Effects of efficient fronto-temporal circuitry on lexical ambiguity resolution: converging evidence from cross-age comparisons in eye-tracking and ERP data

Eye-tracking was used to examine how younger and older adults use syntactic and semantic information to disambiguate noun/verb (NV) homographs (e.g., park). We find that young adults exhibit inflated first fixations to NV-homographs when only syntactic cues are available for disambiguation (i.e., in syntactic prose). This effect is eliminated with the addition of disambiguating semantic information. Older adults (60+) as a group fail to show the first fixation effect in syntactic prose; they instead reread NV homographs longer. This pattern mirrors that in prior event-related potential work (Lee & Federmeier, 2009, 2011), which reported a sustained frontal negativity to NV-homographs in syntactic prose for young adults, which was eliminated by semantic constraints. The frontal negativity was not observed in older adults as a group, although older adults with high verbal fluency showed the young-like pattern. Analyses of individual differences in eye-tracking patterns revealed a similar effect of verbal fluency in both young and older adults: high verbal fluency groups of both ages show larger first fixation effects, while low verbal fluency groups show larger downstream costs (rereading and/or refixating NV homographs). Jointly, the eye-tracking and ERP data suggest that effortful meaning selection recruits frontal brain areas important for suppressing contextually inappropriate meanings, which also slows eye movements. Efficacy of fronto-temporal circuitry, as captured by verbal fluency, predicts the success of engaging these mechanisms in both young and older adults. Failure to recruit these processes requires compensatory rereading or leads to comprehension failures (Lee & Federmeier, in press).

Three Carrier Ambiguity Resolutions : Generalised problems, models and solutions

In this paper, the problems of three carrier phase ambiguity resolution (TCAR) and position estimation (PE) are generalized as real time GNSS data processing problems for a continuously observing network on large scale. In order to describe these problems, a general linear equation system is presented to uniform various geometry-free, geometry-based and geometry-constrained TCAR models, along with state transition questions between observation times. With this general formulation, generalized TCAR solutions are given to cover different real time GNSS data processing scenarios, and various simplified integer solutions, such as geometry-free rounding and geometry-based LAMBDA solutions with single and multiple-epoch measurements. In fact, various ambiguity resolution (AR) solutions differ in the floating ambiguity estimation and integer ambiguity search processes, but their theoretical equivalence remains under the same observational systems models and statistical assumptions. TCAR performance benefits as outlined from the data analyses in some recent literatures are reviewed, showing profound implications for the future GNSS development from both technology and application perspectives.

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to Real-Time Kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least-squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance-covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio-test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.

Fixed failure rate ambiguity validation methods for GPS and compass

Ambiguity resolution plays a crucial role in real time kinematic GNSS positioning which gives centimetre precision positioning results if all the ambiguities in each epoch are correctly fixed to integers. However, the incorrectly fixed ambiguities can result in large positioning offset up to several meters without notice. Hence, ambiguity validation is essential to control the ambiguity resolution quality. Currently, the most popular ambiguity validation is ratio test. The criterion of ratio test is often empirically determined. Empirically determined criterion can be dangerous, because a fixed criterion cannot fit all scenarios and does not directly control the ambiguity resolution risk. In practice, depending on the underlying model strength, the ratio test criterion can be too conservative for some model and becomes too risky for others. A more rational test method is to determine the criterion according to the underlying model and user requirement. Miss-detected incorrect integers will lead to a hazardous result, which should be strictly controlled. In ambiguity resolution miss-detected rate is often known as failure rate. In this paper, a fixed failure rate ratio test method is presented and applied in analysis of GPS and Compass positioning scenarios. A fixed failure rate approach is derived from the integer aperture estimation theory, which is theoretically rigorous. The criteria table for ratio test is computed based on extensive data simulations in the approach. The real-time users can determine the ratio test criterion by looking up the criteria table. This method has been applied in medium distance GPS ambiguity resolution but multi-constellation and high dimensional scenarios haven't been discussed so far. In this paper, a general ambiguity validation model is derived based on hypothesis test theory, and fixed failure rate approach is introduced, especially the relationship between ratio test threshold and failure rate is examined. In the last, Factors that influence fixed failure rate approach ratio test threshold is discussed according to extensive data simulation. The result shows that fixed failure rate approach is a more reasonable ambiguity validation method with proper stochastic model.

Achieving high reliability for ambiguity resolutions with multiple GNSS constellations

Global Navigation Satellite Systems (GNSS)-based observation systems can provide high precision positioning and navigation solutions in real time, in the order of subcentimetre if we make use of carrier phase measurements in the differential mode and deal with all the bias and noise terms well. However, these carrier phase measurements are ambiguous due to unknown, integer numbers of cycles. One key challenge in the differential carrier phase mode is to fix the integer ambiguities correctly. On the other hand, in the safety of life or liability-critical applications, such as for vehicle safety positioning and aviation, not only is high accuracy required, but also the reliability requirement is important. This PhD research studies to achieve high reliability for ambiguity resolution (AR) in a multi-GNSS environment. GNSS ambiguity estimation and validation problems are the focus of the research effort. Particularly, we study the case of multiple constellations that include initial to full operations of foreseeable Galileo, GLONASS and Compass and QZSS navigation systems from next few years to the end of the decade. Since real observation data is only available from GPS and GLONASS systems, the simulation method named Virtual Galileo Constellation (VGC) is applied to generate observational data from another constellation in the data analysis. In addition, both full ambiguity resolution (FAR) and partial ambiguity resolution (PAR) algorithms are used in processing single and dual constellation data. Firstly, a brief overview of related work on AR methods and reliability theory is given. Next, a modified inverse integer Cholesky decorrelation method and its performance on AR are presented. Subsequently, a new measure of decorrelation performance called orthogonality defect is introduced and compared with other measures. Furthermore, a new AR scheme considering the ambiguity validation requirement in the control of the search space size is proposed to improve the search efficiency. With respect to the reliability of AR, we also discuss the computation of the ambiguity success rate (ASR) and confirm that the success rate computed with the integer bootstrapping method is quite a sharp approximation to the actual integer least-squares (ILS) method success rate. The advantages of multi-GNSS constellations are examined in terms of the PAR technique involving the predefined ASR. Finally, a novel satellite selection algorithm for reliable ambiguity resolution called SARA is developed. In summary, the study demonstrats that when the ASR is close to one, the reliability of AR can be guaranteed and the ambiguity validation is effective. The work then focuses on new strategies to improve the ASR, including a partial ambiguity resolution procedure with a predefined success rate and a novel satellite selection strategy with a high success rate. The proposed strategies bring significant benefits of multi-GNSS signals to real-time high precision and high reliability positioning services.

Ambiguity Acceptance Testing : A Comparison of the Ratio Test and Difference Test

Integer ambiguity resolution is an indispensable procedure for all high precision GNSS applications. The correctness of the estimated integer ambiguities is the key to achieving highly reliable positioning, but the solution cannot be validated with classical hypothesis testing methods. The integer aperture estimation theory unifies all existing ambiguity validation tests and provides a new prospective to review existing methods, which enables us to have a better understanding on the ambiguity validation problem. This contribution analyses two simple but efficient ambiguity validation test methods, ratio test and difference test, from three aspects: acceptance region, probability basis and numerical results. The major contribution of this paper can be summarized as: (1) The ratio test acceptance region is overlap of ellipsoids while the difference test acceptance region is overlap of half-spaces. (2) The probability basis of these two popular tests is firstly analyzed. The difference test is an approximation to optimal integer aperture, while the ratio test follows an exponential relationship in probability. (3) The limitations of the two tests are firstly identified. The two tests may under-evaluate the failure risk if the model is not strong enough or the float ambiguities fall in particular region. (4) Extensive numerical results are used to compare the performance of these two tests. The simulation results show the ratio test outperforms the difference test in some models while difference test performs better in other models. Particularly in the medium baseline kinematic model, the difference tests outperforms the ratio test, the superiority is independent on frequency number, observation noise, satellite geometry, while it depends on success rate and failure rate tolerance. Smaller failure rate leads to larger performance discrepancy.

A novel ambiguity acceptance test threshold determination method with controllable failure rate

Ambiguity validation as an important procedure of integer ambiguity resolution is to test the correctness of the fixed integer ambiguity of phase measurements before being used for positioning computation. Most existing investigations on ambiguity validation focus on test statistic. How to determine the threshold more reasonably is less understood, although it is one of the most important topics in ambiguity validation. Currently, there are two threshold determination methods in the ambiguity validation procedure: the empirical approach and the fixed failure rate (FF-) approach. The empirical approach is simple but lacks of theoretical basis. The fixed failure rate approach has a rigorous probability theory basis, but it employs a more complicated procedure. This paper focuses on how to determine the threshold easily and reasonably. Both FF-ratio test and FF-difference test are investigated in this research and the extensive simulation results show that the FF-difference test can achieve comparable or even better performance than the well-known FF-ratio test. Another benefit of adopting the FF-difference test is that its threshold can be expressed as a function of integer least-squares (ILS) success rate with specified failure rate tolerance. Thus, a new threshold determination method named threshold function for the FF-difference test is proposed. The threshold function method preserves the fixed failure rate characteristic and is also easy-to-apply. The performance of the threshold function is validated with simulated data. The validation results show that with the threshold function method, the impact of the modelling error on the failure rate is less than 0.08%. Overall, the threshold function for the FF-difference test is a very promising threshold validation method and it makes the FF-approach applicable for the real-time GNSS positioning applications.

Assessment of commercial network RTK user positioning performance over long inter-station distances

The paper provides an assessment of the performance of commercial Real Time Kinematic (RTK) systems over longer than recommended inter-station distances. The experiments were set up to test and analyse solutions from the i-MAX, MAX and VRS systems being operated with three triangle shaped network cells, each having an average inter-station distance of 69km, 118km and 166km. The performance characteristics appraised included initialization success rate, initialization time, RTK position accuracy and availability, ambiguity resolution risk and RTK integrity risk in order to provide a wider perspective of the performance of the testing systems. ----- ----- The results showed that the performances of all network RTK solutions assessed were affected by the increase in the inter-station distances to similar degrees. The MAX solution achieved the highest initialization success rate of 96.6% on average, albeit with a longer initialisation time. Two VRS approaches achieved lower initialization success rate of 80% over the large triangle. In terms of RTK positioning accuracy after successful initialisation, the results indicated a good agreement between the actual error growth in both horizontal and vertical components and the accuracy specified in the RMS and part per million (ppm) values by the manufacturers. ----- ----- Additionally, the VRS approaches performed better than the MAX and i-MAX when being tested under the standard triangle network with a mean inter-station distance of 69km. However as the inter-station distance increases, the network RTK software may fail to generate VRS correction and then may turn to operate in the nearest single-base RTK (or RAW) mode. The position uncertainty reached beyond 2 meters occasionally, showing that the RTK rover software was using an incorrect ambiguity fixed solution to estimate the rover position rather than automatically dropping back to using an ambiguity float solution. Results identified that the risk of incorrectly resolving ambiguities reached 18%, 20%, 13% and 25% for i-MAX, MAX, Leica VRS and Trimble VRS respectively when operating over the large triangle network. Additionally, the Coordinate Quality indicator values given by the Leica GX1230 GG rover receiver tended to be over-optimistic and not functioning well with the identification of incorrectly fixed integer ambiguity solutions. In summary, this independent assessment has identified some problems and failures that can occur in all of the systems tested, especially when being pushed beyond the recommended limits. While such failures are expected, they can offer useful insights into where users should be wary and how manufacturers might improve their products. The results also demonstrate that integrity monitoring of RTK solutions is indeed necessary for precision applications, thus deserving serious attention from researchers and system providers.

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

Real-time kinematic positioning over long baselines using triple-frequency BeiDou signals

The BeiDou system is the first global navigation satellite system in which all satellites transmit triple-frequency signals that can provide the positioning, navigation, and timing independently. A benefit of triple-frequency signals is that more useful combinations can be formed, including some extrawide-lane combinations whose ambiguities can generally be instantaneously fixed without distance restriction, although the narrow-lane ambiguity resolution (NL AR) still depends on the interreceiver distance or requires a long time to achieve. In this paper, we synthetically study decimeter and centimeter kinematic positioning using BeiDou triple-frequency signals. It starts with AR of two extrawide-lane signals based on the ionosphere-free or ionosphere-reduced geometry-free model. For decimeter positioning, one can immediately use two ambiguity-fixed extrawide-lane observations without pursuing NL AR. To achieve higher accuracy, NL AR is the necessary next step. Despite the fact that long-baseline NL AR is still challenging, some NL ambiguities can indeed be fixed with high reliability. Partial AR for NL signals is acceptable, because as long as some ambiguities for NL signals are fixed, positioning accuracy will be certainly improved.With accumulation of observations, more and more NL ambiguities are fixed and the positioning accuracy continues to improve. An efficient Kalman-filtering system is established to implement the whole process. The formulated system is flexible, since the additional constraints can be easily applied to enhance the model's strength. Numerical results from a set of real triple-frequency BeiDou data on a 50 km baseline show that decimeter positioning is achievable instantaneously.With only five data epochs, 84% of NL ambiguities can be fixed so that the real-time kinematic accuracies are 4.5, 2.5, and 16 cm for north, east, and height components (respectively), while with 10 data epochs more than 90% of NL ambiguities are fixed, and the rea- -time kinematic solutions are improved to centimeter level for all three coordinate components.

Improving the GNSS positioning stochastic model in the presence of ionospheric scintillation

Ionospheric scintillations are caused by time-varying electron density irregularities in the ionosphere, occurring more often at equatorial and high latitudes. This paper focuses exclusively on experiments undertaken in Europe, at geographic latitudes between similar to 50 degrees N and similar to 80 degrees N, where a network of GPS receivers capable of monitoring Total Electron Content and ionospheric scintillation parameters was deployed. The widely used ionospheric scintillation indices S4 and sigma(phi) represent a practical measure of the intensity of amplitude and phase scintillation affecting GNSS receivers. However, they do not provide sufficient information regarding the actual tracking errors that degrade GNSS receiver performance. Suitable receiver tracking models, sensitive to ionospheric scintillation, allow the computation of the variance of the output error of the receiver PLL (Phase Locked Loop) and DLL (Delay Locked Loop), which expresses the quality of the range measurements used by the receiver to calculate user position. The ability of such models of incorporating phase and amplitude scintillation effects into the variance of these tracking errors underpins our proposed method of applying relative weights to measurements from different satellites. That gives the least squares stochastic model used for position computation a more realistic representation, vis-a-vis the otherwise 'equal weights' model. For pseudorange processing, relative weights were computed, so that a 'scintillation-mitigated' solution could be performed and compared to the (non-mitigated) 'equal weights' solution. An improvement between 17 and 38% in height accuracy was achieved when an epoch by epoch differential solution was computed over baselines ranging from 1 to 750 km. The method was then compared with alternative approaches that can be used to improve the least squares stochastic model such as weighting according to satellite elevation angle and by the inverse of the square of the standard deviation of the code/carrier divergence (sigma CCDiv). The influence of multipath effects on the proposed mitigation approach is also discussed. With the use of high rate scintillation data in addition to the scintillation indices a carrier phase based mitigated solution was also implemented and compared with the conventional solution. During a period of occurrence of high phase scintillation it was observed that problems related to ambiguity resolution can be reduced by the use of the proposed mitigated solution.