Apropos laser tracking to GPS satellites

. Laser tracking to GPS satellites (PRN5 and 6) provides an opportunity to compare GPS and laser systems directly and to combine data of both in a single solution. A few examples of this are given in this study. The most important results of the analysis are that (1) daily SLR station coordinate solutions could be generated with a few cm accuracy; (2) coordinates of nine stations were determined in a 2.3-year-long arc solution; (3) the contribution of laser data on the `SLR-GPS' combined orbit, resulting from the simultaneous processing of SLR and GPS data, is significant and (4) laser-only orbits have an accuracy of 10–20 cm, 1-day predictions of SLR orbits differ from IGS orbits by about 20–40 cm, 2-day predictions by 50–60 cm. Received: 1 October 1996 / Accepted: 14 February 1997     

Access to the EGNOS signal in space over mobile-IP

The EGNOS service will provide better positioning availability and accuracy than that from the standalone GPS solutions. However, in order to access the EGNOS service, the end user needs to access the corresponding GEO satellites that broadcast the augmentation information for the region. This is not a problem normally for aviation and maritime applications because an open sky is always available for such applications. However, an open sky is not always available for land applications because of the obstacles in the vicinity of the end users, for example, in the city canyons. The situation gets worse for the regions at high latitudes because the elevation angles to the GEO satellites are rather low (e.g. 4–22° in Finland). This article describes briefly the SISNeT technology, designed and developed by the European Space Agency, which allows accessing the EGNOS SIS via the Internet. It will describe in detail the handheld SISNeT receiver, designed and developed by the Finnish Geodetic Institute under ESA contract. The SISNeT data server is an IP-based server that acquires the EGNOS messages from an EGNOS receiver, and broadcasts them over the Internet in real-time. The handheld receiver consists of a GPS PC-card receiver, a GPRS (or GSM) card phone, and a pocket PC as the host platform. The receiver software is a Windows CE-based package with a multi-process and multi-thread architecture. It simultaneously receives: (1) the EGNOS SIS over a GPRS wireless connection and the Internet and (2) the NMEA messages from a serial connection to a GPS receiver. It decompresses and decodes the EGNOS messages, and utilizes the information in the messages to estimate the EGNOS-corrected coordinates, which are finally delivered to the end user via a virtual COM port. The virtual COM port has been implemented as a stream interface driver in the Pocket PC. It can be accessed in the same way as the physical COM port in a GPS receiver is accessed. Therefore, it is easy to interface to any third-party applications. The test results show that the handheld SISNeT receiver can provide a positioning accuracy of about 1–2 m for the horizontal components, and 2–3 m for the vertical component in real time. Due to the poor performance of the wireless connection, 10–30% of the EGNOS messages can be lost depending on the services provided by the wireless network operators. The impact of the messages lost on the positioning accuracy is about 0.5 m in both the horizontal and vertical components. Electronic Publication     

A GPS-Based Online Control and Alarm System

A global positioning system (GPS)-based online control and alarm system (GOCA) for monitoring of three-dimensional movements has been developed at the Karlsruhe University of Technology. The GOCA hardware consists of an array of GPS sensors and communication units to be placed in the monitoring area. The hardware-dependent control software communicates with the GPS sensors and provides the GPS baseline data and covariance information to the GOCA deformation analysis software. The GOCA center, which comprises both the control software and the GOCA software, may be linked – for example, over a long distance – to another personal computer (PC) that serves as a remote control station. GOCA is able to provide the full capabilities of classical deformation analysis online (with stations grouped into stable points and moving object points). Both types of points may be occupied either continuously or over short periods at different times. The object points are determined with respect to the stable points. A network adjustment is performed for each interval of data collection, and the coordinate and covariance information may optionally be transformed into a specific reference system (e. g., the building system). Unstable reference points are to be detected by statistical tests. The estimated object point time series are filtered with respect to gross errors using robust estimation techniques. Online filters are used to smooth the time series data of critical displacements and to predict other deformation functions. The time series data, as well as prediction results, are displayed graphically for each object point. An example concerning the online monitoring of a slag heap in a coal-mining area is included. ? 2000 John Wiley & Sons, Inc.     

Improving strain rate estimation from velocity data of non-permanent GPS stations: the Central Apennine study case (Italy)

An efficient procedure is proposed to define realistic lower limits of velocity errors of a non-permanent GPS station (NPS), i.e., a station where the antenna is installed and operates for short time periods, typically 10–20 days per year. Moreover, the proposed method is aimed at being independent of standard GPS data processing. The key is to subsample appropriately the coordinate time series of several continuous GPS stations situated nearby or inside the considered NPS network, in order to simulate the NPS behavior and to estimate the velocity errors associated with the subsampling procedure. The obtained data are used as lower limits to accept or correct the error estimates provided by standard data processing. The proposed approach is applied to data from the dense, non-permanent network in the Central Apennine of Italy based on a sequence of solutions for the overlapping time spans 1999–2003, 1999–2004, 1999–2005 and 1999–2007. Both the original and error-corrected velocity patterns are used to compute the strain rate fields. The comparison between the corresponding results reveals large differences that could lead to divergent interpretations about the kinematics of the study area.     

An assessment of Bernese GPS software precise point positioning using IGS final products for global site velocities

We assess the use of precise point positioning (PPP) within the Bernese GPS software (BSW) Version 5.0 over the period from 2000 to 2005. In our strategy, we compute a set of daily PPP solutions for international GNSS service (IGS) reference frame (IGb00) sites by fixing IGS final satellite orbits and clock products, followed by a Helmert transformation of these solutions into ITRF2000, forming a set of continuous position time series over the entire time span. We assess BSW PPP by comparing our set of transformation parameters with those produced by the IGS analysis centre coordinator (ACC) and our position time series with those of the Jet Propulsion Laboratory (JPL) and the Scripps Orbit and Permanent Array Centre at the Scripps Institute of Oceanography (SIO). The distributions of the north (N), east (E) and up (U) daily position differences are characterized by means and SD of +2.2 ± 4.8, −0.6 ± 7.9 and +4.8 ± 17.3 mm with respect to JPL, and of +0.1 ± 4.4, −0.1 ± 7.4 and −0.1 ± 11.8 mm with respect to SIO. Similarly, we find sub-millimetre mean velocity differences and SD for the N, E and U components of 0.9, 1.5 and 2.2 mm/year with JPL, and of 1.2, 1.6 and 2.3 mm/year with SIO. A noise analysis using maximum likelihood estimation (MLE) shows that when estimating global site velocities from our position time series, the series need to be on average up to 1.3 times longer than those of JPL and SIO, before an uncertainty of less than 0.5 mm/year is obtained.     

A case study of using Raman lidar measurements in high-accuracy GPS applications

This paper investigates the impact of rapid small-scale water vapor fluctuations on GPS height determination. Water vapor measurements from a Raman lidar are used for documenting the water vapor heterogeneities and correcting GPS signal propagation delays in clear sky conditions. We use data from four short observing sessions (6 h) during the VAPIC experiment (15 May–15 June 2004). The retrieval of wet delays from our Raman lidar is shown to agree well with radiosonde retrievals (bias and standard deviation (SD) were smaller than 1 and 2.8 mm, respectively) and microwave radiometers (from two different instruments, bias was 6.0/−6.6 mm and SD 1.3/3.8 mm). A standard GPS data analysis is shown to fail in accurately reproducing fast zenith wet delay (ZWD) variations. The ZWD estimates could be improved when mean post-fit phase residuals were removed. Several methodologies for integrating zenith lidar observations into the GPS data processing are also presented. The final method consists in using lidar wet delays for correcting a priori the GPS phase observations and estimating a scale factor for the lidar wet delays jointly with the GPS station position. The estimation of this scale factor allows correcting for a mis-calibration in the lidar data and provides in the same way an estimate of the Raman lidar instrument constant. The agreement of this constant with an independent determination using radiosonde data is at the level of 1–4%. The lidar wet delays were derived by ray-tracing from zenith pointing measurements: further improvement in GPS positioning is expected from slant path lidar measurements that would properly account for water vapor anisotropy.     

Precision real-time navigation of LEO satellites using global positioning system measurements

Continued advancements in remote sensing technology along with a trend towards highly autonomous spacecraft provide a strong motivation for accurate real-time navigation of satellites in low Earth orbit (LEO). Global Navigation Satellite System (GNSS) sensors nowadays enable a continuous tracking and provide low-noise radiometric measurements onboard a user spacecraft. Following the deactivation of Selective Availability a representative real-time positioning accuracy of 10 m is presently achieved by spaceborne global positioning system (GPS) receivers on LEO satellites. This accuracy can notably be improved by use of dynamic orbit determination techniques. Besides a filtering of measurement noise and other short-term errors, these techniques enable the processing of ambiguous measurements such as carrier phase or code-carrier combinations. In this paper a reference algorithm for real-time onboard orbit determination is described and tested with GPS measurements from various ongoing space missions covering an altitude range of 400–800 km. A trade-off between modeling effort and achievable accuracy is performed, which takes into account the limitations of available onboard processors and the restricted upload capabilities. Furthermore, the benefits of different measurements types and the available real-time ephemeris products are assessed. Using GPS broadcast ephemerides a real-time position accuracy of about 0.5 m (3D rms) is feasible with dual-frequency carrier phase measurements. Slightly inferior results (0.6–1 m) are achieved with single-frequency code-carrier combinations or dual-frequency code. For further performance improvements the use of more accurate real-time GPS ephemeris products is mandatory. By way of example, it is shown that the TDRSS Augmentation Service for Satellites (TASS) offers the potential for 0.1–0.2 m real-time navigation accuracies onboard LEO satellites.     

GPS network monitors the Western Alps' deformation over a five-year period: 1993–1998

  The Western Alps are among the best studied collisional belts with both detailed structural mapping and also crustal geophysical investigations such as the ECORS and EGT seismic profile. By contrast, the present-day kinematics of the belt is still largely unknown due to small relative motions and the insufficient accuracy of the triangulation data. As a consequence, several tectonic problems still remain to be solved, such as the amount of N–S convergence in the Occidental Alps, the repartition of the deformation between the Alpine tectonic units, and the relation between deformation and rotation across the Alpine arc. In order to address these problems, the GPS ALPES group, made up of French, Swiss and Italian research organizations, has achieved the first large-scale GPS surveys of the Western Alps. More than 60 sites were surveyed in 1993 and 1998 with a minimum observation of 3 days at each site. GPS data processing has been done by three independent teams using different software. The different solutions have horizontal repeatabilities (N–E) of 4–7 mm in 1993 and 2–3 mm in 1998 and compare at the 3–5-mm level in position and 2-mm/yr level in velocity. A comparison of 1993 and 1998 coordinates shows that residual velocities of the GPS marks are generally smaller than 2 mm/yr, precluding a detailed tectonic interpretation of the differential motions. However, these data seem to suggest that the N–S compression of the Western Alps is quite mild (less than 2 mm/yr) compared to the global convergence between the African and Eurasian plate (6 mm/yr). This implies that the shortening must be accomodated elsewhere by the deformation of the Maghrebids and/or by rotations of Mediterranean microplates. Also, E–W velocity components analysis supports the idea that E–W extension exists, as already suggested by recent structural and seismotectonic data interpretation. Received: 27 November 2000 / Accepted: 17 September 2001     

GPS sensitivity analysis applied to non-permanent deformation control networks

This paper illustrates the surveys and the results obtained in an experiment whose goal is to evaluate the Global Positioning System (GPS) sensitivity and accuracy for deformation control on non-permanent network of different extensions. To this aim a high-precision device was properly built to set up known displacements along three orthogonal axes of a GPS antenna. One of the antennas in the considered GPS networks was moved according to centimeter and sub-centimeter displacements; after careful GPS data processing, it was evaluated whether these simulated deformations were correctly a posteriori detected and at which probability level. This experiment was carried out both on a local (baselines ranging between 3 and 30 km) and on a regional (baselines ranging between 300 and 600 km) GPS network. The results show that in the local network it is possible to identify the displacements at a level of 10 mm in height and at a level of 5 mm in horizontal position. The analysis of the regional network showed that it is fundamental to investigate new strategies to model the troposphere; in fact, it is necessary to improve the precision of the height in order to correctly identify displacements lower than 60–80 mm; on the contrary, horizontal displacements can be evidenced at the level of 20 mm. Received: 27 April 1998 / Accepted: 14 December 1998     

Performance of Singapore Integrated Multiple Reference Station Network (SIMRSN) for RTK Positioning

Conventional RTK positioning is usable, but requires the use of a local base station. It is also restricted by the effects of the de-correlate atmospheric refraction on the GPS signal, which limits the use of the RTK positioning up to distances of 10–15 km from the reference station to the user. With a multiple reference station network approach, precise RTK positioning capability may be extended for a much larger area. The Singapore Integrated Multiple Reference Station Network (SIMRSN) has been established for this purpose. Using an existing method termed linear combination method, the multiple reference station network corrections are generated for the user on an epoch by epoch, satellite-by-satellite basis. A residual-based adaptive Kalman filter is proposed to improve network correction availability. The VRS concept is used to transmit corrections to the user for RTK positioning. Field tests were conducted to demonstrate the general performance of SIMRSN. The tests confirmed that RTK positioning within a multiple reference station network can provide the user with better than 3 cm in horizontal position, the height accuracy is in the range of 1–7 cm, and the average TTF (Time To Fix) are 46 and 76 s during GLC station and LPR station tests, respectively. With this highly efficient survey technique, the user needs only to be equipped with a single GPS receiver. This reduces equipment and manpower costs compared with traditional RTK positioning using a specially set up reference station. The multiple reference station framework also paves the way for various other applications beyond the traditional surveying profession. Electronic Publication     

The International GLONASS Service – Pilot Project

The International GLONASS Service – Pilot Project (IGLOS-PP), a project of the International GPS Service, was launched in order to underscore the importance and benefits of integrating data from multiple systmes and techniques within IGS products. At first this article summarizes the contributing organizations and the available infrastructure. Later on the GLONASS related modeling techniques at the involved IGS Analysis Centers are described and we conclude with some remarks concerning the advantages for the expected user commmunity. ? 2001 John Wiley & Sons, Inc.     

A High-Performance,High-Accuracy RTK GPS Machine Guiadance System

As technology matures, Real Time Kinematic (RTK) global positioning system (GPS) receivers are providing increased performance in accuracy, on-the-fly (OTF) initialization times, measurement speed, and latency. Leica's Dozer 2000 machine guidance system combines an MC1000 GPS sensor, graphic intensive guidance software, a digital terrain model, and a digital site plan. Figure 1 shows the operator's view of the system. The end results is a highly accurate, extremely responsive local navigation system. Engineers can easily upload design information onto a touch-screen machine guidance personal computer (PC) and greatly reduce earthmoving costs while simultaneously recording “as-built” inspection data. The Leica MC1000 machine control sensor is a true 10-Hz, centimeter-level-accuracy, open-architecture GPS sensor specifically designed for machine guidance and control. At the heart of the MC1000's performance are a very stable oven-controlled oscillator (3 × 10⁻¹¹/s short-term stability), a low-power Intel 486-DX4-80 processor, and four user-configurable input/output (I7O) ports. Special algorithms mitigate the effects of multipath and Selective Availability (SA) while providing centimeter accuracy up to 10 times per second with only 30 milliseconds' latency. The high update rate and low latency are essential for machine guidance and control. The MC1000 GPS reference station is capable of outputting RTK and Differential GPS (DGPS) data simultaneously, providing and entire site with GPS information for machine guidance and control, tracking and dispatching of vehicles, and support of survey crews. This article describes how recent advances in technology have combined to produce the Leica Dozer 2000 – a machine guidance system that is ideal for a wide range of earthmoving and inspection applications. ? 2000 John Wiley & Sons, Inc.     

An integrated urban systems model with GIS

The main purpose of this paper is to explore a possible integration for the entire transportation modeling procedure – from data inventory to future demand forecasting – by implementing integrated land use and transportation models with a geographic information system (GIS). In order to make an integrated, procedural modeling system possible, Land Use and Transportation modeling system with GIS (LUTGIS) has been developed and presented in this paper.  There are four sub-systems in LUTGIS: (1) a data inventory system, (2) a traffic analysis zone generation system, (3) an integrated land use and transportation modeling system, and (4) a graphic user interface (GUI) system. Since the main target of this paper is to explore a possible way to create a viable system, LUTGIS integrates currently available and user-friendly computing technologies. For both transportation planners and administrative decision-makers, such an operable system is very desirable for sharing information so they may arrive at a consensus through the use of LUTGIS, an integrated land use and transportation modeling system. Received: 22 October 1998/Accepted 11 July 1999     

GPS measurements of ocean loading and its impact on zenith tropospheric delay estimates: a case study in Brittany, France

 The results from a global positioning system (GPS) experiment carried out in Brittany, France, in October 1999, aimed at measuring crustal displacements caused by ocean loading and quantifying their effects on GPS-derived tropospheric delay estimates, are presented. The loading effect in the vertical and horizontal position time series is identified, however with significant disagreement in amplitude compared to ocean loading model predictions. It is shown that these amplitude misfits result from spatial tropospheric heterogeneities not accounted for in the data processing. The effect of ocean loading on GPS-derived zenith total delay (ZTD) estimates is investigated and a scaling factor of 4.4 between ZTD and station height for a 10° elevation cut-off angle is found (i.e. a 4.4-cm station height error would map into a 1-cm ZTD error). Consequently, unmodeled ocean loading effects map into significant errors in ZTD estimates and ocean loading modeling must be properly implemented when estimating ZTD parameters from GPS data for meteorological applications. Ocean loading effects must be known with an accuracy of better than 3 cm in order to meet the accuracy requirements of meteorological and climatological applications of GPS-derived precipitable water vapor. Received: 16 July 2001 / Accepted: 25 April 2002 Acknowledgments. The authors are grateful to H.G. Scherneck for fruitful discussions and for his help with the ocean loading calculations. They thank H. Vedel for making the HIRLAM data available; D. Jerett for helpful discussions; and the city of Rostrenen, the Laboratoire d'Océanographie of Concarneau, and the Institut de Protection et de S?reté Nucléaire (BERSSIN) for their support during the GPS measurement campaign. Reviews by C.K. Shum and two anonymous referees significantly improved this paper. This work was carried out in the framework of the MAGIC project (http://www.acri.fr/magic), funded by the European Commission, Environment and Climate Program (EC Contract ENV4-CT98–0745). Correspondence to: E. Calais, Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907-1397, USA. e-mail: ecalais@purdue.edu Tel. : +1-765-496-2915; Fax:+1-765-496-1210     

The total optimal search criterion in solving the mixed integer linear model with GNSS carrier phase observations

Existing algorithms for GPS ambiguity determination can be classified into three categories, i.e. ambiguity resolution in the measurement domain, the coordinate domain and the ambiguity domain. There are many techniques available for searching the ambiguity domain, such as FARA (Frei and Beutler in Manuscr Geod 15(4):325–356, 1990), LSAST (Hatch in Proceedings of KIS’90, Banff, Canada, pp 299–308, 1990), the modified Cholesky decomposition method (Euler and Landau in Proceedings of the sixth international geodetic symposium on satellite positioning, Columbus, Ohio, pp 650–659, 1992), LAMBDA (Teunissen in Invited lecture, section IV theory and methodology, IAG general meeting, Beijing, China, 1993), FASF (Chen and Lachapelle in J Inst Navig 42(2):371–390, 1995) and modified LLL Algorithm (Grafarend in GPS Solut 4(2):31–44, 2000; Lou and Grafarend in Zeitschrift für Vermessungswesen 3:203–210, 2003). The widely applied LAMBDA method is based on the Least Squares Ambiguity Search (LSAS) criterion and employs an effective decorrelation technique in addition. G. Xu (J Glob Position Syst 1(2):121–131, 2002) proposed also a new general criterion together with its equivalent objective function for ambiguity searching that can be carried out in the coordinate domain, the ambiguity domain or both. Xu’s objective function differs from the LSAS function, leading to different numerical results. The cause of this difference is identified in this contribution and corrected. After correction, the Xu’s approach and the one implied in LAMBDA are identical. We have developed a total optimal search criterion for the mixed integer linear model resolving integer ambiguities in both coordinate and ambiguity domain, and derived the orthogonal decomposition of the objective function and the related minimum expressions algebraically and geometrically. This criterion is verified with real GPS phase data. The theoretical and numerical results show that (1) the LSAS objective function can be derived from the total optimal search criterion with the constraint on the fixed integer ambiguity parameters, and (2) Xu’s derivation of the equivalent objective function was incorrect, leading to an incorrect search procedure. The effects of the total optimal criterion on GPS carrier phase data processing are discussed and its practical implementation is also proposed.     

Combined processing of the IGS and the IGEX network

 Since the beginning of the International Global Navigation Satellite System (GLONASS) Experiment, IGEX, in October 1998, the Center for Orbit Determination in Europe (CODE) has acted as an analysis center providing precise GLONASS orbits on a regular basis. In CODE's IGEX routine analysis the Global Positioning System (GPS) orbits and Earth rotation parameters are introduced as known quantities into the GLONASS processing. A new approach is studied, where data from the IGEX network are combined with GPS observations from the International GPS Service (IGS) network and all parameters (GPS and GLONASS orbits, Earth rotation parameters, and site coordinates) are estimated in one processing step. The influence of different solar radiation pressure parameterizations on the GLONASS orbits is studied using different parameter subsets of the extended CODE orbit model. Parameterization with three constant terms in the three orthogonal directions, D, Y, and X (D = direction satellite–Sun, Y = direction of the satellite's solar panel axis), and two periodic terms in the X-direction, proves to be adequate for GLONASS satellites. As a result of the processing it is found that the solar radiation pressure effect for the GLONASS satellites is significantly different in the Y-direction from that for the GPS satellites, and an extensive analysis is carried out to investigate the effect in detail. SLR observations from the ILRS network are used as an independent check on the quality of the GLONASS orbital solutions. Both processing aspects, combining the two networks and changing the orbit parameterization, significantly improve the quality of the determined GLONASS orbits compared to the orbits stemming from CODE's IGEX routine processing. Received: 10 May 2000 / Accepted: 9 October 2000     

Precise ionosphere-free single-frequency GNSS positioning

Ionospheric delays can be efficiently eliminated from single-frequency data using a combination of carrier phases and code ranges. Unfortunately, GPS and GLONASS ranges are relatively noisy which can limit the use of the positioning method. Nevertheless, position standard deviations are in the range of 6–8 cm (horizontal) and 7–9 cm (3d) obtained from diurnal data batches from selected IGS reference stations can be further reduced to 2–3 cm (3d) for weekly smoothed averages. GPS data sets collected in Ghana (Africa) reveal a typical level of 10 cm of deviation that must be anticipated under average conditions. Looking at the future of GNSS, the European Galileo system will, in contrast to GPS, provide the broadband signal E5 that is by far less affected by multipath thus providing rather precise range measurements. Simulated processing runs featuring both high ionospheric and tropospheric delay variations show a 3d position precision of 4 cm even for a data batch as short as just 1 h, whereas GPS L1/Galileo E1 performance is close to 13 cm for the same data set.     

Comparison of a GPS-defined global reference frame with ITRF2000

The Global Positioning System is a constellation of 24–28 satellites, which can be used to define a global terrestrial reference frame. Daily offsets between a GPS defined frame and ITRF2000 have been estimated using more than a decade of GPS observations from 1990–2001. A linear fit to the full span of data shows agreement between the two frames at the level of –1 ppb and –0.1 ppb/year for scale, 5 mm and 0 mm/year for the X component of center of mass, –2 mm and –3 mm/year for the Y component, and 4 mm and 6 mm/year for the Z component. GPS is a viable tool for defining the global reference frame either alone, or in combination with other geodetic techniques. Electronic Publication     

GPS IF信号的计算机模拟和实现(英文)

A GPS IF signal computer simulation method is proposed in this article. The carrier Doppler frequency and the total propagation and delay time can be modeled or calculated with the input GPS satellite ephemeris file. The simulated GPS IF signal outputs to a text file for post-processing and analysis. The simulation signal spectrum is compared with the received real GPS IF signal spectrum, and the correctness of the simulation result is verified. Supported by the Research Fund (2008–2009) of State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, the National 863 Program of China (No.2008AA12Z308).     

Adaptive Kalman Filtering for INS/GPS

After reviewing the two main approaches of adaptive Kalman filtering, namely, innovation-based adaptive estimation (IAE) and multiple-model-based adaptive estimation (MMAE), the detailed development of an innovation-based adaptive Kalman filter for an integrated inertial navigation system/global positioning system (INS/GPS) is given. The developed adaptive Kalman filter is based on the maximum likelihood criterion for the proper choice of the filter weight and hence the filter gain factors. Results from two kinematic field tests in which the INS/GPS was compared to highly precise reference data are presented. Results show that the adaptive Kalman filter outperforms the conventional Kalman filter by tuning either the system noise variance–covariance (V–C) matrix `Q' or the update measurement noise V–C matrix `R' or both of them. Received: 14 September 1998 / Accepted: 21 December 1998