535300000510
Is a first order Taylor series expansion, X 'of the sampled data of channel 1 after fractional delay filtering processing'0(k) Sampled data X for channel 00(k) The derivative of (2) is calculated by using the sampling data of the channel 0, and the calculation method is as follows:
X'0(k)＝[-X0(k+2)+8X0(k+1)-8X0(k-1)+X0(k-2)]/[(48×π×f0)/fs] (8)
in the formula f0Is the frequency of the input signal to be measured, fsIs the sampling rate of the TIADC system;
and 5: estimation of the bias error g for channel 1 with an adaptive filter1And the time phase error Δ t1。
As shown in FIG. 3, the adaptive filter includes a weighting coefficient w0Adjusting unit, weighting factor w1Adjusting part, first to second accumulators, sampling data X of channel 00(k) Input weighting factor w0Adjustment component, derivative X 'of sampled data of channel 0'0(k) Input weighting factor w1Adjusting means, weighting factor w0Adjusting unit, weighting factor w1The output of the adjusting component is sent to a first accumulator, and the output of the first accumulator and the first-order Taylor series expansion of the sampling data of the channel 1 after the fractional delay filtering processing
Figure GDA0002725653530000061
Subtracted in a second accumulator, the output of which is used to control the weighting factor w0Adjusting unit, weighting factor w1An adjusting component for adjusting the weighting coefficient w according to a preset adjusting step length0And a weighting factor w1Until the mean square error of the output of the second accumulator is not reduced;
gain error g1The estimated values of (c) are:
Figure GDA0002725653530000062
time phase error Δ t1The estimated values of (c) are:
Figure GDA0002725653530000063
step 6: correcting the placement error and time phase error of channel 1:
Figure GDA0002725653530000064
in the formula (I), the compound is shown in the specification,
Figure GDA0002725653530000065
for the corrected sample data of channel 1,
Figure GDA0002725653530000066
for the system transfer function of the time phase error correction filter,
Figure GDA0002725653530000067
in order to obtain the final calibration data,
Figure GDA0002725653530000068
gain error g for channel 11Is determined by the estimated value of (c),
Figure GDA0002725653530000069
is a time phase error Δ t1An estimate of (d).
Example 2: the difference from the embodiment 1 is that the channel 2 is also included, and the channel 2 adopts the same calibration method as the channel 1 in the embodiment 1.

Claims (3)

1. A TIADC mismatch error calibration method based on adaptive filtering and Taylor series is characterized in that: the method comprises the following steps:
step 1: channel signal acquisition: a standard signal source X (t) sin (w)int) simultaneously inputting a channel 0 and a channel 1; angular frequency w of standard signal sourceinSatisfies the following conditions:
Figure FDA0002725653520000011
Tsfor the sample interval time, channel 0 is the reference channel, and channel 0 and channel 1 are separated by the sample interval time TsInterleaved sampling, communicationTrack 1 sample data X1(k) Comprises the following steps:
X1(k)＝(1+g1)X0(k+0.5-Δt1/2)+o1 (2)
wherein X0(k) Is the sampled data of channel 0, g1,o1,Δt1Respectively is the gain error, the offset error and the time phase error of the channel 1, and k is the number of discrete sampling points of the channel 1, the channel 0 and the fractional delay filter;
step 2: estimating offset error of sampled data for channel 1
Figure FDA0002725653520000012
Figure FDA0002725653520000013
Wherein E is an averaging operation;
and step 3: correction of offset error for channel 1:
Figure FDA0002725653520000014
in the formula
Figure FDA0002725653520000015
The data is the sampling data of the channel 1 after the offset error correction;
and 4, step 4: fractional delay filtering: the offset error corrected sampling data of the channel 1
Figure FDA0002725653520000016
Filtering by an input fractional delay filter, wherein the system transfer function of the fractional delay filter is as follows:
Figure FDA0002725653520000017
wherein h isid(k) K is the number of discrete sampling points of the channel 1, the channel 0 and the fractional delay filter, and M is the length of the filter;
the first order Taylor series expansion of the sampled data of the channel 1 after the fractional delay filtering processing is
Figure FDA0002725653520000018
Figure FDA0002725653520000019
In the formula
Figure FDA0002725653520000021
Is a first order Taylor series expansion, X 'of the sampled data of channel 1 after fractional delay filtering processing'0(k) Sampled data X for channel 00(k) The calculation method of the derivative of (2) is:
X'0(k)＝[-X0(k+2)+8X0(k+1)-8X0(k-1)+X0(k-2)]/[(48×π×f0)/fs] (7)
in the formula f0Is the frequency of the input signal to be measured, fsIs the sampling rate of the TIADC system;
and 5: estimation of the gain error g of channel 1 with an adaptive filter1And the time phase error Δ t1；
Step 6: correction of gain error and time phase error for channel 1:
Figure FDA0002725653520000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002725653520000023
for the corrected sample data of channel 1,
Figure FDA0002725653520000024
for the system transfer function of the time phase error correction filter,
Figure FDA0002725653520000025
in order to obtain the final calibration data,
Figure FDA0002725653520000026
gain error g for channel 11Is determined by the estimated value of (c),
Figure FDA0002725653520000027
is a time phase error Δ t1An estimate of (d).
2. The adaptive filtering and taylor series based TIADC mismatch error calibration method of claim 1, wherein:
the adaptive filter in step 5 comprises a weighting coefficient w0Adjusting unit, weighting factor w1Adjusting part, first to second accumulators, sampling data X of channel 00(k) Input weighting factor w0Adjustment component, derivative X 'of sampled data of channel 0'0(k) Input weighting factor w1Adjusting means, weighting factor w0Adjusting unit, weighting factor w1The output of the adjusting component is sent to a first accumulator, and the output of the first accumulator and the first-order Taylor series expansion of the sampling data of the channel 1 after the fractional delay filtering processing
Figure FDA0002725653520000028
Subtracted in a second accumulator, the output of which is used to control the weighting factor w0Adjusting unit, weighting factor w1An adjusting component for adjusting the weighting coefficient w according to a preset adjusting step length0And a weighting factor w1Until the mean square error of the output of the second accumulator is not reduced;
gain error g1The estimated values of (c) are:
Figure FDA0002725653520000029
time phase error Δ t1The estimated values of (c) are:
Figure FDA00027256535200000210
3. the adaptive filtering and taylor series based TIADC mismatch error calibration method of claim 1, wherein: the method comprises 1 reference channel and more than 1 calibration channel, and each calibration channel adopts the same calibration method as the channel 1.
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