Consideration of time-correlated errors in a Kalman filter applicable to GNSS

An algorithm for considering time-correlated errors in a Kalman filter is presented. The algorithm differs from previous implementations in that it does not suffer from numerical problems; does not contain inherent time latency or require reinterpretation of Kalman filter parameters, and gives full consideration to additive white noise that is often still present but ignored in previous implementations. Simulation results indicate that the application of the new algorithm yields more realistic and therefore useful state and covariance information than the standard implementation. Results from a field test of the algorithm applied to the problem of kinematic differential GPS demonstrate that the algorithm provides slightly pessimistic covariance estimates whereas the standard Kalman filter provides optimistic covariance estimates.     

Temporal impact of selected GPS errors on point positioning

This paper is aimed at investigating the stability of point positions over time in support of applications that require high position stability when differential GPS is not feasible. One such application is the use of a P3-Orion aircraft offshore for magnetic measurement in support of submarine detection. Temporal changes in several GPS errors lead to variability in the computed positions, so it is not the absolute errors, but rather their temporal variations that are of importance. Furthermore, the temporal variability of the different error sources may dictate a certain algorithm approach and processing strategy. This paper analyzes the temporal variations of the broadcast satellite clock model and orbit parameters, as well as ionospheric errors, because these will typically be the dominant errors for real-time point positioning. These three errors are analyzed independently. A tropospheric correction is applied when computing all of the position results, so the tropospheric error itself is not investigated. Satellite clock and orbit errors are analyzed by comparing broadcast and precise post-mission SV clock corrections and orbits. For the ionosphere, the effect is separated using dual-frequency data. The analysis comprises primarily of assessing error behaviors and magnitudes through time and frequency analyses. In this way, the differences in variability of the errors are easily determined. The effect of each error in the position domain is also investigated in addition to the combined effect. Results show that, on a typical day when single frequency data are processed with broadcast orbit and clock data, the root mean square (RMS) of the changes in the position errors over a 50-s interval is about 5.8 cm in northing, 4.0 in easting, and 11.0 cm in height. When using precise orbits and clocks, in addition to dual frequency data, these values improve by 46–56% to 2.7 cm in northing, 2.2 cm in easting, and 4.9 cm in height. Under severe ionospheric activity, the RMS of the errors decrease from 8.1 to 3.3 cm in northing, 5.7 to 2.6 cm in easting, and 17.0 to 4.9 cm in height, which are improvements of 54–71%. Electronic Publication     

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.     

Feasibility assessment of MEMS oscillators for GNSS receivers

We analyze results from using a temperature-sensing MEMS oscillator as frequency source for the front end of a software-based GNSS receiver. Results show that although MEMS oscillators are highly sensitive to temperature, GNSS receivers can still make use of them even without any form of temperature information or compensation. Nevertheless, using a temperature sensor in close proximity to the resonator can significantly decrease acquisition time and improve tracking performance if the temperature measurements are properly filtered to remove noise. In this case, no negative effect on the measured carrier-to-noise density ratio was detected, and phase-locked tracking of strong signals was possible over a temperature range of ?40 to +85 °C.     

Estimation of Clock Stability Using GPS

The recent development of low-cost, high-precision oscillators has allowed many applications in various fields to become financially feasible. The stability of an oscillator is ultimatively what determines its usefulness for a certain application, and is therefore desirable to quantify. Current methods of evaluating stability require a direct comparison of the oscillator under test (OUT) with amore stable reference oscillator, the cost of which often offsets the initial benefit of a low-cost device. However, a relatively inexpensive Global Positioning System (GPS) receiver is capable of exploiting the highly stable GPS time scale, thus obviating the need for an expensive reference oscillator. By allowing the OUT to drive a GPS receiver, and processing the data with precise GPS orbits and clock corrections to eliminate the effects of selective availability (SA), the time series of computed clock offsets provides a measure of the oscillator's stability relative to GPS time. The use of GPS for assessing clock stability in the time domain is evaluated herein via the computation of Allan variance values. Performance of one rubidium and three ovenized crystal oscillator are investigated. Results show the method is limited to time intervals less than about two seconds or longer than about 300 seconds, where the effects of measurement noise and residual SA is less pronounced. ? 2000 John Wiley & Sons, Inc.     

Narrowlane: is it worth it?

The narrowlane (NL) linear carrier phase combination is commonly used to obtain the highest positioning accuracy using the Global Positioning System because it is capable of mitigating the effect of measurement noise and multipath. However, after reviewing the effect of various error sources on linear carrier phase combinations, it is shown herein that it is theoretically possible to obtain marginally better positioning accuracy using the L1 and L2 carrier phase data independently. Numerical results indicate no difference in performance. With this in mind, the paper investigates the practical benefits of the L1 and L2 approach over the NL combination including; less reliance on L2 phase continuity; easier ambiguity resolution; and simpler navigation filter development.All theses from the Department of Geomatics Engineering at the University of Calgary are downloadable from     

A performance comparison of single and dual frequency GPS ambiguity resolution strategies

The impact of observation selection, observation combination and model parameterization on GPS carrier phase ambiguity resolution and position accuracy under operational conditions is investigated. The impact of an ionospheric bias for a generic linear combination of L1 and L2 measurements is assessed and the results are used to clearly outline the desirable characteristics for improving ambiguity resolution versus positioning accuracy performance. Ambiguity resolution performance and position accuracy are shown for widelane (WL), L1-only, and ionospheric-free (IF) combinations. Several techniques for dealing with the ionospheric bias are also presented and compared, including stochastic ionospheric modelling. Multiple carrier phase combination solutions estimated in the same filter are also compared. The concept of an optimal processing strategy—in terms of both reliable ambiguity resolution and high accuracy positions—is presented. In total, eight strategies, which vary in observables and parameters, are tested on several datasets ranging from 13 km to 43 km.     

Choosing the coherent integration time for Kalman filter-based carrier-phase tracking of GNSS signals

Carrier phase–based positioning using Global Navigation Satellite System (GNSS) signals can provide centimeter-level accuracy; however, to do so requires robust, continuous tracking of the phase of the received signal. The phase-locked loop is typically the weakest link in GNSS signal processing, with frequent cycle slips and loss of lock occurring at lower signal-to-noise ratios. One way to improve the signal-to-noise ratio is to increase the coherent integration time; however doing so reduces the loop update rate, thereby degrading performance. This paper investigates this trade-off between sensitivity and loop update rate by investigation of the Kalman filter-based tracking loop. It is shown that it is possible to choose an optimal integration time for a given application. A relatively straightforward procedure is given to determine this optimal value. The results are confirmed through real-time kinematic processing of live satellite signals.     

3D building model-assisted snapshot positioning algorithm

GPS Solutions - A method for constructively using non-line-of-sight GNSS signals from a snapshot of signal samples for positioning of users in urban areas is presented here. Using a 3D building...