CN105137459A - Beidou single frequency cycle slip detection method - Google Patents

Abstract

The invention relates to a Beidou single frequency cycle slip detection method, which belongs to the field of Beidou navigation and positioning data processing. A pseudo range observation value is firstly used for subtracting a carrier phase observation value, the difference value is then differenced between epochs, and a cycle slip detection amount is obtained; then, a Hankel matrix is used for building an attractor track matrix for the cycle slip detection amount, singular value decomposition (SVD) is carried out, and a limited number of effective singular values capable of reflecting abrupt information can be obtained; and finally, SVD inverse operation is used for reconstructing a component signal for each effective singular value, and after the component signals are overlapped, the cycle slip is detected according to the position of the maximum value point in the overlapped signals. Amplitude changes only need to be features, whether cycle slip happens is judged only by a cycle slip detection amount amplitude through SVD processing, the problem that the traditional method is hard to detect small cycle slip can be solved, and small cycle slip with 1 to 5 cycles in the Beidou carrier phase observation value can be effectively detected.

Description

A kind of Big Dipper single-frequency Cycle Slips Detection

Technical field

The present invention relates to a kind of Big Dipper single-frequency Cycle Slips Detection, belong to Beidou navigation locator data process field.

Background technology

The comprehensive networking of triones navigation system is built up, and will provide location, navigation, time service and short message communication service for Global Subscriber.Because it has great importance and using value widely, China just greatly develops, improve correlation technique, as problems such as error analysis and processing, cycle-slip detection and repair, Carrier Phase Ambiguity Resolution.Wherein, Detection of Cycle-slip is high precision BDS Data processing very important link, and in carrier phase data, 10 weeks and above cycle slip are easy to be found, and are less than the cycle slip of 10 weeks, and particularly the little cycle slip of 1 ~ 5 week is not easily found.Polynomial fitting method, Higher Difference Method, Ionosphere Residual Error method and wavelet analysis method etc. are the conventional methods of Detection of Cycle-slip.Wherein, polynomial fitting method needs phase change rate, and some receiver is inapplicable owing to not possessing this kind of measured value, and can not detect the little cycle slip of 1 ~ 5 week; It is also unaccommodated that Higher Difference Method is used for the method for little Detection of Cycle-slip because high order difference between carrier phase epoch by repeatedly doing difference, be also exaggerated noise signal while amplifying cycle slip; Although Ionosphere Residual Error method has the feature to little cycle slip sensitivity, under being only suitable for the environment that ionosphere conversion is slow, Multi-Path Effects is little; Although wavelet analysis method can to Xiao Zhou jump into row detection, wavelet function choose also ununified theoretical standard, in Detection of Cycle-slip, there is significant limitation.Therefore, be necessary to propose a kind of technological means, to solve the problem in fact.

Summary of the invention

The invention provides a kind of Big Dipper single-frequency Cycle Slips Detection, for the problem that the little cycle slip of solution is not easily found.

Technical scheme of the present invention is: a kind of Big Dipper single-frequency Cycle Slips Detection, first uses Pseudo-range Observations ρ _tdeduct carrier phase observation data and its difference is asked between epoch again poor, obtain cycle slip inspected number D (t); Then utilize Hankel matrix to build attractor track matrix A to cycle slip inspected number D (t), and svd process is carried out to A, obtain effective singular value that limited can reflect abrupt information; Finally use SVD inverse operation respectively to each effective singular value reconstruct component signal, according to the position sensing cycle slip of maximum point in superposed signal after being superposed by each component signal.

The concrete steps of described method are as follows:

Step1, by Pseudo-range Observations ρ _tdeduct carrier phase observation data φ _t, and its difference is asked poor in epoch between t again, can cycle slip inspected number D (t) be obtained;

$D\left(t\right)=\frac{({\mathrm{\ρ}}_{t+1}-{\mathrm{\λ\φ}}_{t+1})-({\mathrm{\ρ}}_t-{\mathrm{\λ\φ}}_t)}{\mathrm{\λ}}---\left(1\right)$

In formula, λ is the carrier wavelength of a certain frequency range of the Big Dipper; T is the moment obtaining Pseudo-range Observations and carrier phase observation data, also claims epoch; T+1 is next epoch of t;

Step2, Hankel matrix is utilized to build attractor track matrix A to cycle slip inspected number D (t) that formula (1) obtains;

$A=\left[\begin{array}{cccc}{d}_1& d_2& ...& d_n\\ d_2& d_3& ...& d_{n+1}\\ ...& ...& ...& ...\\ d_m& d_{m+1}& ...& d_N\end{array}\right]---\left(2\right)$

In formula, N is number epoch of observation of the carrier phase chosen, and n is the columns of matrix A and meets 1<n<N; The line number m=N-n+1 of order matrix A, then A ∈ R ^{m × n}; d ₁be cycle slip inspected number corresponding to the 1st epoch, in like manner, d _nbe cycle slip inspected number corresponding to the n-th epoch, d _nbe cycle slip inspected number corresponding to N number of epoch;

Step3, according to formula (3), SVD process is carried out to attractor track matrix A, obtain limited effective singular value;

A＝USV ^T(3)

In formula, U=[u ₁, u ₂..., u _m] ∈ R ^{m × m}, V=[v ₁, v ₂..., v _n] ∈ R ^{n × n}be called the left and right singular matrix of attractor track matrix A, and U and V is orthogonal matrix; u _mfor m column vector of matrix U; v _nfor the n-component column vector of matrix V; S=[diag (σ ₁, σ ₂... σ _q), O] or its transposition, depend on the magnitude relationship of m and n, S ∈ R ^{m × n}, O is null matrix, and q depends on the little person in m and n, and q is the number of effective singular value, and singular value has such relation: σ ₁>=σ ₂>=...>=σ _q> 0, q=min (m, n);

Step4, utilization SVD inverse operation are respectively to effective singular value σ ₁, σ ₂... σ _qreconstruct component signal P ₁, P ₂... P _q:

P _i＝u _iσ _iv _i ^T，i＝1,2,…,q(4)

In formula, u _ifor i-th column vector of matrix U; v _ifor i-th column vector of matrix V;

Step5, according to formula (5) by each component signal P ₁, P ₂... P _qafter superposing, the position sensing cycle slip according to maximum point in superposed signal X:

X＝P ₁+P ₂+...+P _q(5)。

Cycle slip is regarded as the singular point in carrier phase observation data, after SVD process, slackened the impact of stochastic error and measurement noises, determine according to the position of abrupt information in superposed signal the epoch that cycle slip occurs, thus complete the detection of cycle slip.

Principle of work of the present invention is: if there is not cycle slip in Big Dipper carrier phase observation data, then cycle slip inspected number D (t) shows as a level and smooth straight line, owing to being subject to the impact of stochastic error and measurement noises in actual observation, cycle slip inspected number D (t) shows as random error characteristics; When there is cycle slip in carrier phase observation data, the random character of cycle slip inspected number suffers to destroy and just there will be sudden change, and cycle slip value is larger, suddenlys change more obvious.Then for the little cycle slip of 1 ~ 5 week, human eye not easily observes directly this sudden change, and svd (SingularValueDecomposition, SVD) has good de-noising function, can extract abrupt information.Cycle slip is regarded as the singular point in carrier phase observation data, after SVD slackens the impact of stochastic error and measurement noises, in the signal after reconstructing component signal superposition according to SVD, the epoch that cycle slip occurs is determined in the position of abrupt information, thus completes the detection of cycle slip.

Step based on the Big Dipper single-frequency Cycle Slips Detection of SVD is as follows:

1, Hankel matrix is utilized to the process that cycle slip inspected number D (t) builds attractor track matrix A to be:

First determine line number and the columns of Hankel matrix, namely determine the size of m and n.SVD decomposes quantity of information that the component that obtains comprises directly by corresponding singular value σ _qsize determine, σ _qthe quantity of information of less this respective components of expression is less.Therefore, singular value contribution rate ζ can be defined _qcomprehensively weigh the quantity of information of respective components:

${\mathrm{\&zeta;}}_q=\frac{{\mathrm{\&sigma;}}_q}{{\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_2+...+{\mathrm{\&sigma;}}_q}---\left(6\right)$

The size of m and n can be determined according to (6) formula.By choosing several m, from singular value curve map, if quickly fall to zero or close to zero from a certain moment singular value, so known from then on j component starts, follow-up component does not have significance, and this just can determine matrix column number n=j, is determined the line number of matrix A by m=N-n+1.

2, after Hankel matrix has built, theoretical according to svd, matrix A is represented, containing u by formula below _iand v _iand σ _i:

$A=\underset{i=1}{\overset{q}{\&Sigma;}}{u}_i{\mathrm{\&sigma;}}_i{v_i}^T=\underset{i=1}{\overset{q}{\&Sigma;}}{A}_i---\left(7\right)$

U in formula _i∈ R ^{m × 1}, v _i∈ R ^{n × 1}.Matrix A equals q sub-matrix A after SVD decomposes _isum.

Under Hankel matrix, choose an effectively singular value and carry out SVD inverse transformation and try to achieve component signal, the linear superposition of each component signal consisted of inverse transformation just obtains signal originally.

The invention has the beneficial effects as follows: only need be changed to feature with amplitude, can judge whether there occurs cycle slip from the cycle slip inspected number amplitude through SVD process, solve the problem that classic method is difficult to detect little cycle slip, effectively can detect the little cycle slip of in Big Dipper carrier phase observation data 1 ~ 5 week.

Accompanying drawing explanation

Fig. 1 is the inventive method process flow diagram;

Fig. 2 is singular value curve map (n=4) in the present invention;

Fig. 3 opens test case figure in the present invention;

Fig. 4 is cycle slip inspection spirogram when not adding cycle slip in the present invention;

Fig. 5 is the attractor track matrix A to cycle slip inspected number structure in the present invention;

Fig. 6 is four component signal P in the present invention ₁, P ₂, P ₃, P ₄figure;

Fig. 7 is that cycle slip inspected number after adding 1 week cycle slip in the present invention is through SVD process figure;

Fig. 8 is that cycle slip inspected number after adding 2 weeks cycle slips in the present invention is through SVD process figure;

Fig. 9 is that cycle slip inspected number after adding 3 weeks cycle slips in the present invention is through SVD process figure;

Figure 10 is that cycle slip inspected number after adding 4 weeks cycle slips in the present invention is through SVD process figure;

Figure 11 is that cycle slip inspected number after adding 5 weeks cycle slips in the present invention is through SVD process figure.

Embodiment

Embodiment 1: as shown in figs. 1-11, a kind of Big Dipper single-frequency Cycle Slips Detection, first uses Pseudo-range Observations ρ _tdeduct carrier phase observation data and its difference is asked between epoch again poor, obtain cycle slip inspected number D (t); Then utilize Hankel matrix to build attractor track matrix A to cycle slip inspected number D (t), and svd process is carried out to A, obtain effective singular value that limited can reflect abrupt information; Finally use SVD inverse operation respectively to each effective singular value reconstruct component signal, according to the position sensing cycle slip of maximum point in superposed signal after being superposed by each component signal.

The concrete steps of described method are as follows:

Step1, by Pseudo-range Observations ρ _tdeduct carrier phase observation data φ _t, and its difference is asked poor in epoch between t again, can cycle slip inspected number D (t) be obtained;

$D\left(t\right)=\frac{({\mathrm{\&rho;}}_{t+1}-{\mathrm{\&lambda;\&phi;}}_{t+1})-({\mathrm{\&rho;}}_t-{\mathrm{\&lambda;\&phi;}}_t)}{\mathrm{\&lambda;}}---\left(1\right)$

In formula, λ is the carrier wavelength of a certain frequency range of the Big Dipper; T is the moment obtaining Pseudo-range Observations and carrier phase observation data, also claims epoch; T+1 is next epoch of t;

Step2, Hankel matrix is utilized to build attractor track matrix A to cycle slip inspected number D (t) that formula (1) obtains;

$A=\left[\begin{array}{cccc}{d}_1& d_2& ...& d_n\\ d_2& d_3& ...& d_{n+1}\\ ...& ...& ...& ...\\ d_m& d_{m+1}& ...& d_N\end{array}\right]---\left(2\right)$

In formula, N is number epoch of observation of the carrier phase chosen, and n is the columns of matrix A and meets 1<n<N; The line number m=N-n+1 of order matrix A, then A ∈ R ^{m × n}; d ₁be cycle slip inspected number corresponding to the 1st epoch, in like manner, d _nbe cycle slip inspected number corresponding to the n-th epoch, d _nbe cycle slip inspected number corresponding to N number of epoch;

Step3, according to formula (3), SVD process is carried out to attractor track matrix A, obtain limited effective singular value;

A＝USV ^T(3)

In formula, U=[u ₁, u ₂..., u _m] ∈ R ^{m × m}, V=[v ₁, v ₂..., v _n] ∈ R ^{n × n}be called the left and right singular matrix of attractor track matrix A, and U and V is orthogonal matrix; u _mfor m column vector of matrix U; v _nfor the n-component column vector of matrix V; S=[diag (σ ₁, σ ₂... σ _q), O] or its transposition, depend on the magnitude relationship of m and n, S ∈ R ^{m × n}, O is null matrix, and q depends on the little person in m and n, and q is the number of effective singular value, and singular value has such relation: σ ₁>=σ ₂>=...>=σ _q> 0, q=min (m, n);

Step4, utilization SVD inverse operation are respectively to effective singular value σ ₁, σ ₂... σ _qreconstruct component signal P ₁, P ₂... P _q:

P _i＝u _iσ _iv _i ^T，i＝1,2,…,q(4)

In formula, u _ifor i-th column vector of matrix U; v _ifor i-th column vector of matrix V;

Step5, according to formula (5) by each component signal P ₁, P ₂... P _qafter superposing, the position sensing cycle slip according to maximum point in superposed signal X:

X＝P ₁+P ₂+...+P _q(5)。

Embodiment 2: as shown in figs. 1-11, a kind of Big Dipper single-frequency Cycle Slips Detection, first uses Pseudo-range Observations ρ _tdeduct carrier phase observation data and its difference is asked between epoch again poor, obtain cycle slip inspected number D (t); Then utilize Hankel matrix to build attractor track matrix A to cycle slip inspected number D (t), and svd process is carried out to A, obtain effective singular value that limited can reflect abrupt information; Finally use SVD inverse operation respectively to each effective singular value reconstruct component signal, according to the position sensing cycle slip of maximum point in superposed signal after being superposed by each component signal.

Embodiment 3: as shown in figs. 1-11, a kind of Big Dipper single-frequency Cycle Slips Detection, first uses Pseudo-range Observations ρ _tdeduct carrier phase observation data and its difference is asked between epoch again poor, obtain cycle slip inspected number D (t); Then utilize Hankel matrix to build attractor track matrix A to cycle slip inspected number D (t), and svd process is carried out to A, obtain effective singular value that limited can reflect abrupt information; Finally use SVD inverse operation respectively to each effective singular value reconstruct component signal, according to the position sensing cycle slip of maximum point in superposed signal after being superposed by each component signal.

Described method specific experiment process is as follows:

Step 1, open the double star five frequently test case " 502449091t.13O " from the navigation of Shanghai compass in ancient China with UltraEdit software, as shown in Figure 3, its sample frequency is 1Hz, and observation duration is 1h.Select the Big Dipper (COMPASS, C01) the Pseudo-range Observations ρ of front 300 epoch _tand carrier phase observation data as test case;

Step 2, the COMPASS Pseudo-range Observations ρ of 300 epoch that will select _tand carrier phase observation data copy in two row of Excel table respectively, wherein, 1 row are Pseudo-range Observations ρ entirely _t, another row are carrier phase observation data entirely

Step 3, use Pseudo-range Observations ρ _tdeduct carrier phase observation data and its difference is asked poor in epoch between t again, can cycle slip inspected number D (t) be obtained, cycle slip inspected number D (t) be imported in MATLAB software and be shown as figure, as shown in Figure 4.According to Fig. 4, when not adding cycle slip, because carrier phase observation data is subject to the impact of stochastic error and measurement noises, cycle slip inspected number D (t) is made to show as random error characteristics in time series.

Step 4, utilize Hankel matrix to construct attractor track matrix A to cycle slip inspected number D (t) can to obtain as shown in Figure 5, matrix A is the matrix (wherein Fig. 5 only provides partial data) of 297 × 4.

Step 5, SVD process is carried out to attractor track matrix A obtain effective singular value σ ₁, σ ₂... σ _qbe respectively 6.6662,6.5793,5.7076,3.9478.Namely effective singular value number is 4.

Step 6, SVD inverse operation is carried out to 4 effective singular values and reconstruct obtains 4 component signal P ₁, P ₂, P ₃, P ₄, 4 component signals as shown in Figure 6.As shown in Figure 6, the noise of 4 components obtained through SVD process weakens to some extent, shows as its amplitude less, and contrast known with Fig. 4, these 4 components more intactly remain the information of former cycle slip inspected number D (t) simultaneously.

Step 7, by formula (5) by 4 component signal P ₁, P ₂, P ₃, P ₄superpose, obtain superposed signal X, due to the carrier phase observation data obtained in not containing cycle slip, the superposed signal X now obtained obviously distinguishes with former cycle slip inspected number D (t) nothing.

In order to verify that context of methods effectively can detect 1 ~ 5 week cycle slip, artificially press formula (8) at carrier phase observation data φ _tany epoch, t added 1 ~ 5 week cycle slip respectively time, repeated execution of steps 3 ~ step 7, can obtain Fig. 7 ~ Figure 11:

${{\mathrm{\&phi;}}_t}^{\&prime;}=\left\{\begin{array}{cc}{\mathrm{\&phi;}}_t;& t=1-t_1\\ {\mathrm{\&phi;}}_t+{\mathrm{\&Delta;n}}_1;& t=t_1+1-t_2\\ {\mathrm{\&phi;}}_t+{\mathrm{\&Delta;n}}_2;& t=t_2+1,...\end{array}\right.---\left(8\right)$

In formula, n ₁, n ₂represent t respectively ₁, t ₂the size of the cycle slip added, t ₁, t ₂represent the moment adding cycle slip.

As can be seen from Figure 7, after adding 1 week cycle slip 100 epoch of carrier phase observation data, cycle slip inspected number D (t), after SVD process, obviously can be found out that the threshold value located in 100 epoch has exceeded 1 week, there occurs sudden change, namely there occurs cycle slip.

As can be seen from Figure 8, after adding 2 weeks cycle slips 150 epoch of carrier phase observation data, cycle slip inspected number D (t) is after SVD process, obviously can find out that the threshold value located in 150 epoch has exceeded 1.5 weeks, reached for-1.575 weeks, knownly there occurs sudden change, namely there occurs cycle slip.

As can be seen from Figure 9, after adding 3 weeks cycle slips 200 epoch of carrier phase observation data, cycle slip inspected number D (t) is after SVD process, obviously can find out that the threshold value located in 200 epoch has exceeded 2 weeks, reached for-2.216 weeks, there occurs sudden change, can be judged as there occurs cycle slip.

As can be seen from Figure 10, after adding 4 weeks cycle slips 250 epoch of carrier phase observation data, cycle slip inspected number D (t) is after SVD process, obviously can find out that the threshold value located in 250 epoch has exceeded 2.5 weeks, reached for-2.83 weeks, sudden change is comparatively obvious, and namely cycle slip is comparatively obvious.

As can be seen from Figure 11, after adding 5 weeks cycle slips 220 epoch of carrier phase observation data, cycle slip inspected number D (t), after SVD process, obviously can be found out that the threshold value located in 220 epoch has exceeded 3.5 weeks, can judge to there occurs cycle slip.

In sum, a kind of Big Dipper single-frequency Cycle Slips Detection, by using Pseudo-range Observations ρ _tdeduct carrier phase observation data and its difference is asked between epoch again poor, obtain cycle slip inspected number D (t); Then utilize Hankel matrix to build attractor track matrix A to cycle slip inspected number D (t), and svd (SVD) process is carried out to A, obtain effective singular value that can reflect abrupt information; Finally use SVD inverse operation respectively to effective singular value reconstruct component signal, according to the position sensing cycle slip of maximum point in superposed signal after being superposed by each component signal.

By reference to the accompanying drawings the specific embodiment of the present invention is explained in detail above, but the present invention is not limited to above-mentioned embodiment, in the ken that those of ordinary skill in the art possess, various change can also be made under the prerequisite not departing from present inventive concept.

Claims (2)

1. a Big Dipper single-frequency Cycle Slips Detection, is characterized in that: first use Pseudo-range Observations ρ _tdeduct carrier phase observation data and its difference is asked between epoch again poor, obtain cycle slip inspected number D (t); Then utilize Hankel matrix to build attractor track matrix A to cycle slip inspected number D (t), and svd process is carried out to A, obtain effective singular value that limited can reflect abrupt information; Finally use SVD inverse operation respectively to each effective singular value reconstruct component signal, according to the position sensing cycle slip of maximum point in superposed signal after being superposed by each component signal.

2. Big Dipper single-frequency Cycle Slips Detection according to claim 1, is characterized in that: the concrete steps of described method are as follows:

Step1, by Pseudo-range Observations ρ _tdeduct carrier phase observation data φ _t, and its difference is asked poor in epoch between t again, can cycle slip inspected number D (t) be obtained;

$D\left(t\right)=\frac{({\mathrm{\&rho;}}_{t+1}-{\mathrm{\&lambda;\&phi;}}_{t+1})-({\mathrm{\&rho;}}_t-{\mathrm{\&lambda;\&phi;}}_t)}{\mathrm{\&lambda;}}---\left(1\right)$

In formula, λ is the carrier wavelength of a certain frequency range of the Big Dipper; T is the moment obtaining Pseudo-range Observations and carrier phase observation data, also claims epoch; T+1 is next epoch of t;

Step2, Hankel matrix is utilized to build attractor track matrix A to cycle slip inspected number D (t) that formula (1) obtains;

$A=\left[\begin{array}{cccc}{d}_1& d_2& ...& d_n\\ d_2& d_3& ...& d_{n+1}\\ ...& ...& ...& ...\\ d_m& d_{m+1}& ...& d_N\end{array}\right]---\left(2\right)$

In formula, N is number epoch of observation of the carrier phase chosen, and n is the columns of matrix A and meets 1<n<N; The line number m=N-n+1 of order matrix A, then A ∈ R ^{m × n}; d ₁be cycle slip inspected number corresponding to the 1st epoch, in like manner, d _nbe cycle slip inspected number corresponding to the n-th epoch, d _nbe cycle slip inspected number corresponding to N number of epoch;

Step3, according to formula (3), SVD process is carried out to attractor track matrix A, obtain limited effective singular value;

A＝USV ^T(3)

In formula, U=[u ₁, u ₂..., u _m] ∈ R ^{m × m}, V=[v ₁, v ₂..., v _n] ∈ R ^{n × n}be called the left and right singular matrix of attractor track matrix A, and U and V is orthogonal matrix; u _mfor m column vector of matrix U; v _nfor the n-component column vector of matrix V; S=[diag (σ ₁, σ ₂... σ _q), O] or its transposition, depend on the magnitude relationship of m and n, S ∈ R ^{m × n}, O is null matrix, and q depends on the little person in m and n, and q is the number of effective singular value, and singular value has such relation: σ ₁>=σ ₂>=...>=σ _q> 0, q=min (m, n);

Step4, utilization SVD inverse operation are respectively to effective singular value σ ₁, σ ₂... σ _qreconstruct component signal P ₁, P ₂... P _q:

P _i＝u _iσ _iv _i ^T，i＝1,2,…,q(4)

In formula, u _ifor i-th column vector of matrix U; v _ifor i-th column vector of matrix V;

Step5, according to formula (5) by each component signal P ₁, P ₂... P _qafter superposing, the position sensing cycle slip according to maximum point in superposed signal X:

X＝P ₁+P ₂+...+P _q(5)。