Position Bias Research Articles

A New Type of Red-Green-Blue Composite and Its Application in Tropical Cyclone Center Positioning

Weak tropical cyclone (TC) center positioning is difficult work in operational forecasting. In the present study, a TC-red-green-blue (TC-RGB) composite was designed by using satellite multichannel observations (reflectance, brightness temperature, and brightness temperature differences). Compared with single channel images, TC-RGB composites can clearly show the exposed low-level circulation (LLC) of weak TCs under large vertical wind shear. Based on the guidelines of TC-RGB composites for TC center positioning, we repositioned 83 western North Pacific (WNP) TC cases during 2017–2019. Then, the comparisons of TC center positions were made between the TC-RGB composite and the Regional Specialized Meteorological Centre-Tokyo (RSMC-Tokyo), the Joint Typhoon Warning Center (JTWC) and the China Meteorological Administration-Shanghai Typhoon Institute (CMA-STI). Via case analysis of TC Kalmaegi (2019), it was found that the best-track data from the RSMC-Tokyo, JTWC and CMA-STI would have over 100 km biases at the early stage of TC life history. Taking all the 83 TC cases into account, the results show that the average center position biases and standard deviations for weak TCs under small vertical wind shear in the daytime are 5 km larger than those under large vertical wind shear at nighttime. When considering the 83 TC cases with clear LLC centers, the difference of these two biases is 10 km. The average biases are mostly above 20 km in the areas south of 18° N and north of 36° N over the WNP. Conversely, in the areas between 18° N and 36° N over the WNP, they are mostly below 20 km.

Dynamic is optimal: Effect of three alternative auto-complete on the usability of in-vehicle dialing displays and driver distraction

Objective Auto-complete (AC) has become ubiquitous on domain-specific systems and is mainly divided into two types (static-AC and dynamic-AC). Specifically, static-AC only presents the possible completions not changing with user input in the suggestion list for users to select. Dynamic-AC constantly filters out inconsistent content with user input and shows the possible completions at the top of the suggestion list. However, the details of the driver’s interactions with AC in the vehicle are poorly understood. Therefore, we investigated the effect of three alternative AC (non-AC, static-AC, and dynamic-AC) on the usability of in-vehicle dialing displays and driver distraction. As a reference, the baseline task (only driving) was also surveyed in each AC condition. Methods A simulated driving experiment consisting of 24 participants was conducted. The primary task was a lane-keeping task with speed ranging between 60 and 120 km/h over the stretch. The secondary task was dialing an 11-digit phone number. Usability metrics (task completion time and number of errors) and driver distraction metrics (NASA-reduced task load index (NASA-RTLX), mean speed, lateral position variation, total glance time, number of glances, mean glance time, and number of glances over 1.6 s) in each condition were measured. A series of one-way repeated measure analyses of variance was used to examine whether and which type of AC can maximize the usability of in-vehicle dialing displays and minimize driver distraction. Results Generally, the AC-based in-vehicle dialing display gains a more positive effect. Specifically, we observed that among the three alternative AC conditions, dynamic-AC performed optimally on usability metrics similar to previous studies and various driver distraction metrics, notwithstanding it is still not up to the level of the baseline condition. However, static-AC did not exhibit the advantages described in previous studies except for fewer errors and NASA-RTLX owing to the possibility of position bias and boundary effect. Conclusions This study provides valuable insights into drivers’ interactions with AC-based in-vehicle dialing displays and broadened its applications in safety-critical situations. More importantly, it informs the design of a more effective in-vehicle system, which positively contributes to mitigating driver distraction and preventing traffic accidents.

Integration of adeno-associated virus (AAV) into the genomes of most Thai and Mongolian liver cancer patients does not induce oncogenesis

BackgroundEngineered versions of adeno-associated virus (AAV) are commonly used in gene therapy but evidence revealing a potential oncogenic role of natural AAV in hepatocellular carcinoma (HCC) has raised concerns. The frequency of potentially oncogenic integrations has been reported in only a few populations. AAV infection and host genome integration in another type of liver cancer, cholangiocarcinoma (CCA), has been studied only in one cohort. All reported oncogenic AAV integrations in HCC come from strains resembling the fully sequenced AAV2 and partly sequenced AAV13. When AAV integration occurs, only a fragment of the AAV genome is detectable in later DNA or RNA sequencing. The integrated fragment is typically from the 3’ end of the AAV genome, and this positional bias has been only partly explained. Three research groups searched for evidence of AAV integration in HCC RNAseq samples in the Cancer Genome Atlas (TCGA) but reported conflicting results.ResultsWe collected and analyzed whole transcriptome and viral capture DNA sequencing in paired tumor and non-tumor samples from two liver cancer Asian cohorts from Thailand (N = 147, 47 HCC and 100 intrahepatic cholangiocarcinoma (iCCA)) and Mongolia (N = 70, all HCC). We found only one HCC patient with a potentially oncogenic integration of AAV, in contrast to higher frequency reported in European patients. There were no oncogenic AAV integrations in iCCA patients. AAV genomic segments are present preferentially in the non-tumor samples of Thai patients.By analyzing the AAV genome positions of oncogenic and non-oncogenic integrated fragments, we found that almost all the putative oncogenic integrations overlap the X gene, which is present and functional only in the strain AAV2 among all fully sequenced strains. This gene content difference could explain why putative oncogenic integrations from other AAV strains have not been reported.We resolved the discrepancies in previous analyses of AAV presence in TCGA HCC samples and extended it to CCA. There are 12 TCGA samples with an AAV segment and none are in Asian patients. AAV segments are present in preferentially in TCGA non-tumor samples, like what we observed in the Thai patients.ConclusionsOur findings suggest a minimal AAV risk of hepatocarcinogenesis in Asian liver cancer patients. The partial genome presence and positional bias of AAV integrations into the human genome has complicated analysis of possible roles of AAV in liver cancer.

The Position of Distractors in Multiple-Choice Test Items: The Strongest Precede the Weakest

Middle bias has been reported for responses to multiple-choice test items used in educational assessment. It has been claimed that this response bias probably occurs because test developers tend to place correct responses among middle options, tests thus presenting a middle-biased distribution of answer keys. However, this response bias could be driven by strong distractors being more frequently located among middle options. In this study, the frequency of responses to a Chilean national examination used to rank students wanting to access higher education was used to categorize distractors based on attractiveness level. The distribution of different distractor types (best distractor, non-functioning distractors…) was analyzed across 110 tests of 80 five-option items administered to assess several disciplines in five consecutive years. Results showed that the strongest distractors were more frequently found among middle options, most commonly at option C. In contrast, the weakest distractors were more frequently found at the last option (E). This pattern did not substantially vary across disciplines or years. Supplementary analyses revealed that a similar position bias for distractors could be observed in tests administered in countries other than Chile. Thus, the location of different types of distractors might provide an alternative explanation for the middle bias reported in literature for tests’ responses. Implications for test developers, test takers, and researchers in the field are discussed.

Electrostatic switch of magnetic anisotropy in the composite with iron-metal granule and barium-titanate matrix

This work investigates electrostatic switch of magnetic anisotropy in the composite with iron-metal granule and barium-titanate matrix theoretically. As the spontaneous polarization is switched downward or upward in barium-titanate matrix, the parallel or perpendicular magnetizing is preferred in iron-metal granule respectively. This demagnetizing anisotropy originates from the long-range electrostatic interaction in matrix body, which induces the inharmonic magnetic moment on granule surface. The effects of position bias and composite size are delicately studied. The cross-section map displays distorted electric polarization in barium-titanate matrix, and demagnetizing energy gradient in iron-metal granule. This work predicts the electrostatic switch of magnetic anisotropy in metal/oxide composite, which would develop the integrated device and functional material.

Theoretical analysis of beamforming steering vector formulations for acoustic source localization

In three-dimensional acoustic source localization, setting the steering vector is an important choice. Four steering vector formulations are frequently used. In the noiseless case, two of them yield a correct estimation of the position, the two others yielding correct estimation of the amplitude of the source, assuming its position is known. Here, noisy measurements are considered, and the steering vector formulations are compared in terms of bias and variance of the estimated position and amplitude, allowing a more informative assessment of their performances. An approximated value of the position bias of the biased formulations is given. Maximum likelihood estimation of the parameters of the source is derived, showing that it involves the combination of two steering vector formulations, for position estimation, followed by amplitude estimation. This analysis does not rely on the specific form of the Green function, and remains relevant for general propagation media.

Aerodynamic Influence of a Bleed on the Last Stage of a Low-Pressure Compressor and S-Duct

Abstract This paper uses computational fluid dynamics to investigate the effect of an engine handling bleed situated on the outer casing downstream of the last rotor stage of a low-pressure compressor and upstream of the outlet guide vane and S-shaped duct. The model, validated against existing experimental data, utilized an unsteady Reynolds-averaging Navier–Stokes (RANS) solver incorporating a Reynolds stress closure to examine the unsteady component interactions. The results showed that at bleed rates less than 25% of the mainstream flow, the bleed effects were negligible. However, at higher bleed rates, performance was significantly degraded. A uniform flow extraction hypothesis was employed to separate the positional bias effects of the bleed from the bulk flow diffusion. This revealed that the bleed-induced radial flow distortion can significantly affect the outlet guide vane (OGV) loading distribution, which thereby dictates the position and type of stall within the OGV passage. Extraction of the rotor tip leakage via the shroud bleed, combined with the radial flow distortion, contributed to a 28% reduction in duct loss at 10% bleed and up to 50% reduced loss at 25% bleed. The actual amount of flow required to be extracted for an OGV stall to develop was 30%. That was independent of the bleed location and the type of stall. For bleeds up to 20%, the S-duct displayed a remarkable resilience and consistency of flow variables at duct exit. However, a stalled OGV deteriorated the radial flow uniformity that was presented to the high-pressure compressor.

A cost‐efficient joint target location and clock bias estimation technique using multiple time step measurements in mobile bistatic sonar

Active localization of a stationary target is one key issue in applications of bistatic sonar based on bistatic range (BR) measurement. However, the complex underwater environment makes achieving the synchronization between the transmitted station and the received station difficult. For solving the synchronization problem, this study relies on mobile bistatic sonar to acquire measurement information at multiple time steps. After that, the target location and clock bias are jointly estimated by solving a non-linear least square problem. To this end, a recursive scheme is proposed to optimise the measurement cost and reduce the impact of the initial value to achieve accurate estimation by taking full advantage of the redundant measurement information. Orthogonal transformation is used to ensure computational efficiency and numerical reliability. The Cramer–Rao Lower Bound (CRLB) is also derived as a lower bound on the error in estimating the target position and clock bias. Simulation results show that the proposed method achieves the CRLB performance and optimises the measurement cost over the small error region under Gaussian noise.

Analysis of shape uses local apparent position rather than physical position.

Objects are often identified by the shapes of their boundaries. Here, by measuring threshold amplitudes for detection of sinusoidal modulation of local position, orientation and centrifugal speed in a closed path of Gabor patches, we show that the positions of such boundaries are misperceived to accommodate local illusions of orientation context and motion induced positional bias. These two types of illusion are shown to occur independently, but the misperception of position is additive. We conclude that, in the analysis of shape, the visual system uses the apparent rather than the veridical boundary conformation.

Obligate movements of an active site–linked surface domain control RNA polymerase elongation and pausing via a Phe pocket anchor

The catalytic trigger loop (TL) in RNA polymerase (RNAP) alternates between unstructured and helical hairpin conformations to admit and then contact the NTP substrate during transcription. In many bacterial lineages, the TL is interrupted by insertions of two to five surface-exposed, sandwich-barrel hybrid motifs (SBHMs) of poorly understood function. The 188-amino acid, two-SBHM insertion in Escherichia coli RNAP, called SI3, occupies different locations in elongating, NTP-bound, and paused transcription complexes, but its dynamics during active transcription and pausing are undefined. Here, we report the design, optimization, and use of a Cys-triplet reporter to measure the positional bias of SI3 in different transcription complexes and to determine the effect of restricting SI3 movement on nucleotide addition and pausing. We describe the use of H2O2 as a superior oxidant for RNAP disulfide reporters. NTP binding biases SI3 toward the closed conformation, whereas transcriptional pausing biases SI3 toward a swiveled position that inhibits TL folding. We find that SI3 must change location in every round of nucleotide addition and that restricting its movements inhibits both transcript elongation and pausing. These dynamics are modulated by a crucial Phe pocket formed by the junction of the two SBHM domains. This SI3 Phe pocket captures a Phe residue in the RNAP jaw when the TL unfolds, explaining the similar phenotypes of alterations in the jaw and SI3. Our findings establish that SI3 functions by modulating TL folding to aid transcriptional regulation and to reset secondary channel trafficking in every round of nucleotide addition.

Expression Characteristics Analysis of CesA/Csl genes in Flax During the Fast Growing Stage

ABSTRACT Expression characteristics of predicted CesA/Csl genes of fiber flax variety ‘Diana’ were investigated using RNA-seq data obtained during the fast-growing stage. First, flax stem anatomic analysis revealed differing developmental processes from bottom to top, with middle and lower stem fiber cells exhibiting significantly thickened cell walls. Moreover, stem cellulose/hemicellulose content exhibited positional biases, with a top-to-bottom increase in cellulose content and bottom-to-top increase in hemicellulose content observed. Most CesA/Csl genes were predominantly expressed in stems, roots, and less in leaves. The correlations between the expression levels of CesA/Csl genes and the contents of cellulose and hemicellulose were analyzed. The expression levels of LuCesA4, LuCesA8A and LuCesA8B genes showed significantly positive correlations with cellulose content (P < 0.05), while expression levels of two LuCesA3, three LuCesA6, two LuCslA2, and four LuCslC genes revealed significantly positive correlations with hemicellulose content (P < 0.05). CesA/Csl protein interaction network analysis revealed five transcription factors (TFs) that had high protein–protein interaction (PPI) scores with CesA/Csl proteins: LuNAC10 (Lus10015392), LuNAC12 (Lus10001664), LuNAM (Lus10017915), LuMyb42 (Lus10038913), LuMyb46 (Lus10027369). Therefore, these TFs may play critical regulatory roles in cellulose/hemicellulose synthesis. This study provides a theoretical foundation for investigating flax fiber cell wall synthesis and regulatory mechanisms.

One‐way deep indoor positioning system for conventional GNSS receiver using paired transmitters

<h3>Abstract</h3> Generally, GNSS-based indoor navigation systems use repeaters or pseudolites. However, these methods are vulnerable to multipath errors and require additional information, including the repeater or pseudolite position. In this study, we propose a novel one-way indoor positioning system using GNSS signal transmitters. Our system uses paired transmitters, each of which broadcasts the same set of satellite signals. The autocorrelation functions of the combined signals are analyzed as the overlap of each individual autocorrelation function. The estimated position can be determined along the track between the transmitters. The multipath error is absorbed by the clock bias and does not cause position bias error. Furthermore, the proposed system can be applied in current commercial GNSS receivers directly. A theoretical analysis of the pseudorange, user position, multipath error, and signal power is included and supported by simulation results. A field test was conducted to confirm the feasibility of the proposed system.

Spatial asymmetries (\u201cpseudoneglect\u201d) in free visual exploration\u2014modulation of age and relationship to line bisection

When humans visually explore an image, they typically tend to start exploring its left side. This phenomenon, so-called pseudoneglect, is well known, but its time-course has only sparsely been studied. Furthermore, it is unclear whether age influences pseudoneglect, and the relationship between visuo-spatial attentional asymmetries in a free visual exploration task and a classical line bisection task has not been established. To address these questions, 60 healthy participants, aged between 22 and 86, were assessed by means of a free visual exploration task with a series of naturalistic, colour photographs of everyday scenes, while their gaze was recorded by means of a contact-free eye-tracking system. Furthermore, a classical line bisection task was administered, and information concerning handedness and subjective alertness during the experiment was obtained. The results revealed a time-sensitive window during visual exploration, between 260 and 960 ms, in which age was a significant predictor of the leftward bias in gaze position, i.e., of pseudoneglect. Moreover, pseudoneglect as assessed by the line bisection task correlated with the average gaze position throughout a time-window of 300–1490 ms during the visual exploration task. These results suggest that age influences visual exploration and pseudoneglect in a time-sensitive fashion, and that the degree of pseudoneglect in the line bisection task correlates with the average gaze position during visual exploration in a time-sensitive manner.

Cascade Submodular Maximization: Question Selection and Sequencing in Online Personality Quiz

Personality quiz is a powerful tool that enables costumer segmentation by actively asking them questions, and marketers are using it as an effective method of generating leads and increasing e‐commerce sales. We study the problem of how to select and sequence a group of quiz questions so as to optimize the quality of customer segmentation. We assume that the customer will sequentially scan the list of questions. After reading a question, the customer makes two, possibly correlated, random decisions: (i) she first decides whether to answer this question or not, and then (ii) decides whether to continue reading the next question or not. We further assume that the utility of questions that have been answered can be captured by a monotone and submodular function. In general, our problem falls into the category of non‐adaptive active learning‐based customer profiling. Note that under our model, the probability of a question being answered depends on the location of that question, as well as the set of other questions placed ahead of that question, this makes our problem fundamentally different from existing studies on submodular optimization. We develop a series of question selection and sequencing strategies with provable performance bound. Although we focus on the application of quiz design in this study, our results apply to a broad range of applications, including assortment optimization with position bias effect.

Accuracy in WiFi Access Point Position Estimation Using Round Trip Time.

WiFi Round Trip Time (RTT) unlocks meter level accuracies in user terminal positions where no other navigation systems, such as Global Navigation Satellite Systems (GNSS), are able to (e.g., indoors). However, little has been done so far to obtain a scalable and automated system that computes the position of the WiFi Access Points (WAP) using RTT and that is able to estimate, in addition to the position, the hardware biases that offset the WiFi ranging measurements. These biases have a direct impact on the ultimate position accuracy of the terminals. This work proposes a method in which the computation of the WiFi Access Points positions and hardware biases (i.e., products) can be estimated based on the ranges and position fixes provided by user terminals (i.e., inverse positioning) and details how this can be improved if raw GNSS measurements (pseudoranges and carrier phase) are also available in the terminal. The data setup used to obtain a performance assessment was configured in a benign scenario (open sky with no obstructions) in order to obtain an upper boundary on the positioning error that can be achieved with the proposed method. Under these conditions, accuracies better than 1.5 m were achieved for the WAP position and hardware bias. The proposed method is suitable to be implemented in an automated manner, without having to rely on dedicated campaigns to survey 802.11mc-compliant WAPs. This paper offers a technique to automatically estimate both mild-indoor WAP products (where terminals have both Wi-Fi RTT and GNSS coverage) and deep-indoor WAP (with no GNSS coverage where the terminals obtain their position exclusively from previously estimated mild-indoor WAPs).

Market segmentation in online platforms

This paper studies ranking policies in a stylized trial-offer marketplace model, in which a single firm offers multiple products and has consumers who express heterogeneous preferences. Consumer trials are influenced by past purchases, the inherent appeal of the products, and the ranking of each product. Consumer purchases conditional on trying the product are dependent on the inherent quality for the given consumer segment. The platform owner needs to devise a ranking policy to display the products to maximize the number of purchases in the long run, and to decide whether to display the number of past purchases. The model proposed attempts to understand the impact of market segmentation in a trial-offer market with position bias and social influence. Under our model, consumer choices are based on a very general choice model known as the mixed multinomial logit model, which embeds product appeal, ranking, and past purchases into the taste parameters. We analyze the long-term dynamics of this highly complex stochastic model and we quantify the expected benefits of market segmentation as well as the value of social influence. When past purchases are displayed, consumer heterogeneity makes buyers try the sub-optimal products, reducing the overall sales rate. We show that consumer heterogeneity makes the ranking problem NP-hard. We then analyze the benefits of market segmentation. We find tight bounds to the expected benefits of offering a distinct ranking to each consumer segment. Finally, we show that the market segmentation strategy always benefits from social influence when the average quality ranking is used. One of the managerial implications is that the firm is better off using an aggregate ranking policy when the variety of consumer preference is limited, but it should perform a market segmentation policy when consumers are highly heterogeneous. We also show that this result is robust to relatively small consumer classification mistakes; when these are large, an aggregate ranking is preferred.

Quantitative examination of an unconventional form of the filled-space illusion.

The spatial interval containing some visual elements (fillers) seems to be longer than an empty interval of the same length, and the effect persists for most observers. This illusion of interrupted spatial extent (or the filled-space illusion) can be observed even in extremely simplified line drawings, but its origin is still not completely understood. Recently, we proposed a quantitative explanation for the results of experiments with stimuli containing either continuous or discrete filling: the illusion may be associated with the integration of distractor-induced effects near the endpoints (terminators) of the stimulus intervals. Subsequent analysis of the principles underlying the explanation allowed us to hypothesize the appearance of illusory effects caused by previously unknown stimulus modifications. To test the suggestions, in the present study we performed experiments with three-dot stimuli that contain a distracting circle (either outline or uniformly filled) surrounding one of the lateral terminators. It has been demonstrated that the illusion magnitude varies predictably with the size of the circle, and there is no significant difference between the data obtained for stimuli with the outline and filled distractors. To more thoroughly examine the illusion, the central angle of circular distracting arcs (real or imaginary) was used as an independent variable in supplementary experiments. A rather successful theoretical interpretation of the experimental results supports the suggestion that perceptual positional biases induced by additional context-evoked neural excitation can be considered as one of the main causes of the filled-space illusion.

Visuoproprioceptive conflict in hand position biases tactile localization on the hand surface.

The location of touch can be represented in a somatotopic reference frame and, combined with proprioceptive information, in an external reference frame. There is evidence that body position influences where individuals feel touch on the skin surface, indicating that proprioceptive information affects tactile localization in a somatotopic reference frame. In conditions with visual and proprioceptive mismatch of body position, where do individuals feel touch on the body? We used the mirror box illusion to address this question. Participants placed 1 hand on each side of a mirror aligned with the body midline, such that the hand reflection in the mirror looked like the hand hidden behind the mirror. The illusion creates a spatial mismatch between the actual hidden hand position and where the participant perceives their hand to be (the mirror image location). Across three experiments, localization judgments on the hidden hand were consistently and systematically biased toward the actual hand position relative to the viewed hand position. These findings provide evidence that proprioceptive estimates of limb position influence tactile localization and are discussed in relation to two models of tactile localization. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Autonomous Ground Vehicle Path Planning in Urban Environments Using GNSS and Cellular Signals Reliability Maps: Models and Algorithms

In this article, autonomous ground vehicle (AGV) path planning is considered. The AGV is assumed to be equipped with receivers capable of producing pseudorange measurements to overhead global navigation satellite systems (GNSS) satellites and to cellular base stations in its environment. Parameters of the cellular pseudoranges related to the transmitter clock bias are estimated in an initialization step in an open-sky environment. The AGV fuses these pseudoranges to produce an estimate about its own states. The AGV is also equipped with a three-dimensional building map of the environment. Starting from a known starting point, the AGV desires to reach a known target point by taking the shortest distance, while minimizing the AGV's position estimation error and guaranteeing that the AGV's position estimation uncertainty is below a desired threshold. Toward this objective, a so-called signal reliability map is first generated, which provides information about regions where large errors due to poor GNSS line-of-sight or cellular signal multipath are expected. The vehicle uses the signal reliability map to calculate the position mean-squared error (MSE). An analytical expression for the AGV's state estimates is derived, which is used to find an upper bound on the position bias due to multipath. An optimal path planning generation approach, which is based on Dijkstra's algorithm, is developed to optimize the AGV's path while minimizing the path length and position MSE, subject to keeping the position estimation uncertainty and position estimation bias due to multipath below desired thresholds. The path planning approach yields the optimal path together with a list of feasible paths and reliable GNSS satellites and cellular base stations to use along these paths.

Influence of the inhomogeneous troposphere on GNSS positioning and integer ambiguity resolution

The tropospheric delay is one of many error sources that affect the Global Navigation Satellite System (GNSS) positioning solutions. The widely used troposphere models assume a homogeneous atmosphere so that only the zenith delay needs to be determined and is mapped through an elevation-dependent mapping function. This procedure is to reduce the computational burden and keep the positioning model full-rank. However, this assumption fails for a realistic description of the troposphere, which is always asymmetrical at a certain elevation angle, especially during a weather event when the weather conditions are very complex. These imperfectly modelled tropospheric delays may influence the positioning accuracy and integer ambiguity resolution performance. In this case, this contribution aims to investigate the effects of the model errors due to the asymmetrical troposphere on GNSS estimations. The Numerical Weather Prediction (NWP) model is applied to generate the actual ray-tracing tropospheric delay in Western Europe, and the tropospheric model errors are calculated in a normal weather condition and a weather event condition by comparing the slant delay calculated from the NWP model and the mapping function. Case studies on the same GNSS station are conducted in two weather conditions: a normal troposphere condition and a weather event with heavy rainfall. The results based on the case studies show that the troposphere in the normal weather condition is nearly homogeneous that the azimuthal-dependent discrepancies of the tropospheric delay are less than 1cm at a very low elevation angle; meanwhile, the discrepancies between different azimuthal angles can reach to more than 25cm in the weather event. A single-frequency Single Point Positioning (SPP) model and a Precise Point Positioning (PPP) model that preserves the integer property of ambiguity are chosen for studying the estimation biases caused by the troposphere model errors. It turns out that almost all horizontal positioning biases of SPP and PPP are less than 1cm in the normal weather condition; however, the scales of the horizontal and 3D biases are concentrated in 1 to 10cm in the weather event for these two models. This contribution also contains the study of the actual integer ambiguity resolution success rate in the presence of the tropospheric model errors by applying the Monte Carlo simulation, and the success rates of PPP in the normal weather condition are consistent with the theoretical values calculated with the ideal troposphere which is totally symmetrical. However, the actual success rates in the weather event are extremely low at some epochs due to the tropospheric model errors, which means that wrong fixing may occur since the theoretical values cannot take into account these model errors. Note that the horizontal tropospheric gradients are not involved in the processing, which means that an optimistic performance might be expected if the gradients are considered.