Real-time cycle slip detection and repair method for pseudo-satellite single-frequency observation

Abstract

The invention relates to a real-time cycle slip detection and restoration method for pseudo-satellite single-frequency observation, and the method comprises the following steps: data collection: obtaining observation data of adjacent epochs based on navigation signals of a receiver and a transmitter, and building a single-frequency carrier observation equation; carrying out time sequence differential processing, and carrying out subtraction on carrier phase observation values of adjacent epochs in combination with correction parameters; constructing a least square adjustment model, and performing parameter estimation by using the difference observed quantity; calculating a residual error after the test; introducing a statistical hypothesis to perform cycle slip detection and repair; and outputting a result. A least square adjustment model is constructed based on a time sequence difference model, and cycle slip detection and repair are realized through chi-square test of a post-test residual error, so that ambiguity initialization and position errors caused by false detection and missing detection are reduced, and the positioning precision and reliability of a pseudo satellite are improved.

Description

Technical Field

[0001] The present invention relates to the field of surveying and mapping science and technology, and in particular to a real-time cycle slip detection and repair method for pseudolite single-frequency observation. Background Art

[0002] As a simulated satellite device, pseudolites can transmit positioning signals that are completely consistent with GNSS satellites. Their signals do not need to pass through the ionosphere and have a very low altitude angle. They can effectively improve the geometric distribution of satellites and the positioning accuracy of GNSS receivers. They can serve as an effective supplement, backup and enhancement solution in the event of GNSS satellite failure or performance degradation.

[0003] In order to obtain high-precision positioning results, carrier phase measurement must be used in positioning. However, cycle slips in carrier phase observations are a unique problem, which is a limiting factor in improving positioning accuracy. Only phase data after eliminating the influence of cycle slips can be used for precise positioning. Often, the receiver's observation of pseudolites is seriously affected by the multipath effect, and cycle slips are more frequent, which in turn causes frequent parameter initialization, resulting in increased position errors and reduced positioning accuracy. The current more mature GNSS cycle slip algorithm is a dual-frequency-based cycle slip detection and repair method, which is generally suitable for post-processing and is not fully applicable to pseudolites. The cycle slip detection and repair algorithm for pseudolites single-frequency observations is still imperfect. Therefore, establishing a universal single-frequency cycle slip detection and repair method is of great significance for high-precision positioning. Summary of the invention

[0004] In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a real-time cycle slip detection and repair method for pseudolite single-frequency observation, so as to solve one or more problems in the prior art.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A real-time cycle slip detection and repair method for pseudolite single-frequency observation, characterized in that it comprises the following steps:

[0007] Data acquisition: based on the navigation signals of the receiver and transmitter, the observation data of adjacent epochs are obtained and the single-frequency carrier observation equation is established;

[0008] Timing difference processing, making the difference between the carrier phase observations of adjacent epochs;

[0009] Construct the least squares adjustment model and use differential observations to estimate parameters;

[0010] Post-test residual calculation;

[0011] Introducing statistical assumptions to detect and repair cycle slips;

[0012] Result output.

[0013] Furthermore, the calculation formula for the differential observation value between epochs in the time series difference processing is as follows:

[0014]

[0015] Where: represents the phase observation value of the receiver r to the pseudo-satellite s after the known value correction, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) represents the receiver clock error, c represents the speed of light, represents the carrier phase ambiguity, λ is the wavelength of the phase observation, represents the observation error.

[0016] Furthermore, the steps of constructing the least squares adjustment model are as follows:

[0017] The observation vector is obtained by differential observation values;

[0018] Assume no cycle slips and estimate unknown parameters;

[0019] The least squares estimation method is used to obtain the solution of the parameters to be estimated.

[0020] Furthermore, the calculation formula of the observation vector is as follows:

[0021]

[0022]

[0023] Where: Y(t) is the observation vector, represents the phase observation value of receiver r to pseudo-satellite n after the known quantity correction, h(i) is the observation model, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) represents the receiver clock error, represents the observation error.

[0024] Furthermore, the estimated unknown parameters are the receiver position, the receiver clock error and the carrier phase ambiguity; the partial derivatives of the estimated parameters are calculated at the approximate values ​​of the unknown parameters to obtain the design matrix, and the design matrix expression is shown in the following formula:

[0025]

[0026] Where: H(t) is the design matrix, A unit vector representing the direction in which the receiver is pointing towards the satellite.

[0027] Furthermore, the expression of the solution of the parameter to be estimated is as follows:

[0028]

[0029] Where: is the least squares estimation result, θ0(t) is the approximate value at the linear expansion, H(t) is the design matrix, R(t) is the measurement noise covariance matrix, and h(·) is the observation model.

[0030] Furthermore, the post-test residual calculation includes the following steps:

[0031] Evaluate the parameter estimation results to obtain the estimation error covariance;

[0032] The posterior residual of the observation equation and its covariance matrix are shown as follows:

[0033]

[0034] Where: Y(t) is the observation vector, h(·) is the observed model after verification.

[0035] Furthermore, the step of introducing statistical assumptions to detect and repair cycle slips includes the following steps:

[0036] Construct the overall hypothesis test quantity;

[0037] Determine whether there is a cycle slip. If not, output the result. Otherwise, make a judgment for each satellite.

[0038] Determine the satellites that have cycle slips, remove them, and then perform adjustment calculations again until there are no cycle slips;

[0039] The cycle slip amount is estimated and repaired using the a posteriori residuals of adjacent epochs of the satellite where the cycle slip occurred.

[0040] Furthermore, the expression of the constructed overall hypothesis test quantity is shown as follows:

[0041] K(t)=z(t) T ·M -1 (t)·z(t)

[0042] Where: z(t) is the posterior residual, M(t) is the covariance.

[0043] Furthermore, the cycle slip estimation expression is as follows:

[0044]

[0045] In the formula: round() means rounding, z s (i) is the posterior residual of satellite s, and λ is the wavelength of the phase observation.

[0046] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0047] The technical solution of the present invention is to detect and repair the single-frequency carrier phase observation value of the pseudolite system in real time. By constructing a least square adjustment model based on a time series difference model, the detection and repair of cycle slips are realized through the chi-square test of the post-test residual, thereby reducing the ambiguity initialization and position error caused by false detection and missed detection, and improving the positioning accuracy and reliability of pseudolite. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A structural schematic diagram of a real-time cycle slip detection and repair method for pseudolite single-frequency observation according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical scheme and advantages of the present invention clearer, the following is a further detailed description of a real-time cycle slip detection and repair method for pseudo-satellite single-frequency observation proposed by the present invention in combination with the accompanying drawings and specific embodiments. According to the following description, the advantages and features of the present invention will be clearer. It should be noted that the accompanying drawings are in a very simplified form and use non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention. In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, please refer to the accompanying drawings. It should be noted that the structure, proportion, size, etc. illustrated in the drawings of this specification are only used to match the content disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the limiting conditions for the implementation of the present invention, so they have no technical substantive significance. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effect that the present invention can produce and the purpose that can be achieved, should still fall within the scope of the technical content disclosed by the present invention.

[0050] See also Figure 1 , a real-time cycle slip detection and repair method for pseudolite single-frequency observation, comprising the following steps:

[0051] Step 1: Data acquisition: Based on the navigation signals of the receiver and transmitter, the observation data of adjacent epochs are obtained and the single-frequency carrier observation equation is established.

[0052] The navigation signal from the pseudo-satellite transmitter s is received by the receiver r, and it is captured and tracked at time t to obtain the carrier phase observation. Combined with the signal propagation delay and various measurement errors, the single-frequency carrier observation equation at time t can be obtained as shown in the following equation 1:

[0053]

[0054] Where: represents the phase observation value of the receiver r to the pseudo-satellite s, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) and δt s (t) represents the clock difference between the receiver and the satellite, represents the multipath error in the observations, represents the carrier phase ambiguity, λ is the wavelength of the phase observation, represents the observation error.

[0055] For pseudo-satellite systems, unlike navigation satellites, atmospheric delay can be ignored.

[0056] Furthermore, the above where r = [x r ,y r ,z r ] represents the receiver coordinates, s = [x s ,y s ,z s ] represents pseudo-satellite coordinates.

[0057] Step 2: Perform time difference processing to make the difference between the carrier phase observation values ​​at adjacent epochs, i.e., time t and time t-1, to ensure that the satellite has not experienced a cycle slip in adjacent epochs. Otherwise, continue to search forward for the nearest epoch where the satellite has not experienced a cycle slip.

[0058] The calculation formula of the difference observation value between epochs in the time series difference processing is shown in the following formula 2:

[0059]

[0060] Where: represents the phase observation value of the receiver r to the pseudo-satellite s after the known value correction, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) and δt s (t) represents the clock difference between the receiver and the satellite, c represents the speed of light, represents the multipath error in the observations, represents the carrier phase ambiguity, λ is the wavelength of the phase observation, represents the observation error.

[0061] Furthermore, △δt r (t) = δt r (t)-δt r (t-1), △δt s (t-1) = δt s (t)-δt s (t-1), Among them, the carrier phase observation values ​​between two adjacent epochs are differenced, the pseudo-satellite coordinates and clock errors have been externally calibrated, the receiver coordinates and clock errors at time t-1 can be obtained from the filter, and the multipath changes between adjacent epochs can be ignored.

[0062] Furthermore, by using the known terms in the inter-epoch differential observations, the above formula 2 can be transformed into the following formula 3:

[0063]

[0064] Where: represents the phase observation value of the receiver r to the pseudo-satellite s after the known value correction, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) represents the receiver clock error, c represents the speed of light, represents the carrier phase ambiguity, λ is the wavelength of the phase observation, Represents the observation error. Among them, the parameters receiver position, receiver clock error and carrier phase ambiguity are unknown.

[0065] Step 3: Construct a least squares adjustment model and use differential observations to estimate parameters.

[0066] Step 3.1: Obtain the observation vector by differencing the observations.

[0067] For continuous carrier phase measurement, when no cycle slip occurs in the carrier phase measurement, the change in carrier phase ambiguity is zero. Assuming that in this case, all visible satellites s = [1, 2, 3, ..., n] are used simultaneously, the inter-epoch carrier phase difference components are constructed as shown in equations 4 and 5:

[0068]

[0069]

[0070] Where: represents the phase observation value of the receiver r to the pseudo-satellite n after the known quantity correction, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) represents the receiver clock error, represents the observation error.

[0071] Step 3.2: Assume no cycle slips and estimate the unknown parameters.

[0072] Furthermore, the estimated unknown parameters are recorded as The design matrix is ​​obtained by calculating the partial derivative of the estimated parameters at the approximate value as shown in Equation 6:

[0073]

[0074] Where: The unit vector representing the direction of the receiver pointing to the satellite can be expressed as

[0075] Step 3.3: The least squares estimation is used to obtain the solution of the parameters to be estimated.

[0076] The least squares estimation is performed on the above equations (4) and (5), and the measurement error vector is The covariance matrix can be expressed as R(t)=E{ε(t)ε T (t)}. The solution of the estimated parameter can be expressed as shown in the following equation 7:

[0077]

[0078] Where: is the least squares estimation result, θ0(t) is the approximate value at the linear expansion, H(t) is the design matrix, R(t) is the measurement noise covariance matrix, and h(·) is the observation model.

[0079] Step 4: Calculate the post-test residual.

[0080] Step 4.1: Evaluate the parameter estimation results to obtain the estimation error covariance.

[0081] Said The calculation formula of the estimated error covariance is shown in Equation 8:

[0082]

[0083] Where: θ(t) is the estimated unknown parameter, is the least squares estimation result, H(t) is the design matrix, and R(t) is the measurement noise covariance matrix.

[0084] Step 4.2: Derive the posterior residuals of the observation equation and its covariance matrix.

[0085] The observation equation posterior residual z(t) and its covariance matrix M(t) can be expressed as shown in the following equations 9 and 10 respectively:

[0086]

[0087] Where: Y(t) is the observation vector, h(·) is the observed model after verification.

[0088] Furthermore, when no cycle slip occurs, the posterior residual z(t) is a variable that conforms to the zero-mean normal distribution and has a covariance of M(t). However, when a cycle slip occurs in the carrier phase measurement, the ambiguity variation is introduced into the measurement error, and the mean of the posterior residual normal distribution changes due to the cycle slip. Therefore, the cycle slip can be detected and repaired by performing statistical hypothesis tests on the posterior residual z(t).

[0089] Step 5: Introduce statistical assumptions to detect and repair cycle slips.

[0090] Step 5.1: Construct the overall hypothesis test quantity.

[0091] Furthermore, the overall hypothesis test expression is constructed as shown in Equation 11:

[0092] K(t)=z(t) T ·M -1 (t)·z(t) (11)

[0093] Where: z(t) is the post-test residual, M(t) is the covariance, and K(t) obeys the χ2 equation with n degrees of freedom. 2 distributed.

[0094] Step 5.2: Determine whether a cycle slip exists.

[0095] If a pseudosatellite has a cycle slip in the observation equation, the posterior residual will lose the zero mean distribution condition, so we can make the assumption that all satellites have no cycle slips, denoted by H χ,0 , there is a satellite cycle slip, denoted as H χ,1 .

[0096] After determining the significance level (e.g., a significance level of α = 0.05 indicates a 5% risk of concluding that there is an association between variables when there is no association in fact), a judgment can be made on the cycle slip situation: Then deny H χ,0 , it is concluded that the association between the variables is statistically significant and that a cycle slip exists.

[0097] Step 5.3: Determine the satellites with cycle slips and remove them for post-detection verification

[0098] To further determine the satellite that has cycle slips, the posterior residuals of each satellite are traversed and χ is constructed. 2 (1) distribution, that is, for the s-th satellite, the same formula (11) is used to construct like It is determined that this satellite has a cycle slip.

[0099] Furthermore, to verify the detection results, the adjustment can be performed again after removing the corresponding satellite. If there is no abnormality in the residual statistics after verification, it means that the detection is correct.

[0100] Step 5.4: Estimate and repair the cycle slip of satellites with cycle slips using the post-validation residuals of adjacent epochs.

[0101] If the above statistical test detects that there is a cycle slip in the carrier phase measurement of the sth satellite, then the cycle slip value is The posterior residual z of the adjacent epochs can be used s (t) is estimated, the cycle slip amount The estimated expression is shown in Equation 12:

[0102]

[0103] In the formula: round() means rounding, z s (i) is the posterior residual of satellite s, and λ is the wavelength of the phase observation.

[0104] Step 6: Output the results.

[0105] The repaired cycle slip amount is again substituted into the above formula (4), and after repeated calculations until there is no cycle slip satellite, the repaired carrier phase data is output again to improve positioning accuracy.

[0106] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0107] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A real-time cycle slip detection and repair method for pseudolite single-frequency observation, characterized in that: The steps include: Data acquisition: based on the navigation signals of the receiver and transmitter, the observation data of adjacent epochs are obtained and the single-frequency carrier observation equation is established; Timing difference processing, making the difference between the carrier phase observations of adjacent epochs; Construct the least squares adjustment model and use differential observations to estimate parameters; Post-test residual calculation; Introducing statistical assumptions to detect and repair cycle slips; Result output.

2. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 1, characterized in that: The calculation formula for the difference observation value between epochs in the time series difference processing is as follows: Where: represents the phase observation value of the receiver r to the pseudo-satellite s after the known value correction, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) represents the receiver clock error, c represents the speed of light, represents the carrier phase ambiguity, λ is the wavelength of the phase observation, represents the observation error.

3. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 2, characterized in that: The steps of constructing the least squares adjustment model are as follows: The observation vector is obtained by differential observation values; Assume no cycle slips and estimate unknown parameters; The least squares estimation method is used to obtain the solution of the parameters to be estimated.

4. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 3, characterized in that: The calculation formula of the observation vector is shown as follows: Where: Y(t) is the observation vector, represents the phase observation value of receiver r to pseudo-satellite n after the known quantity correction, h(i) is the observation model, represents the geometric distance between the pseudo-satellite and the phase center of the receiver antenna, δt r (t) represents the receiver clock error, represents the observation error.

5. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 4, characterized in that: The estimated unknown parameters are the receiver position, the receiver clock error and the carrier phase ambiguity; the partial derivatives of the estimated parameters are calculated at the approximate values ​​of the unknown parameters to obtain the design matrix, and the design matrix expression is shown in the following formula: Where: H(t) is the design matrix, A unit vector representing the direction in which the receiver is pointing towards the satellite.

6. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 5, characterized in that: The expression of the parameter solution to be estimated is shown in the following formula: Where: is the least squares estimation result, θ0(t) is the approximate value at the linear expansion, H(t) is the design matrix, R(t) is the measurement noise covariance matrix, and h(·) is the observation model.

7. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 1, characterized in that: The post-test residual calculation comprises the following steps: Evaluate the parameter estimation results to obtain the estimation error covariance; The posterior residual of the observation equation and its covariance matrix are shown as follows: M(t)=E{z(t)z T (t)}=H(t)P(t)H T (t)+R(t) Where: Y(t) is the observation vector, h(·) is the observed model after verification.

8. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 1, characterized in that: The method of introducing statistical hypothesis to detect and repair cycle slips includes the following steps: constructing an overall hypothesis test quantity; Determine whether there is a cycle slip. If not, output the result. Otherwise, make a judgment for each satellite. Determine the satellite with a cycle slip and remove it. Then detect and verify and adjust the calculation again until there is no cycle slip. The cycle slip amount is estimated and repaired using the a posteriori residuals of the adjacent epochs of the satellite where the cycle slip occurred.

9. A real-time cycle slip detection and repair method for pseudolite single-frequency observation as claimed in claim 8, characterized in that: The expression of the constructed overall hypothesis test quantity is shown as follows: K(t)=z(t) T ·M -1 (t)·z(t) Where: z(t) is the posterior residual, M(t) is the covariance.

10. A real-time cycle slip detection and repair method for pseudolite single-frequency observation according to claim 9, characterized in that: The cycle slip estimation expression is as follows: In the formula: round() means rounding, z s (i) is the posterior residual of satellite s, and λ is the wavelength of the phase observation.

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