西南交通大学测量工程系：《GPS卫星定位技术与方法（GPS技术与应用）》课程教学资源（课件讲稿）Data Processing（1/2）.pdf_大学文库

1 Dr. Guoqing Zhou 9. Data Processing (1) CET 318 Book: p. 203-276 1. Data Pre-Processing 1.1 Data Handling 1. Downloading 2. Data Management 3. Data Exchange 1. RINEX format consists of: (1) The observation data file containing the range data; (2) The meteorological data file; and (3) The navigation message file. 2. RINEX Data Format 1. RINEX observation data file • Header section • Data section 2. RINEX meteorological data file • Header section • Data section 3. RINEX navigation message file • Header section • Data section 1.2 Cycle Slip Detection and Repair 1. Definition of Cycle Slips During tracking, at a given epoch, the observed accumulated phase ∆ϕ ∑ ∑ = = = = = + + i t i t N i 1 i 1 ∆ϕ 2π ϕ The initial integer number N of cycles between the satellite and the receiver is unknown. This phase ambiguity N remains constant as long as no loss of the signal lock occurs. In this event, the integer counter is re-initialized which causes a jump in the instantaneous accumulated phase by an integer number of cycles. This jump is called cycle slip. 2. Causes of Cycle Slips 1. Obstructions of the satellite signal due to trees, buildings, bridges, mountains, etc. This source is the most frequent one. 2. Low SNR due to bad ionospheric conditions, multipath, high receiver dynamics, or low satellite elevation. 3. Failure in the receiver software, which leads to incorrect signal processing. 4. Malfunctioning satellite oscillators, but these cases are rare. 3. Testing Quantities The formulation of testing quantities is based on measured carrier phases and code ranges. Phase and integrated Doppler combination Single frequency phase and Doppler Phase and code range combination Single frequency phase and code range Dual frequency phases (L1 and L2) Phase combinations Single frequency phase (L1 or L2) Raw phase Required data Testing quantity Single receiver tests enable in situ cycle slip detection and repair by the internal software of the receiver. For a single site, the testing quantities are

2 4. Detection and Repair Each of the described testing quantities allows the location of cycle slips by checking the difference of two consecutive epoch values. This also yields an approximate size of the cycle slip. One of the methods for cycle slip detection is the scheme of differences. 1. Detection of Cycle Slip Interpolation Techniques: A method is to fit a curve through the testing quantities before and after the cycle slip. Prediction Method: At a certain epoch, the function value (i.e., one of the testing quantities) for the next epoch is predicted based on the information obtained from preceding function values. 2. Determination of Size of Cycle Slip • Kalman filtering • Linear regression • Least square method 3. Repair of Cycle Slip Cycle slip repair using the ionospheric residual are 1. Based on the measurement noise assumption, the separation of the cycle slips is unambiguosuly possible for up to ±4 cycles. 2. A smaller measurement noise increase the separability. 3. For a larger cycle slips, another method should be used in order to avoid wrong choices in ambiguous situation. 2. Ambiguity Resolution 2.1 General Aspects Iono λ 1 ρ f δ N - λ 1 Φ = + ∆ + ∆ The ambiguity inherent with phase measurements depends upon both receiver and satellite. The model for phase is If we consider the ambiguity, N as an integer value, the ambiguity is said to be resolved or fixed. Ambiguity fixing strengthens the baseline solution, but sometimes solutions with fixed ambiguities (i.e., integer values) and float ambiguities (i.e., real values) may agree within a few millimeters 1. Ambiguity Measurement The use of double-differences instead of single-differences for carrier phase processing can eliminate the clock terms and the isolation of the ambiguities is possible. Why? 2. Double-Differences For high accuracy of the carrier phase observable, the ambiguities must be resolved to their correct integer value since one cycle on the L1 carrier may translate, in the maximum, to a 19 cm position error. It should be stressed here that integer ambiguity resolution may not always be possible. 3. Effect of Ionosphere, Troposphere and Other Minor

4. Satellite Geometry and Measurement Time 5. Multipath and Length of Baseline Satellite Geometry: The number of satellites tracked at ultipath is station dependent, it may be significant for any instant translates into a better dilution of precision nort baselines. As in the case of atmospheric and orbital alue. Thus if a receiver tracks seven or eight satellites. it Tors for long baselines, multipath has the effect of both is preferable since redundant satellites aid in the efficiency ontaminating the station coordinates and ambiguities and reliability of ambiguity resolution Multipath is also a critical factor for ambiquity resolution. Length of measurement Time: The information content of the carrier phase is a function of time which is directly 6. Major Steps of Ambiguity Resolution correlated to the movement of the satellite The Main First Step is the generation of potential integer The time is a critical component of ambiguity resolution mbiguity combinations that should be considered by the even under good geometric conditions. Example: every 15 seconds for one hour, every second for A combination is comprised of an integer ambiquity for. four minutes, a total of 240 measurements per satellite. egeach of the domble-difiference satellite nairs. Search Space is the volume of uncertainty which surrounds the approximate coordinates of the unknown The Second Major Step is the identification of the antenna location correct integer ambiguity combination. Static positioning: it can be realized from the so- called float ambiguity solution, The Third Major Step is the a validation(verification) Kinematic positioning: it is realized from a code of the ambiguities ange solution ize of the Search Space will affect the efficiency, i.e Integer ambiguity combinations to assess, which in tum ncreases the computational burden. This is typically important for kinematic applications. It is necessary to balance computational load with a conservative search space sIze 2.2 Basic Approaches Characteristics of Single-Frequency: 1. With Single Frequency Phase Data For only one frequency(Ll or L2)available, the most direct 1. The unmodeled errors affect all estimated parameters Therefore the integer nature of the ambiguities is lost and 1. Establishing model by Eq(9.14), hey are estimated as real values. teger values, a sequential adjustment could be performed ordinates, clock parameters, etc. )is estimated along with N in a common adjustment. 3. After an initial adjustment, the ambiguity with a computed value closest to an integer and with minimum standard When using double-differences over short baselines, this approach is sually successful. The critical factor is the ionospheric refraction bias is then fixed, and the adjustment is repeated(with one which must be modeled and which may prevent a correct resolution less unknown) to fix another ambiguity and so on

3 Satellite Geometry: The number of satellites tracked at any instant translates into a better dilution of precision value. Thus, if a receiver tracks seven or eight satellites, it is preferable since redundant satellites aid in the efficiency and reliability of ambiguity resolution. Length of Measurement Time: The information content of the carrier phase is a function of time which is directly correlated to the movement of the satellite. 4. Satellite Geometry and Measurement Time The time is a critical component of ambiguity resolution even under good geometric conditions. Example: every 15 seconds for one hour; every second for four minutes, a total of 240 measurements per satellite. Since multipath is station dependent, it may be significant for short baselines. As in the case of atmospheric and orbital errors for long baselines, multipath has the effect of both contaminating the station coordinates and ambiguities 6. Major Steps of Ambiguity Resolution Multipath is also a critical factor for ambiguity resolution. 5. Multipath and Length of Baseline The Main First Step is the generation of potential integer ambiguity combinations that should be considered by the algorithm. A combination is comprised of an integer ambiguity for, e.g., each of the double-difference satellite pairs. Search Space is the volume of uncertainty which surrounds the approximate coordinates of the unknown antenna location. • Static positioning: it can be realized from the socalled float ambiguity solution, • Kinematic positioning: it is realized from a code range solution. Size of the Search Space will affect the efficiency, i.e., computational speed. • A larger search space gives a higher number of potential integer ambiguity combinations to assess, which in turn increases the computational burden. This is typically important for kinematic applications. It is necessary to balance computational load with a conservative search space size. The Second Major Step is the identification of the correct integer ambiguity combination. The Third Major Step is the a validation (verification) of the ambiguities. 2.2 Basic Approaches 1. With Single Frequency Phase Data For only one frequency (L1 or L2) available, the most direct approach is. 1. Establishing model by Eq. (9.14), 2. Linearizing the model, 3. Solving the model, a number of unknowns (e.g., point coordinates, clock parameters, etc.) is estimated along with N in a common adjustment. When using double-differences over short baselines, this approach is usually successful. The critical factor is the ionospheric refraction which must be modeled and which may prevent a correct resolution of all ambiguities. 1. The unmodeled errors affect all estimated parameters. Therefore, the integer nature of the ambiguities is lost and they are estimated as real values. 2. To fix ambiguities to integer values, a sequential adjustment could be performed. 3. After an initial adjustment, the ambiguity with a computed value closest to an integer and with minimum standard error is considered to be determined most reliably. This bias is then fixed, and the adjustment is repeated (with one less unknown) to fix another ambiguity and so on. Characteristics of Single-Frequency:

4 2. With Dual Frequency Phase Data Why Dual Frequency: because of the various possible linear combinations. fL1-L2 = 347.82 MHz, λL1-L2 = 86.2 cm λorg = 19~24.4 cm Wide Lane and Narrow Lane Techniques: Wide Lane Signal: Φ w = Φ L1 − Φ L 2 Significant increase compared to the original wavelengths • The increased wide lane wavelength provides an increased ambiguity spacing. • This is the key to easier resolution of the integer ambiguities. Φ L1− L 2 = Φ L1 − Φ L 2 L1 L 2 L1 L 2 f = f − f − NL1−L 2 = NL1 − NL 2 The adjustment based on the wide lane model gives wide lane ambiguities NL1-L2 which are more easily resoled than the base carrier ambiguities. ( ) (1 ) 2 1 1 2 1 1 2 1 1 1 1 2 1 2 L L L L L L L L L L L L L L f f f b f b f f N = Φ − Φ − N + − − − − − − To compute the ambiguities for the measured phases, we can get What is b? please see p. 105, Eq.6.73 1 2 1 2 1 2 1 1 1 1 2 1 2 ( ) L L L L L L L L L L L L L f f f f b f f N N + = Φ − Φ − + − − − After ionospheric Geometry-free linear phase combination The disadvantage of this combination is • The corresponding ambiguity is no longer an integer. • The ionosphere is a problem or the ionospheric influence is eliminated which destroys the integer nature of the ambiguities. The use of other linear combinations ranging from narrow lane with a 10.7 cm wavelength to extra wide with a 172.4 cm wavelength. Characteristics of Dual-Frequency: 3. By Combining Dual Frequency Carrier Phase and Code Data The most unreliable factor of the wide lane technique is the influence of the ionosphere which increases with baseline length. This drawback can be eliminated by a combination of phase and code data. 1 1 1 1 N b a L L L L f Φ = f − + 1 1 1 b a L L L f R = f + carrier phases code ranges 2 2 2 2 N b a L L L L f Φ = f − + 2 2 2 b a L L L f R = f + What is a, b? please see p. 105, Eq.6.74 4 equations contain 4 unknowns, geometry term, a and ionosphere term b and ( )( ) 1 2 1 2 1 2 1 2 1 2 L L L L L L L L L L R R f f f f N + + − − = Φ − − This rather elegant equation allows for the determination of the wide lane ambiguity NL1-L2 for each epoch and each site. It is independent of the baseline length and of the ionospheric effects. By a series derivation, we finally get Note that even if all systematic effects cancel out, the multipath effect remains and affects phase and code differently. 4. By Combining Triple Frequency Carrier Phase and Code Data This technique for ambiguity resolution based on three carriers is denoted as Three-Carries Ambiguity Resolution-TCAR. 1 1 1 1 N b a L L L L f Φ = f − + 1 1 1 b a L L L f R = f + carrier phases code ranges 2 2 2 2 N b a L L L L f Φ = f − + 2 2 2 b a L L L f R = f + What is a, b? please see p. 105, Eq.6.74 5 5 5 5 N b a L L L L f Φ = f − + 5 5 5 b a L L L f R = f + Similarly 6 equations contain 5 unknowns

5 3. Search Techniques 1. A Standard Approach When processing the data based on double-differences by least squares adjustment, the ambiguities are estimated as real or floating point numbers. The first double-difference solution is called the float ambiguity solution. The output is the best estimate of the station coordinates as well as double-difference ambiguities. Shore baseline (e.g., 5km), and long observation span (1 hr), the float ambiguities close to integers. Ambiguity resolution in this case is merely used to refine the achievable positioning accuracy. For example: 2. Ambiguity Resolution On-the-Fly (AROF, OTF, OTR) Code ranges are used to define the search space for the kinematic case. A relative code range position is used as the best estimate of antenna location, and the associated standard deviations are used to define the size of the search space (a cube, a cylinder, or an ellipsoid). To reduce the number of integer ambiguity combinations, the code solution should be as accurate as possible which means that receiver selection becomes important. • Low noise, • Narrow correlator-type code ranges They have a resolution at 10 cm range and improved multipath reduction compared with standard C/A-code receivers. The OTF techniques have common features like, e.g., the determination of an initial solution. A summary of the main features is given in Table 9.5 p. 228. Please see the Table 9.5, p. 228. 3. Ambiguity Function Method ρ ( ) N δ ( ) 1 AB j j AB t f t AB AB j Φ = + − λ ρ ( ) N δ ( ) 1 AB j j AB t f t AB AB j Φ − = − λ {2 πN ( ) 2ππf ( ) ρ ( )} λ 2π {2 πΦ ( ) AB j AB i t t i t t j AB j AB e e − − = 2 πN 2 πfδ ( )} ρ ( )} λ 2π {2 πΦ ( ) j AB j AB i t i i t t e e e j AB j AB − − = cos α sin α iα e = + i 2 πfδ ( ) ρ ( )} λ 2π {2 πΦ ( ) AB j AB i t i t t e e j AB − − = For one epoch and one satellite The basic principle by Counselman and Gourevitch is 4. Least Squares Ambiguity Search Technique Basic principles: is the separation of the satellites into a primary and a secondary group. 1. The primary group consists of four satellites, which should have a good PDOP, the possible ambiguity sets are determined. 2. The remaining secondary satellites are used to eliminate candidates of the possible ambiguity sets. Approximation: This technique requires an approximation for the position (due to the linearization of the observation equation) which may be obtained from a code range solution. Search Area: The search area may be established by surrounding the approximate position by a 3δ region

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. 237-244

6 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