Geometry‐specified troposphere decorrelation for subcentimeter real‐time kinematic solutions over long baselines

Real‐time kinematic (RTK) GPS techniques have been extensively developed for applications including surveying, structural monitoring, and machine automation. Limitations of the existing RTK techniques that hinder their applications for geodynamics purposes are twofold: (1) the achievable RTK accuracy is on the level of a few centimeters and the uncertainty of vertical component is 1.5–2 times worse than those of horizontal components and (2) the RTK position uncertainty grows in proportional to the base‐torover distances. The key limiting factor behind the problems is the significant effect of residual tropospheric errors on the positioning solutions, especially on the highly correlated height component. This paper develops the geometry‐specified troposphere decorrelation strategy to achieve the subcentimeter kinematic positioning accuracy in all three components. The key is to set up a relative zenith tropospheric delay (RZTD) parameter to absorb the residual tropospheric effects and to solve the established model as an ill‐posed problem using the regularization method. In order to compute a reasonable regularization parameter to obtain an optimal regularized solution, the covariance matrix of positional parameters estimated without the RZTD parameter, which is characterized by observation geometry, is used to replace the quadratic matrix of their “true” values. As a result, the regularization parameter is adaptively computed with variation of observation geometry. The experiment results show that new method can efficiently alleviate the model’s ill condition and stabilize the solution from a single data epoch. Compared to the results from the conventional least squares method, the new method can improve the longrange RTK solution precision from several centimeters to the subcentimeter in all components. More significantly, the precision of the height component is even higher. Several geosciences applications that require subcentimeter real‐time solutions can largely benefit from the proposed approach, such as monitoring of earthquakes and large dams in real‐time, high‐precision GPS leveling and refinement of the vertical datum. In addition, the high‐resolution RZTD solutions can contribute to effective recovery of tropospheric slant path delays in order to establish a 4‐D troposphere tomography.

A Systematic Review of kinematic models used in foot & ankle biomechanics

Over the past decade our understanding of foot function has increased significantly[1,2]. Our understanding of foot and ankle biomechanics appears to be directly correlated to advances in models used to assess and quantify kinematic parameters in gait. These advances in models in turn lead to greater detail in the data. However, we must consider that the level of complexity is determined by the question or task being analysed. This systematic review aims to provide a critical appraisal of commonly used marker sets and foot models to assess foot and ankle kinematics in a wide variety of clinical and research purposes.

Experimental studies of wireless communication and GNSS kinematic positioning performance in high-mobility vehicle environments

In order to support intelligent transportation system (ITS) road safety applications such as collision avoidance, lane departure warnings and lane keeping, Global Navigation Satellite Systems (GNSS) based vehicle positioning system has to provide lane-level (0.5 to 1 m) or even in-lane-level (0.1 to 0.3 m) accurate and reliable positioning information to vehicle users. However, current vehicle navigation systems equipped with a single frequency GPS receiver can only provide road-level accuracy at 5-10 meters. The positioning accuracy can be improved to sub-meter or higher with the augmented GNSS techniques such as Real Time Kinematic (RTK) and Precise Point Positioning (PPP) which have been traditionally used in land surveying and or in slowly moving environment. In these techniques, GNSS corrections data generated from a local or regional or global network of GNSS ground stations are broadcast to the users via various communication data links, mostly 3G cellular networks and communication satellites. This research aimed to investigate the precise positioning system performances when operating in the high mobility environments. This involves evaluation of the performances of both RTK and PPP techniques using: i) the state-of-art dual frequency GPS receiver; and ii) low-cost single frequency GNSS receiver. Additionally, this research evaluates the effectiveness of several operational strategies in reducing the load on data communication networks due to correction data transmission, which may be problematic for the future wide-area ITS services deployment. These strategies include the use of different data transmission protocols, different correction data format standards, and correction data transmission at the less-frequent interval. A series of field experiments were designed and conducted for each research task. Firstly, the performances of RTK and PPP techniques were evaluated in both static and kinematic (highway with speed exceed 80km) experiments. RTK solutions achieved the RMS precision of 0.09 to 0.2 meter accuracy in static and 0.2 to 0.3 meter in kinematic tests, while PPP reported 0.5 to 1.5 meters in static and 1 to 1.8 meter in kinematic tests by using the RTKlib software. These RMS precision values could be further improved if the better RTK and PPP algorithms are adopted. The tests results also showed that RTK may be more suitable in the lane-level accuracy vehicle positioning. The professional grade (dual frequency) and mass-market grade (single frequency) GNSS receivers were tested for their performance using RTK in static and kinematic modes. The analysis has shown that mass-market grade receivers provide the good solution continuity, although the overall positioning accuracy is worse than the professional grade receivers. In an attempt to reduce the load on data communication network, we firstly evaluate the use of different correction data format standards, namely RTCM version 2.x and RTCM version 3.0 format. A 24 hours transmission test was conducted to compare the network throughput. The results have shown that 66% of network throughput reduction can be achieved by using the newer RTCM version 3.0, comparing to the older RTCM version 2.x format. Secondly, experiments were conducted to examine the use of two data transmission protocols, TCP and UDP, for correction data transmission through the Telstra 3G cellular network. The performance of each transmission method was analysed in terms of packet transmission latency, packet dropout, packet throughput, packet retransmission rate etc. The overall network throughput and latency of UDP data transmission are 76.5% and 83.6% of TCP data transmission, while the overall accuracy of positioning solutions remains in the same level. Additionally, due to the nature of UDP transmission, it is also found that 0.17% of UDP packets were lost during the kinematic tests, but this loss doesn't lead to significant reduction of the quality of positioning results. The experimental results from the static and the kinematic field tests have also shown that the mobile network communication may be blocked for a couple of seconds, but the positioning solutions can be kept at the required accuracy level by setting of the Age of Differential. Finally, we investigate the effects of using less-frequent correction data (transmitted at 1, 5, 10, 15, 20, 30 and 60 seconds interval) on the precise positioning system. As the time interval increasing, the percentage of ambiguity fixed solutions gradually decreases, while the positioning error increases from 0.1 to 0.5 meter. The results showed the position accuracy could still be kept at the in-lane-level (0.1 to 0.3 m) when using up to 20 seconds interval correction data transmission.

A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services

Currently, the GNSS computing modes are of two classes: network-based data processing and user receiver-based processing. A GNSS reference receiver station essentially contributes raw measurement data in either the RINEX file format or as real-time data streams in the RTCM format. Very little computation is carried out by the reference station. The existing network-based processing modes, regardless of whether they are executed in real-time or post-processed modes, are centralised or sequential. This paper describes a distributed GNSS computing framework that incorporates three GNSS modes: reference station-based, user receiver-based and network-based data processing. Raw data streams from each GNSS reference receiver station are processed in a distributed manner, i.e., either at the station itself or at a hosting data server/processor, to generate station-based solutions, or reference receiver-specific parameters. These may include precise receiver clock, zenith tropospheric delay, differential code biases, ambiguity parameters, ionospheric delays, as well as line-of-sight information such as azimuth and elevation angles. Covariance information for estimated parameters may also be optionally provided. In such a mode the nearby precise point positioning (PPP) or real-time kinematic (RTK) users can directly use the corrections from all or some of the stations for real-time precise positioning via a data server. At the user receiver, PPP and RTK techniques are unified under the same observation models, and the distinction is how the user receiver software deals with corrections from the reference station solutions and the ambiguity estimation in the observation equations. Numerical tests demonstrate good convergence behaviour for differential code bias and ambiguity estimates derived individually with single reference stations. With station-based solutions from three reference stations within distances of 22–103 km the user receiver positioning results, with various schemes, show an accuracy improvement of the proposed station-augmented PPP and ambiguity-fixed PPP solutions with respect to the standard float PPP solutions without station augmentation and ambiguity resolutions. Overall, the proposed reference station-based GNSS computing mode can support PPP and RTK positioning services as a simpler alternative to the existing network-based RTK or regionally augmented PPP systems.

A kinematic analysis of the hand function

Background The evaluation of the hand function is an essential element within the clinical practice. The usual assessments are focus on the ability to perform activities of daily life. The inclusion of instruments to measure kinematic variables provides a new approach to the assessment. Inertial sensors adapted to the hand could be used as a complementary instrument to the traditional assessment. Material: clinimetric assessment (Upper Limb Functional Index, Quick Dash), antrophometric variables (eight and weight), dynamometry (palm preasure) was taken. Functional analysis was made with Acceleglove system for the right hand and computer system. The glove has six acceleration sensor, one on each finger and another one on the reverse palm. Method Analytic, transversal approach. Ten healthy subject made six task on evaluation table (tripod pinch, lateral pinch and tip pinch, extension grip, spherical grip and power grip). Each task was made and measure three times, the second one was analyze for the results section. A Matlab script was created for the analysis of each movement and detection phase based on module vector. Results The module acceleration vector offers useful information of the hand function. The data analysis obtained during the performance of functional gestures allows to identify five different phases within the movement, three static phase and tow dynamic, each module vector was allied to one task. Conclusion Module vector variables could be used for the analysis of the different task made by the hand. Inertial sensor could be use as a complement for the traditional assessment system.

A kinematic and electromyographic study of grip force

Background The hand is an element of great importance to humans, as it enables us to have different grips. Its analysis, based on an accelerometer and electromyography, is critical in order to determine its operation. The processing and analysis of variables obtained by these devices offer a different approach in functional assessment. Therefore, knowledge of the muscles and elements of the hand in the grip force will offer a better approach for different interventions. Method The functionality of the hand of seven healthy subjects was parameterized and synchronized in real time based on grip force. The AcceleGlove was used to register accelerometric (fingers and palm) values and the Mega ME6000 was used for the surface electromyography and maximum voluntary contraction for the hand and forearm muscles. A computer script based on “R” and MATLAB software was developed to enable the correct interpretation of the main variables (variation of acceleration and maximum peak value of electromyography). Results The muscles of greater activity in grip was found in the hypothenar region (0.313 ± 0.148%) and the flexor ulnaris carpi (0.360 ± 0.118%), based on maximum voluntary contraction. Reference values in the module vector of the palm have proved an essential element for the identification of the movement phases. The ring and index fingers were the elements with the greatest variation of acceleration in the movement phases. Conclusion: Parameterization of the force grip and fragmentation of the registered data has been made possible due to the development of a technical procedure.

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.

Wide area kinematic positioning with BeiDou triple frequency signals

A key challenge of wide area kinematic positioning is to overcome the effects of the varying hardware biases in code signals of the BeiDou system. Based on three geometryfree/ionosphere-free combinations, the elevation-dependent code biases are modelled for all BeiDou satellites. Results from the data sets of 30-day for 5 baselines of 533 to 2545 km demonstrate that the wide-lane (WL) integer-fixing success rates of 98% to 100% can be achieved within 25 min. Under the condition of HDOP of less than 2, the overall RMS statistics show that ionospheric-free WL single-epoch solutions achieve 24 to 50 cm in the horizontal direction. Smoothing processing over the moving window of 20 min reduces the RMS values by a factor of about 2. Considering distance-independent nature, the above results show the potential that reliable and high precision positioning services could be provided in a wide area based on a sparsely distributed ground network.

Kinematic flow patterns in slow deformation of a dense granular material

The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using in situ imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediately underneath the punch; and formation of distinct shear bands adjoining the stagnation zone. The transient and steady state stagnation zone geometry, as well as the strength of the vortices and strain rates in the shear bands, are obtained from the experimental data. All of these results are well-reproduced in exact-scale non-smooth contact dynamics simulations. Full 3D numerical particle positions from the simulations allow extraction of flow features that are extremely difficult to obtain from experiments. Three examples of these, namely material free surface evolution, deformation of a grain column below the punch and resolution of velocities inside the primary shear band, are highlighted. The variety of flow features observed in this model problem also illustrates the difficulty involved in formulating a complete micromechanical analytical description of the deformation.

An evaluation of orogenic kinematic evolution utilizing crystalline and magnetic anisotropy in granitoids

The Silurian-Devonian Galway Granite Complex (GGC ~425-380Ma) is defined here as a suite of granitoid plutons that comprise the Main Galway Granite Batholith and the Earlier Plutons. The Main Batholith is a composite of the Carna Pluton in the west and the Kilkieran Pluton in the east and extends from Galway City ~130km to the west. The Earlier Plutons are spatially, temporally and structurally distinct, situated northwest of the Main Batholith and include the Roundstone, Omey, Inis and Letterfrack Plutons. The majority of isotopic and structural data currently available pertain to the Kilkieran Pluton, several tectonic models have already been devised for this part of the complex. These relate emplacement of the Kilkieran Pluton to extension across a large east-west Caledonian lineament, i.e. the Skird Rocks Fault, during late Caledonian transtension. No chronological data have been published that directly and accurately date the emplacement of the Carna Pluton or any of the Earlier Plutons. There is also a lack of data pertaining to the internal structure of these intrusions. Accordingly, no previous study has established the mechanisms of emplacement for the Earlier Plutons and only limited work is available for the Carna Pluton. As a consequense of this, constituents of the GGC have not previously been placed in a context relative to each other or to regional scale Silurio-Devonian kinematics. The current work focuses on the Omey, Roundstone and Carna Plutons. Here, results of detailed field and Anisotropy of Magnetic Susceptibiliy (AMS) fabric studies are presented. This work is complemented by geological mapping that focuses on fault dynamics and contact relationships. Interpretation of AMS data is aided by rock magnetic experiment data and petrographic microstructural evaluations of representative samples. A new geological map of the the Omey Pluton demonstrates that this intrusion has a defined roof and base which are gently inclined parallel to the fold hinge of the Connemara Antiform. AMS and petrographic data show the intrusion is cross cut by NNW-SSE shear zones that extend into the country rock. These pre-date and were active during magma emplacement. It is proposed that the Omey pluton was emplaced as a discordant phacolith. Pre-existing subvertical D5 faults in the host rock were reactived during emplacement, due to regional sinistral transpression, and served as centralised ascent conduits. A central portion of the Roundstone Pluton was mapped in detail for the first time. Two facies are identified, G1 forms the majority of the pluton and coeval G2 sheets cross cut G1 at the core of the pluton. NNW-SSE D5 faults mapped in the country rock extend across the pluton. These share a geometrical relationship with the distribution of submagmatic strain in the pluton and parallel the majoity of mapped subvertical G2 dykes. These data indicate that magma ascent was controlled by NNW-SSE conduits that are inherently related to those identifed in the Omey Pluton. It is proposed that the Roundstone Pluton is a punched laccolith, the symmetry and structure of which was controlled by pre-exising host rock structures and regional sinistral transpressive stress which presided during emplacement. Field relationships show the long axis of the Carna Pluton lies parallel to mulitple NNW-SSE shear zones. These are represented on a regional scale by the Clifden-Mace Fault which cross cuts the core of this intrusion. AMS and petrographic data show concentric emplacement fabrics were tectonically overprinted as magma cooled from the magmatic state due to this faulting. It is proposed that the Clifden-Mace Fault system was active during ascent and emplacement of the magma and that pluton inflation only terminated as this controlling structure went into compression due to the onset of regional transtension. U-Pb zircon laser ablation inductively coupled mass spectrometry (LA-ICP-MS) data has been compiled from four sample sites. New geochronological data from the Roundstone Pluton (RD1 = ± 3.2Ma) represent the oldest age determination obtained from any member of the GGC and demonstrates that this pluton predates the Carna Pluton by ~10Ma and probably intruded synchronously with the Omey Pluton (~422.5 ± 1.7Ma). Chronological data from the Carna Pluton (CN2 = 412.9 ± 2.5Ma; CN3 = 409.8 ± 7.2Ma; CN4 = 409.6 ± 3.6Ma) represent the first precise magma crystallisation age for this intrusion. This work shows this pluton is 10Ma older than the Kilkieran Pluton and that the supply of magma into the Carna Pluton had terminated by ~409Ma. Chronological, magnetic and field data have been utilised to evaluate the kinematic evolution of the Caledonides of western Ireland throughout the construction of the GGC. It is proposed that the GGC was constructed during four distinct episodes. The style of emplacement and the conduits used for magma transport to the site of emplacement was dependent on the orientation of local structures relative to the regional ambiant stress field. This philosophy is used to critically evaluate and progress existing hypotheses on the transition from regional transpression to regional transtension at the end of the Caledonian Orogeny.

Improved kinematic sensing for motion control applications

New compensation methods are presented that can greatly reduce the slit errors (i.e. transition location errors) and interval errors induced due to non-idealities in optical incremental encoders (square-wave). An M/T-type, constant sample-time digital tachometer (CSDT) is selected for measuring the velocity of the sensor drives. Using this data, three encoder compensation techniques (two pseudoinverse based methods and an iterative method) are presented that improve velocity measurement accuracy. The methods do not require precise knowledge of shaft velocity. During the initial learning stage of the compensation algorithm (possibly performed in-situ), slit errors/interval errors are calculated through pseudoinversebased solutions of simple approximate linear equations, which can provide fast solutions, or an iterative method that requires very little memory storage. Subsequent operation of the motion system utilizes adjusted slit positions for more accurate velocity calculation. In the theoretical analysis of the compensation of encoder errors, encoder error sources such as random electrical noise and error in estimated reference velocity are considered. Initially, the proposed learning compensation techniques are validated by implementing the algorithms in MATLAB software, showing a 95% to 99% improvement in velocity measurement. However, it is also observed that the efficiency of the algorithm decreases with the higher presence of non-repetitive random noise and/or with the errors in reference velocity calculations. The performance improvement in velocity measurement is also demonstrated experimentally using motor-drive systems, each of which includes a field-programmable gate array (FPGA) for CSDT counting/timing purposes, and a digital-signal-processor (DSP). Results from open-loop velocity measurement and closed-loop servocontrol applications, on three optical incremental square-wave encoders and two motor drives, are compiled. While implementing these algorithms experimentally on different drives (with and without a flywheel) and on encoders of different resolutions, slit error reductions of 60% to 86% are obtained (typically approximately 80%).

Excess open solar magnetic flux from satellite data: 1. Analysis of the third perihelion Ulysses pass

We use the third perihelion pass by the Ulysses spacecraft to illustrate and investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the potential effects of small-scale structure in the heliospheric field (giving fluctuations in the radial component on timescales smaller than 1 h) and kinematic time-of-flight effects of longitudinal structure in the solar wind flow. We show that the flux excess is explained by neither very small-scale structure (timescales < 1 h) nor by the kinematic “bunching effect” on spacecraft sampling. The observed flux excesses is, however, well explained by the kinematic effect of larger-scale (>1 day) solar wind speed variations on the frozen-in heliospheric field. We show that averaging over an interval T (that is long enough to eliminate structure originating in the heliosphere yet small enough to avoid cancelling opposite polarity radial field that originates from genuine sector structure in the coronal source field) is only an approximately valid way of allowing for these effects and does not adequately explain or account for differences between the streamer belt and the polar coronal holes.

Modulation of event-related desynchronization during kinematic and kinetic hand movements

Background Event-related desynchronization/synchronization (ERD/ERS) is a relative power decrease/increase of electroencephalogram (EEG) in a specific frequency band during physical motor execution and mental motor imagery, thus it is widely used for the brain-computer interface (BCI) purpose. However what the ERD really reflects and its frequency band specific role have not been agreed and are under investigation. Understanding the underlying mechanism which causes a significant ERD would be crucial to improve the reliability of the ERD-based BCI. We systematically investigated the relationship between conditions of actual repetitive hand movements and resulting ERD. Methods Eleven healthy young participants were asked to close/open their right hand repetitively at three different speeds (Hold, 1/3 Hz, and 1 Hz) and four distinct motor loads (0, 2, 10, and 15 kgf). In each condition, participants repeated 20 experimental trials, each of which consisted of rest (8–10 s), preparation (1 s) and task (6 s) periods. Under the Hold condition, participants were instructed to keep clenching their hand (i.e., isometric contraction) during the task period. Throughout the experiment, EEG signals were recorded from left and right motor areas for offline data analysis. We obtained time courses of EEG power spectrum to discuss the modulation of mu and beta-ERD/ERS due to the task conditions. Results We confirmed salient mu-ERD (8–13 Hz) and slightly weak beta-ERD (14–30 Hz) on both hemispheres during repetitive hand grasping movements. According to a 3 × 4 ANOVA (speed × motor load), both mu and beta-ERD during the task period were significantly weakened under the Hold condition, whereas no significant difference in the kinetics levels and interaction effect was observed. Conclusions This study investigates the effect of changes in kinematics and kinetics on resulting ERD during repetitive hand grasping movements. The experimental results suggest that the strength of ERD may reflect the time differentiation of hand postures in motor planning process or the variation of proprioception resulting from hand movements, rather than the motor command generated in the down stream, which recruits a group of motor neurons.

GHASP: an H alpha kinematic survey of spiral and irregular galaxies - IX. The near-infrared, stellar and baryonic Tully-Fisher relations

We studied, for the first time, the near-infrared, stellar and baryonic Tully-Fisher relations for a sample of field galaxies taken from a homogeneous Fabry-Perot sample of galaxies [the Gassendi HAlpha survey of SPirals (GHASP) survey]. The main advantage of GHASP over other samples is that the maximum rotational velocities were estimated from 2D velocity fields, avoiding assumptions about the inclination and position angle of the galaxies. By combining these data with 2MASS photometry, optical colours, HI masses and different mass-to-light ratio estimators, we found a slope of 4.48 +/- 0.38 and 3.64 +/- 0.28 for the stellar and baryonic Tully-Fisher relation, respectively. We found that these values do not change significantly when different mass-to-light ratio recipes were used. We also point out, for the first time, that the rising rotation curves as well as asymmetric rotation curves show a larger dispersion in the Tully-Fisher relation than the flat ones or the symmetric ones. Using the baryonic mass and the optical radius of galaxies, we found that the surface baryonic mass density is almost constant for all the galaxies of this sample. In this study we also emphasize the presence of a break in the NIR Tully-Fisher relation at M(H,K) similar to -20 and we confirm that late-type galaxies present higher total-to-baryonic mass ratios than early-type spirals, suggesting that supernova feedback is actually an important issue in late-type spirals. Due to the well-defined sample selection criteria and the homogeneity of the data analysis, the Tully-Fisher relation for GHASP galaxies can be used as a reference for the study of this relation in other environments and at higher redshifts.

Transition redshift: new kinematic constraints from supernovae

The transition redshift (deceleration/acceleration) is discussed by expanding the deceleration parameter to first order around its present value. A detailed study is carried out by considering two different parametrizations, q = q(0) + q(1)z and q = q(0) + q(1)z(1 + z)(-1), and the associated free parameters (q(0), q(1)) are constrained by three different supernovae (SNe) samples. A previous analysis by Riess et al. using the first expansion is slightly improved and confirmed in light of their recent data (Gold07 sample). However, by fitting the model with the Supernova Legacy Survey (SNLS) type Ia sample, we find that the best fit to the redshift transition is z(t) = 0.61, instead of z(t) = 0.46 as derived by the High-z Supernovae Search (HZSNS) team. This result based in the SNLS sample is also in good agreement with the sample of Davis et al., z(t) = 0.60(-0.11)(+0.28) (1 sigma). Such results are in line with some independent analyses and accommodate more easily the concordance flat model (Lambda CDM). For both parametrizations, the three SNe Ia samples considered favour recent acceleration and past deceleration with a high degree of statistical confidence level. All the kinematic results presented here depend neither on the validity of general relativity nor on the matter-energy contents of the Universe.