Use of a reduced IMU to aid a GPS receiver with adaptive tracking loops for land vehicle navigation

A reduced inertial measurement unit (IMU) consisting of only one vertical gyro and two horizontal accelerometers or three orthogonal accelerometers can be used in land vehicle navigation systems to reduce volume and cost. In this paper, a reduced IMU is integrated with a Global Positioning System (GPS) receiver whose phase lock loops (PLLs) are aided with the Doppler shift from the integrated system. This approach is called tight integration with loop aiding (TLA). With Doppler aiding, the noise bandwidth of the PLL loop filters can be narrowed more than in the GPS-only case, which results in improved noise suppression within the receiver. In this paper, first the formulae to calculate the PLL noise bandwidth in a TLA GPS/reduced IMU are derived and used to design an adaptive PLL loop filter. Using a series of vehicle tests, results show that the noise bandwidth calculation formulae are valid and the adaptive loop filter can improve the performance of the TLA GPS/reduced IMU in both navigation performance and PLL tracking ability.     

MEMS IMU辅助的高性能GPS接收机设计

高性能稳健性的GPS卫星接收机仍然是当前研究和发展的热点。在高动态条件下,GNSS接收机设计总是涉及到跟踪动态性能所要求的环路带宽和噪声所要求的环路带宽一对矛盾体。以微惯性测量单元(MIMU)辅助的GPS接收机为实例,设计了MIMU辅助的GPS接收机搜索算法和跟踪算法,同时为减少GPS接收机对惯性器件的性能的依赖,设计了基于MIMU辅助的最优GPS接收机的环路带宽。通过仿真和车载试验对所设计的方法进行验证,仿真和试验结果表明,MIMU辅助的GPS接收机动态性能取决于MIMU的性能指标和环路的带宽,而抗干扰性能至少有13 dB的提高;跑车试验中,商用GPS接收机和研制的GPS接收机精度大体相当。同时系统还能够提供姿态角信息。     

Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration

 Ten days of GPS data from 1998 were processed to determine how the accuracy of a derived three-dimensional relative position vector between GPS antennas depends on the chord distance (denoted L) between these antennas and on the duration of the GPS observing session (denoted T). It was found that the dependence of accuracy on L is negligibly small when (a) using the `final' GPS satellite orbits disseminated by the International GPS Service, (b) fixing integer ambiguities, (c) estimating appropriate neutral-atmosphere-delay parameters, (d) 26 km ≤ L ≤ 300 km, and (e) 4 h ≤T ≤ 24 h. Under these same conditions, the standard error for the relative position in the north–south dimension (denoted S _n and expressed in mm) is adequately approximated by the equation S _n =k _n /T ^0.5 with k _n =9.5 ± 2.1 mm · h^0.5 and T expressed in hours. Similarly, the standard errors for the relative position in the east–west and in the up-down dimensions are adequately approximated by the equations S _e =k _e /T ^0.5 and S _u =k _u /T ^0.5, respectively, with k _e =9.9 ± 3.1 mm · h^0.5 and k _u =36.5 ± 9.1 mm · h^0.5. Received: 5 February 2001 / Accepted: 14 May 2001     

一种SINS/GPS深组合导航系统技术问题分析

为了满足高动态用户及强干扰条件下的应用需求,提出了一种基于卫星信号矢量跟踪的SINS/GPS深组合导航方法,设计了基于FPGA硬件平台的实施方案。利用组合卡尔曼滤波器反馈回路取代了传统接收机中独立、并行的跟踪环路,能够同时完成所有可视卫星信号的跟踪和导航信息处理;通过矢量跟踪算法对所有可视卫星信号进行集中处理,能够增强跟踪通道对信号载噪比变化的适应能力,从而提高接收机在强干扰或信号中断条件下的跟踪性能;根据SINS导航参数和星历信息推测GPS伪码相位和多普勒频移等参数,用以辅助卫星信号的捕获和跟踪,能够大大缩短接收机的搜索捕获时间,并增强接收机在高动态条件下的跟踪性能。基于矢量跟踪的深组合方法不仅在GPS信号短暂中断期间,能够保证系统的导航精度和可靠性,而且在强干扰环境中能够维持较好的伪码相位和载波频率跟踪性能。     

A globally applicable, season-specific model for estimating the weighted mean temperature of the atmosphere

In GPS meteorology, the weighted mean temperature is usually obtained by using a linear function of the surface temperature T _s. However, not every GPS station can measure the surface temperature. The current study explores the characteristics of surface temperature and weighted mean temperature based on the global pressure and temperature model (GPT) and the Bevis T _m–T _s relationship (T _m =?a?+?bT _s). A new global weighted mean temperature (GWMT) model has been built which directly uses three-dimensional coordinates and day of the year to calculate the weighted mean temperature. The data of year 2005–2009 from 135 radiosonde stations provided by the Integrated Global Radiosonde Archive were used to calculate the model coefficients, which have been validated through examples. The result shows that the GWMT model is generally better than the existing liner models in most areas according to the statistic indexes (namely, mean absolute error and root mean square). Then we calculated precipitable water vapor, and the result shows that GWMT model can also yield high precision PWV.     

GGOS-D: homogeneous reprocessing and rigorous combination of space geodetic observations

In preparation of activities planned for the realization of the Global Geodetic Observing System (GGOS), a group of German scientists has carried out a study under the acronym GGOS-D which closely resembles the ideas behind the GGOS initiative. The objective of the GGOS-D project was the investigation of the methodological and information-technological realization of a global geodetic-geophysical observing system and especially the integration and combination of the space geodetic observations. In the course of this project, highly consistent time series of GPS, VLBI, and SLR results were generated based on common state-of-the-art standards for modeling and parameterization. These series were then combined to consistently and accurately compute a Terrestrial Reference Frame (TRF). This TRF was subsequently used as the basis to produce time series of station coordinates, Earth orientation, and troposphere parameters. In this publication, we present results of processing algorithms and strategies for the integration of the space-geodetic observations which had been developed in the project GGOS-D serving as a prototype or a small and limited version of the data handling and processing part of a global geodetic observing system. From a comparison of the GGOS-D terrestrial reference frame results and the ITRF2005, the accuracy of the datum parameters is about 5?C7?mm for the positions and 1.0?C1.5?mm/year for the rates. The residuals of the station positions are about 3?mm and between 0.5 and 1.0?mm/year for the station velocities. Applying the GGOS-D TRF, the offset of the polar motion time series from GPS and VLBI is reduced to 50 ??as (equivalent to 1.5?mm at the Earth??s surface). With respect to troposphere parameter time series, the offset of the estimates of total zenith delays from co-located VLBI and GPS observations for most stations in this study is smaller than 1.5?mm. The combined polar motion components show a significantly better WRMS agreement with the IERS 05C04 series (96.0/96.0???as) than VLBI (109.0/100.7???as) or GPS (98.0/99.5???as) alone. The time series of the estimated parameters have not yet been combined and exploited to the extent that would be possible. However, the results presented here demonstrate that the experiences made by the GGOS-D project are very valuable for similar developments on an international level as part of the GGOS development.     

Geocentre motion measured with DORIS and SLR, and predicted by geophysical models

Geocentre motion signals measured by satellite geodesy and those predicted from the observed mass redistribution in the ocean, atmosphere and terrestrial waters over 1993.1–2003.0 are analysed and compared under two viewpoints: the amplitudes and phases of the seasonal components, and the spectral signature of the non-seasonal components. The geodetic signals partly match the geophysical variations in the seasonal band, with possible remaining annual and semi-annual errors in both techniques, at the millimetre level in the equatorial plane for Satellite laser ranging (SLR) and Doppler Orbitography and radiopositioning integrated on Satellite (DORIS), and at the centimetre level in T _z (Z-axis translation) for DORIS. Unlike SLR, the DORIS annual signatures in all three geocentre components have strongly varying amplitudes after 1996. The amplitude of the annual geophysical signal in T _y is slowly growing with time. All three geophysical fluids contribute to this effect. The magnitude of the geophysically derived long-term geocentre motion is of the same magnitude in the T _x , T _y and T _z directions, with a 0.5–1.0 mm Allan standard deviation for the 1-year sampling time, while the geodetic values are 2 mm in the equatorial plane for both SLR and DORIS, 4 mm for SLR and 9 mm for DORIS in the T _z direction. The mismatch of the geodetic signal with the geophysical one in the inter-annual band is suggested to be due partly to excessive geodetic noise and partly to underestimated geophysical signal.     

Evaluation of the ITRF2008 GPS vertical velocities using satellite antenna z-offsets

We develop a method to evaluate the terrestrial reference frame (TRF) scale rate error using Global Positioning System (GPS) satellite antenna phase center offset (APCO) parameters and apply it to ITRF2008. We search for the TRF in which z-APCO parameters have the smallest drift. In order to provide realistic error bars for the z-APCO drifts, we pay attention to model periodic variations and auto-correlated noise processes in the z-APCO time series. We will show that the GPS scale rate with respect to a frame is, as a first approximation, proportional to the estimated mean z-APCO trend if that frame is used to constrain station positions. Thus, an ITRF2008 scale rate error between ?0.27 and ?0.06 mm/yr depending on the GPS analysis center can be estimated, which demonstrates the high quality of the newly constructed ITRF2008. We will also demonstrate that the traditional estimates of the GPS scale rate from 7-parameter similarity transformations are consistent with our newly derived GPS scale rates with respect to ITRF2008 within two sigmas. We find using International GNSS Service (IGS) products that the traditional approach is relevant for scale rate determination even if some of the z-APCO values supplied by the IGS were not simultaneously calibrated. As the scale rate is related to the accuracy of vertical velocities, our estimates supply a conservative evaluation that can be used for error budget computation.     

Performance analysis of a Kalman filter carrier phase tracking loop

GPS Solutions - The equivalent bandwidth of a Kalman filter (KF) tracking loop for a Global Navigation Satellite System receiver is widely used to compare the performance of the KF with that of the...     

Ultra-tight GPS/INS/PL integration: a system concept and performance analysis

The architecture of the ultra-tight GPS/INS/PL integration is the key to its successful performance; the main feature of this architecture is the Doppler feedback to the GPS receiver tracking loops. This Doppler derived from INS, when integrated with the carrier tracking loops, removes the Doppler due to vehicle dynamics from the GPS/PL signal thereby achieving a significant reduction in the carrier tracking loop bandwidth. The bandwidth reduction provides several advantages such as: improvement in anti-jamming performance, and increase in post correlated signal strength which in turn increases the dynamic range and accuracy of measurements. Therefore, any degradation in the derived Doppler estimates will directly affect the tracking loop bandwidth and hence its performance. The quadrature signals from the receiver correlator, I (in-phase) and Q (quadrature), form the measurements, whereas the inertial sensor errors, position, velocity and attitude errors form the states of the complementary Kalman filter. To specify a reliable measurement model of the filter for this type of integrated system, a good understanding of GPS/PL signal characteristics is essential. It is shown in this paper that phase and frequency errors are the variables that relate the measurements and the states in the Kalman filter. The main focus of this paper is to establish the fundamental mathematical relationships that form the measurement model, and to show explicitly how the system error states are related to the GPS/PL signals. The derived mathematical relationships encapsulated in a Kalman filter, are tested by simulation and shown to be valid.

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Combining consecutive short arcs into long arcs for precise and efficient GPS Orbit Determination

The final products of theCODE Analysis Center (Center for Orbit Determination in Europe) of theInternational GPS Service for Geodynamics (IGS) stem fromoverlapping 3-day-arcs. Until 31 December, 1994 these long arcs were computedfrom scratch, i.e. by processing three days of observations of about 40 stations (by mid 1995 about 60 stations were used) of the IGS Global Network in our parameter estimation program GPSEST. Becauseone-day-arcs have to be produced first (for the purpose of error detection etc.) the actual procedure was rather time-consuming. In the present article we develop the mathematical tools necessary to form long arcs based on the normal equation systems of consecutive short arcs (one-day-solutions in the case of CODE). The procedure in its simplest version is as follows:

• Each short arc is described bysix initial conditions and a number of dynamical orbit parameters (e.g. radiation pressure parameters). The resulting long arc in turn shall be based onn consecutive short arcs and described bysix initial conditions and again the same number of dynamical parameters as in the short arcs..
• By asking position and velocity to be continuous at the boundaries of the short arcs we obtain a long arc which is actually defined by one set of initial conditions andn sets of dynamical parameters (ifn short arcs are combined)..
• By asking the dynamical parameters to be identical in consecutive short arcs, the resulting long arc is characterized by exactly the same number of orbit parameters as each of the short arcs.
• This procedure isnot yet optimized becauseformally all n sets of orbit parameters have to be set up and solved for in the long arc solution (although they are not independent). In order to allow for an optimized solution we derive all necessary relations to eliminate the unnecessary parameters in the combination. Each long arc is characterized by the actual number of independent orbit parameters. The resulting procedure isvery efficient.

From the point of view of the result the new procedure iscompletely equivalent to an actual re-evaluation of all observations pertaining to the long arc. It is much more efficient and flexible, however because it allows us to construct 2-day-arcs, 3-day-arcs, etc. based on the previously stored daily normal equation systems without requiring much additional CPU time. The theory is developed in the first four sections. Technical aspects are dealt with in appendices A and B. The actual implementation into the Bernese GPS Software system and test results are given in section 5.     

Truncation error formulas for the geoidal height and the deflection of the vertical

A general formula giving Molodenskii coefficientsQ _n of the truncation errors for the geoidal height is introduced in this paper. A relation betweenQ _n andq _n, Cook’s truncation function, is also obtained. Cook (1951) has treated the truncation errors for the deflection of the vertical in the Vening Meinesz integration. Molodenskii et al. (1962) have also derived the truncation error formulas for the deflection of the vertical. It is proved in this paper that these two formulas are equivalent.     

Characterization of periodic variations in the GPS satellite clocks

The clock products of the International Global Navigation Satellite Systems (GNSS) Service (IGS) are used to characterize the timing performance of the GPS satellites. Using 5-min and 30-s observational samples and focusing only on the sub-daily regime, approximate power-law stochastic processes are found. The Block IIA Rb and Cs clocks obey predominantly random walk phase (or white frequency) noise processes. The Rb clocks are up to nearly an order of magnitude more stable and show a flicker phase noise component over intervals shorter than about 100 s. Due to the onboard Time Keeping System in the newer Block IIR and IIR-M satellites, their Rb clocks behave in a more complex way: as an apparent random walk phase process up to about 100 s and then changing to flicker phase up to a few thousand seconds. Superposed on this random background, periodic signals have been detected in all clock types at four harmonic frequencies, n × (2.0029 ± 0.0005) cycles per day (24 h coordinated universal time or UTC), for n = 1, 2, 3, and 4. The equivalent fundamental period is 11.9826 ± 0.0030 h, which surprisingly differs from the reported mean GPS orbital period of 11.9659 ± 0.0007 h by 60 ± 11 s. We cannot account for this apparent discrepancy but note that a clear relationship between the periodic signals and the orbital dynamics is evidenced for some satellites by modulations of the spectral amplitudes with eclipse season. All four harmonics are much smaller for the IIR and IIR-M satellites than for the older blocks. Awareness of the periodic variations can be used to improve the clock modeling, including for interpolation of tabulated IGS products for higher-rate GPS positioning and for predictions in real-time applications. This is especially true for high-accuracy uses, but could also benefit the standard GPS operational products. The observed stochastic properties of each satellite clock type are used to estimate the growth of interpolation and prediction errors with time interval.     

Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity

We develop a new approach for cycle slip detection and repair under high ionospheric activity using undifferenced dual-frequency GPS carrier phase observations. A forward and backward moving window averaging (FBMWA) algorithm and a second-order, time-difference phase ionospheric residual (STPIR) algorithm are integrated to jointly detect and repair cycle slips. The FBMWA algorithm is proposed to detect cycle slips from the widelane ambiguity of Melbourne–Wübbena linear combination observable. The FBMWA algorithm has the advantage of reducing the noise level of widelane ambiguities, even if the GPS data are observed under rapid ionospheric variations. Thus, the detection of slips of one cycle becomes possible. The STPIR algorithm can better remove the trend component of ionospheric variations compared to the normally used first-order, time-difference phase ionospheric residual method. The combination of STPIR and FBMWA algorithms can uniquely determine the cycle slips at both GPS L ₁ and L ₂ frequencies. The proposed approach has been tested using data collected under different levels of ionospheric activities with simulated cycle slips. The results indicate that this approach is effective even under active ionospheric conditions.     

GPS radio occultation measurements on ionospheric electron density from low Earth orbit

Since the proof-of-concept GPS/Meteorology (GPS/MET) experiment successfully demonstrated active limb sounding of the Earth’s neutral atmosphere and ionosphere via GPS radio occultation (RO) from low Earth orbit, the developments of electron density (n _e) retrieval techniques and powerful processing systems have made a significant progress in recent years. In this study, the researches of n _e profiling from space-based GPS RO observations are briefly reviewed. Applying to the Formosat-3/Constellation Observing System for Meteorology, Ionosphere and Climate (FS3/COSMIC) data, we also present a compensatory Abel inversion technique including the effects of large-scale horizontal gradients and/or inhomogeneous ionospheric n _e obtained from an improved near real-time phenomenological model of the TaiWan Ionospheric Model. The results were evaluated by the ionosonde foF2 and foE data and showed improvements of rms foF2 difference from 29.2 to 16.5% in relative percentage and rms foE difference from 54.2 to 32.7% over the standard Abel inversion.     

Noise-signal index threshold: a new noise-reduction technique for generation of reference spectra and efficient hyperspectral image classification

Reference spectra of terrestrial targets are usually collected using field spectro-radiometers for mineral abundance mapping and target detection. These spectra often have noise that masks characteristic absorption and reflection features and affects the efficiency of material mapping. This work aims at obtaining an empirical technique for reduction of high-frequency noise from field spectra. The proposed noise correction technique uses a ‘normalized’ measure R_n , where R_n  = (L_n  ? F_n )/L_n for each band (n) calculated from field and laboratory spectra of test material, with F_n and L_n being the depth of the absorption feature in field and laboratory spectra, respectively. On the basis of the assumption of the constancy of this ratio in neighbouring bands, an empirical algorithm that approximates the ratio R_n of a noisy band to the corrected ratio of an adjacent band is used to obtain the noise-corrected field spectra. The classification accuracy increases significantly when noise reduced field spectra are used as reference spectra.     

Methodology for comparing two carrier phase tracking techniques

The carrier phase tracking loop is the primary focus of the current work. In particular, two carrier phase tracking techniques are compared, the standard phase tracking loop, i.e., the phase lock loop (PLL), and the extended Kalman filter (EKF) tracking loop. In order to compare these two different techniques and taking into consideration the different models adopted in each, it is important to bring them to one common ground. In order to accomplish this, the equivalent PLL for a given EKF has to be determined in terms of steady-state response to both thermal noise and signal dynamics. A novel method for experimentally calculating the equivalent bandwidth of the EKF is presented and used to evaluate the performance of the equivalent PLL. Results are shown for both the L1 and L5 signals. Even though the two loops are designed to track equivalent dynamics and to have equivalent carrier phase standard deviations, the EKF outperforms the equivalent PLL in terms of both the transient response and sensitivity.     

Improved amplitude- and phase-scintillation indices derived from wavelet detrended high-latitude GPS data

Accuracy and validity of scintillation indices estimated using the power and phase of the GPS signal depend heavily on the detrending method used and the selection of the cutoff frequency of the associated filter. A Butterworth filter with a constant cutoff frequency of 0.1?Hz is commonly used in detrending GPS data. In this study, the performance of this commonly used filter is evaluated and compared with a new wavelet-based detrending method using GPS data from high latitudes. It was observed that in detrending high-latitude GPS data, a wavelet filter performed better than Butterworth filters as the correlation between amplitude- and phase-scintillation indices in S ₄ and ?? _? improved significantly from 0.53, when using a Butterworth filter, to 0.79, when using the wavelet filtering method. We also introduced an improved phase-scintillation index, ?? _CHAIN, which we think is comparatively a better parameter to represent phase scintillations at high latitudes as the correlation between S ₄ and ?? _CHAIN was as high as 0.90. During the analysis, we also noted that the occurrence of the ??phase scintillation without amplitude scintillation?? phenomenon was significantly reduced when scintillation indices were derived using the wavelet-based detrending method. These results seem to indicate that wavelet-based detrending is better suited for GPS scintillation signals and also that ?? _CHAIN is a better parameter for representing GPS phase scintillations at high latitudes.     

A USRP2-based reconfigurable multi-constellation multi-frequency GNSS software receiver front end

We present a multi-constellation multi-band GNSS software receiver front end based on USRP2, a general purpose radio platform. When integrated with appropriate daughter boards, the USRP2 can be used to collect raw intermediate frequency (IF) data covering the entire GNSS family of signals. In this study, C++ class-based software receiver processing functions were developed to process the IF data for GPS L1, L2C, and L5 and GLONASS L1 and L2 signals collected by the USRP2 front end. The front end performance is evaluated against the outputs of a high end custom front end driven by the same local oscillator and two commercial receivers, all using the same real signal sources. The results show that for GPS signals, the USRP2 front end typically generates carrier-to-noise ratio (C/N ₀) at 1–3 and 1–2 dB below that of the high end front end and a NovAtel receiver, respectively. For GLONASS signals, the USRP2 C/N ₀ outputs are comparable to those of a Septentrio receiver. The carrier phase noise from the USRP2 outputs is similar to those of the benchmarking devices. These results demonstrate that the USRP2 is a suitable front end for applications, such as ionosphere scintillation studies.     

Anomaly analysis of 18 years of newly merged GPS ephemeris from four IGS data centers

The merged GPS navigation files from the International GNSS Service (IGS) data centers, i.e., the Crustal Dynamics Data Information System (CDDIS), the Bundesamt für Kartographie und Geodäsie (BKG), the Scripps Institution of Oceanography (SIO), and the Institut Geographique National (IGN) are occasionally contaminated by anomalies and inconsistent user range accuracy (URA). This contamination impairs the performance assessment of GPS service, especially the system integrity. We remerged these files starting Day of Year (DOY) 1, 2000 using all available navigation data files from IGS stations. To effectively get the upper bound URA, a frequency-dependent pattern recognition method was developed. In addition, a comprehensive comparison between the navigation data remerged by us and those provided by the four IGS data centers was performed. The compared results revealed that T_GD and Issue of Data Clock (IODC) were the dominating anomalies in the merged navigation data from CDDIS and SIO for the first several years after 2000, and M₀, Ω₀, ω, and a_f0 were the dominant anomalies in the merged data from IGN. In addition to a number of missing records, many records with incorrect PRN (pseudo-random noise number), identifying a GPS satellite, were found in files from the IGS data centers. Although the number of anomalies in the merged files from CDDIS has continued to decrease in recent years, they have not disappeared and would affect system-level assessment and scientific applications to a certain extent. The results also revealed that our remerged files were more complete, clean, compact and consistent, making them more suitable for GPS system performance assessment and related research studies. Moreover, those data are now openly available.