Least-squares Ambiguity Decorrelation Adjustment Method Research Articles

Real-time GNSS attitude determination by a direct approach with efficiency and robustness

Estimating attitude directly from multi-antenna carrier phase measurements is known as the direct approach of global navigation satellite system attitude determination. Without the process of resolving baseline vectors in advance, this approach makes full use of raw observations. However, the known baseline constraints would be missing when the least squares method is used in the direct approach, of which the corresponding model contains no baseline parameter. The constraint information is important for real-time ambiguity resolution. Therefore, we propose using an adaptively robust Kalman filter for the direct approach, in which the predicted attitude plays the role of an attitude constraint. An observation model parameterized by the multiplicative quaternion error vector and the integer ambiguities is derived, accompanied with a state model consisting of the quaternion error vector, the ambiguities and the angular rate. Since the state vector contains three different types of parameters, the filter uses an adaptive matrix consisting of different adaptive factors instead of a single factor. The factor of the quaternion error vector is determined by a three-section function containing the ratio value from the ratio-test of ambiguity resolution. The factors of the ambiguities are calculated by the detected cycle slip. The equivalent weight matrix of the filtering can resist the influence of outliers in harsh environment. By the direct approach with the proposed adaptively robust filtering, the accuracy of the float solution and the variance-covariance matrix are significantly improved, and the ambiguity can be efficiently searched and fixed using the standard least-squares ambiguity decorrelation adjustment method. The proposed algorithm is suitable for real-time applications since no time-consuming and complex searching of ambiguity resolution is required. Finally, the efficiency and robustness of the algorithm is validated by a field test.

EFFECT OF SPATIAL CORRELATION ON THE PERFORMANCES OF MODERNIZED GPS AND GALILEO IN RELATIVE POSITIONING

In the context of processing GNSS (Global Navigation Satellite System) data, it is known that the estimation of the ionospheric delays decreases the strength of the observation model and makes significant the time required to fix the ambiguities namely in case of long baselines. However, considering the double-differenced (DD) ionospheric delays as stochastic quantities, the redundancy in this case increases and leads to the reduction of time of fixing the ambiguities. The approach developed in the present paper makes two considerations: 1) the DD ionospheric delays are assumed as stochastic quantities and, 2) the spatial correlation of errors is accounted for based on a simple model of correlation. A simulation is made and aims to study the effect of these two mentioned considerations on the performances of the three multifrequency GNSSs; modernized GPS, Galileo and BDS which are not yet in full capability. For each GNSS, dual-frequency combinations of frequencies as well as triple-frequency combination are investigated in the simulation. The performances studied include: the time to fix the ambiguities with high success rate and the precision of coordinates in static relative positioning with varying baseline length. A method is developed to derive what we call the spatial correlation model which approximately gives the covariance between the individual errors belonging to two stations. Furthermore, the stochastic models that follow from accounting and neglecting the spatial correlation are developed. The LAMBDA (Least-squares Ambiguity Decorrelation Adjustment) method is implemented for ambiguity decorrelation. The results show that the time to fix the ambiguities caused by accounting the spatial correlation is less than the time of fix without the spatial correlation. Also, a slight superiority of Galileo in terms of performances is seen compared to the other GNSS. For all the dualfrequency combinations investigated, when processing a baseline length of 500 km with accounted spatial correlation, the time needed to successfully fix the ambiguities lies between 5 and 9 min, whereas it becomes only between 2.5 and 3 min for all the triple-frequency combinations, this is with a sampling time of 5 s. In addition, for all different combinations, the coordinates precision is less than 8 mm even for 500 km. We think that these high performances result from: 1) the precise codes of future GNSS signals, 2) the high redundancy in the observations equation and, 3) taking into account the spatial correlation in the definition of the stochastic model.

Parameterization-switching GNSS attitude determination considering the success rate of ambiguity resolution

The two key elements of GNSS attitude determination are the correct integer ambiguity resolution (IAR) and the choice of appropriate method. The least-squares ambiguity decorrelation adjustment method is normally used to fix ambiguities using float estimates. However, it is difficult to get all ambiguities fixed in real time. Therefore, a method of partial ambiguity resolution which considers the success rate of IAR and makes full use of the ambiguity information at each epoch is proposed. The ambiguities after decorrelation can be divided into fixed ambiguities and unfixed ambiguities considering the fixing success rate. At the next epoch, the fixed ones are treated as constants, while the float estimates of the unfixed ones, along with the corresponding covariance matrix, are treated as prior information or pseudo-measurements. The parameters of the attitude determination problem can be baseline coordinates (BCs) or attitude angles (AAs). BC parameterization, without considering the baseline constraints, has the merit of resulting in a linear model; however, it involves parameter redundancy, which reduces the model strength. AA parameterization, although avoiding parameter redundancy, brings in nonlinearity and hence linearization errors in the least-squares solution. The linearization errors decrease as the number of fixed ambiguities increases. A switching-parameterization method is proposed; namely, at any epoch, as long as there are at least three fixed double-difference ambiguities, AA parameterization is adopted, otherwise BC is adopted. Even with AA, BC is firstly estimated and then transformed to attitude estimates at which the nonlinear measurement equations are linearized and solved. To verify the performance of the proposed method, a comparative study is implemented with BC and AA methods in the static experiment. The results show that the proposed method can fix ambiguity faster and have better stability and accuracy. In addition, the yaw angle is consistent with the actual running route of the vehicle in the kinematic experiment.

GNSS ambiguity resolution with ratio and fixed failure ratio tests for long baseline network RTK under ionospheric activity

To perform network RTK positioning, a user must receive and apply the information generated from a network. Corrections are generated for the user to consider the atmospheric delays (ionosphere and troposphere) between ther location and the network stations. In order to generate reliable corrections and send them to users, one must resolve the ambiguities in the processing step of the network stations. Ambiguities are the number of integer cycles of the carrier phase in the first data collection epoch and are introduced as parameters to be estimated in the processing. Thus, the ambiguity resolution process becomes a prerequisite for obtaining high accuracy in network RTK positioning. This process can be divided into two steps: estimation and validation. The estimation step aims to obtain the integer values of ambiguities and in the validation step it is inferred if the estimated integer value may or may not be accepted. In this work, the LAMBDA (Least squares AMBiguity Decorrelation Adjustment) method was used to obtain the integer ambiguity estimate and for the validation the Ratio and FF-RT (Fixed Failure Ratio Test) tests were used. The objective of this work was to investigate the performance of the ambiguities validation tests for long baselines. The results showed that the FF-RT test presented the highest fixed ambiguity percentages when compared to the Ratio test in all analyzed periods. Thus, for long baselines positioning, in periods of either weak or strong ionospheric activity, the use of the FF-RT test will cause a greater number of fixed ambiguities to be used in the process of generating the corrections for the user.

Effect of selection of combined observations on cycle-slip repair success rate for BDS triple-frequency signals

Modern global navigation satellite systems introduce additional frequencies that benefit the performance of cycle-slip detection and repair. However, recent related studies have focused on the success rate (SR) of cycle-slip detection rather than that of repair. This study considered common combinations of triple-frequency observations and analyzed their advantages/disadvantages in detail. To detect and repair cycle slip, combinations of the two main forms of observation were constructed based on the classic least-squares ambiguity decorrelation adjustment (LAMBDA) method, with consideration of residual ionospheric variations. A large volume of simulation data was used to test the cycle-slip repair SR of different combinations of observations under different ionospheric conditions. Theoretical and experimental results showed that using different forms of two geometry-free (GF) phase or two extra-wide-lane (EWL) combinations to fix the cycle-slip solution using the LAMBDA method was irrelevant to the cycle-slip repair SR of the 1EWL & 2GF and 2EWL & 1GF phase combination forms, respectively. Under the same ionospheric conditions, the performance of 2EWL & 1GF phase combinations was significantly better than that of 1EWL & 2GF phase combinations in terms of cycle-slip repair SR. The difference was mainly reflected in the performance of cycle-slip detection. The larger the maximum threshold of ionospheric variation (MTIV) value of GF phase combination observations, which represents the ability to resist the insensitive cycle-slip group ±(1, 1, 1), the lower the cycle-slip repair SR for those combinations. Therefore, the optimal strategy would be to employ strong GF phase combinations with a large MTIV value to detect cycle slip, and to employ excellent GF phase combinations with a high SR to repair cycle slip.

Improving ambiguity resolution success rate in the joint solution of GNSS-based attitude determination and relative positioning with multivariate constraints

Usually, the global navigation satellite system (GNSS)-based attitude determination and the GNSS-based relative positioning are treated as separate problems. In this contribution, the two problems are resolved as a combined solution of a joint model with multivariate constraints, in which the known geometry of the antenna array on the rover platform is used as constraints, thereby improving the parameter estimation in not only the attitude determination but also the relative positioning. The objective function of the joint model is decomposed and then reduced so that only the terms concerning the constraints are retained, thus transforming the objective function into the exact form of that of the GNSS-based multivariate constrained attitude determination model. Then the multivariate constrained least-squares ambiguity decorrelation adjustment method together with the efficient shrinkage or expansion with bounds strategies, which are shown to work well in the attitude determination, can be extended to the joint model. In experimental validation, the joint model is tested with both simulated and real GPS/BDS datasets in terms of ambiguity resolution success rate and the precision of solutions. The results confirm that the joint model ensures the highest ambiguity resolution success rate among the existing unaided GNSS-based relative positioning methods, and the improvement is more obvious when the observation model is weaker, for example, when the number of available satellites is fewer or when the precision of observations is poorer, thus showing an overall best performance in both reliability and precision aspects.

Influence of Pseudorange Biases on Single Epoch GNSS Integer Ambiguity Resolution

Model strength and biases are two main factors for GNSS integer ambiguity resolution. Due to the nonideal GNSS signal, the receiver's observations will be biased. In GNSS relative positioning, the double difference pseudorange bias cannot be eliminated due to the different receiver's technical parameters between base and rover stations, which are generally ignored. This paper investigates single epoch ambiguity resolution performance in the presence of pseudorange biases. Specifically, two commonly ambiguity resolution methods are used, including the bootstrapped and the Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) methods. A transfer model of pseudorange biases affecting integer ambiguity resolution is proposed to analyze the influence of pseudorange biases theoretically. The theoretical analysis and simulation results show that the pseudorange biases can affect the float ambiguities and decrease the success rate of integer ambiguity resolution. The simulation result shows that the performance of bootstrapped method may exceed the LAMBDA method in the presence of pseudorange biases. Further, a real data experiment is conducted to confirm the influence of pseudorange biases on ambiguity resolution. Both the simulations and the experimental results show that decimeter-level pseudorange biases can also decrease the success rate of ambiguity. The real data experiment indicates that with the pseudorange biases modified, the success rate of ambiguity fixing may increase up by 5% in zero baseline. The better the geometry of the observations, the robuster the ambiguity resolution against pseudorange biases.

Rotation Matrix Method Based on Ambiguity Function for GNSS Attitude Determination.

Global navigation satellite systems (GNSS) are well suited for attitude determination. In this study, we use the rotation matrix method to resolve the attitude angle. This method achieves better performance in reducing computational complexity and selecting satellites. The condition of the baseline length is combined with the ambiguity function method (AFM) to search for integer ambiguity, and it is validated in reducing the span of candidates. The noise error is always the key factor to the success rate. It is closely related to the satellite geometry model. In contrast to the AFM, the LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) method gets better results in solving the relationship of the geometric model and the noise error. Although the AFM is more flexible, it is lack of analysis on this aspect. In this study, the influence of the satellite geometry model on the success rate is analyzed in detail. The computation error and the noise error are effectively treated. Not only is the flexibility of the AFM inherited, but the success rate is also increased. An experiment is conducted in a selected campus, and the performance is proved to be effective. Our results are based on simulated and real-time GNSS data and are applied on single-frequency processing, which is known as one of the challenging case of GNSS attitude determination.

BeiDou phase bias estimation and its application in precise point positioning with triple-frequency observable

At present, the BeiDou system (BDS) enables the practical application of triple-frequency observable in the Asia-Pacific region, of many possible benefits from the additional signal; this study focuses on exploiting the contribution of zero difference (ZD) ambiguity resolution (AR) to the precise point positioning (PPP). A general modeling strategy for multi-frequency PPP AR is presented, in which, the least squares ambiguity decorrelation adjustment (LAMBDA) method is employed in ambiguity fixing based on the full variance-covariance ambiguity matrix generated from the raw data processing model. Because of the reliable fixing of BDS L1 ambiguity faces more difficulty, the LAMBDA method with partial ambiguity fixing is proposed to enable the independent and instantaneous resolution of extra wide-lane (EWL) and wide-lane (WL). This mechanism of sequential ambiguity fixing is demonstrated for resolving ZD satellite phase bias and performing triple-frequency PPP AR with two reference station networks with a typical baseline of up to 400 and 800 km, respectively. Tests show that about $$90\,\%$$ of the EWL and WL phase bias of BDS has a consistency of better than 0.1 cycle, and this value decreases to $$<$$ 80 % for L1 phase bias for Experiment I, while all the solutions of Experiment II have a similar RMS of about 0.12 cycles. In addition, the repeatability of the daily mean phase bias agree to 0.093 cycles and 0.095 cycles for EWL and WL on average, which is much smaller than 0.20 cycles of L1. To assess the improvement of fixed PPP brought by applying the third frequency signal as well as the above phase bias, various ambiguity fixing strategy are considered in the numerical demonstration. It is shown that the impact of the additional signal is almost negligible when only float solution involved. It is also shown that by fixing EWL and WL together, as opposed to the single ambiguity fixing, will leads to an improvement in PPP accuracy by about $$20.6\,\%$$ on average. Attributed to the efficient resolution of EWL $$+$$ WL within about 2 min in Experiment I, the 0.5 m level positioning can be achieved in 10 min for both horizontal and vertical, compared to 50 min for horizontal and 30 min for vertical by the NONE/EWL/WL fixed solution. While, for Experiment II, the improvement in the convergence can only be seen for the horizontal as the TTFF takes about 40 min for EWL and WL to be resolved.

Benefits of the third frequency signal on cycle slip correction

Cycle slip detection and correction are important issues when carrier phase observations are used in high-precision GNSS data processing and have, therefore, been intensively investigated. Along with the GNSS modernization, the cycle slip correction (CSC) problem has been raised to deal with more signals from multi-frequencies. We extend the geometry-based approach by integrating time-differenced pseudorange and carrier phase observations to estimate the integer number of triple-frequency cycle slips together with the receiver clock offset, ionospheric delay variations and receiver displacements. The Least-squares AMBiguity Decorrelation Adjustment method can be employed. The benefit of the third frequency observation on the cycle slip estimate is first investigated with simulation tests. The results show that adding the third frequency observation can significantly improve the model strength and that a reliable triple-frequency CSC with a theoretical success rate of higher than 99.9 % can still be achieved, even under the condition that the range or ionosphere delay variation is poorly defined. The performance of triple-frequency CSC is validated with real triple-frequency BDS data since all BDS satellites in orbit are transmitting triple-frequency signals. The results show that the fixing rate of CSC can reach 99.1 % in static precise point positioning (PPP) and 98.8 % in the kinematic case. PPP solutions with cycle slip-uncorrected and cycle slip-corrected data sets are compared to validate the correctness of triple-frequency CSC. The standard deviations of the PPP solution in east, north and vertical component, respectively, can be improved by 31.1, 30.7 and 37.6 % for static, and by 42.0, 53.8 and 39.7 % for kinematic after cycle slips are corrected. The performance of dual- and triple-frequency CSC is also compared. Results show that the performance of dual-frequency CSC is slightly worse than that of triple-frequency CSC. These results demonstrate that the performance of CSC can be significantly improved with triple-frequency observations.

Ambiguity-Free Method for Fast and Precise GNSS Differential Positioning

AbstractMethods based on integer ambiguity determination, such as the least-squares ambiguity decorrelation adjustment (LAMBDA) method, are currently used for precise global navigation satellite system (GNSS) differential positioning. In the present paper, the author proposes an ambiguity-free method based on a dedicated mixed (stochastic/deterministic) optimization algorithm that, unlike the LAMBDA method, is capable of providing reliable and accurate results using few observation epochs (e.g., 1-cm accuracy with just two epochs), having the additional advantages of insensitivity to cycle slips and impossibility of wrong ambiguity fixation. In addition, it is demonstrated that the application of the linear (deterministic) part of this algorithm yields the correct baseline results much more easily and quickly than methods requiring integer ambiguity determination, provided the initial approximate coordinates are accurate to a few centimeters. However, the use of ambiguity-free methods requires that the in...

Enhanced algorithm based on persistent scatterer interferometry for the estimation of high-rate land subsidence

Persistent scatterer interferometry (PSI) techniques using amplitude analysis and considering a temporal deformation model for PS pixel selection are unable to identify PS pixels in rural areas lacking human-made structures. In contrast, high rates of land subsidence lead to significant phase-unwrapping errors in a recently developed PSI algorithm (StaMPS) that applies phase stability and amplitude analysis to select the PS pixels in rural areas. The objective of this paper is to present an enhanced algorithm based on PSI to estimate the deformation rate in rural areas undergoing high and nearly constant rates of deformation. The proposed approach integrates the strengths of all of the existing PSI algorithms in PS pixel selection and phase unwrapping. PS pixels are first selected based on the amplitude information and phase-stability estimation as performed in StaMPS. The phase-unwrapping step, including the deformation rate and phase-ambiguity estimation, is then performed using least-squares ambiguity decorrelation adjustment (LAMBDA). The atmospheric phase screen (APS) and nonlinear deformation contribution to the phase are estimated by applying a high-pass temporal filter to the residuals derived from the LAMBDA method. The final deformation rate and the ambiguity parameter are re-estimated after subtracting the APS and the nonlinear deformation from that of the initial phase. The proposed method is applied to 22 ENVISAT ASAR images of southwestern Tehran basin captured between 2003 and 2008. A quantitative comparison with the results obtained with leveling and GPS measurements demonstrates the significant improvement of the PSI technique.

A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS

The upcoming modernization of the GPS signals will allow for measurements on an additional third frequency L5 located at 1176.45 MHz. To take advantage of carrier-phase measurements on this new signal, the strategies for integer ambiguity resolution, required for centimeter-level accuracy, may need to be revised. The Least-squares Ambiguity Decorrelation Adjustment method remains perhaps the most powerful tool for finding the best combinations based on a complete decorrelation of the variance–covariance matrix related to the ambiguities. However, the computational load of that method plus the opportunity to comprehensively study the interaction of multiple frequencies suggest a reconsideration of approaches using predefined combinations between frequencies is not out of place. In this paper a systematic investigation is made of all possible triple-frequency geometry-free carrier-phase combinations which retain the integer nature of the ambiguities. The concept of the lane-number is presented to unambiguously describe the wavelength of a particular combination. The propagation of the observation noise and of the ionospheric bias on these combinations is presented. These noise and ionospheric amplification factors are analysed with respect to the resulting wavelength, in an effort to highlight optimal combinations characterized by a long wavelength, low noise and limited ionospheric impact.

Estimation of Relative Satellite Position Using Transformed Differential Carrier-Phase GPS Measurements

Techniques for applying differential carrier-phase global positioning systems to satellite formation clusters with large (approximately 100 km or more) baselines are described. Because satellites in the cluster may move relative to each other, it is imperative that the carrier-phase ambiguities be resolved quickly and accurately. We propose a transformation of the m-vector carrier-phase measurement equations that restricts the geometric nonlinearities to a one-dimensional subspace and an almost universal linearization of the position state and integer ambiguities in the remaining m - 1 dimensional subspace. We then show that all of the measurement equations can be processed with an unscented Kalman filter to quickly compute very accurate floating-point valued estimates of the system state and error covariance. By an integer-preserving transformation found in the least-squares ambiguity decorrelation adjustment method, the number of possible hypotheses for the double-differenced wide-lane ambiguity candidates can be reduced. For the hypotheses set applying a multiple hypothesis Wald sequential probability test, using a specially conditioned form of the transformed global positioning system measurements, quickly and almost optimally determines the correct value of the carrier-phase double-differenced ambiguity. Once the double-differenced wide-lane ambiguities are obtained, the L 1 double-differenced ambiguities are resolved by using L 1 and L 2 carrier-phase measurements based on wide-lane integers in the unscented Kalman filter, then using the least-squares ambiguity decorrelation adjustment method for determining the hypotheses, followed by the multiple hypothesis Wald sequential probability test for resolving the L 1 double-differenced ambiguities. Finally, using the L 1 carrier-phase measurements, the unscented Kalman filter produces the relative position estimates. These techniques are then demonstrated on a simulation of a formation of two satellites in low Earth orbits.

Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods

This paper investigates single epoch ambiguity resolution performance using Galileo four frequency data. Two commonly used ambiguity resolution methods are used in the tests, including the Cascade Ambiguity Resolution (CAR) and the Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) methods. For CAR method, four optimal combinations are carefully selected according to their wavelength to noise ratios and success rate for ambiguity fixing. The test results show, in general, the LAMBDA method performs better than the CAR method. The speed of ambiguity resolution is closely related to the carrier phase measurement precision. With carrier phase measurement precision of 3 mm, single epoch ambiguity resolution can be achieved at every epoch with simulated 1-s interval 24-h Galileo data (total epochs 86,400). With the increase of carrier phase noise, ambiguity resolution performances become worse. When the noise level is increased to 12 mm, single epoch ambiguity resolution can only be achieved about 50% of epochs.

Batch Algorithm for Global-Positioning-System Attitude Determination and Integer Ambiguity Resolution

A new algorithm has been developed for simultaneous determination of attitude and carrier phase integer ambiguities based on data from an array of global-positioning-system (GPS) antennas. The purpose of the algorithm is to reduce the required number of tracked GPS satellites and antenna baselines needed to correctly resolve the ambiguities. This new motion-based method relies on data from several sample times. The vehicle must rotate about one or more axes among the samples. The solution algorithm works in two stages. It first solves a nonlinear least-squares problem in which the single-differenced carrier-phase ambiguities are allowed to vary as continuous real numbers. The second stage solves a nonlinear least-squares problem that restricts the ambiguities to be integers. This latter algorithm uses a combined Newton/Levenberg‐Marquardt method to deal with attitude quaternion nonlinearities, and it uses the least-squares ambiguity decorrelation adjustment method to deal with the integers. The second-stage algorithm is very accurate, but it needs to use initial guesses generated from first-stage algorithm solutions to find the global optimum. If the maneuver is large enough, then this new method can reliably solve difficult attitude/ambiguity-resolution problems. This capability has been demonstrated using Monte Carlo simulation. In one set of cases, the new algorithm correctly resolves ambiguities and achieves an accuracy of 4 deg or better when using two GPS satellite signals received by three antennas that are arrayed along 1-m baselines.

Some properties of decorrelation techniques in the ambiguity space

The most recent contributions to ambiguity resolution techniques have mainly focused on resolution in the ambiguity domain. Two techniques utilizing a decorrelation approach are compared. These techniques are the least-squares ambiguity decorrelation adjustment method and the lattice basis reduction. The latter is also known as the LLL method. The main focus in this article is on the decorrelation performance of these state-of-the-art techniques, which are aiming at ambiguity space decorrelation through unimodular transformations. The performances of the two-decorrelation techniques are compared through their ability in making the ambiguity space as orthogonal as possible.

Integration of LAMBDA Ambiguity Resolution with Kalman Filter for Relative Navigation of Spacecraft

: A general theoretical approach to finding a minimum-mean-squared-error solution to a set of linear measurement equations involving unknown continuous and integer states was published in 1993 [1]. This development was followed by the publication [2–4] of a practical method, known as the LAMBDA (least-squares ambiguity decorrelation adjustment) method, for efficiently implementing part of this approach, namely, the resolution of the integer states. This paper provides a method of implementing the general approach using a Kalman filter and some augmenting calculations. The result is an optimum filter in a recursive form. When the LAMBDA method is used to facilitate the integer-resolution calculations, the entire filter is computationally efficient, and has the potential for wide application. Extensions to prediction and smoothing are straightforward. An example of the application of this filter for relative navigation of space vehicles on the basis of GPS carrier and code measurements is described, and computer simulation results are provided.

Performance of the LAMBDA Method for Fast GPS Ambiguity Resolution

This paper provides an overview of the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method for the estimation of integer GPS ambiguities. The method's performance is discussed, together with the theoretical concepts on which it is based. The method is based on the integer least-squares principle and requires no application-dependent restrictions or assumptions. The actual integer estimation is preceded by a decorrelation step in order to make it more efficient. Especially for short time spans, a large gain in efficiency is obtained. The decorrelation of the ambiguities enables one to refrain from any approximation as far as the shape of the search space is concerned; i.e., the search is performed within the ellipsoidal space induced by the covariance matrix of the float ambiguities. The decorrelated ambiguities also make it possible to scale the search space such that, to a large degree of accuracy, it contains only the k best vectors of integer ambiguities.

On the GPS widelane and its decorrelating property

In this contribution we consider the popular widelaning technique from the viewpoint of ambiguity decorrelation. It enables us to cast the technique into the framework of the least-squares ambiguity decorrelation adjustment (LAMBDA) and to analyse its relative merits. In doing so, we will provide answers to the following three questions. Does the widelane decorrelate? Does it explicitly appear in the automated transformation step of the LAMBDA method? Can one do better than the widelane? It is shown that all three questions can be answered in the affirmative. This holds true for the ionosphere-fixed case, the ionosphere-float case, as well as for the ionosphere-weighted case.