CN105260587B - A kind of method of interference signal in removal coherent signal - Google Patents

A kind of method of interference signal in removal coherent signal Download PDF

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CN105260587B
CN105260587B CN201510563569.3A CN201510563569A CN105260587B CN 105260587 B CN105260587 B CN 105260587B CN 201510563569 A CN201510563569 A CN 201510563569A CN 105260587 B CN105260587 B CN 105260587B
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CN105260587A (en
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王泽�
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Hangzhou Normal University
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Hangzhou Normal University
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Abstract

The invention discloses a kind of method for removing interference signal in coherent signal.It comprises the following steps：Acquisition module collects two groups of data-signals that are mutually related, and is sent to CPU；Collect two groups of data-signals are formed characteristic vector by CPU in three-dimensional data spaceWithCPU calculatesWithCommon groundIndependent sectorAnd independent sectorThe data output that computer will calculate.The present invention can extract the independent sector of each coherent signal, and not interrelated between independent sector, remove the interference information in signal.

Description

A kind of method of interference signal in removal coherent signal
Technical field
The present invention relates to signal processing technology field, more particularly to a kind of method for removing interference signal in coherent signal.
Background technology
To certain correlation often be present between the measurement data of same object different qualities.Medical science or cognitive science or To complicated event, such as cerebral apoplexy or aphasis or atmosphere pollution etc. in the other research practices of person, carry out accurate analysis and Never ipsilateral or direction gathered data are required for during description, is often interfered between these data, you are part of me has in me You, it is difficult to assess the independent information each provided.It is untreated for example two kinds of phenomenons of soil desertification and drought influence each other If them can not be determined to environmental ecology each independent influence and joint effect.Cerebral arterial thrombosis clinical diagnosis and assessment In generally to measure brain blood flow and the free diffusing degree of brain water molecule, but both indexs cerebral apoplexy patient (or its His patient) brain in can influence each other, can not determine that each of which is assessed disease forecasting if untreated and be provided Independent information.For another example in aphasis assessment, measure voice mistake and be difficult to accomplish not done by other side mutually during phonetic system mistake Disturb.
Traditional way be these correlated variables pairwise orthogonals are mapped then take remainder as it is respective it is independent into Point, this extracting method is that ensure that residual components (output) and (the input change of other original variable of each variable in fact Amount) between be orthogonal and independent, between these residual components still correlation and it is related between correlation and initial data Property it is essentially equal simply symbol become it is anti-.This conventional art can not obtain the common component of correlated variables simultaneously.Thus need A new technology is developed to be used for extracting coherent signal each independent composition and common composition.By two or more correlations Variable, which resolves into, to be overlapped the technologies of component and mutually orthogonal residual components and can be referred to as the independent element extraction of coherent signal Take.
The content of the invention
The purpose of the present invention is to overcome existing method to map coherent signal pairwise orthogonal, then takes remainder as each From independent sector, it only ensure that between the independent sector of each signal and other primary signal it is independent, and these independences Still be mutually related technical problem between part, there is provided a kind of method for removing interference signal in coherent signal, it can The independent sector of each coherent signal is extracted, and it is not interrelated between independent sector, remove the interference information in signal.
The method of interference signal, comprises the following steps in a kind of removal coherent signal of the present invention：
S1：Acquisition module collects two groups of data-signals that are mutually related, and is sent to CPU；
S2：CPU is handled the data-signal received, by the every group of data-signal collected three A characteristic vector is formed in dimension data space, the characteristic vector that two groups of data-signals are formed is respectivelyWith
S3：Assuming that in the presence of three independent componentsMeet equation below：
⊥ represents vertical relation, thenWithCommon ground beIndependent sector be Independence Part is
S4：Assuming that in three-dimensional data space,Starting point be A, terminal B, Starting point A, terminal For C,Starting point be A, terminal D,Starting point be D, terminal B,'s Starting point is D, terminal C,Point G on straight line BC be present so that straight line AG perpendicular to straight line BC, i.e. AG ⊥ BC, by In AD ⊥ DB and AD ⊥ DC, so straight line AD is perpendicular to plane DBC, because straight line BC is on plane DBC, so AD ⊥ BC, knot AG ⊥ BC are closed, straight line BC are obtained perpendicular to plane ADG, so DG ⊥ BC；
S5：Point P on straight line AG be present so that straight line DP is perpendicular to straight line AG, i.e. DP ⊥ AG, because straight line BC is perpendicular to flat Face ADG, then straight line BC is perpendicular to straight line DP, i.e. DP ⊥ BC, so straight line DP is perpendicular to plane ABC；
S6：Following relationship is obtained by the relation between above-mentioned vector：
So as to be calculated：
| | | | 2 norms of vector are represented, | | represent The length of line segment；
S7：Following relationship is also obtained by the relation between above-mentioned vector：
I.e.
| AP |=| AG |-| PG |；
Calculate | AP |, | DP |, | CG | value, so that it is determined that uniquelyAnd
S8：Calculate withWithVertical unit vectorSo as to calculateAccording toCalculate
S9：The common ground that CPU will calculateIndependent sectorAnd independent sectorOutput.
In the technical program, two groups of coherent signals are exactly resolved into weight by the method for removing interference signal in coherent signal Part and mutually orthogonal independent sector are closed, independent sector is extracted, these independent sectors do not associate between each other, Signal is not interfered with independent sector.Coherent signal, which decomposes to be equal on vector space, finds three vectors And meet following relation： Perpendicular toWithPerpendicular to Relation can is mutually perpendicular to more than and finds out these three vectors not in same high dimensional plane, their intersection point does not also exist WithOn the high dimensional plane of construction.This method be exactly based on fromWithLooked for outside the plane formedWithBe total to Same partMethod solve coherent signal independent element extraction problem.Using vector algebra geometric knowledge,It can divide Solution is located at into oneWithComponent and a component perpendicular to the plane in plane, this method exactly first obtain this two Then they are added and draw common ground by the length of individual component with directionValue, there is common groundValue can calculates Independent sectorAnd independent sectorValue.CPU is by common groundIndependent sectorAnd independent sectorIt is output to display screen and shows or be output to next equipment and is analyzed.
Preferably, when acquisition module collect it is more than two be mutually related data-signal when, acquisition module will gather Data-signal be sent to CPU, CPU is from two groups or more number that is mutually related collected It is believed that number in arbitrarily extract two groups of data-signals, perform step S2 to S8 and calculate common ground and two independent sectors, connect And one group of data-signal is arbitrarily extracted from untreated data-signal, the data-signal and the common ground calculated are made For two coherent signals, the independent sector that step S2 to S8 calculates new common ground and the data-signal is performed, is so followed Common ground and independent sector between newest common ground and one group of untreated data-signal that ring extraction obtains every time, Finished until all data-signals are all processed, then CPU is by all independent sectors and the common portion finally obtained Divide output.
For two or more coherent signal, it can appoint and take two signals, seek the common ground again after obtaining common ground and appoint The new common ground and independent sector of one remaining untreated signal of meaning, so circulation are until each signal processed one Untill secondary.The common ground finally calculated is exactly the common ground of all signals, and CPU is by all independent sectors Display screen is output to the common ground finally obtained shows or be output to next equipment and analyzed.
Preferably, work as, will by pre-processing when invalidWithIt is normalized, i.e.,So that their norm is 1, so thatSet up.
Preferably, calculated in the step S8 withWithVertical unit vectorMethod include following step Suddenly：Take any one random vectorUsing Gram-Schmidt orthogonalization procedures respectively by it and the orthogonal normalizing of x1 and x2 difference Change, comprise the following steps：
Represent andDirection identical unit vector,Represent andDirection identical unit vector,Expression is askedWithInner product,Expression is askedWithInner product.
Preferably, obtained independent sector and common ground are subjected to low-pass filtering treatment.Suppress the independence extracted High-frequency Interference composition in part and common ground, makes data smoother.
The present invention substantial effect be：The independent sector of each coherent signal can be extracted, and between independent sector It is not interrelated, remove the interference information in signal.
Brief description of the drawings
Fig. 1 is polar plot of the coherent signal of the present invention in three-dimensional data space；
Fig. 2 is data collecting module collected to two groups of signals that coefficient correlation is 0.566；
Fig. 3 is to handle the common ground that two groups of signals obtain in Fig. 2 using prior artIndependent sectorAnd independence Part
Fig. 4 is to handle the common ground that two groups of signals obtain in Fig. 2 using the method for the present inventionIndependent sectorWith Independent sector
Fig. 5 is the signal to being obtained after each signal progress low-pass filtering treatment in Fig. 4；
Fig. 6 is data collecting module collected to two groups of signals that coefficient correlation is 0.5331；
Fig. 7 is to handle the common ground that two groups of signals obtain in Fig. 6 using prior artIndependent sectorAnd independence Part
Fig. 8 is to handle the common ground that two groups of signals obtain in Fig. 6 using the method for the present inventionIndependent sectorWith Independent sector
Embodiment
Below by embodiment, and with reference to accompanying drawing, technical scheme is described in further detail.
Embodiment：The method of interference signal in a kind of removal coherent signal of the present embodiment, as shown in figure 1, including following Step：
S1：Acquisition module collects two groups of data-signals that are mutually related, and every group of data-signal includes three sampled values, and It is sent to CPU；
S2：CPU is handled the data-signal received, by the every group of data-signal collected three A characteristic vector is formed in dimension data space, the characteristic vector that two groups of data-signals are formed is respectivelyWith
S3：Assuming that in the presence of three independent componentsMeet equation below：
⊥ represents vertical relation, thenWithCommon ground beIndependent sector be Independence Part is
S4：Assuming that in three-dimensional data space,Starting point be A, terminal B, Starting point A, terminal For C,Starting point be A, terminal D,Starting point be D, terminal B,Starting point be D, terminal C,Point G on straight line BC be present so that straight line AG is perpendicular to straight Line BC, i.e. AG ⊥ BC, due to AD ⊥ DB and AD ⊥ DC, so straight line AD is perpendicular to plane DBC, because straight line BC is in plane DBC On, so AD ⊥ BC, with reference to AG ⊥ BC, obtain straight line BC perpendicular to plane ADG, so DG ⊥ BC；
S5：Point P on straight line AG be present so that straight line DP is perpendicular to straight line AG, i.e. DP ⊥ AG, because straight line BC is perpendicular to flat Face ADG, then straight line BC is perpendicular to straight line DP, i.e. DP ⊥ BC, so straight line DP is perpendicular to plane ABC；
S6：Following relationship is obtained by the relation between above-mentioned vector：
So as to be calculated：
| | | | 2 norms of vector are represented, | | represent The length of line segment；
S7：Following relationship is also obtained by the relation between above-mentioned vector：
I.e.
| AP |=| AG |-| PG |；
Calculate | AP |, | DP |, | CG | value, so that it is determined that uniquelyAnd
S8：Calculate withWithVertical unit vectorSo as to calculateAccording toCalculate
S9：The common ground that CPU will calculateIndependent sectorAnd independent sectorOutput.
When, will by pre-processing when invalidWithReturned One change is handled, i.e.,So that their norm is 1, so thatSet up.
Calculated in step S8 withWithVertical unit vectorMethod comprise the following steps：Take any one Random vectorIt and x1 and x2 are distinguished into orthonomalization, including following step respectively using Gram-Schmidt orthogonalization procedures Suddenly：
Represent andDirection identical unit vector,Represent andDirection identical unit vector,Expression is askedWithInner product,Expression is askedWithInner product.
Remove coherent signal in interference signal method be exactly by every group of relevant data signals in three-dimensional data space shape Into a characteristic vector (vector algebra method), two groups of relevant data signals are resolved into intersection and mutually orthogonal only Vertical part, independent sector is extracted, these independent sectors are not associated between each other, and letter is not interfered with independent sector Number.Coherent signal, which decomposes to be equal on vector space, finds three vectorsAnd meet following relation：Perpendicular toWithPerpendicular toIt is mutually perpendicular to close more than It is that can finds out these three vectors not in same high dimensional plane, their intersection point does not also existWithThe higher-dimension of construction is put down On face.This method be exactly based on fromWithLooked for outside the plane formedWithCommon groundMethod come Solves coherent signal independent element extraction problem.Using vector algebra geometric knowledge,One can be resolved into be located atWithComponent and a component perpendicular to the plane in plane, this method exactly first obtain length and the side of the two components It is added to and then by them and draws common groundValue, there is common groundValue can calculates independent sectorAnd independence PartValue.CPU is by common groundIndependent sectorAnd independent sectorIt is output to display screen display Show or be output to next equipment and analyzed.
In the present embodiment, data collecting module collected to coefficient correlation is 0.566 two groups of signals, as shown in Figure 2.
The common ground obtained using prior artIndependent sectorAnd independent sectorAs shown in figure 3, they Between coefficient correlation, as shown in Table 1：
Table one
Two groups of direct correlations of the respective independent sector of data of original that prior art is drawn are former two groups of data dependences Negative, directly prove that this method based on linear regression can not extract separate independent sector at all.While we It can be seen that there is also very strong correlation between common ground and independent sector.
The common ground obtained using this methodIndependent sectorAnd independent sectorAs shown in figure 4, they it Between coefficient correlation, as shown in Table 2：
Table two
The common ground of this method extraction is can be seen that from table twoIndependent sectorAnd independent sectorBetween do not have There is correlation.
As can be seen from Figure 4 the result that this method obtains has the composition of the higher-order of oscillation along X direction, and this is due to pair In the case of more than 3 data collection points, the result of complete orthogonal decomposition may have several groups.In actual applications, we Have in the result that may want to decompose a certain component be along for transverse axis it is smoother, therefore, by obtained independent sector and Common ground carries out low-pass filtering treatment, suppresses the High-frequency Interference composition in the independent sector and common ground extracted, makes number According to common ground that is smoother, obtainingIndependent sectorAnd independent sectorAs shown in figure 5, the correlation between them Coefficient, as shown in Table 3：
Table three
When acquisition module collect it is more than two be mutually related data-signal when, acquisition module is by the data-signal of collection Be sent to CPU, CPU from collect two groups or more be mutually related in data-signal and appoint Meaning extracts two groups of data-signals, performs step S2 to S8 and calculates common ground and two independent sectors, then from untreated Data-signal in arbitrarily extract one group of data-signal, it is related as two using the data-signal to the common ground calculated Signal, the independent sector that step S2 to S8 calculates new common ground and the data-signal is performed, so circulation extraction is each Common ground and independent sector between obtained newest common ground and one group of untreated data-signal, until all numbers It is believed that number all processed finish, then CPU exports all independent sectors and the common ground finally obtained.
For two or more coherent signal, it can appoint and take two signals, seek the common ground again after obtaining common ground and appoint The new common ground and independent sector of one remaining untreated signal of meaning, so circulation are until each signal processed one Untill secondary.The common ground finally calculated is exactly the common ground of all signals, and CPU is by all independent sectors Display screen is output to the common ground finally obtained shows or be output to next equipment and analyzed.
In the present embodiment, data collecting module collected to coefficient correlation is 0.5331 two groups of signals, as shown in fig. 6, Fig. 6 In,It is the language testing data extracted from 50 people, abscissa represents number, and ordinate represents to repeat to read aloud not recognizing The ratio that Chinese character is misread for a period of time；It is the language testing data extracted from 50 people, abscissa represents number, indulges and sits Mark represents that playback distinguishes the error rate that described word occurs；The relative coefficient of both different pieces of informations is 0.5331.
The common ground obtained using prior artIndependent sectorAnd independent sectorAs shown in fig. 7, they Between coefficient correlation, as shown in Table 4,
Table four
Two groups of direct correlations of the respective independent sector of data of original that prior art is drawn are former two groups of data dependences Negative, directly prove that this method based on linear regression can not extract separate independent sector at all.While we It can be seen that there is also very strong correlation between common ground and independent sector.
The common ground obtained using this methodIndependent sectorAnd independent sectorAs shown in figure 8, they it Between coefficient correlation, as shown in Table 5,
Table five
It can be seen that from table five, common groundIndependent sectorAnd independent sectorCoefficient correlation between any two All it is 0, so the common ground of this method extractionIndependent sectorAnd independent sectorBetween there is no correlation.
Be for assess voice extraction and function of pronunciation,It is to assess the speech recognition under the help of no vision Function.Common groundCharacterize the function that words and voice combine together of brain.Independent sectorCharacterize and seek Look for and express the function of the contact, independent sectorWhat is represented is the function of establishing this semantic connection procedure of voice.

Claims (4)

  1. A kind of 1. method for removing interference signal in coherent signal, it is characterised in that comprise the following steps：
    S1：Acquisition module collects two groups of data-signals that are mutually related, and is sent to CPU；
    S2：CPU is handled the data-signal received, by the every group of data-signal collected in three dimensions According to one characteristic vector of formation in space, the characteristic vector that two groups of data-signals are formed is respectivelyWith
    S3：Assuming that in the presence of three independent componentsMeet equation below：
    <mrow> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <mover> <mrow> <mi>u</mi> <mi>c</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>+</mo> <mover> <mrow> <mi>u</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>;</mo> </mrow>
    <mrow> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <mover> <mrow> <mi>u</mi> <mi>c</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>+</mo> <mover> <mrow> <mi>u</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>;</mo> </mrow>
    <mrow> <mover> <mrow> <mi>u</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;perp;</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>;</mo> </mrow>
    <mrow> <mover> <mrow> <mi>u</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;perp;</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>;</mo> </mrow>
    <mrow> <mover> <mrow> <mi>u</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;perp;</mo> <mover> <mrow> <mi>u</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>;</mo> </mrow>
    ⊥ represents vertical relation, thenWithCommon ground beIndependent sector be Independent sector be
    S4：Assuming that in three-dimensional data space,Starting point be A, terminal B, Starting point A, terminal C, Starting point be A, terminal D, Starting point be D, terminal B, Rise Point is D, terminal C,Point G on straight line BC be present so that straight line AG is perpendicular to straight line BC, i.e. AG ⊥ BC, due to AD ⊥ DB and AD ⊥ DC, so straight line AD is perpendicular to plane DBC, because straight line BC is on plane DBC, so AD ⊥ BC, with reference to AG ⊥ BC, straight line BC are obtained perpendicular to plane ADG, so DG ⊥ BC；
    S5：Point P on straight line AG be present so that straight line DP is perpendicular to straight line AG, i.e. DP ⊥ AG, because straight line BC is perpendicular to plane ADG, then straight line BC is perpendicular to straight line DP, i.e. DP ⊥ BC, so straight line DP is perpendicular to plane ABC；
    S6：Following relationship is obtained by the relation between above-mentioned straight line：
    <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>=</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>-</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>;</mo> </mrow>
    <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mi>c</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>=</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>;</mo> </mrow>
    <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mi>c</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>=</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>;</mo> </mrow>
    So as to be calculated：
    <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>-</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>)</mo> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <mo>;</mo> </mrow>
    <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>-</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>)</mo> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <mo>;</mo> </mrow>
    <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mi>c</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>-</mo> <mover> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>)</mo> <mo>/</mo> <mn>2</mn> </mrow> </msqrt> <mo>;</mo> </mrow>
    | | | | 2 norms of vector are represented, | | represent line segment Length；
    S7：Following relationship is also obtained by the relation between above-mentioned straight line：
    I.e.
    <mrow> <mo>|</mo> <mi>A</mi> <mi>G</mi> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mi>c</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mi>D</mi> <mi>G</mi> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </msqrt> <mo>;</mo> </mrow>
    <mrow> <mfrac> <mrow> <mo>|</mo> <mi>P</mi> <mi>G</mi> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mi>D</mi> <mi>G</mi> <mo>|</mo> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>D</mi> <mi>G</mi> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mi>A</mi> <mi>G</mi> <mo>|</mo> </mrow> </mfrac> <mo>;</mo> </mrow>
    | AP |=| AG |-| PG |；
    <mrow> <mo>|</mo> <mi>D</mi> <mi>P</mi> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mo>|</mo> <mi>D</mi> <mi>G</mi> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>|</mo> <mi>P</mi> <mi>G</mi> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </msqrt> <mo>;</mo> </mrow>
    <mrow> <mo>|</mo> <mi>C</mi> <mi>G</mi> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>u</mi> <mn>2</mn> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mo>|</mo> <mi>D</mi> <mi>G</mi> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </msqrt> <mo>;</mo> </mrow>
    Calculate | AP |, | DP |, | CG | value, so that it is determined that uniquelyAnd
    S8：Calculate withWithVertical unit vectorSo as to calculateAccording toCalculate
    Calculate withWithVertical unit vectorMethod comprise the following steps：Take any one random vectorProfit It and x1 and x2 are distinguished into orthonomalization respectively with Gram-Schmidt orthogonalization procedures, comprised the following steps：
    <mrow> <mover> <mrow> <mi>e</mi> <mi>o</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>=</mo> <mfrac> <mover> <mrow> <mi>r</mi> <mi>o</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mrow> <mi>r</mi> <mi>o</mi> </mrow> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow>
    Represent andDirection identical unit vector,Represent andDirection identical unit vector,Table Show and askWithInner product,Expression is askedWithInner product；
    S9：The common ground that CPU will calculateIndependent sectorAnd independent sectorOutput.
  2. A kind of 2. method for removing interference signal in coherent signal according to claim 1, it is characterised in that：When collection mould Block collect it is more than two be mutually related data-signal when, the data-signal of collection is sent to central processing list by acquisition module Member, CPU from collect two groups or more be mutually related in data-signal and arbitrarily extract two groups of data Signal, perform step S2 to S8 and calculate common ground and two independent sectors, it is then any from untreated data-signal One group of data-signal is extracted, using the data-signal and the common ground calculated as two coherent signals, performs step S2 The independent sector of new common ground and the data-signal is calculated to S8, so circulation extraction obtains newest common every time Common ground and independent sector between part and one group of untreated data-signal, until all data-signals all have been processed Finish, then CPU exports all independent sectors and the common ground finally obtained.
  3. A kind of 3. method for removing interference signal in coherent signal according to claim 1, it is characterised in that：When, will by pre-processing when invalidWithIt is normalized, i.e.,So that their norm is 1, so that Set up.
  4. 4. the method for interference signal in a kind of removal coherent signal according to claim 1 or 2 or 3, it is characterised in that：Will Obtained independent sector and common ground carries out low-pass filtering treatment.
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