5. Fast Ambiguity Resolution Approach (FARA) In The First SteD: real values for double-difference The Main Characteristics of fara e estimated based on carrier phase (1)to use statistical information from the initial adjustme measurements and calculated by an adjustment procedure which also computes the (2)to use information of the var arance matrix to reject Cofactor matrix of the unknown parameters Posteriori variance of unit weight (a posteriori variance 3)to apply statistical hypothesis testing to select the correct set of integer ambiguities ce matrix of the un 1. computing the float carrier phase solution, Standard deviations of the ambiguities 3. computing a fixed solution for each ambiguity set, and 4. statistically testing the fixed solution with the smallest In The Second Step: the criteria for selecting possible ambiguity ranges(set) based on confidence intervals of the real In The Third Step: least squares adjustments with fixed values of the ambiguities. accepted ambiguity set yielding adjusted (1)First Criterion: The quality of the initial solution of the components and a posteriori variance factors irst step affects the possible ambiguity ranges. In more detail, the search range for this ambiguity is koN(k from In The Fourth Step I. The solution with the smallest a posteriori (2)A Second Criterion: the use of the correlation of the variance is further investigated 2. The baseline components of this solution are N=N-N compared with the float solution 3. If the solutio 4. The compatibility may be checked by a X teger sets. An even more impressive reduction is achieved if distribution which tests the compatibility of the a dual frequency phase measurements are available. sterioni variance with the a priori variance. 5. Fast Ambiguity Search Filter(FASF) 6. Least Squares Ambiguity Decorrelation Adjustment FASF is comprised of basically three components Teunissen proposed the idea and further developed the least ()A Kalman filter is applied to predict a state vector squares ambiguity decorrelation adjustment(LAMBDA) which is treated as observable Understanding the principle of this method must have a (2)The search of the ambiguities is performed at every strong background in linear algebra epoch until they are fixed, and are computed decorrelated related to ea Interested students can read through from p. 237-2446 5. Fast Ambiguity Resolution Approach (FARA) The Main Characteristics of FARA (1) to use statistical information from the initial adjustment to select the search range, (2) to use information of the variance-covariance matrix to reject ambiguity sets that are not acceptable from the statistical point of view, and (3) to apply statistical hypothesis testing to select the correct set of integer ambiguities. The FARA Algorithm 1. computing the float carrier phase solution, 2. choosing ambiguity sets to be tested, 3. computing a fixed solution for each ambiguity set, and 4. statistically testing the fixed solution with the smallest variance. In The First Step: real values for double-difference ambiguities are estimated based on carrier phase measurements and calculated by an adjustment procedure which also computes the • Cofactor matrix of the unknown parameters • Posteriori variance of unit weight (a posteriori variance factor) • Variance-covariance matrix of the unknown parameters • Standard deviations of the ambiguities In The Second Step: the criteria for selecting possible ambiguity ranges (set) based on confidence intervals of the real values of the ambiguities. (1) First Criterion: The quality of the initial solution of the first step affects the possible ambiguity ranges. In more detail, the search range for this ambiguity is kδN (k from Student's t-distribution). (2) A Second Criterion: the use of the correlation of the ambiguities. 2 N N N 2 Nij Ni i j j Nij = Ni − N j δ = δ − 2δ + δ This criterion significantly reduces the number of possible integer sets. An even more impressive reduction is achieved if dual frequency phase measurements are available. In The Third Step: least squares adjustments with fixed ambiguities are performed for each statistically accepted ambiguity set yielding adjusted baseline components and a posteriori variance factors. In The Fourth Step: 1. The solution with the smallest a posteriori variance is further investigated. 2. The baseline components of this solution are compared with the float solution. 3. If the solution is compatible, it is accepted. 4. The compatibility may be checked by a X2- distribution which tests the compatibility of the a posteriori variance with the a priori variance. 5. Fast Ambiguity Search Filter (FASF) FASF is comprised of basically three components: (1)A Kalman filter is applied to predict a state vector which is treated as observable, (2)The search of the ambiguities is performed at every epoch until they are fixed, and (3)The search ranges for the ambiguities are computed recursively and are related to each other. 6. Least Squares Ambiguity Decorrelation Adjustment Teunissen proposed the idea and further developed the least squares ambiguity decorrelation adjustment (LAMBDA). Understanding the principle of this method must have a strong background in linear algebra. Interested students can read through from p. 237-244         21 12 11 12 Q Q Q Q         12 11 0 0 W decorrelated W