Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #1

MULTIPLE HYPOTHESIS SEQUENTIAL PROBABILITY RATIO TESTS FOR RESOLVING INTEGER AMBIGUITY IN GPS:
J.D. Wolfe, J.L. Speyer, W.R. Williamson, UCLA MAE Dept.

In this paper, we present two statistical techniques appropriate for the "validation" of integer ambiguities and the detection of cycle slips. The multiple hypothesis Wald sequential probability ratio test (SPRT) can find the conditional probability that each set of integer biases under consideration is the true bias condition. The multiple hypothesis Shiryayev SPRT determines the conditional probability that the integer biases have jumped from the nominal bias condition to each member of a collection of other bias conditions. Hence, the Wald SPRT is a method for validating the integer ambiguities during the initial ambiguity resolution, while the Shiryayev SPRT can be used to monitor for cycle slips.

Each of these multiple hypothesis SPRTs (MHSPRTs) makes use of two measurement residuals. One is geometric combination of the carrier phase measurements, and the other is generated by differencing the carrier phase measurements with code measurements.

Prior work on cycle slip monitoring has focused solely on the detection of the occurrence of a cycle slip in the fastest time, balanced against the probability of issuing a false alarm. Once a disruption has occurred, the ambiguity resolution process must restart from scratch. The Shiryayev SPRT bypasses this problem, as it announces the location of the biases after the jump, in addition to the time of the cycle slip.

The calculations for the MHSPRTs are not linked to any particular distribution, unlike prior efforts. Only the probability density functions of the measurement residuals are required. Hence, the techniques can correctly compensate for non-Gaussian errors in measurement such as multipath.

For each hypothesis under consideration, the MHSPRTs yield the probability of that hypothesis being the correct one. The "state" of the MHSPRT recursions is the vector of all of these probabilities. Information from past measurements is embedded in this state. This recursive, probabilistic framework makes it very straightforward to add new hypotheses into the set of possible bias conditions while retaining information from prior measurements. In contrast, there is no way to do this for other techniques, since they are based on cumulative sums.

Results from successful simulations and field experiments will be presented, showing the efficacy of these techniques.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #2

FAST AMBIGUITY CONVERGENCE IN CARRIER PHASE-BASED PRECISE POINT POSITIONING:
Y. Gao, X. Shen, The University of Calgary, Canada; P. Heroux, Natural Resources Canada

Precise Point Positioning (PPP) is a technology currently under development with a strong interest from the GPS community in recent years. Using currently available precise satellite orbit and clock products from organizations such as the International GPS Service (IGS) and Natural Resources Canada (NRCan), PPP has the potential to provide decimetre to centimetre accurate position results in a stand-alone mode on a global scale. Differs from the traditional differential positioning techniques that require access to observations from one or more reference stations with known coordinates, PPP doesn't involve observation differencing. As the continuous improvement of the precise products in precision and timeliness and the permanent turn-off of the Satellite Selectivity (SA), PPP will be feasible for real-time decimetre to centimetre accurate positioning and navigation in the near future.

This paper will report recent research results in the development of a PPP system. Since the carrier phase is the principal observable, fast ambiguity convergence will be the most critical part in order for the system to be feasible for real-time application. The characteristics of the residual errors after the use of precise and clock correction and other error mitigation models must therefore be investigated before a proper model can be developed for optimal position and ambiguity determination. In this paper, observation combinations suitable for PPP have been developed to eliminate the influence of the ionosphere while minimizing the increase of the measurement noise level. This step is essential for fast ambiguity convergence. With the newly developed observable combination, a stochastic model has been developed to further strengthen the model to account for possible significant residual errors in the observations and subsequently to improve the performance of ambiguity convergence. Once fast ambiguity convergence is reached, effort to fix the ambiguity can then be made to further improve the obtainable position accuracy. On the occasion of a slow ambiguity convergence, a search technique has been developed to accelerate the convergence. Numerical results will be presented to support the analysis using IGS precise orbit and clock products and NRCan's real-time orbit and clock products. Test results in both static and kinematic modes have indicated that decimetre to centimetre position accuracy is obtainable using the developed PPP system.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #3

RELIABILITY ANALYSIS OF A QUASI-INSTANTANEOUS AMBIGUITY FIXING METHOD:
T. Cunha, P. Tome, S. Cunha, L. Bastos, University of Porto, Portugal

This paper describes a method for L1 ambiguity determination that requires only a few seconds of data (typically 3 to 10, depending on the specific conditions), for DGPS kinematic applications. This methodology is based on dual frequency data and is suitable for situations where the data rate is relatively high (1 Hz or higher), which is typical for most kinematic surveys. The proposed methodology takes into consideration the fact that some parameters are better estimated at a higher sampling frequency. Based on this and a few other strategies described in this paper, a reduced ambiguity search space is generated. The selection of the best candidate takes into account, among other factors, the residuals of both L1 and L2 carrier phase measurements, making use of the correlation that exists between them regarding the unique antenna position and the wide-lane ambiguity. This set of algorithms was implemented as a user-friendly computer application, which is able to process data both in real-time and post-processing mode.

This paper demonstrates the reliability of this method by presenting results obtained from several tests, under different conditions, and with sufficient trials to withdraw statistical conclusions about its performance. The ionospheric influence is also analyzed together with the behavior of the method with increasing baseline length. The issue of employing multiple reference stations is also addressed, with test data analysis indicating a performance improvement of the method over larger areas.

Almost instantaneous high-precision positioning can benefit many surveying applications. Achieving a sub-decimeter precision with only a few seconds of observation improves the productivity of any land survey, like, for example, photogrametric point surveying or kinematic surveys where the obstruction of satellite signals can occur quite frequently. When operating in real-time, the developed software allows the user to view graphically the quality of the estimated position on-line. For short-static applications, this feature enables the user to survey a point only during the strictly necessary time and not for a predefined, and usually over-determined, interval.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #4

SURVEY QUALITY REAL-TIME GPS: SOLVING THE TIME TO FIX VS. RELIABILITY PARADOX:
S. Han, R. Johnson, Ashtech Precision Products, Magellan Corporation

Carrier phase ambiguity resolution is the corner stone of modern real-time GPS surveying systems. Availability of fixed ambiguity solutions is the difference between waiting and working. Evaluation of the time to fix in a variety of real-world conditions is often a primary motivator when GPS system buying decisions are made, but solving the paradox of speed versus reliability continues to be one of the greatest challenges facing real-time GPS surveying.

In an effort to translate GPS receiver technology to fast, reliable centimeter level solutions for surveyors, scientists and engineers are required to push the limits of real-time carrier phase performance. Operational constraints of real world environments, such as extended baseline length, signal multipath and organic obstructions require not only strong mathematical and statistical modeling, but progressive stochastic modeling techniques as well.

Advanced, adaptive stochastic modeling in addition to careful statistical modeling as implemented in the Ashtech Instant-RTK technology and featured in the new Z-Xtreme GPS receiver demonstrates unprecedented success in solving the ambiguity resolution speed vs. reliability paradox. Tests on short to medium length baselines with open sky show typical <5 sec ambiguity resolution with 99.9% reliability, and tests on longer baselines, and baselines with significant tree obstructions, maintain 99.9% reliability with impressive time to fix.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #5

A COMPUTATIONALLY EFFICIENT AMBIGUITY RESOLUTION TECHNIQUE:
R. Hatch, T. Sharpe, P. Rosenboom, NavCom Technology, Inc.

NavCom Technology, a wholly owned subsidiary of John Deere, has developed real-time kinematic (RTK) or carrier-phase differential GPS software to embed within their NCT-2000D dual-frequency GPS receiver. First, measurement domain techniques are used to minimize multipath distortion in two ways. A weighted average is formed of the code measurements at L1 and L2, which statistically reduces both the multipath and the temporal correlation of that multipath. In addition, the weighting is chosen such that the resulting code measurement is affected by ionospheric refraction exactly the same as the wide-lane carrier phase. This allows a smoothing process to be implemented as an expanding recursive average, which automatically reduces the multipath-and the longer the ambiguity resolution process takes, the lower the multipath corruption of the code measurements.

In the next step of the processing, the smoothed code measurements are used to set wide-lane ambiguity values to the nearest integer. Using these values a wide-lane base position is computed together with the associated residuals. From the geometry information, the sensitivity or S-matrix is computed. The S-matrix indicates how each residual would change given a specific change in the individual carrier-phase measurements. For RTK positioning the S-matrix can be quantized to reflect a change of one whole-cycle in the ambiguity value. This allows very rapid and efficient computation of the RMS residuals corresponding to the search across different ambiguity combinations.

In a final step of the processing, the narrow-lane carrier-phase ambiguity values are computed and the S-matrix is used to search the two integer values which are closest to the computed value. The solution with the smallest residual is selected as the tentative solution. Several tests are implemented to prevent an incorrect set of ambiguity values from being selected. Ambiguities are declared resolved when these tests are passed successfully.

Scoring runs, which measure the time to resolve the ambiguity values, will be shown for different baseline separation distances. The new ambiguity resolution process is very efficient computationally and the number of one-second epochs needed to resolve the ambiguities averages less than eight. With the computer loading from higher priority tasks, the ambiguity resolution logic can take nearly twice real time. Thus, ambiguity resolution within the NCT 2000D receiver generally takes less than 15 seconds on average.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #6

A NEW GEOMETRICAL APPROACH FOR INTEGER AMBIGUITY RESOLUTION, WHICH CAN GUARANTEE CORRECTNESS OF THE SOLUTIONS:
C. Kee, D. Kim, Seoul National University, Korea

Real-Time Kinematic GPS positioning is widely used for many applications. It can provide static & kinematic positioning accuracy to centimeter level. Resolving ambiguities is the key to precise positioning. Integer ambiguity resolution is the process of resolving the unknown cycle ambiguities of double difference carrier phase data as integers. Two important points of resolving ambiguities as integer numbers are efficiency and reliability.

Many groups have proposed a lot of ambiguity resolution techniques. However, there is no one that can guarantee correctness of the solution. We cannot determine whether it is right solution or not with existing techniques. In real-time positioning, the reliability of solution is a very critical problem that is directly related to safety.

This paper proposes a reliable and effective ambiguity resolution. We found a new method to resolve ambiguity by using geometrical formulation. Our approach can prevent wrong fixes and give a confidence level of solution. We can say that the solution is right or wrong when it is resolved, because we check candidates of solution probabilistically. It can be also used as a built-in integrity monitoring system.

Together with this algorithm, we devised a new method to check candidates more efficiently. We found that computational loads were reduced to one-tenth on the average with this method. It can eliminate unnecessary checking of candidates, so as a result we can get a computational efficiency.

In this paper, we described the procedure for our new algorithms and showed the results of simulations. The performance of our approach was compared with those of existing approaches.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #7

FLIGHT TEST OF A MULTIPLE FILTER APPROACH FOR PRECISE DGPS POSITIONING AND CARRIER-PHASE AMBIGUITY RESOLUTION:
P.E. Henderson, Air Force Institute of Technology School of Engineering

ION Sponsored Student Paper
Precise relative positioning obtained using differential GPS depends on accurately determining the carrier-phase integer ambiguities. In order to achieve high precision, many current static and kinematic surveying algorithms use a floating-point solution until enough information becomes available to fix the carrier-phase ambiguities accurately. However, in dynamic environments where many brief measurement outages or cycle slips are possible, these algorithms may never gain enough information to fix the ambiguities with the confidence required for a fixed-integer solution.

A mew method is presented that uses a multiple model Kalman filter to resolve the carrier-phase integer ambiguities . This method starts with the floating-point results, yet smoothly and rapidly attains the precision of the correct fixed-integer solution, eliminating the need to decide when to switch from the floating to the fixed-integer solution. This method is based on a theoretically correct blending of solutions from multiple filters, each of which hypothesizes a different ambiguity set. This new technique is computationally efficient, providing a robust navigation solution useful in demanding applications such as precision landing and autonomous navigation.

This paper describes the new algorithm and explains its differences and advantages over current approaches. The paper also presents the results of flight tests and discusses possible improvements to the new algorithm.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Paper #8

SINGLE EPOCH AMBIGUITY RESOLUTION FOR HIGHWAY AND RACETRACK APPLICATIONS:
J.W. Sinko, SRI International

The development of reliable RTK GPS for vehicles operating in the highway environment will enable many new safety, efficiency, and convenience applications. An obvious application is a lane departure warning system that would eventually be augmented to support fully automated highways. On the racetrack RTK GPS can be used to measure and optimize vehicle handling characteristics and driver performance. Real time centimeter-level accuracy GPS for highway and motor racing applications requires specialized algorithms. The greatest difficulty encountered is the frequent obscurations that cause the GPS receiver to loose track of satellite signals. Of particular concern is the frequent loss of L2 carrier phase data for many seconds, and even after track is reestablished, the accuracy is degraded for several seconds. Test results of reacquisition times for receivers from several manufacturers are included.

This paper presents a new single epoch ambiguity resolution technique that is optimized for the highway environment. The term single epoch ambiguity resolution is somewhat of a misnomer in that most GPS receivers have smoothing filters which introduce a significant correlation between successive epochs when sampling rates are 1 Hz or higher. Also, multipath errors are highly correlated in time. Autocorrelation functions for the residuals after correct ambiguity resolution are shown. The single-epoch method eliminates the prolonged carrying of wrong integer solutions that occasionally happens with Kalman filter and other multiple epoch algorithms. After encountering an obstacle, the single epoch method provides a solution as soon as the receiver recovers an adequate number of signals, although the probability of selecting the correct integers will improve after the receiver has had a few seconds of settling time. Over short baselines (a few kilometers) and with 6 or more satellites available, ambiguities are resolved correctly over 99% of the time. In clear areas (i.e. a racetrack in Buttonwillow, CA) correct single epoch ambiguity resolution has been demonstrated over 99.8% of the time.

Vehicular applications can use altitude aiding to significantly help in resolving the ambiguities. Code differential GPS gives the location on the road with sufficient accuracy that an accurate height can be found from a detailed road database and used as a constraint in finding the solution. The algorithm has been tested in a series of rooftop static tests during which the antennas were covered for short periods of time. On a relatively clear stretch of freeway with only one overpass, correct ambiguity resolution was demonstrated 88% of the time without altitude aiding and 96% of the time with altitude aiding. Over a more obscured stretch of freeway with trees and hills, ambiguities were correctly resolved 62% of the time without altitude aiding and 91% of the time with altitude aiding.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Alternate #1

ACCURACY ANALYSIS OF AIRBORNE KINEMATIC POSITIONING AND ATTITUDE DETERMINATION USING THE NGS CORS AND THE IGS DATA:
M.M.R. Mostafa, J. Hutton, B. Scherzinger, Applanix Corporation

In some aerial survey applications, the required accuracy of aircraft position and attitude information is relaxed, yet having a GPS base station becomes a problem in some situations. In this paper, the potential of using GPS with no base station for aerial survey applications is discussed. Either The NGS CORS network stations and/or the IGS precise ephemeris, satellite clock corrections, and ionospheric and tropospheric information, are processed in conjunction with the airborne GPS raw observables to determine the aircraft position and velocity. The GPS post-processed data is then used to aid the inertial data processing in a closed loop fashion to end up with a full resolution of the trajectory parameters, namely position, velocity and attitude. The interpolated aircraft position and attitude parameters are then used to generate Exterior Orientation data to support aerial mapping. Flight test data were collected in January 2001 using the Applanix POS/AV system (S/A is off). Processed results are compared against two references. The first is a reference trajectory computed using a carrier phase DGPS solution integrated with the inertial data (using a nearby base station). The second is a reference trajectory computed using a traditional photogrammetric aerotriangulation. All GPS and integrated GPS/Inertial processing was done using the Applanix POSPacTM software. Test results and analysis are presented in some detail.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Alternate #2

MODULAR GPS/IMU AIDED KINEMATIC CARRIER PHASE TRACKING (KCPT) SOFTWARE PACKAGE - ARCHITECTURE AND RESULTS:
K. Taylor, A. Brown, D. Sullivan, NAVSYS Corporation

NAVSYS has developed a modularized, integrated GPS/IMU KCPT software package that offers the ultimate in flexibility with regard to hardware configuration, software operation and performance control. The truly modular design accepts GPS data from a variety of GPS receivers, including the NAVSYS Advanced GPS receiver (AGR) as well as devices from Novatel and Rockwell Collins. It also has the capability to use a variety of IMU's, including RLG, FOG and MEMS devices. Using the package, we are able to fuse GPS data, using either narrow-laning or wide-laning processing, with the inertial data to provide a more robust ambiguity resolution solution while constantly monitoring the integrity of the solutions.

This paper describes the approach used to modularize the software components to achieve maximum robustness and integrity, and demonstrates solution performance with different system configurations.
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Session D3: CARRIER PHASE-BASED POSITIONING II
Alternate #3

SINGLE-FREQUENCY RTK SYSTEM USING LOW-COST GPS RECEIVER:
S. Park, Y. Cho, J. Gil, ELEXTECH, Korea

Over the last decade, RTK has undergone tremendous improvement and can now routinely deliver centimeter accuracy. But RTK systems are too expensive equipment.
This paper presents effective and reliable approach for RTK algorithm with L1 C/A GPS receiver. This RTK system used LSAST and FASF to resolve integer ambiguity.

A carrier phase-based GPS positioning system based on a low-cost hardware configuration is described. We present a algorithm for real-time kinematic applications, implementation technique and test results. To evaluate the performance of the low-cost RTK system, the static and dynamic experiments were conducted.
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