CN107462909A - A kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase - Google Patents
A kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase Download PDFInfo
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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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
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Abstract
The present invention relates to a kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase, belongs to Beidou navigation field of signal processing.The present invention subtracts pseudorange method first with phase and calculates construction cycle slip signal, is tentatively detected；Then matrix dimension is set according to singular value curve, Hankel matrixes is constructed to cycle slip signal, cycle slip signal is subjected to SVD decomposition；Finally calculate the coefficient correlation of original cycle slip signal and its SVD component signal and the coefficient correlation of SVD component signals and single-frequency carrier phase signal not plus during cycle slip, sensitive factor and its Difference Spectrum are built again, sensitive SVD components are selected accordingly, because sensitive factor upsets singular value order therefore the positioning factor is set, by positioning mutation singular value corresponding to the sensitive component signal of factor extraction and carrying out signal reconstruction；Mutated site in reconstruction signal determines that the epoch of cycle slip occurs.The present invention can detect less cycle slip signal, and also the epoch that cycle slip signal occur more accurately can be positioned.
Description
Technical field
The present invention relates to a kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase, belong to Beidou navigation signal processing technology
Field.
Background technology
Triones navigation system (BDS) is global positioning satellite and the communication system of Chinese independent development capability and energy independent operating
System.At present, the system is successfully used widely in many fields, and provides positioning, navigation and the time service service of correlation.
But during application, because carrier phase is disturbed by various factors, make the precision of navigator fix not accurate enough, and it is all
It is to improve the committed step of satellite navigation positioning precision to jump detection.
Cycle slip signal is regarded as the exceptional value in signal, the method that many abnormal signals detect is applied to Detection of Cycle-slip
In, as empirical mode decomposition (Empirical Mode Decomposition, EMD), local average decompose (Local Mean
Decomposition, LMD), SVD (Singular Value Decomposition, SVD) etc., when detecting cycle slip, these are calculated
Method has respective limitation, and the cycle slip signal that EMD can not be larger to the sampling interval detects, and LMD visits to non-stationary signal
Accuracy during survey is relatively low, and SVD has positive effect in the higher cycle slip signal of detection signal to noise ratio.These methods substantially can be brighter
Aobvious detects cycle slip signal, but certain defect also be present on the problem of quick and precisely epoch of cycle slip occurs for positioning.Therefore will
A kind of new method is proposed to solve problem above.
The content of the invention
The invention provides a kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase, for solving to occurring compared with Xiao Zhou
The epoch for jumping signal positions the problem of not accurate enough.
The technical scheme is that：A kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase, subtracts first with phase
Pseudorange method calculates construction cycle slip signal, is tentatively detected；Then matrix dimension is set according to singular value curve, to cycle slip signal
Hankel matrixes are constructed, cycle slip signal is subjected to SVD decomposition；Finally calculate the phase of original cycle slip signal and its SVD component signal
The coefficient correlation of relation number and SVD component signals and single-frequency carrier phase signal not plus during cycle slip, then build sensitive factor and its
Difference Spectrum, sensitive SVD components are selected accordingly, because sensitive factor upsets singular value order therefore the positioning factor is set, by fixed
Location factor extracts mutation singular value corresponding to sensitive component signal and carries out signal reconstruction；Mutation position in reconstruction signal
Put the epoch for determining that cycle slip occurs.
The Cycle Slips Detection of the Big Dipper single-frequency carrier phase comprises the following steps that：
Step1, first with carrier phase observational equation subtract pseudorange observation equation, obtain formula (1)：
Formula (1) is asked poor between epoch, i.e., phase subtracts the counted cycle slip valuation of pseudorange method
In formula,For carrier phase observation data；R is Pseudo-range Observations；ρ is that satellite arrives the distance between receiver；dIφ,
dIRThe respectively ionosphere delay of carrier phase and pseudorange；λ is carrier wavelength；N is the integer ambiguity in carrier phase；
dmφ,dmRThe respectively multipath effect of carrier phase and pseudorange；εφ,εRRespectively carrier phase observation data and Pseudo-range Observations
Measurement error；T is epoch, and cycle slip valuation Δ N (t-1) is cycle slip signal；
Step2, using Hankel matrix creation analysis matrixes, by cycle slip signal x=(x1,x2,···xN) form matrix
A, wherein signal x are discrete digital signal, and the Hankel matrixes of construction are as follows：
Wherein, 1 ＜ n ＜ N, make m=N-n+1, then A ∈ Rm×n；
The decomposition of cycle slip signal is realized using SVD decomposition methods, formula (3) is rewritten into column vector uiAnd viThe form of expression：
A=σ1u1v1 T+σ2u2v2 T+···+σquqvq T (4)
(4) in formula, ui∈Rm×1, vi∈Rn×1, i=1,2, q, make Ai=σiuivi T, then Ai∈Rm×n, original matrix A
It is to be represented by q sub- matrix linear superpositions, and each AiOne-component signal can be obtained；
Step3, the coefficient correlation for calculating original cycle slip signal and its SVD component signal and SVD component signals be not with adding week
The coefficient correlation of single-frequency carrier phase signal during jump, sensitive component signal choosing is carried out according to the similarity of the two coefficient correlations
Select, comprise the following steps that：
Step3.1, calculate original cycle slip signal x(t)Coefficient correlation μ between SVD component signalsn(n=1,
2,···,N)；
The coefficient correlation η of single-frequency carrier phase signal when Step3.2, calculating SVD component signals be not with adding cycle slipn(n=1,
2,···,N)；
Two coefficient correlation μ are tried to achieve in Step3.3, joint step Step3.1 and Step3.2n、ηnSubtract each other to obtain sensitive phase
Close coefficient gamman=μn-ηn, n=1,2, N；
Step3.4, calculate original cycle slip signal x(t)Sensitive factorγ is sequence
{γn, n=1,2, N；
Step3.5, by SVD component signals according to the descending arrangement of sensitive factor order, select the SVD components letter of sensitivity
Number, obtain cycle slip component signal sequence { yn, n=1,2 ..., N, σ1'≥σ'2,…,σ'n,…,σ'N-1≥σ'N；
Step3.6, make poor, construction sensitive factor Difference Spectrum with two adjacent sensitive factors：Make dn=σ 'n-σ'n+1, i=
1,2, q-1, then diForm vectorial B=[d1 d2 … dq-1], therefore the position of unusual value mutation is in max (dn) place,
Sequence number n according to corresponding to the sensitiveness of each component adaptively finds out maximum difference, corresponding to preceding n SVD component signals
Be cycle slip sensitivity component signal；
Step3.7, due to sensitive factor sequence by from big to small order arrangement be disturbed the order of original singular value,
So set the positioning factor, by positioning the singular value before factor extraction corresponding to n sensitive SVD component signals；
Step4, according to the construction features of Hankel matrixes obtain component signalIt is A shown in formula (5)iSquare
The transposition of first row vector of battle array and last column vector is end to end to be formed, wherein Pi,1∈R1×n, Hi,n∈R(m-1)×1；
It is superimposed to obtain reconstruction signal, i.e. formula (6) according to the n obtained in the step Step3.7 sensitive component signals
X=P1+P2+···+Pn (6)
Mutated site in reconstruction signal determines that the epoch of cycle slip occurs.
The beneficial effects of the invention are as follows：
With reference to traditional SVD to small Detection of Cycle-slip clear advantage, based on the Big Dipper single frequency carrier phase for considering sensitive factor SVD
The Cycle Slips Detection of position, SVD decomposition is carried out to cycle slip signal, pass through the sensitive cycle slip point of sensitive factor and positioning predictor selection
The corresponding mutation singular value of amount carries out signal reconstruction, can more accurately orient the epoch that small cycle slip occurs.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the original detection limit that cycle slip is not added with the present invention；
Fig. 3 is the singular value curve in the present invention；
Fig. 4 is the original cycle slip signal at single epoch after addition cycle slip and six component signals after SVD is decomposed
Figure；
Fig. 5 is the sensitive factor and difference spectrogram added at single epoch after cycle slip；
Fig. 6 is the positioning factor graph added at single epoch after cycle slip；
Fig. 7 is the component reconstruct signal graph added at single epoch after cycle slip；
Fig. 8 is the original cycle slip signal at two epoch after addition cycle slip and six component signals after SVD is decomposed
Figure；
Fig. 9 is the sensitive factor and difference spectrogram added at two epoch after cycle slip；
Figure 10 is the positioning factor graph added at two epoch after cycle slip；
Figure 11 is the component reconstruct signal graph added at two epoch after cycle slip.
Embodiment
Embodiment 1：Shown in Fig. 1-3, a kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase, subtract puppet first with phase
Construction cycle slip signal is calculated away from method, is tentatively detected；Then matrix dimension is set according to singular value curve, to cycle slip signal structure
Hankel matrixes are made, cycle slip signal is subjected to SVD decomposition；It is related to its SVD component signal finally to calculate original cycle slip signal
The coefficient correlation of single-frequency carrier phase signal when coefficient and SVD component signals be not with adding cycle slip, then build sensitive factor and its difference
Open score, sensitive SVD components are selected accordingly, because sensitive factor upsets singular value order therefore the positioning factor is set, pass through positioning
The factor extracts mutation singular value corresponding to sensitive component signal and carries out signal reconstruction；Mutated site in reconstruction signal
It is determined that the epoch of cycle slip occurs.
Further, the Cycle Slips Detection of the Big Dipper single-frequency carrier phase comprises the following steps that：
Step1, first with carrier phase observational equation subtract pseudorange observation equation, obtain formula (1)：
Formula (1) is asked poor between epoch, i.e., phase subtracts the counted cycle slip valuation of pseudorange method
In formula,For carrier phase observation data；R is Pseudo-range Observations；ρ is that satellite arrives the distance between receiver；dIφ,
dIRThe respectively ionosphere delay of carrier phase and pseudorange；λ is carrier wavelength；N is the integer ambiguity in carrier phase；
dmφ,dmRThe respectively multipath effect of carrier phase and pseudorange；εφ,εRRespectively carrier phase observation data and Pseudo-range Observations
Measurement error；T is epoch, and cycle slip valuation Δ N (t-1) is cycle slip signal；
Step2, using Hankel matrix creation analysis matrixes, by cycle slip signal x=(x1,x2,···xN) form matrix
A, wherein signal x are discrete digital signal, and the Hankel matrixes of construction are as follows：
Wherein, 1 ＜ n ＜ N, make m=N-n+1, then A ∈ Rm×n；
The decomposition of cycle slip signal is realized using SVD decomposition methods, formula (3) is rewritten into column vector uiAnd viThe form of expression：
A=σ1u1v1 T+σ2u2v2 T+···+σquqvq T (4)
(4) in formula, ui∈Rm×1, vi∈Rn×1, i=1,2, q, make Ai=σiuivi T, then Ai∈Rm×n, original matrix A
It is to be represented by q sub- matrix linear superpositions, and each AiOne-component signal can be obtained；
Step3, the coefficient correlation for calculating original cycle slip signal and its SVD component signal and SVD component signals be not with adding week
The coefficient correlation of single-frequency carrier phase signal during jump, sensitive component signal choosing is carried out according to the similarity of the two coefficient correlations
Select, comprise the following steps that：
Step3.1, calculate original cycle slip signal x(t)Coefficient correlation μ between SVD component signalsn(n=1,
2,···,N)；
The coefficient correlation η of single-frequency carrier phase signal when Step3.2, calculating SVD component signals be not with adding cycle slipn(n=1,
2,···,N)；
Two coefficient correlation μ are tried to achieve in Step3.3, joint step Step3.1 and Step3.2n、ηnSubtract each other to obtain sensitive phase
Close coefficient gamman=μn-ηn, n=1,2, N；
Step3.4, calculate original cycle slip signal x(t)Sensitive factorγ is sequence
{γn, n=1,2, N；
Step3.5, by SVD component signals according to the descending arrangement of sensitive factor order, select the SVD components letter of sensitivity
Number, obtain cycle slip component signal sequence { yn, n=1,2 ..., N, σ1'≥σ'2,…,σ'n,…,σ'N-1≥σ'N；
Step3.6, make poor, construction sensitive factor Difference Spectrum with two adjacent sensitive factors：Make dn=σ 'n-σ'n+1, i=
1,2, q-1, then diForm vectorial B=[d1 d2 … dq-1], therefore the position of unusual value mutation is in max (dn) place,
Sequence number n according to corresponding to the sensitiveness of each component adaptively finds out maximum difference, corresponding to preceding n SVD component signals
Be cycle slip sensitivity component signal；
Step3.7, due to sensitive factor sequence by from big to small order arrangement be disturbed the order of original singular value,
So set the positioning factor, by positioning the singular value before factor extraction corresponding to n sensitive SVD component signals；
Step4, according to the construction features of Hankel matrixes obtain component signalIt is A shown in formula (5)iSquare
The transposition of first row vector of battle array and last column vector is end to end to be formed, wherein Pi,1∈R1×n, Hi,n∈R(m-1)×1；
It is superimposed to obtain reconstruction signal, i.e. formula (6) according to the n obtained in the step Step3.7 sensitive component signals
X=P1+P2+···+Pn (6)
Mutated site in reconstruction signal determines that the epoch of cycle slip occurs.
Embodiment 2：A kind of Cycle Slips Detection of Big Dipper single-frequency carrier phase, subtract pseudorange method meter first with phase
Construction cycle slip signal is calculated, is tentatively detected；Then matrix dimension is set according to singular value curve, cycle slip signal is constructed
Hankel matrixes, cycle slip signal is subjected to SVD decomposition；Finally calculate the phase relation of original cycle slip signal and its SVD component signal
The coefficient correlation of single-frequency carrier phase signal when number and SVD component signals be not with adding cycle slip, then build sensitive factor and its difference
Spectrum, select sensitive SVD components accordingly, due to sensitive factor by singular value order upset thus sets position the factor, by position because
Son extracts mutation singular value corresponding to sensitive component signal and carries out signal reconstruction；Mutated site in reconstruction signal is true
Surely the epoch of cycle slip occurs.
Step 1, the frequency test case 502036091t.13O of double star five to be navigated from Shanghai Sinan is opened with UltraEdit,
Choose the 1200 groups of carrier phase observation datas and Pseudo-range Observations of wherein Big Dipper B3 frequency ranges, sampling interval of the frequency range is 1s, ripple
A length of 0.236m；
Step 2, the carrier phase of selected frequency range is observed into data pseudorange observation data duplication into Excel forms first,
Pseudo-range Observations are subtracted with carrier phase observation data, the difference tried to achieve is asked poor between epoch, obtains original cycle slip signal, due to
Calculated in Excel forms, import data to and the file of .xls forms is converted into .mat forms, structure when in MATLAB
The original cycle slips detection amount (cycle slip signal) made is as shown in Figure 2；It can be seen that to fetch the ripple of different amplitudes in be present in fig. 2
Dynamic, these fluctuations are due to caused by random error, and random error destroys its time series, cause detection limit to occur by a small margin
Mutation.
Step 3, cycle slip signal is used to Hankel matrix creation analysis matrix progress singular value decomposition, according to singular value point
Cloth curve, carry out the dimension of effective selection matrix, as shown in figure 3, singular value after m=6 declines rapidly as can be seen from Figure
Or close to zero, illustrate that follow-up singular value component is meaningless, so the present invention is constructed cycle slips detection amount by m=6
Hankel matrixes；
Step 4, component signal of the calculating after SVD is decomposed are with the coefficient correlation of original cycle slip signal and after SVD is decomposed
Component signal and a certain normal signal (not plus during cycle slip single-frequency carrier phase signal) coefficient correlation, structure structure it is sensitive because
Son and its Difference Spectrum, select more sensitive SVD components accordingly, and can eliminate unobvious using sensitive factor obtains cycle slip component signal,
Select obvious component signal to carry out signal reconstruction, more accurately detect that the epoch of cycle slip occurs；
Step 5, due to sensitive factor by singular value order upset thus set positioning the factor, by position the factor extract it is former
Singular value is mutated corresponding to individual more sensitive component signal and carries out signal reconstruction；
It is artificial in 1200 groups of carrier phase data in order to verify that this method can effectively detect the small cycle slip of 1~7 week
The middle cycle slip for adding different all numbers；
In order to verify the validity of the sensitive factor in this method, the cycle slip of different all numbers will be added at multiple epoch,
To verify that sensitive factor selects the validity of sensitive component；
Epoch adds 2 weeks cycle slips at 220 as can be seen from Figure 4, and six component signals as shown in Figure 4 are resolved into through SVD,
First three component signal has obvious cycle slip signal as can be seen from Figure 4, but not can determine that point corresponding to which singular value
It is most obvious to measure signal cycle slip, therefore can be seen that unusual value mutation is most obvious at sensitive factor sequence 1 according to sensitive factor Fig. 5, so
The position that corresponding positioning factor graph 6 finds out former sequence corresponding to positioning factor sequence 1 place afterwards is 2, then adds at an epoch
When entering cycle slip, the singular value that reconstruction signal only have selected corresponding to second component signal is reconstructed, reconstruction signal such as Fig. 7 institutes
Showing, the reconstruction signal can not verify the sensitivity of sensitive factor selection mutation singular value because positioning singular value catastrophe point is very few,
Cause reconstruction signal meaningless, but small cycle slip can be detected；
Add the cycle slip of 3 weeks and 7 weeks simultaneously in 230 epoch and 880 epoch as can be seen from Figure 8, resolved into through SVD such as Fig. 8
Six shown component signals, as can be seen from Figure 8 preceding four component signals have obvious cycle slip signal, therefore according to sensitive factor
Fig. 9 can select preceding four sensitive components, and then the position of former sequence is according to corresponding to positioning factor graph 10 finds out sensitive component
1st, 2,3,4, finally carry out signal reconstruction with this four singular values.Signal reconstruction figure is as shown in figure 11.
Above in conjunction with accompanying drawing to the present invention embodiment be explained in detail, but the present invention be not limited to it is above-mentioned
Embodiment, can also be before present inventive concept not be departed from those of ordinary skill in the art's possessed knowledge
Put that various changes can be made.
Claims (2)
- A kind of 1. Cycle Slips Detection of Big Dipper single-frequency carrier phase, it is characterised in that：Subtract pseudorange method first with phase to calculate Cycle slip signal is constructed, is tentatively detected；Then matrix dimension is set according to singular value curve, Hankel is constructed to cycle slip signal Matrix, cycle slip signal is subjected to SVD decomposition；Finally calculate the coefficient correlation and SVD of original cycle slip signal and its SVD component signal The coefficient correlation of single-frequency carrier phase signal when component signal is not with adding cycle slip, then sensitive factor and its Difference Spectrum are built, accordingly Sensitive SVD components are selected, because sensitive factor upsets singular value order therefore the positioning factor is set, it is quick by positioning factor extraction Singular value is mutated corresponding to sense component signal and carries out signal reconstruction；Mutated site in reconstruction signal determines that week occurs The epoch of jump.
- 2. the Cycle Slips Detection of Big Dipper single-frequency carrier phase according to claim 1, it is characterised in that：The Big Dipper list The Cycle Slips Detection of frequency carrier phase comprises the following steps that：Step1, first with carrier phase observational equation subtract pseudorange observation equation, obtain formula (1)：<mrow> <mi>N</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>&lambda;</mi> </mfrac> <mo>&lsqb;</mo> <mi>&lambda;</mi> <mi>&phi;</mi> <mo>-</mo> <mi>R</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>dI</mi> <mi>&phi;</mi> </msub> <mo>-</mo> <msub> <mi>dI</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>dm</mi> <mi>&phi;</mi> </msub> <mo>-</mo> <msub> <mi>dm</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>&epsiv;</mi> <mi>&phi;</mi> </msub> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>Formula (1) is asked poor between epoch, i.e., phase subtracts the counted cycle slip valuation of pseudorange method<mrow> <mtable> <mtr> <mtd> <mrow> <mi>&Delta;</mi> <mi>N</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mo>&lsqb;</mo> <mi>R</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>/</mo> <mi>&lambda;</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>In formula,For carrier phase observation data；R is Pseudo-range Observations；ρ is that satellite arrives the distance between receiver；dIφ,dIRPoint Not Wei carrier phase and pseudorange ionosphere delay；λ is carrier wavelength；N is the integer ambiguity in carrier phase；dmφ,dmR The respectively multipath effect of carrier phase and pseudorange；εφ,εRThe respectively measurement of carrier phase observation data and Pseudo-range Observations Error；T is epoch, and cycle slip valuation Δ N (t-1) is cycle slip signal；Step2, using Hankel matrix creation analysis matrixes, by cycle slip signal x=(x1,x2,···xN) matrix A is formed, its Middle signal x is discrete digital signal, and the Hankel matrixes of construction are as follows：Wherein, 1 ＜ n ＜ N, make m=N-n+1, then A ∈ Rm×n；The decomposition of cycle slip signal is realized using SVD decomposition methods, formula (3) is rewritten into column vector uiAnd viThe form of expression：A=σ1u1v1 T+σ2u2v2 T+···+σquqvq T (4)(4) in formula, ui∈Rm×1, vi∈Rn×1, i=1,2, q, make Ai=σiuivi T, then Ai∈Rm×n, original matrix A be by Q sub- matrix linear superpositions represent, and each AiOne-component signal can be obtained；When Step3, the coefficient correlation for calculating original cycle slip signal and its SVD component signal and SVD component signals be not with adding cycle slip The coefficient correlation of single-frequency carrier phase signal, sensitive component signal selection is carried out according to the similarity of the two coefficient correlations, Comprise the following steps that：Step3.1, calculate original cycle slip signal x(t)Coefficient correlation μ between SVD component signalsn(n=1,2, N)；The coefficient correlation η of single-frequency carrier phase signal when Step3.2, calculating SVD component signals be not with adding cycle slipn(n=1, 2,···,N)；Two coefficient correlation μ are tried to achieve in Step3.3, joint step Step3.1 and Step3.2n、ηnSubtract each other to obtain sensitive phase relation Number γn=μn-ηn, n=1,2, N；Step3.4, calculate original cycle slip signal x(t)Sensitive factorγ is sequence { γn, n= 1,2,···,N；Step3.5, by SVD component signals according to the descending arrangement of sensitive factor order, select the SVD component signals of sensitivity, Obtain cycle slip component signal sequence { yn, n=1,2 ..., N, σ1'≥σ'2,…,σ'n,…,σ'N-1≥σ'N；Step3.6, make poor, construction sensitive factor Difference Spectrum with two adjacent sensitive factors：Make dn=σ 'n-σ'n+1, i=1, 2, q-1, then diForm vectorial B=[d1 d2 … dq-1], therefore the position of unusual value mutation is in max (dn) place, root The sequence number n corresponding to maximum difference is adaptively found out according to the sensitiveness of each component, corresponding to preceding n SVD component signals As cycle slip sensitivity component signal；Step3.7, due to sensitive factor sequence by from big to small order arrangement be disturbed the order of original singular value, so The positioning factor is set, by positioning the singular value before factor extraction corresponding to n sensitive SVD component signals；Step4, according to the construction features of Hankel matrixes obtain component signalIt is A shown in formula (5)iMatrix first The transposition of individual row vector and last column vector is end to end to be formed, wherein Pi,1∈R1×n, Hi,n∈R(m-1)×1；<mrow> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>It is superimposed to obtain reconstruction signal, i.e. formula (6) according to the n obtained in the step Step3.7 sensitive component signalsX=P1+P2+···+Pn (6)Mutated site in reconstruction signal determines that the epoch of cycle slip occurs.
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