Reliable ambiguity resolving method for Beidou weak observation

Abstract

The invention discloses a Beidou weak observation-oriented ambiguity reliable resolving method, which comprises the following steps of: judging a weak observation degree and a noise level in an observed quantity through an observation equation method matrix condition number and a unit weight variance, introducing regularization in an integer least square (ILS) search process when the weak observation is serious and the noise in the observed quantity is relatively large, and calculating the ambiguity reliability of the Beidou weak observation. Otherwise, regularization is not adopted. And an elastic positioning scheme is further formed based on the ratio value, the ambiguity residual quadratic form and the BIE estimation optimal solution weight as judgment conditions. When the ratio value is high, an ambiguity fixed solution is adopted; and when the ratio value is low, the residual quadratic forms of the optimal ambiguity solution and the suboptimal solution are similar, and the weight of the optimal ambiguity solution estimated by the BIE is too high, a BIE solution (LBIE) based on Laplace distribution is adopted, and otherwise, a BIE solution (GBIE) based on Gaussian distribution is adopted. According to the method, regularization is introduced into ILS search, and GBIE, LBIE and ILS estimation are integrated to form an elastic positioning scheme, so that the accuracy and reliability of ambiguity calculation for a single Beidou weak observation scene are improved.

Description

Technical Field

[0001] The invention belongs to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, and specifically relates to a reliable ambiguity resolution method for Beidou weak observation. Background Art

[0002] Reliable resolution of GNSS carrier phase integer ambiguity is the core prerequisite for achieving high-quality navigation and positioning services. Currently, the ILS method is the most widely used method for resolving carrier phase ambiguity because it has the highest success rate.

[0003] The ILS estimation process mainly follows: (1) Use LS estimation to calculate the floating-point solution of ambiguity and its related VC matrix in the real number domain; (2) Based on the integer characteristics of ambiguity, use the floating-point solution of ambiguity and its VC matrix to search for the optimal integer candidate vector, that is, the ambiguity fixed solution; (3) Reliability test of the ambiguity fixed solution. Among the commonly used reliability test methods, the R-ratio test is widely used because of its easy-to-obtain statistics and simple operation. (4) If the fixed solution is evaluated to be reliable enough, the unknown parameters such as the baseline coordinates are updated accordingly, otherwise the floating-point solution is maintained.

[0004] Although the reliability verification method guarantees the stability of ambiguity estimation to a large extent, it inevitably has inherent defects in the setting of empirical thresholds. That is, if the empirical threshold is set too strictly, "discarding true" errors will occur frequently, and excessive use of floating-point solutions will lead to a significant decrease in positioning accuracy; if the empirical threshold is set too loosely, "accepting false" errors will occur frequently, which will lead to a sharp decrease in positioning reliability, and the use of erroneous fixed solutions may cause serious positioning errors. To overcome the above limitations, BIE estimation has been widely used. BIE estimation is obtained by probability-weighted calculation of all vectors in integer space, with minimum mean square error (MMSE). At the same time, the variance of BIE estimation can be used as an evaluation indicator of its own reliability, without the need for conventional ambiguity reliability verification steps, overcoming the dilemma of empirical threshold selection.

[0005] For single BeiDou observation, in weak observation environments such as canyons where the number of satellites is limited and the satellite configuration is poor, the observation equation becomes ill-conditioned. At this time, when the observed quantity contains a certain degree of systematic error, it is absorbed by the ambiguity floating-point solution through LS estimation, causing the floating-point solution to have deviations, and the matching of the floating-point solution with its posterior variance will decrease. This problem greatly increases the probability of selecting the wrong optimal integer candidate vector, and the risk of serious deviations in some ambiguities in the selected optimal solution is significantly increased. At the same time, the rationality of the weight allocation of the ambiguity candidate vector is destroyed, which can easily lead to the optimal solution with serious deviations having too high a weight, and the contribution of other candidate solutions to the BIE estimation is almost negligible. The BIE solution is approximately consistent with the fixed solution, resulting in significant positioning errors. At the same time, the excessively high weight of the wrong optimal solution will make the posterior variance of the BIE estimate similar to that of the fixed solution, which is too optimistic about the estimation result, unable to effectively characterize the actual positioning error, and loses the early warning capability. To this end, the present invention introduces the regularization idea into the ambiguity search process, and combines the ILS, GBIE, and LBIE estimation strategies to propose a reliable ambiguity resolution method for Beidou weak observation, which improves the accuracy and stability of the positioning solution. Summary of the invention

[0006] To solve the above problems, the present invention discloses a reliable ambiguity resolution method for Beidou weak observation, introduces a regularization strategy in the LAMBDA algorithm search process, and combines ILS, GBIE, and LBIE estimation methods to weaken the negative impact of ill-posed problems on BIE estimation, improve the accuracy of LAMBDA algorithm search under weak observation conditions, and improve the rationality of weight allocation of BIE estimation ambiguity candidate solutions, thereby improving the accuracy and reliability of positioning solution in a single Beidou weak observation environment.

[0007] To achieve the above object, the technical solution of the present invention is as follows:

[0008] A reliable ambiguity resolution method for Beidou weak observation includes the following steps:

[0009] Step 1: Establish a satellite positioning observation model;

[0010] Step 2: Check the weak observation degree and observation noise level;

[0011] Step 3: If the degree of weak observation and the level of observation noise are high, add a regularization strategy to the LAMBDA algorithm;

[0012] Step 4: R-ratio value check. If the ratio value is greater than the threshold, the fuzzy fixed solution is used, otherwise the BIE solution is used.

[0013] Step 5: If the BIE solution is adopted, perform a rationality check on the BIE estimation weight allocation. If the rationality check passes, keep the BIE estimation based on Gaussian distribution, otherwise change to the BIE estimation based on Laplace distribution;

[0014] Step 6: Output the positioning solution.

[0015] The specific steps are:

[0016] Step 1. Establish satellite positioning observation model

[0017]

[0018] Where ε is the random error vector; L is the order double difference observation vector; a is the nth order double difference ambiguity vector; b is the other c unknown parameter vectors including the baseline coordinates; A and B are the corresponding k×n and k×c order design matrices respectively; D LL is the variance matrix of the observation vector L, and N is the normal distribution.

[0019] Step 2. Verification of weak observation degree and observation noise level.

[0020] The standard least squares (LS) method is used to solve the floating point solution and its variance-covariance (VC) matrix:

[0021]

[0022] is the variance of a, is the ab covariance, is the ba covariance, is the variance of b.

[0023] Calculate the VC matrix after ambiguity floating point resolution The condition number of and the unit weight variance of the floating-point solution:

[0024]

[0025] Where num is The condition number of num and σ is the unit weight variance. If num and σ are greater than the corresponding thresholds, the weak observation degree and the observation noise level are judged to be too high and regularization must be performed. Otherwise, it is judged not to be performed. k, n, and c are the orders.

[0026] Step 3. If the degree of weak observation and the level of observation noise are high, add a regularization strategy to the LAMBDA algorithm.

[0027] The objective function of the integer least squares ILS search is:

[0028]

[0029] For single Beidou observation, when the positioning scene is more complex, such as in urban canyons and natural canyons, satellite signals are susceptible to reflection, diffraction and occlusion, multipath errors are serious, cycle jumps occur frequently, and the observations contain many unmodeled errors. The ambiguity is estimated by LS to absorb the systematic errors in some of the observations. At the same time, the number of single Beidou observation satellites in complex scenes is small, the satellite geometry is not good, and the ill-posed problems in geodetic measurement are more prominent. At this time, the problem of mismatch between the ambiguity floating point solution and the variance is serious, and the posterior VC matrix of the ambiguity floating point solution usually has a more significant singularity. The tiny systematic error in the observation may cause the ambiguity candidate solution with serious deviation in the integer vector search process to be selected as the optimal solution. At the same time, this optimal solution obtains too high a weight distribution under the assumption of GBIE Gaussian distribution, resulting in a serious deviation between the fixed solution and the BIE solution.

[0030] The following regularized estimation criterion is established based on the integer least squares criterion:

[0031]

[0032] In the formula, R is the regularization matrix and ξ is the regularization parameter. Based on the Tikhonov regularization principle, the regularization matrix R is selected as:

[0033]

[0034] Among them, R is an n×n diagonal matrix, and the diagonal element r is The minimum value among the main diagonal elements of .

[0035] When the posterior VC matrix of the floating-point solution is determined, the corresponding regularization matrix R can be obtained. A large number of examples have verified that selecting the regularization parameter ξ as 0.0005 can achieve good positioning optimization effects.

[0036] Step 4. R-ratio value test, if the ratio value is greater than the threshold, the ambiguity fixed solution is used, otherwise the BIE solution is used.

[0037] Based on the integer nature of ambiguity, the floating point solution of ambiguity is used Its VC matrix Using the LAMBDA algorithm to obtain the optimal solution for ambiguity is to fix the ambiguity solution The calculation formula of ratio is:

[0038]

[0039] where a 2is the suboptimal solution of ambiguity searched by the LAMBDA algorithm. When ratio is greater than the set threshold, the ambiguity fixed solution is considered to have sufficient reliability and is Compute fixed solutions for other unknown parameters including the baseline coordinates:

[0040]

[0041] When the ratio is less than the set threshold, the ambiguity candidate solutions searched by LAMBDA are weighted averaged to obtain the ambiguity GBIE solution:

[0042]

[0043] Where t is the total number of candidate integer vectors, z j is the candidate solution for the ambiguity searched by the LAMBDA algorithm, represented by a G Further obtain other unknown parameters of GBIE:

[0044]

[0045] Step 5. Perform a rationality check on the BIE estimation weight allocation. If the rationality check passes, keep the BIE estimation based on Gaussian distribution (GBIE), otherwise change to the BIE estimation based on Laplace distribution (LBIE);

[0046] The relative amount of the residual quadratic form of the optimal solution and the suboptimal solution of fuzziness is defined as:

[0047]

[0048] The weight of the optimal solution to fuzziness is:

[0049]

[0050] When p best When is greater than a certain threshold and μ is less than a certain threshold, the GBIE estimation weight distribution is considered unreasonable, the weight distribution function is changed to the Laplace distribution function, and the LBIE solution is calculated:

[0051]

[0052] e is the scale factor of the Laplace distribution; after verification by a large number of examples, selecting the regularization parameter ξ as 0.0005 can achieve a good positioning optimization effect. Otherwise, the GBIE estimation result is maintained.

[0053] Step 6. Output the positioning solution.

[0054] If the R-ratio test determines that the fixed solution has sufficient reliability, the fixed solution is output; if the fixed solution is determined to be unreliable and the BIE estimation weight allocation rationality test passes, the GBIE solution is output; if the fixed solution is determined to be unreliable and the BIE estimation weight allocation rationality test fails, the LBIE solution is output.

[0055] The beneficial effects of the present invention are:

[0056] The present invention proposes a reliable ambiguity resolution method for Beidou weak observation. In the scenario where the weak observation degree is serious and the observation noise is large, a regularization strategy is introduced in the LAMBDA algorithm search process, which overcomes the influence of the ill-posed problem on the BIE estimation performance to a certain extent and improves the correctness of the ambiguity candidate vector selection. At the same time, the ILS, GBIE, and LBIE estimation methods are combined, and the ILS estimation is used when the ratio value is high, and the BIE estimation is used when the ratio value is low. At the same time, the GBIE and LBIE estimations are selected according to the weight distribution rationality judgment results to maintain the reliable performance of the BIE estimation, thereby improving the accuracy and stability of the positioning solution in a single Beidou weak observation environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is an implementation flow chart of the present invention;

[0058] Figure 2 Comparison of positioning errors between traditional BIE and optimized BIE estimation in easting (E), northing (N), and elevation (U). DETAILED DESCRIPTION

[0059] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0060] As shown in the figure, the present embodiment of the present invention discloses a reliable ambiguity resolution method for Beidou weak observation, and the specific steps are as follows:

[0061] Step 1. Establish satellite positioning observation model

[0062]

[0063] Where ε is the random error vector; L is the order double difference observation vector; a is the nth order double difference ambiguity vector; b is the other c unknown parameter vectors including the baseline coordinates; A and B are the corresponding k×n and k×c order design matrices respectively; D LL is the variance matrix of the observation vector L.

[0064] Step 2. Verification of weak observation degree and observation noise level.

[0065] Use LS estimation to solve the floating point solution and its VC matrix:

[0066]

[0067] Calculate the VC matrix after ambiguity floating point resolution The condition number of and the unit weight variance of the floating-point solution:

[0068]

[0069] Where num is The condition number of num and σ is the unit weight variance. If num and σ are greater than the corresponding thresholds, the weak observation degree and the observation noise level are judged to be too high and regularization must be performed. Otherwise, it is judged not to be performed.

[0070] Step 3. If the degree of weak observation and the level of observation noise are high, add a regularization strategy to the LAMBDA algorithm.

[0071] The objective function of the integer least squares ILS search is:

[0072]

[0073] For single Beidou observation, when the positioning scene is more complex, such as in urban canyons and natural canyons, satellite signals are susceptible to reflection, diffraction and occlusion, multipath errors are serious, cycle jumps occur frequently, and the observations contain many unmodeled errors. The ambiguity is estimated by LS to absorb the systematic errors in some of the observations. At the same time, the number of single Beidou observation satellites in complex scenes is small, the satellite geometry is not good, and the ill-posed problems in geodetic measurement are more prominent. At this time, the problem of mismatch between the ambiguity floating point solution and the variance is serious, and the posterior VC matrix of the ambiguity floating point solution usually has a more significant singularity. The tiny systematic error in the observation may cause the ambiguity candidate solution with serious deviation in the integer vector search process to be selected as the optimal solution. At the same time, this optimal solution obtains too high a weight distribution under the assumption of GBIE Gaussian distribution, resulting in a serious deviation between the fixed solution and the BIE solution.

[0074] The following regularized estimation criterion is established based on the integer least squares criterion:

[0075]

[0076] In the formula, R is the regularization matrix and ξ is the regularization parameter. Based on the Tikhonov regularization principle, the regularization matrix R is selected as:

[0077]

[0078] Among them, R is an n×n diagonal matrix, and the diagonal element r is The minimum value among the main diagonal elements of .

[0079] When the posterior VC matrix of the floating-point solution is determined, the corresponding regularization matrix R can be obtained. A large number of examples have verified that selecting the regularization parameter ξ as 0.0005 can achieve good positioning optimization effects.

[0080] Step 4. R-ratio value test, if the ratio value is greater than the threshold, the ambiguity fixed solution is used, otherwise the BIE solution is used.

[0081] Based on the integer nature of ambiguity, the floating point solution of ambiguity is used Its VC matrix Using the LAMBDA algorithm to obtain the optimal solution for ambiguity is to fix the ambiguity solution The calculation formula of ratio is:

[0082]

[0083] where a 2 is the suboptimal solution of ambiguity searched by the LAMBDA algorithm. When ratio is greater than the set threshold, the ambiguity fixed solution is considered to have sufficient reliability and is Compute fixed solutions for other unknown parameters including the baseline coordinates:

[0084]

[0085] When the ratio is less than the set threshold, the ambiguity candidate solutions searched by LAMBDA are weighted averaged to obtain the ambiguity GBIE solution:

[0086]

[0087] Where t is the total number of candidate integer vectors. G Further obtain other unknown parameters of GBIE:

[0088]

[0089] Step 5. If the BIE solution is adopted, perform a rationality check on the BIE estimation weight allocation. If the rationality check passes, keep the BIE estimation based on Gaussian distribution (GBIE), otherwise change to the BIE estimation based on Laplace distribution (LBIE);

[0090] The relative amount of the residual quadratic form of the optimal solution and the suboptimal solution of fuzziness is defined as:

[0091]

[0092] The weight of the optimal solution to fuzziness is:

[0093]

[0094] When p best When μ is greater than a certain threshold and μ is less than a certain threshold, the rationality test fails, and the GBIE estimated weight distribution is considered unreasonable. The weight distribution function is changed to the Laplace distribution function, and the LBIE solution is calculated:

[0095]

[0096] Where e is the scale factor of the Laplace distribution. A large number of experiments have shown that taking e = 3 can achieve a better optimization effect of LBIE. If the rationality test passes, the GBIE estimation result is maintained.

[0097] Step 6. Output the positioning solution.

[0098] If the R-ratio test determines that the fixed solution has sufficient reliability, the fixed solution is output; if the fixed solution is determined to be unreliable and the BIE estimation weight allocation rationality test passes, the GBIE solution is output; if the fixed solution is determined to be unreliable and the BIE estimation weight allocation rationality test fails, the LBIE solution is output.

Claims

1. A reliable ambiguity resolution method for Beidou weak observation, characterized in that: include: Step 1: Establish a satellite positioning observation model; Step 2: Check the weak observation degree and observation noise level; Step 3: If the weak observation degree and observation noise level are high, add a regularization strategy to the LAMBDA algorithm; Step 4: R-ratio value check. If the ratio value is greater than the threshold, the fuzzy fixed solution is used, otherwise the BIE solution is used. Step 5: If the BIE solution is adopted, perform a rationality check on the BIE estimation weight allocation. If the rationality check passes, keep the BIE estimation based on Gaussian distribution, otherwise change to the BIE estimation based on Laplace distribution; Step 6: Output the positioning solution.

2. The reliable ambiguity resolution method for Beidou weak observation as claimed in claim 1, characterized in that: Step 1: Establishing a satellite positioning observation model; Where ε is the random error vector; L is the order double difference observation vector; a is the nth order double difference ambiguity vector; b is the other c unknown parameter vectors including the baseline coordinates; A and B are the corresponding k×n and k×c order design matrices respectively; D LL is the variance matrix of the observation vector L.

3. The reliable ambiguity resolution method for Beidou weak observation as claimed in claim 1, characterized in that: The weak observation degree and observation noise level test described in step 2; Use standard least squares to find the floating-point solution and its variance-covariance matrix: Calculate the floating-point resolution of the ambiguity and its variance-covariance matrix The condition number of and the unit weight variance of the floating-point solution: Where num is The condition number of num and σ is the unit weight variance. If num and σ are respectively greater than the corresponding thresholds, it is determined that the weak observation degree and the observation noise level are too high and regularization must be performed. Otherwise, it is determined not to be performed.

4. The reliable ambiguity resolution method for Beidou weak observation as claimed in claim 1, characterized in that: As described in step 3, if the weak observation degree and observation noise level are high, a regularization strategy is added to the LAMBDA algorithm; The following regularized estimation criterion is established based on the integer least squares criterion: In the formula, R is the regularization matrix, ξ is the regularization parameter; based on the Tikhonov regularization principle, the regularization matrix R is selected as: Among them, R is an n×n diagonal matrix, and the diagonal element r is The minimum value among the main diagonal elements of ; When the posterior variance-covariance matrix of the floating-point solution is determined, the corresponding regularization matrix R is obtained; the regularization parameter ξ is 0.0005.

5. The reliable ambiguity resolution method for Beidou weak observation according to claim 1, characterized in that: The R-ratio value test described in step 4, if the ratio value is greater than the threshold, the fuzzy fixed solution is adopted, otherwise the BIE solution is adopted; Based on the integer nature of ambiguity, the floating point solution of ambiguity is used and its variance-covariance matrix Using the LAMBDA algorithm to obtain the optimal solution for ambiguity is to fix the ambiguity solution The calculation formula of ratio is: Where a2 is the suboptimal solution of ambiguity searched by the LAMBDA algorithm; when ratio is greater than the set threshold, the ambiguity fixed solution is considered to have sufficient reliability and is Compute fixed solutions for other unknown parameters including the baseline coordinates: When the ratio is less than the set threshold, the ambiguity candidate solutions searched by LAMBDA are weighted averaged to obtain the ambiguity GBIE solution: Where t is the total number of candidate integer vectors; G Further obtain other unknown parameters of GBIE:

6. The reliable ambiguity resolution method for Beidou weak observation according to claim 1, characterized in that: If the BIE solution is adopted as described in step 5, a rationality check of the BIE estimation weight distribution is performed. If the rationality check passes, the BIE estimation based on Gaussian distribution is maintained, otherwise it is changed to the BIE estimation based on Laplace distribution; The relative amount of the residual quadratic form of the optimal solution and the suboptimal solution of fuzziness is defined as: The weight of the optimal solution to fuzziness is: When p best When μ is greater than a certain threshold and μ is less than a certain threshold, the rationality test fails, and the GBIE estimated weight distribution is considered unreasonable. The weight distribution function is changed to the Laplace distribution function, and the LBIE solution is calculated: Where e is the scale factor of the Laplace distribution; e = 3 can achieve the optimization effect of LBIE; if the rationality test passes, the GBIE estimation result is maintained.

7. The reliable ambiguity resolution method for Beidou weak observation according to claim 1, characterized in that: The output positioning solution described in step 6; If the R-ratio test determines that the fixed solution has sufficient reliability, the fixed solution is output; if the fixed solution is determined to be unreliable and the BIE estimation weight allocation rationality test passes, the GBIE solution is output; if the fixed solution is determined to be unreliable and the BIE estimation weight allocation rationality test fails, the LBIE solution is output.

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