Geocentric Frame Research Articles

Early Emergence of Agreement in Yucatec Maya Sign Language

In many sign languages, space is used to express grammatical features. However, verb agreement in space is noticeably slow to appear in emerging sign languages. Many reasons have been proposed to explain this delay or even absence: the reduced size of the community, the recent creation of the sign language and the lack of exposure to a fully formed language. To examine the way space is used to express agreement in Yucatec Maya Sign Language (YMSL), a new signed language from the peninsula of Yucatán (Mexico), a task was conducted using video stimuli created to elicit ditransitive constructions showing transfer events, such as events of giving or taking. Results show that agreement is present early in YMSL, even from the first generation of deaf signers. While many signers used single agreement constructions, the second generation of deaf children systematically employed double agreement constructions, placing them on the high end of the evolutionary path proposed for verb agreement in sign languages. I argue that cultural habits of the surrounding community, namely the preference for a geocentric frame of reference among Yucatec Maya speakers, is what facilitates the early emergence of the use of space to express agreement in YMSL.

Reference frames in language and cognition: cross-population mismatches

AbstractNumerous studies have found evidence of a speech community’s referential practices in discourse being predictive of its members’ behavior in nonverbal tasks. In this article, we discuss a series of exceptions to this alignment pattern, drawing on data from eleven populations of Asia, Europe, the Middle East, North and Central America, and Oceania. These exceptions have not been discussed in conjunction with one another and the striking commonalities across the findings of these studies have gone unnoticed: (a) in discourses referring to small-scale space, either intrinsic frame use is dominant or both relative and geocentric frames are used frequently in addition to intrinsic frames; and (b) in recall/recognition memory, geocentric coding is more common than egocentric coding (in tasks that involve stationary stimulus configurations) in nine of the populations, while in the remaining two, there is evidence of extensive intrinsic coding even in nonverbal cognition. We discuss these findings in light of Haun’s innate geocentrism hypothesis (Haun, D. B. M., C. Rapold, J. Call, G. Janzen & S. C. Levinson. 2006. Cognitive cladistics and cultural override in hominid spatial cognition.Proceedings of the National Academy of Sciences103(46). 17568–17573). Our data offers partial support for this hypothesis, but simultaneously calls into question whether any extrinsic reference frames are available innately.

Directionals, topography, and cultural construals of landscape in Lamaholot

AbstractThis paper investigates “directionals” or geocentric spatial terms in Lamaholot, examining the interaction between directionals, topographic environment, and cultural construals of landscape. Lamaholot is an Austronesian language of eastern Indonesia spoken on the volcanic island of Flores. The Lewotobi dialect, with which this paper is concerned, is spoken on the coastal area between Mt. Lewotobi and the Solor Sea. Reflective of this topographic environment, this language has “directionals” or grammatical terms defined with respect to landmarks:rae‘mountainward’,lau‘seaward’,wəli‘parallel with the coast’,teti‘upward’, andlali‘downward’. After describing how the spatial orientation represented by directionals is embedded in linguistic and sociocultural practices in Lamaholot-speaking communities, this paper shows that directionals exhibit intriguing diversity in interpretation and morphosyntax: they constitute a coordinate system for geocentric frame of reference, refer to different directions depending on different construals of landscape, and can appear in various syntactic positions. It is argued that this diversity can be understood in terms of a complex interplay of topographic environment, sociocultural practices, language uses, and linguistic repertoire, as assumed in the Sociotopographic Model (Palmer, Bill, Jonathon Lum, Jonathan Schlossberg & Alice Gaby. 2017. How does the environment shape spatial language? Evidence for sociotopography.Linguistic Typology21(3). 457–491). Thus, the directional system in Lamaholot makes a strong case for a sociotopographic approach to spatial language.

Stellar Aberration from Earth and from a Satellite

In his endeavor to find a concrete evidence in favor of the Copernican picture of the solar system, the English astronomer James Bradley made a series of astronomical observations during the period (1725-1728) aiming to detect a stellar parallax. His findings, which manifested indeed an annual apparent cyclic motion of a star, were however at conflict with what is expected in a parallax. To his surprise, the result of every measurement obtained corresponded to what he expected to get in a measurement done three months earlier. Bradley realized that he was witnessing a new physical effect, and he presented an explanation that conceived light as a corpuscular stream travelling at finite velocity. Despite that Bradley’s explanation of the stellar aberration effect was inadequate, the equation which he derived to quantify the aberration angle, predicted a better estimation of light velocity, and the aberration phenomenon itself was a concrete support of heliocentrism. Stellar aberration as well as some other optical experiments, whose explanations posed challenges to the existing physical theories in the late nineteenth century paved the way for the emergence of the special theory of relativity. In the current work we employ the theory of universal space and time to show that a given direction in a frame of reference is tilted when observed in a moving frame by an angle that depends on the direction itself and the velocity of the moving frame. The latter fact is utilized to explain stellar aberration, determine the deviation of a star’s vision direction from its true one, and deduce its apparent position at any instant as a function of its latitude and time. The novel concept of aberration correction vector is employed to derive the apparent elliptic path of an observed celestial object at any time. The concept of graded inertial frames is introduced and utilized to deal with aberration when observed from a satellite in a similar way to its treatment when observed from Earth. The transformation matrix between a geocentric frame and a satellite’s non-rotating frame is derived and used to transform temporary Earthly vision directions to the satellite’s frame. Furthermore, the transformed vectors are adopted as transient fixed directions relative to which the vision directions of a star from the satellite are specified throughout one revolution. Satellites connective matrices are constructed to make geometric information regarding the celestial sphere in one frame immediately usable by observers on Earth and in all other satellites.

Operation and reliability of an onboard GNSS receiver during an in-flight test

This article presents and describes the operational capabilities of an onboard GNSS receiver to determine the reliability of the in-flight navigation parameters. An analysis was made of the operation reliability of an autonomous single-frequency Thales Mobile Mapper receiver in air navigation as compared to the technical operation of a dual-frequency Topcon HiperPro receiver. To this end, this work contains a comparison of the aircraft flight navigation parameters based on readings obtained from the Thales Mobile Mapper and Topcon HiperPro receivers. In particular, the comparison concerned the reliability of coordinate determination and flight speed parameters of an aircraft. The research experiment was conducted using a Cessna 172 aircraft, a property of the Military University of Aviation in Dęblin, Poland. Technical operation of the GNSS satellite receivers was tested in the flights of the Cessna 172 aircraft around the EPDE military airport in Dęblin. Based on the results obtained from the tests, it was found that the operational reliability of the Thales Mobile Mapper in the operational phase of the in-flight test ranged from -3.8 to +6.9 m in the XYZ geocentric frame and from -2.2 to +8.1 m in the BLh ellipsoidal frame, respectively. On the other hand, the accuracy of the Cessna 172 aircraft positioning when using the Thales Mobile Mapper receiver was higher than 1.7 m in the XYZ geocentric frame and higher than 2 m in the BLh ellipsoidal frame, respectively. Furthermore, the reliability of the Cessna 172 flight speed determination was from -3.4 to +2.4 m/s.

Accurate Mapping Method for UAV Photogrammetry Without Ground Control Points in the Map Projection Frame

Unmanned aerial vehicle (UAV) photogrammetry without ground control points (GCPs) can effectively improve production efficiency and reduce production costs; this method is especially advantageous in areas that are difficult for people to reach. However, there are a series of problems in UAV photogrammetry without GCPs. One of the main problems is that the accurate camera parameters cannot be obtained through the on-the-job calibration method; furthermore, the inaccurate principal distance will have a serious impact on the elevation accuracy of object points. The other one is that the projection deformation and earth curvature also have impacts on the elevation accuracy, when the mapping task is carried out in the map projection frame. This article explains the specific reasons of elevation errors and proposes an effective solution. First, the camera self-calibration is performed in a geocentric frame with control strips. Then, the exterior orientation elements of the images are calculated in the map projection frame without control strips. Finally, the elevation errors that are caused by the map projection deformation and the earth’s curvature are corrected. The experimental results show that the proposed method can achieve accurate mapping, and the elevation accuracy has been significantly improved.

Semi-annual, annual and Universal Time variations in the magnetosphere and in geomagnetic activity: 4. Polar Cap motions and origins of the Universal Time effect

We use theam,an, asand theaσgeomagnetic indices to the explore a previously overlooked factor in magnetospheric electrodynamics, namely the inductive effect of diurnal motions of the Earth’s magnetic poles toward and away from the Sun caused by Earth’s rotation. Because the offset of the (eccentric dipole) geomagnetic pole from the rotational axis is roughly twice as large in the southern hemisphere compared to the northern, the effects there are predicted to be roughly twice the amplitude of those in the northern hemisphere. Hemispheric differences have previously been discussed in terms of polar ionospheric conductivities generated by solar photoionization, effects which we allow for by looking at the dipole tilt effect on the time-of-year variations of the indices. The electric field induced in a geocentric frame is shown to also be a significant factor and gives a modulation of the voltage applied by the solar wind flow in the southern hemisphere that is typically a ±30% diurnal modulation for disturbed intervals rising to ±76% in quiet times. For the northern hemisphere these are 15% and 38% modulations. Motion away from/towards the Sun reduces/enhances the directly-driven ionospheric voltages and reduces/enhances the magnetic energy stored in the tail and we estimate that approximately 10% of the effect appears in directly driven ionospheric voltages and 90% in changes of the rate of energy storage or release in the near-Earth tail. The hemispheric asymmetry in the geomagnetic pole offsets from the rotational axis is shown to be the dominant factor in driving Universal Time (UT) variations and hemispheric differences in geomagnetic activity. Combined with the effect of solar wind dynamic pressure and dipole tilt on the pressure balance in the near-Earth tail, the effect provides an excellent explanation of how the observed Russell-McPherron pattern with time-of-yearFandUTin the driving power input into the magnetosphere is converted into the equinoctialF-UTpattern in average geomagnetic activity (after correction is made for dipole tilt effects on ionospheric conductivity), added to a pronouncedUTvariation with minimum at 02–10 UT. In addition, we show that the predicted and observedUTvariations in average geomagnetic activity has implications for the occurrence of the largest events that also show the nettUTvariation.

About the Free and Forced Nutation: The Daily Nutation

To explain the nutation phenomenon, Euler chose a geocentric frame of coordinates to present his dynamical equations. In accordance with his formulas, the nutation is caused by a momentum relative to the Earth's center, due to certain external forces. Further, Poinsot presented a special case of the Euler's equations, when any momentum of those certain external forces does not exist. Due to a problematic approximation, Poinsot announced that in this case may take place a nutation period of 10 month, named “free period”, to distinguish it from the Euler's dynamical solution, known as “forced nutation”. After Poinsot, the notion of “free nutation” was extended also to those nutation phenomena which have only a geophysical origin, without a momentum of certain external forces. Usually, the daily nutation is considered as being a free nutation phenomenon. In order to search for a forced daily nutation component, the daily trajectory of the Earth-Moon barycenter inside the Earth is used (a simple scheme of this barycenter trajectory is presented in a geocentric system of axes). Finally, if the ecliptic line is accepted to be described by the Earth-Moon barycenter, it must be accepted, too, that a torque due the Sun and the Moon acts during a sideral day interval on diurnal Earth rotation around its axis. Due to the small value of the nutation constant, a period of 18,6 years is needed to correctly and completely detect the forced daily nutation; this phenomenon permanently presents very fine variations depending on the longitude of the ascending lunar node, the Moon’s declination and the Sun’s ecliptic longitude.

3D Localisation of Target using Elevation Angle Algorithm with the use of Ground Radars

A new novel method based on elevation angle algorithm (EAA) is proposed in this paper, to obtain 3D position of target using range and azimuth measurements of two ground 2D radars. The EAA estimates optimal target elevation angle wrt contributing radar by solving a non-linear optimisation problem using Levenberg-Marquardt method in geo-centric frame such as earth-centred-earth-fixed. The target position in geodetic frame (WGS84) is then obtained using slant range, azimuth and estimated elevation angle. The proposed method is evaluated using simulated but realistic radar data and accuracy of estimated position is found to be comparable with true position (error within acceptable limit). The method is also evaluated with real data from actual ground 2D radars and estimated target position is found to be comparable with reference navigation data (GPS) on-board of target. For each radar, corresponding Extended Kalman filter (EKF) is used to handle noisy, asynchronous measurements and to provide estimated range and azimuth at common reference time for altitude estimation using proposed EAA method. In case of real data, the estimated altitude is found to be comparable GPS altitude with error less than 5 % of true altitude. From the study, it is found that EAA is suitable to estimate target position using measurements from only two contributing asynchronous 2D radars in real-time as compared to some other techniques such triangulation and Trilateration where at-least three radars are required to get the position of target. This method can be useful to utilise network of vintage long range 2D radars to determine target position and to fill the gap wherever/whenever target is out of detection range of 3D radars. In addition, EAA method is compared with commonly used methodology such range only localisation and results are presented.

The Application of the BSSD Iono-Free Linear Combination Method in the Processing of Aircraft Positioning

Abstract The article presents the results of research into the use of the differentiation technique of BSSD (Between Satellite Single Difference) observations for the Iono-Free LC combination (Linear Combination) in the GPS system for the needs of aircraft positioning. Within the conducted investigations, a positioning algorithm for the BSSD Iono-Free LC positioning method was presented. In addition, an experimental test was conducted, in which raw observational data and GPS navigation data were exploited in order to recover the aircraft position. The examination was conducted for the Cessna 172 and the on-board dual-frequency receiver Topcon HiperPro. The experimental test presents the results of average errors of determining the position of the Cessna 172 in the XYZ geocentric frame and in the ellipsoidal BLh frame. Furthermore, the article presents the results of DOP (Dilution of Precision) coefficients, the test of the Chi square internal reliability test and the HPL and VPL confidence levels in GNSS precision approach (PA) in air transport. The calculations were performed in the original APS software (APS Aircraft Positioning Software) developed in the Department of Air Navigation of the Faculty of Aeronautics at the Polish Air Force University.

Free falling inside flattened spheroids: Gravity tunnels with no exit

A “gravity tunnel” is the name given to a fictitious deep shaft drilled inside the Earth so that objects dropped from the surface of the Earth would free fall without ever touching the walls. It is well known that because of the rotation of the Earth, such tunnels are not straight lines but instead they emerge westward of the antipodal point, when the Earth is approximated as a rotating sphere. In this article, we determine the shape of gravity tunnels by taking into account the polar flattening of the Earth resulting from its rotation. The Earth is described as a McLaurin spheroid, an exact equilibrium shape for a rotating homogeneous deformable body that provides a fair description of the actual shape of the Earth. It turns out that the gravitational force acting on an object located inside the spheroid has a simple form (it is harmonic), so that it is straightforward to compute analytically the free fall trajectories. This study follows a procedure presented several times in this journal and elsewhere, i.e., the trajectory is first computed in the geocentric (non-rotating) frame, and it is then analysed in the terrestrial (rotating) frame. We find that when the flattening of the Earth is taken into account, gravity tunnels have no exit: an object dropped from a point of the surface (other than on the equator or a pole) never reaches the surface again, unless the flattening has very specific (and unnatural) values. We also compute the deviations from the vertical for short falls and compare them to standard eastwards and southwards deviation expressions obtained with other modelizations of the gravity of the rotating Earth, in particular, for a rotating spherical body.

Effect of Hindi, Sanskrit and Urdu medium schooling on spatial language and encoding

Spatial cognition refers to the process through which people acquire knowledge of the location of objects in their surrounding environment. Studies suggest that people use different spatial frames of reference to describe the location of objects in space. The present study examines the frames of reference used by 10–15-year-old students attending Hindi, Sanskrit and Urdu medium schools at Varanasi in performing spatial cognitive tasks. Traditional schools, such as Sanskrit and Urdu medium schools, provide substantial experience and training in the use of a geocentric frame of reference based on cardinal directions (i.e., north, south, east and west). In view of this, it was expected that children attending these schools would use a geocentric frame of reference more than those attending Hindi medium school. Using a variety of procedures, the spatial frames of reference used in description and encoding of objects by students in Hindi, Sanskrit and Urdu medium schools were assessed. The results indicated that traditional Sanskrit and Urdu medium school students used more geocentric language for description of spatial objects and they also engaged in greater geocentric encoding of those objects than the students of Hindi medium schools.

Aircraft positioning using PPP method in GLONASS system

PurposeThe purpose of the study is focused on implementation of Global Navigation Satellite System (GLONASS) technique in civil aviation for recovery of aircraft position using Precise Point Positioning (PPP) method in kinematic mode.Design/methodology/approachThe aircraft coordinates of Cessna 172 plane in XYZ geocentric frame were obtained based on GLONASS code and phase observations for PPP method. The numerical computations were executed in post-processing mode in the RTKPOST module in RTKLIB program. The mathematical scheme of equation observation of PPP method was solved using Kalman filter in stochastic processing.FindingsIn paper, the average accuracy of aircraft position is about 0.308 m for X coordinate, 0.274 m for Y coordinate, 0.379 m for Z coordinate. In case of the mean radial spherical error (MRSE) parameter, the average value equals to 0.562 m. In paper, the accuracy of aircraft position in BLh geodesic frame were also showed and described.Research limitations/implicationsThe PPP method can be applied for determination the coordinates of receiver, receiver clock bias, Zenith Wet Delay (ZWD) parameter and ambiguity term for each satellite.Practical implicationsThe PPP method is a new technique for aircraft positioning in air navigation. The PPP method can be also used in receiver autonomous integrity monitoring (RAIM) module in aircraft-based augmentation system (ABAS) system in air transport. The typical accuracy for recovery the aircraft position is about cm ÷ dm level using the PPP method.Social implicationsThe paper is destined for people who work in area of geodesy, navigation, aviation and air transport.Originality/valueThe work presents the original research results of implementation the GLONASS satellite technique for recovery the aircraft position in civil aviation. Currently, the presented research PPP method is used in precise positioning of aircraft in air navigation based on global positioning system and GLONASS solutions.

Quasi-experimental research in culture sensitive psychology

The research presented in this article follows up on several aspects of Gustav Jahoda’s long and fruitful career: (1) his early fieldwork on cognitive development in Africa, particularly in the area of spatial skills; (2) his interest in cross-cultural psychology as a research method; and (3) his insistence on bringing anthropology and psychology together. The topic of our research is the development of a so-called “geocentric” frame of spatial reference. This is a cognitive style, in which individuals describe and represent small-scale table-top space in terms of large-scale geographic dimensions. We explore the development with age of geocentric language and cognition, and the relationships between the two. We also explore the many environmental and socio-cultural variables that favor the use of this frame. We demonstrate how we untangled several of these variables by using a succession of within-society group comparisons, in several societies where a geocentric frame is in common usage (Bali, Indonesia, India, and Nepal). Our research program unfolds like a detective story, where one finding that is difficult to interpret because of several confounded variables leads to another quasi-experimental group comparison that suggests another hypothesis, which is then tested in a further session of field-work. In each case, we emphasize how important it was to have extensive linguistic and ethnographic knowledge before implementing psychological tests. The research design is not cross-cultural as such (we hardly ever perform comparisons between societies), but culturally sensitive within a series of societies; in other words, as Dasen and Jahoda (1986 , p. 413) defined it, “cross-cultural developmental psychology is not just comparative: essentially it is an outlook that takes culture seriously.”

One-step solution to local tie vector determination at co-located GNSS/VLBI sites

The local tie vector, which connects the different space geodetic techniques at a co-located site, plays an important role in the realization of the International Terrestrial Reference Frame (ITRF). This paper presents a new method to determine the tie vector between the GNSS and very long baseline interferometry tracking points. The parameters of the local tie vector and the axes offsets are introduced into constraint equations. The parameters are then resolved using the 3D constrained least squares adjustment. With the surveying data collected at two different sites (Kunming and Urumqi) in China, the proposed method can precisely determine the local tie vectors in a geocentric frame. The root mean square error (RMSE) is (1.2, 2.3 and 1.5 mm) and (1.0, 1.5 and 1.4 mm) for the three coordinate components at the sites in Kunming and Urumqi, respectively. The offset between the primary and secondary axes of the VLBI telescopes is estimated to be 7.5 mm in Kunming’s site and 4.0 mm in Urumqi’s site, and the corresponding RMSE is 1.8 mm and 2.0 mm for the two sites, respectively.

Competing perspectives on frames of reference in language and thought

A study found that Dutch-speaking children who prefer an egocentric (left/right) reference frame when describing spatial relationships, and Hai||om-speaking children who use a geocentric (north/south) frame had difficulty recreating small-scale spatial arrays using their language-incongruent system (Haun, Rapold, Janzen, & Levinson, 2011). In five experiments, we reconciled these results with another study showing that English (egocentric) and Tseltal Mayan (geocentric) speakers can flexibly use both systems (Abarbanell, 2010; Li, Abarbanell, Gleitman, & Papafragou, 2011). In replicating and extending Haun et al. (Experiment 1), English- but not Tseltal-speaking children could use their language-incongruent system when the instructions used their non-preferred frame of reference. Perseveration due to task order may explain the discrepancies between present English- and previous Dutch-speaking children, while not understanding task instructions using left/right language may explain why present Tseltal- and previous Hai||om-speaking children had difficulty with their language-incongruent systems. In support, Tseltal-speaking children could use an egocentric system when the instructions were conveyed without left/right language (Experiments 2–4), and many did not know left/right language (Experiment 5). These findings help reconcile seemingly conflicting sets of results and suggest that task constraints, rather than language, determine which system is easier to use (Experiment 2 vs. 3).

A Direct Georeferencing Method for Terrestrial Laser Scanning Using GNSS Data and the Vertical Deflection from Global Earth Gravity Models

Terrestrial laser scanning is an efficient technique in providing highly accurate point clouds for various geoscience applications. The point clouds have to be transformed to a well-defined reference frame, such as the global Geodetic Reference System 1980. The transformation to the geocentric coordinate frame is based on estimating seven Helmert parameters using several GNSS (Global Navigation Satellite System) referencing points. This paper proposes a method for direct point cloud georeferencing that provides coordinates in the geocentric frame. The proposed method employs the vertical deflection from an external global Earth gravity model and thus demands a minimum number of GNSS measurements. The proposed method can be helpful when the number of georeferencing GNSS points is limited, for instance in city corridors. It needs only two georeferencing points. The validation of the method in a field test reveals that the differences between the classical georefencing and the proposed method amount at maximum to 7 mm with the standard deviation of 8 mm for all of three coordinate components. The proposed method may serve as an alternative for the laser scanning data georeferencing, especially when the number of GNSS points is insufficient for classical methods.

Exploring the Moon gravity to escape from the Earth–Moon system

Escape trajectories from the Earth–Moon system can be obtained through a single gravity assist maneuver of a spacecraft with the Moon. This paper presents a semi-analytical study of variations in the semi-major axis and the eccentricity of a spacecraft for a geocentric frame—before and after a close encounter of the spacecraft with the Moon. Studies on the swing-by dynamics between a spacecraft and the Moon were performed in order to establish a set of initial conditions in terms of eccentricities and semi-major axes of geocentric initial orbits. This way, it was possible identify which orbits, launched from Earth parking orbits, accomplish swing-bys with the Moon and generate escape trajectories.

Variance–Covariance Matrix of Transformed GPS Positions: Case Study for the NAD 83 Geodetic Datum

AbstractThis investigation introduces a rigorous mathematical transformation of variance–covariance matrices between a global geocentric frame and a plate-fixed geodetic frame. A practical example between the geocentric frame of International GNSS Service 2008 (IGS08) epoch 2005.00 and the geodetic frame North American Datum of 1983 (NAD 83) (2011) epoch 2010.00 was implemented. Although the theory is general, the transformation used here is controlled by the assumptions implicit in the definition of NAD 83. However, the same approach could be extended to future definitions of fixed-plate datums used by geodetic organizations for charting and mapping applications. Consequently, because the transformation between these two specific frames is assumed by definition to be a one-to-one errorless transformation, the uncertainties for the 14 Helmert transformation parameters between the two frames are assumed to be zero. Nevertheless, the formulation is complete and applicable to other specific datum-transformat...

KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization

AbstractThe current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at today's millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi‐instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.