An ANN–RTS smoother scheme for accurate INS/GPS integrated attitude determination

Digital mobile mapping, the method that integrates digital imaging with direct geo-referencing, has developed rapidly over the past 15 years. The Kalman filter (KF) is considered an optimal estimation tool for real-time INS/GPS integrated kinematic positioning and orientation determination. However, the accuracy requirements of general mobile mapping applications cannot be easily achieved even when using the KF scheme. Therefore, this study proposes an intelligent scheme combining ANN and RTS backward smoother to overcome the limitations of KF and to enhance the overall accuracy of attitude determination for tactical grade and MEMS INS/GPS integrated systems.

Kalman-filter-based GPS clock estimation for near real-time positioning

In this article, an algorithm for clock offset estimation of the GPS satellites is presented. The algorithm is based on a Kalman-filter and processes undifferenced code and carrier-phase measurements of a global tracking network. The clock offset and drift of the satellite clocks are estimated along with tracking station clock offsets, tropospheric zenith path delay and carrier-phase ambiguities. The article provides a brief overview of already existing near-real-time and real-time clock products. The filter algorithm and data processing scheme is presented. Finally, the accuracy of the orbit and clock product is assessed with a precise orbit determination of the MetOp satellite and compared to results gained with other real-time products.

Pitch and roll attitude estimation of a small-scaled helicopter using single antenna GPS with gyroscopes

A method is presented for estimating the roll and pitch attitude of a small-scaled unmanned helicopter based on the velocity measurements of the global positioning system (GPS). The small-scaled helicopter is a radio controlled (RC) model which is readily available and affordable for academic laboratories as a research platform. Only one single antenna GPS receiver is equipped on the RC helicopter to acquire the velocity measurements needed for the attitude estimation. The velocity information is recorded by the onboard computer for post-processing. An attitude and heading reference system (AHRS) is used to provide the reference attitudes. The required angular rates and heading for this study are also given by the gyroscopes and compass of the AHRS for the sake of system’s simplification. The Kalman filter is applied to estimate the helicopter’s accelerations by using the GPS velocity measurements. The estimated accelerations form the fundamental elements of synthesizing the pseudo-roll and the pseudo-pitch. With some legitimate simplifications and assumptions, the relation between the helicopter’s attitudes and the accelerations estimated from the GPS velocity measurements can be developed. Furthermore, to enhance the accuracy of the pseudo-attitudes, the angular rates acquired from the gyroscopes are incorporated into the estimation algorithm of pseudo-attitudes by using a complementary filter.

Simplified equivalent multiple baseline solutions with elevation-dependent weights

Since the assumption of all stations tracking the same satellites with identical weights was previously employed by Shen and Xu (GPS Solut 12:99–108, 2008) to derive the simplified GNSS single- and double-differenced equivalent equations, this supplementary paper expands these simplified equations in the case of each station tracking different satellites with elevation-dependent weights. Numerical experiments are performed to demonstrate the computational efficiency of the simplified equivalent algorithm relative to the traditional method in various scenarios of multi-baseline solutions with tracking different satellites. The fast computational speed of the simplified equivalent algorithm will potentially benefit the local, regional and even global GNSS multi-baseline solutions as well as the combined GNSS application.

Tracking and orbit determination performance of the GRAS instrument on MetOp-A

The global navigation satellite system receiver for atmospheric sounding (GRAS) on MetOp-A is the first European GPS receiver providing dual-frequency navigation and occultation measurements from a spaceborne platform on a routine basis. The receiver is based on ESA’s AGGA-2 correlator chip, which implements a high-quality tracking scheme for semi-codeless P(Y) code tracking on the L1 and L2 frequency. Data collected with the zenith antenna on MetOp-A have been used to perform an in-flight characterization of the GRAS instrument with focus on the tracking and navigation performance. Besides an assessment of the receiver noise and systematic measurement errors, the study addresses the precise orbit determination accuracy achievable with the GRAS receiver. A consistency on the 5 cm level is demonstrated for reduced dynamics orbit solutions computed independently by four different agencies and software packages. With purely kinematic solutions, 10 cm accuracy is obtained. As a part of the analysis, an empirical antenna offset correction and preliminary phase center correction map are derived, which notably reduce the carrier phase residuals and improve the consistency of kinematic orbit determination results.

A constrained LAMBDA method for GPS attitude determination

An improved method to obtain fixed integer ambiguity in GPS attitude determination is presented. Known conditions are utilized as constraints to acquire attitude information when the float solution and its variance–covariance matrix are not accurate enough. The searching ellipsoidal region is first expanded to compensate for errors caused by the inaccurate float solution. Then the constraints are used to shrink the region to a proper size, which maintains the true integer ambiguity. Experimental results demonstrate that this scheme gives a fast search time and a higher success rate in determining the fixed integer ambiguity than the unconstrained method. The accuracy of attitude angles is also improved.

Analysis of high-frequency multipath in 1-Hz GPS kinematic solutions

High-frequency multipath would be problematic for studies at seismic or antenna dynamical frequencies as one could mistakenly interpret them as signals. A simple procedure to identify high-frequency multipath from global positioning system (GPS) time series records is presented. For this purpose, data from four GPS base stations are analyzed using spectral analyses techniques. Additional data, such as TEQC report files of L1 pseudorange multipath, are also used to analyze the high-frequency multipath and confirmation of the high-frequency multipath inferred from the phase records. Results show that this simple procedure is effective in identification of high-frequency multipath. The inferred information can aid interpretation of multipath at the GPS site, and is important for a number of reasons. For example, the information can be used to study GPS site selections and/or installations.

Single-frequency precise point positioning with optimal filtering

The accuracy of standalone GPS positioning improved significantly when Selective Availability was turned off in May 2000. With the availability of various public GPS related products including precise satellite orbits and clocks, and ionosphere maps, a single-frequency standalone user can experience even a further improvement of the position accuracy. Next, using carrier phase measurements becomes crucial to smoothen the pseudorange noise. In this contribution, the most critical sources of error in single-frequency standalone positioning will be reviewed and different approaches to mitigate the errors will be considered. An optimal filter (using also carrier phase measurements) will be deployed. The final approach will then be evaluated in a decently long static test with receivers located in different regions of the world. Kinematic experiments have also been performed in various scenarios including a highly dynamic flight trial. The accuracy, in general, can be confirmed at 0.5 m horizontal and 1 m vertical, with static tests. Ultimate results demonstrate an accuracy close to 2 dm (95%) for the horizontal position components and 5 dm (95%) for the vertical in the flight experiment.

GPS scintillation over the European Arctic during the November 2004 storms

Small-scale irregularities in the background electron density of the ionosphere can cause rapid fluctuations in the amplitude and phase of radio signals passing through it. These rapid fluctuations are known as scintillation and can cause a Global Positioning System (GPS) receiver to lose lock on a signal. This could compromise the integrity of a safety of life system based on GPS, operating in auroral regions. In this paper, the relationship between the loss of lock on GPS signals and ionospheric scintillation in auroral regions is explored. The period from 8 to 14 November 2004 is selected for this study, as it includes both geomagnetically quiet and disturbed conditions. Phase and amplitude scintillation are measured by GPS receivers located at three sites in Northern Scandinavia, and correlated with losses of signal lock in receivers at varying distances from the scintillation receivers. Local multi-path effects are screened out by rejection of low-elevation data from the analysis. The results indicate that losses of lock are more closely related to rapid fluctuations in the phase rather than the amplitude of the received signal. This supports the idea, suggested by Humphreys et al. (2005) (performance of GPS carrier tracking loops during ionospheric scintillations. Proceedings Internationsl Ionospheric Effects Symposium 3–5 May 2005), that a wide loop bandwidth may be preferred for receivers operating at auroral latitudes. Evidence from the Imaging Riometer for Ionospheric Studies (IRIS) appears to suggest that, for this particular storm, precipitation of particles in the D/E regions may be the mechanism that drives the rapid phase fluctuations in the signal.

Critical network infrastructure analysis: interdiction and system flow

Effective management of critical network infrastructure requires the assessment of potential interdiction scenarios. Optimization approaches have been essential for identifying and evaluating such scenarios in networked systems. Although a primary function of any network is the distribution of flow between origins and destinations, the complexity and difficulty of mathematically abstracting interdiction impacts on connectivity or flow has been a challenge for researchers. This paper presents an optimization approach for identifying interdiction bounds with respect to connectivity and/or flow associated with a system of origins and destinations. Application results for telecommunications flow are presented, illustrating the capabilities of this approach.

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Carrier phase-based integrity monitoring for high-accuracy positioning

Pseudorange-based integrity monitoring, for example receiver autonomous integrity monitoring (RAIM), has been investigated for many years and is used in various applications such as non-precision approach phase of flight. However, for high-accuracy applications, carrier phase-based RAIM (CRAIM), an extension of pseudorange-based RAIM (PRAIM) must be used. Existing CRAIM algorithms are a direct extension of PRAIM in which the carrier phase ambiguities are estimated together with the estimation of the position solution. The main issues with the existing algorithms are reliability and robustness, which are dominated by the correctness of the ambiguity resolution, ambiguity validation and error sources such as multipath, cycle slips and noise correlation. This paper proposes a new carrier phase-based integrity monitoring algorithm for high-accuracy positioning, using a Kalman filter. The ambiguities are estimated together with other states in the Kalman filter. The double differenced pseudorange, widelane and carrier phase observations are used as measurements in the Kalman filter. This configuration makes the positioning solution both robust and reliable. The integrity monitoring is based on a number of test statistics and error propagation for the determination of the protection levels. The measurement noise and covariance matrices in the Kalman filter are used to account for the correlation due to differencing of measurements and in the construction of the test statistics. The coefficient used to project the test statistic to the position domain is derived and the synthesis of correlated noise errors is used to determine the protection level. Results from four cases based on limited real data injected with simulated cycle slips show that residual cycle slips have a negative impact on positioning accuracy and that the integrity monitoring algorithm proposed can be effective in detecting and isolating such occurrences if their effects violate the integrity requirements. The CRAIM algorithm proposed is suitable for use within Kalman filter-based integrated navigation systems.

Fast direct GPS P-Code acquisition

GPS P-Code has a higher chipping rate, better accuracy, and anti-jamming property than C/A code. Traditionally, GPS P-Code acquisition depends on handover from C/A code. This potentially needs long acquisition time. Moreover, when C/A code is not available, it is no longer possible to acquire GPS P-Code through handover from C/A code. The purpose of this paper is to describe a new overlap average method to facilitate hardware design of fast direct P-Code acquisition. It allows the rapid code phase search to acquire GPS P-Code signals, and also decreases the hardware resource requirement. The small size FFT in the proposed methods is very promising for fast FPGA hardware system design using FFT cores. The simulation results and theoretical analysis are included demonstrating the overall performance of the proposed method.

Correction of apparent position shifts caused by GNSS antenna changes

Antenna changes at GNSS reference stations frequently produce discontinuities in the coordinate time series. These apparent position shifts are mainly caused by changes of carrier-phase multipath effects and different errors in the antenna phase center corrections. A monitoring method was developed and successfully tested, which requires additional GNSS observations from a local, temporary reference station. Changes of carrier-phase measurement errors due to the antenna change are determined and stored in L1 and L2 phase maps. These phase maps provide corrections to be applied either to the observation data obtained before the antenna change or to the observation data obtained after the antenna change. The observation corrections are able to remove coordinate discontinuities independent of the selected coordinate estimation algorithm.

Bringing GPS into harsh environments for fully automated deformation monitoring

Engineering projects that require deformation monitoring frequently utilize geodetic sensors to measure displacements of target points located in the deformation zone. In situations where control stations and targets are separated by a kilometer or more, GPS can offer higher precision position updates at more frequent intervals than can normally be achieved using total station technology. For large-scale deformation projects requiring the highest precision, it is therefore advisable to use a combination of the two sensors. In response to the need for high precision, continuous GPS position updates in harsh deformation monitoring environments, a software has been developed that employs triple-differenced carrier-phase measurements in a delayed-state Kalman filter. Two data sets were analyzed to test the capabilities of the software. In the first test, a GPS antenna was displaced using a translation stage to mimic slow deformation. In the second test, data collected at a large open pit mine were processed. It was shown that the delayed-state Kalman filter developed could detect millimeter-level displacements of a GPS antenna. The actual precision attained depends upon the amount of process noise infused at each epoch to accommodate the antenna displacements. Higher process noise values result in quicker detection times, but at the same time increase the noise in the solutions. A slow, 25 mm displacement was detected within 30 min of the full displacement with sigma values in E, N and U of ±10 mm or better. The same displacement could also be detected in less than 5 h with sigma values in E, N and U of ±5 mm or better. The software works best for detecting long period deformations (e.g., 20 mm per day or less) for which sigma values of 1–2 mm are attained in all three solution components. It was also shown that the triple-differenced carrier-phase observation can be used to significantly reduce the effects of residual tropospheric delay that would normally plague double-differenced observations in harsh GPS environments.

Reliability checking for GNSS baseline and network processing

Reliability analysis is inseparably connected with the formulation of failure scenarios, and common test statistics are based on specific assumptions. This is easily overlooked when processing observation differences. Poor failure identification performance and misleading pre-analysis results, mainly meaningless minimum detectable biases and external reliability measures, are the consequence. A reasonable failure scenario for use with differenced GNSS observations is formulated which takes into account that individual outliers in the original data affect more than one processed observation. The proper test statistics and reliability indicators are given for use with correlated observations and both batch processing and Kalman filtering. It is also shown that standardized residuals and redundancy numbers fail completely when used with double differenced observations.

Analyzing the shear strength parameters of the Chiu-fen-erh-shan landslide: integrating strong-motion and GPS data to determine the best-fit accelerogram

This study adopts the Chiu-fen-erh-shan landslide as a case study for incorporating comprehensive accelerograph and global positioning system (GPS) data to determine the best-fit acceleration data for analyzing a rock avalanche. Previous investigations indicate that the distance from an accelerograph to a landslide site is crucial to determining the best-fit acceleration data to use in conducting a seismic analysis. Unfortunately, the Chiu-fen-erh-shan landslide and its nearest accelerograph station are located in different geological zones. Thus, GPS data were compared to the displacements derived from the accelerograms of nearby monitoring stations to help select the best accelerograph data. This emphasizes that a high density distribution of accelerographs and GPS installations are essential to acquire the best data for the seismic analysis, especially in complex geological zones. After applying the best-fit accelerogram to Newmark’s sliding model and an empirical displacement attenuation formula to back-calculate the shear strength parameters of the sliding surface, a cohesion of 0 kPa and friction angle of the sliding surface of 24.8° were found for this landslide.

Use of C-Band frequencies for satellite navigation: benefits and drawbacks

Although not considered for the first generation of European Galileo satellites, the use of C-Band frequencies for navigation purposes may be taken into account for a future generation of Galileo. For this reason, a frequency band of 20 MHz bandwidth (5,010–5,030 MHz) has been allocated in the course of the World Radio Communications Conference 2000 held in Istanbul, Turkey. The use of C-Band navigation signals offers both advantages and drawbacks. One example is the ionospheric path delay which is inversely proportional to the (squared) carrier frequency and is therefore significantly smaller at C-Band. On the other hand, the use of C-Band frequencies results in increased attenuation effects such as free space loss or rainfall attenuation. It is therefore necessary to provide a detailed analysis of the effects of C-Band frequencies on the navigation process. In order to assess the feasibility of using C-Band frequencies, various aspects of signal propagation and satellite signal tracking at C-Band are examined in the context of this article. In particular, aspects like free space loss, atmospheric effects, foliage attenuation, code and carrier tracking performance, code noise, phase noise and multipath are discussed with respect to their performance at C-Band. In order to allow comparison with the current GPS system, the performance at C-Band is compared to the L-Band performance under similar or identical conditions. The results of this analysis will finally be discussed with respect to their impact on satellite payload and receiver design.

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Ionospheric climatology derived from gps occultation observations made by the ionospheric occultation experiment

The ionospheric occultation experiment (IOX) is a GPS occultation sensor with an ionospheric mission focus. IOX measurements of GPS L1 and L2 carrier phase during Earth limb views of setting GPS satellites are used together with the Abel transform to determine vertical profiles of electron density from which F-region peak parameters are determined. Data from a four and a half month period beginning in November 2001 are statistically binned and compared with a climatological model. To account for potential errors in interpretation that could arise from violation of the Abel transform assertion of spherical symmetry, the data are compared to both the climatology and to statistics of simulated ionospheric inversions using the climatological model. General characteristics of the climatology are reproduced by the occultation data. However, several significant discrepancies between the model and the data are observed during this near-solar maximum time period. In particular, average mid-latitude daytime densities are shown to be higher than the climatological prediction and the height of F2 layer in the post-sunset equatorial region is underestimated by up to 150 km.

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A data archive of GPS navigation messages

Since 18 June 2007 navigation data messages transmitted by the GPS constellation are recorded by five receivers within GeoForschungsZentrum’s global groundstation network. We describe the recording, processing, validation, analysis and archiving of the navigation data. During the 197 days between 18 June 2007 and 31 December 2007 a total of 125,723,666 subframes were collected. By taking into consideration that the same data set frequently is observed by two or more receivers concurrently, 65,153,955 unique subframes could be extracted from the observations. With an estimated 88,099,200 subframes transmitted by the constellation during this time period a data yield of about 74% was achieved. Simulation studies suggest that with two additional GPS receivers, which are scheduled for addition to the network in 2008, about 95% of the transmitted subframes will be retrieved. The message data archive is open to the scientific community for non-commercial purposes and may be accessed through GFZ’s Information System and Data Center ().

Hidden negative spatial autocorrelation

Mostly lip service treatments of negative spatial autocorrelation (NSA) appear in the literature, although spatial scientists confront it in practice. NSA was detected serendipitously in recalcitrant empirical analyses containing a sizeable amount of global positive spatial autocorrelation (PSA) unaccounted for by standard spatial statistical models, and labeled hidden because conventional spatial statistical tools detected only PSA while giving absolutely not hint of NSA existing. The meaning of this phenomenon is explored empirically, with findings including: a better understanding of NSA, spatial filter model construction guidelines, effective illustrations of NSA, and how hidden NSA furnishes a diagnostic for model misspecification.