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.     

Shipborne GPS attitude determination during MMST-93

The attitude parameters of a ship underway were measured using a configuration of four 10-channel NovAtel Model 951 narrow-correlator-spacing receivers. These C/A code receivers have output rates of up to 10 Hz and maintain effective carrier phase lock under relatively harsh ship dynamics. The attitude parameters are calculated independently at each epoch using differential carrier phase measurements, carrier phase ambiguities are resolved on-the-fly by constraining the approximately known distances between the antennas that are rigidly mounted on the ship. Carrier phase thermal noise and multipath are minimized by mounting the antennas as far apart as possible. The four-antenna configuration provides redundancy and further improves accuracy. During the Matthew Motion Sensor Trials (MMST-93) conducted off the coast of Halifax, Nova Scotia, in June-July 1993, the GPS-derived attitude parameters were compared with those obtained with a Honeywell HG1050 ring laser gyro inertial navigation system (INS) which provides roll and pitch with an accuracy of 15 arcsecs and heading with an accuracy of 2 arcmins. To simulate rough weather conditions, sharp maneuvers were performed to induce roll angles in excess of 10°. No accuracy degradation nor any loss of GPS measurements occurred. The RMS agreement between GPS and INS derived attitude parameters is better than 2 arcmins in heading, 1 arcmin in pitch and 3 arcmins in roll. This level of accuracy demonstrates the capability of GPS for cost-effective shipborne attitude determination at an accuracy level of 0.05     

Variations in the onset of bottom-water intrusions over the entrance sill of a fjord

Puget Sound is a fjord-like estuary and bottom-water intrusions are major circulation features which play a dominant role in the replacement of water below still depth. New observations on the inside and outside of the entrance sill show that, while intrusions occur during neap tides as previously thought, the onset of the intrusions is a results off fluctuations in the horizontal density gradient caused by salinity variations across the sill. Salinity changes outside the sill in the Strait of Juan de Fuca estuary appear to be the result of storms on the Pacific Coast causing reversals of surface flow and variations in deep flow more than 135 km from the coast. Previous observations have shown deep salinity variations midway along the straight, but these are the first to show this effect can penetrate the full length of the Strait causing near-bottom salinity variations of sufficient magnitude to influence flow into Puget Sound. This influence probably occurs from the onset of storms in autumn through subsidence in spring, although occasional large storms occur in summer. Although Puget Sound is more characteristic of a fjord, the simple model calculations here suggest similar processes may occur in lower-layer flow at the mouth of coastal plain estuaries.     

A comparison of P code and high performance C/A code GPS receivers for on the fly ambiguity resolution

Carrier phase ambiguity resolution on the fly is investigated using two receiver technologies, namely dual-frequency P code and high performance, single frequency, C/A code receivers. Both receiver types were used simultaneously in a series of land kinematic trials. A least-squares search technique is used to find the correct double difference carrier phase ambiguities. Both C/A and single frequency P code technologies are found to be equivalent and capable of resolving the integer ambiguities on the fly using some 30 to 200 seconds of data under benign multipath conditions. Successful ambiguity resolution on the fly results in cm-level accuracy kinematic positioning. The ambiguity resolution time required and success rate are however found to be strongly dependent on the level of carrier phase multipath and, as a consequence, on the error variance assigned to the carrier phase measurements. The use of widelaning with the dual frequency P code results in ambiguity resolution in seconds. The performance of widelaning is also superior in a comparatively high carrier phase multipath environment.     

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     

Precise aircraft single-point positioning using GPS post-mission orbits and satellite clock corrections

Summary Aircraft single point position accuracy is assessed through a comparison of the single point coordinates with corresponding DGPS-derived coordinates. The platform utilized for this evaluation is a Naval Air Warfare Center P-3 Orion aircraft. Data was collected over a period of about 40 hours, spread over six days, off Florida's East Coast in July 94, using DGPS reference stations in Jacksonville, FL, and Warminster, PA. The analysis of results shows that the consistency between aircraft single point and DGPS coordinates obtained in single point positioning mode and DGPS mode is about 1 m (rms) in latitude and longitude, and 2 m (rms) in height, with instantaneous errors of up to a few metres due to the effect of the ionosphere on the single point L1 solutions.     

Critical error effects and analysis in carrier phase-based airborne GPS positioning over large areas

For high accuracy airborne differential GPS positioning over large areas, i.e. a monitor-remote separation over 50 km, residual errors from the atmosphere and orbit, as well as multipath effects are the main error sources which limit the potential positioning accuracy. The effects of these critical errors are quantified and analyzed using test data collected during an airborne positioning campaign. Four Trimble 4000 SSE receivers were used, with two serving as monitors and the other two as remote receivers installed in the aircraft. Monitor-aircraft separations of up to 200 km were experienced during the test. A formula is derived for analytical estimation of orbital error effects. Results and discussions relevant to the critical error analysis are presented with emphasis on their effects on the positioning results.     

The formation of Mg i 4571 Å in the solar atmosphere

An analysis of the 4571 Å line of neutral magnesium is presented in which one-dimensional macroscopic velocity fields are included. It is shown that gradients over restricted heights in the vertical and horizontal components of the velocity field of order -0.005 s^–1 and -0.004 s^–1 (such that velocity towards the observer decreases as height increases), respectively, result in asymmetries in the computed line profile similar to those observed. The heights in the solar atmosphere at which these velocity gradients exist are shown to be very critical in reproducing the observations. It was found that the best results were obtained when the gradients existed in the height range from 200 km to 300 km below the temperature minimum. The results indicate that for the Mg i 4571 Å line model calculations that do not include one-dimensional flow velocities may safely be compared with frequency-averaged observations.     

Comparing the Correlative Holdridge Model to Mechanistic Biogeographical Models for Assessing Vegetation Distribution Response to Climatic Change

A well-established and widely used correlative climate-vegetation model (Holdridge Life Zone model) was compared to three mechanistic simulation models (BIOME2, Dynamic Global Phytogeography Model (DOLY), and Mapped Atmosphere-Plant-Soil System (MAPSS)) for the conterminous United States under contemporary climate and a set of future climates prescribed by three Global Circulation Model experiments. Output from the mechanistic models were from the Vegetation/Ecosystem Modeling and Analysis Project (VEMAP) intercomparison. Holdridge modeling approaches, using a Simple implementation (vegetation distribution based on biotemperature and precipitation alone) or a Full implementation (vegetation distribution based on biotemperature, precipitation, altitudinal region, latitudinal belt, and transitional vegetation zones), represented current potential natural U.S. vegetation poor to fair, respectively. The more sophisticated mechanistic models were superior at reproducing potential vegetation under current climate compared to Holdridge, although there was significant variability among these models. The Holdridge implementations generally showed similar or greater climate sensitivity with respect to spatial redistribution of vegetation compared to the mechanistic models run both with and without doubled CO₂ levels; however, the sensitivity of the Holdridge model depended on the implementation. Reduced sensitivity of the mechanistic models arises from direct (physiological) CO₂ effects and other compensating feedbacks not captured by the Holdridge model. The greater degree of physical realism in the mechanistic models makes them the model class of choice for climate impact assessment. However, under circumstances of limited data availability, computation resources, and access to mechanistic models and model expertise, simple correlational models such as Holdridge may be the only method that can be applied. The paper makes some recommendations on the use of the Holdridge model for impact assessment if it is the only available model.