There are many scenarios where an integrated INS/GNSS navigation system may be required to operate in a high interference or weak signal environment. The GPS receiver may exploit the inertial aiding by operating with narrow tracking loop bandwidths in order to increase interference resistance. However, where a low grade INS is used, wider bandwidths are desirable to calibrate the INS errors effectively. This is important for GPS tracking loop aiding and sole-means inertial navigation during jamming. To obtain both effective INS calibration and jamming resistance, an adaptive tightly-coupled (ATC) INS/GPS integration architecture has been developed. The ATC technique has been assessed by simulation, showing that it provides a significant anti-jam margin over an INS/GPS with fixed tracking bandwidths selected for INS calibration. Compared to the deep (or ultra-tightly-coupled) integration techniques currently under development, ATC is a low cost anti-jam integration technique as it does not require a complete re-design of the navigation architecture. When there is too much interference for any GNSS signals to be tracked, the INS provides sole-means navigation. Thus, it is important to optimise the calibration of the INS when GNSS signals are available. To this end, the effects of estimating higher order inertial instrument errors and satellite range biases within the INS/GPS integration filter have been assessed.

The solution for the receiver's position and clock bias using four or more GPS pseudorange measurements involve nonlinear quadratic equations. One of the popular techniques attempts to linearise the equations and solve them by the least-squares (LS) scheme based on an iterative gradient approach. For real-time applications when the solution is to be obtained within a time of the order of a hundred nanoseconds, a digital computer often cannot comply with the desired computation time, or its use is too expensive. In this paper, two ordinary differential equation formulation schemes and corresponding circuits of neuron-like analog processors will be employed for GPS navigation processing. The circuits of simple neuron-like analog processors are employed essentially for solving systems of linear equations based on the criterion of mean square error minimization, which is commonly utilized for determining positioning solutions in the GPS receivers. Experiments on single epoch and thereafter dynamic positioning will be conducted by computer simulation to validate the usefulness of the proposed scheme. The solutions will be assessed and compared to those provided by the conventional method in which pseudo-inverse matrix calculation by digital computer is involved.

Map Matching (MM) algorithms are usually employed for a range of transport telematics applications to correctly identify the physical location of a vehicle travelling on a road network. Two essential components for MM algorithms are (1) navigation sensors such as the Global Positioning System (GPS) and dead reckoning (DR), among others, to estimate the position of the vehicle, and (2) a digital base map for spatial referencing of the vehicle location. Previous research by the authors (Quddus et al., 2003; Ochieng et al., 2003) has developed improved MM algorithms that take account of the vehicle speed and the error sources associated with the navigation sensors and the digital map data previously ignored in conventional MM approaches. However, no validation study assessing the performance of MM algorithms has been presented in the literature. This paper describes a generic validation strategy and results for the MM algorithm previously developed in Ochieng et al. (2003). The validation technique is based on a higher accuracy reference (truth) of the vehicle trajectory as determined by high precision positioning achieved by the carrier-phase observable from GPS. The results show that the vehicle positions determined from the MM results are within 6 m of the true positions. The results also demonstrate the importance of the quality of the digital map data to the map matching process.

This paper presents the results of an experiment to investigate the impact of helicopter rotor blades on GPS signal reception. An offshore transport helicopter was equipped with a measurement system including a TSO-C129 compliant receiver and a custom research receiver. GPS signals passing through rotor discs of this aircraft were found to suffer a reduction in received signal strength, leading to potential navigation and RAIM availability concerns. The phenomenon will vary between installations and receiver types. Test procedures to identify the occurrence of the phenomenon in operational GPS installations are presented, together with possible in-service monitoring programs to assess the impact on the navigation function.

Map matching has been widely applied in car navigation systems as an efficient method to display the location of vehicles on maps. Various map-matching algorithms have been proposed. Inevitably, the correctness of the map matching is closely related to the accuracy of positioning sensors, such as GPS or Dead Reckoning (DR), and the complexity of the road network and map, especially in urban areas where the GPS signal may be constantly blocked by buildings and the road network is complicated. The existing map matching algorithms cannot resolve the positioning problems under all circumstances. They sometimes give the wrong position estimates of the car on road; the result is called mismatching. In order to improve the quality of map matching, a deep understand of the accuracy of sensor errors on mismatching is important. This paper analyses various factors that may affect the quality of map matching based on extensive tests in Hong Kong. Suggestions to improve the success rate of map matching are also provided.

Traditionally, navigation has been taught with methods employing Napier's rules for spherical triangles while methods derived from vector analysis and calculus appear to have been avoided in the teaching environment. In this document, vector methods are described that allow distance and azimuth at any point on a great circle to be determined. These methods are direct and avoid reliance on the formulae of spherical trigonometry. The vector approach presented here allows waypoints to be established without the need to either ascertain the position of the vertex or select the nearest pole; the method discussed here requires only one spherical triangle having an apex at the North Pole and is also easy to implement on a small computer.

The integration of the Global Positioning System (DGPS) with an Inertial Navigation System (INS) has been implemented for several years. In an integrated INS/DGPS system, the DGPS provides positions while the INS provides attitudes. In case of DGPS outages (signal blockages), the INS is used for positioning until the DGPS signals are available again. One of the major issues that limit the INS accuracy, as a stand-alone navigation system, is the level of sensor noise. The problem with inertial data is that the required signal is buried into a large window of high frequency noise. If such noise component could be removed, the overall inertial navigation accuracy is expected to improve considerably. The INS sensor outputs contain actual vehicle motion and sensor noise. Therefore, the resulting position errors are proportional to the existing sensor noise and vehicle vibrations. In this paper, wavelet techniques are applied for de-noising the inertial measurements to minimize the undesirable effects of sensor noise and other disturbances. To test the efficiency of inertial data de-noising, two road vehicle INS/DGPS data sets are utilized. Compared to the obtained position errors using the original inertial measurements, the results showed that the positioning performance using de-noised data improves by 34%–63%.

The paper discusses the development of an adaptive Kalman filter for pipeline surveying applications. Various measurement models are developed and numerically tested using a real natural gas pipeline dataset. Since, for tactical-grade IMUs, odometer-derived velocity measurements alone cannot yield good results, two non-holonomic constraints are augmented to make the three-direction measurement model. Smoothing computation is also applied to yield the best trajectory using all the information contained in the past, current and future measurements. The trajectory errors are within 10–20 m for extreme cases, and within 10 m for most cases. RMS of the trajectory errors is expected to be about 2·5 m.

Precise GPS simulated data requires accurate simulation of the two major sources of error in GPS measurements, namely the ionospheric and tropospheric delays. The ionospheric delay modelling has been handled in a previous work (Farah, 2002). In this paper the simulation of the tropospheric delay is discussed. The suggested model should be accurate in estimating the tropospheric delay as well as capable of simulating high spatial variations of the troposphere resulting in more realistic simulated GPS data. In this paper, the EGNOS tropospheric correction model is considered as a possible tool for simulating the tropospheric delay in order to obtain more realistic simulated GPS data. Comparing the total tropospheric zenith delays from the EGNOS model with the CODE-tropospheric product has allowed the quality of the EGNOS model to be assessed. Four IGS-tracking stations have been selected for this study. Data from four non-consecutive weeks in different seasons over a period of one year were tested to assess the seasonal variation of the weather conditions. It is shown that the EGNOS model agrees well with the CODE-estimations with a mean zenith delay difference of approximately 2 cm. The maximum zenith delay difference between the EGNOS model and the CODE-estimations was in the range of 5 cm to 16 cm, which agrees well with previous studies. A second study has investigated the behaviour of the EGNOS model with other established tropospheric models such as the Saastamoinen, the Hopfield, the Marini and the Magnet model for three IGS-stations. It can be concluded from this study that the EGNOS model shows better agreement with the IGS estimations than the Magnet model and compares well with other models. The major shortcoming in the EGNOS model is its inability to simulate the variations in the troposphere over small regions. This shortcoming could be overcome by using the theory of Gaussian Random Fields, which has been previously used to model real life phenomena such as surface roughness (Chan, 1999). This paper was first presented at ION GPS 2003, the 16th Technical Meeting of the Satellite Division of the Institute of Navigation held at Portland Oregon, USA.

An adaptive Kalman filtering approach is proposed for attitude determination to replace the fixed (conventional) Kalman filtering approach. The filter is used to adaptively reflect system dynamics changes or rapid changes in vehicle trajectory. The estimation procedure is carried out through the use of a measurement residual sequence. The sequence is used as a piece-wise stationary process inside an estimation window. The measurement noise covariance matrix and the system noise matrix are adaptively estimated. An extended Kalman filter approach with iteration of the states within-an-epoch was performed to overcome the non-linearity of the observation equations. A test was performed to evaluate the proposed technique. Different trajectory scenarios are presented to show the difference in performance between the adaptive Kalman filter and the conventional one. Results show that the proposed adoptive filtering approach has a better performance than the conventional filter.

I was amused by the Cross Track Distance at Mid-Longitude problem posed by Paul Hickley in The Journal of Navigation57, 320. Thinking about it, I came up with a solution. My method gives an astonishingly accurate, though approximate, answer which is found without any appeal to any formula of spherical trigonometry.

The quality of kinematic navigation and positioning depends on the quality of the model describing the vehicle movements and the reliability of the observations. An adaptive Kalman filtering is introduced. Three kinds of adaptive factors based on the discrepancy between the geometrical positions and the kinematic model predictions and a variance component ratio between model predictions and observations are described. A new exponential adaptive factor is established. The theoretical curves of the adaptive factors are drawn and a practical example is given. The errors of four adaptive filtering results and the corresponding curves of the adaptive factors are also drawn. It is shown, by comparison and analysis, that all of the four adaptive factors can control the influences of the vehicle disturbances in movements on the navigation results. The results derived by the adaptive factor constructed by the variance component ratio are slightly better than those derived by other adaptive factors.

The objective of this paper is to describe recent progress in the area of the Ground Based Augmentation System (GBAS) σpr_gnd establishment to ensure aircraft precision approach navigation integrity. In particular, this paper details: (1) the development and testing of a new adaptive binning algorithm for processing GBAS reference station empirical data to account for ranging error non-stationarity; (2) an introduction of a practical empirical method to quantify and compensate for the effects of seasonal variations of ranging error; and (3) the synthesis of these empirical results with existing theoretical ground-multipath models toward a quantitative establishment σpr_gnd for GBAS.

I wish to respond to Paul Hickley's invitation in his article on “Great Circle Versus Rhumb Line Cross-Track Distance at Mid-Longitude” in the May 2004 Journal of Navigation. It seemed an ideal teaser for an erstwhile Maps and Charts lecturer, albeit 45 years ago, to play with on his 81st birthday last week! Since it was a question for pilots, did not require knowledge of spherical trig, and was answerable in 2 minutes and 12 seconds I thought, as did Paul, that there must be a fairly simple solution. Mine follows.

In this paper, a simplified and direct computation method formulated by the fixed coordinate system and relative meridian concept in conjunction with vector algebra is developed to deal with the classical problems of celestial navigation. It is found that the proposed approach, the Simultaneous Equal-altitude Equation Method (SEEM), can directly calculate the Astronomical Vessel Position (AVP) without an additional graphical procedure. The SEEM is not only simpler than the matrix method but is also more straightforward than the Spherical Triangle Method (STM). Due to tedious computation procedures existing in the commonly used methods for determining the AVP, a set of optimal computation procedures for the STM is also suggested. In addition, aimed at drawbacks of the intercept method, an improved approach with a new computation procedure is also presented to plot the celestial line of position without the intercept. The improved approach with iteration scheme is used to solve the AVP and validate the SEEM successfully. Methods of solving AVP problems are also discussed in detail. Finally, a benchmark example is included to demonstrate these proposed methods.

Precision inertial navigation depends not only on the quality of the inertial sensors (accelerometers and gyros), but also on the accuracy of the gravity compensation. With a view toward the next-generation inertial navigation systems, based on sensors whose errors contribute as little as a few metres per hour to the navigation error budget, we have analyzed the required quality of gravity compensation to the navigation solution. The investigation considered a standard compensation method using ground data to predict the gravity vector at altitude for aircraft free-inertial navigation. The navigation effects of the compensation errors were examined using gravity data in two gravimetrically distinct areas and a navigation simulator with parameters such as data noise and resolution, supplemental global gravity model noise, and on-track interpolation method. For a typical flight trajectory at 5 km altitude and 300 km/hr aircraft speed, the error in gravity compensation contributes less than 5 m to the position error after one hour of free-inertial navigation if the ground data are gridded with 2 arcmin resolution and are accurate to better than 5 mGal.

I am grateful to both Dr Ponsonby and Sqn Ldr Hoare for their responses to my original article and would like to thank them for replying. It is interesting that they have come up with such different approaches, one based on solid geometry (but not spherical trigonometry) and the other based on a map projection, which both give exact or near-exact answers.

Use of a sphere to represent the Earth in the teaching of navigation has the advantage that the mathematics is relatively simple and has sufficient accuracy for most practical purposes. It also allows relatively simple instructional material to be developed for plane and Mercator sailing. Unfortunately, and as remarked by Williams [1], bad practice based on an error of principle has pervaded some navigation texts for some time. This error has passed into various instructional settings where it has gone un-noticed or un-remarked. The error lies in the un-rigorous use of meridional parts for the spheroidal earth together with latitude differences for the spherical earth in the teaching of plane and Mercator sailing. This is exemplified in [2, example1, p 585]. It is often argued that the resulting error in calculated distance or mid-latitude caused by this un-rigorous treatment is small and within what practical course keeping allows. However, permitting the discrepancy to remain unexplained is a disservice to students of navigation. Students should be given a clear explanation of the differences between the fictitious though useful spherical model of the earth and the spheroidal earth as presently described by WGS84. Teaching of plane and Mercator sailings should be based upon either the spherical model or upon the spheroidal model but not on parts taken from both.

Tracking dynamics on the GPS signal is still a big challenge to the receiver designer as the operating conditions are becoming more volatile. Optimizing the stand-alone system for dynamics generally degrades the accuracy of measurements. Therefore, an inertial navigation system (INS) is integrated with GPS to address this issue. Doppler derived from INS can be used to aid the carrier tracking loop for improving the performance under dynamic conditions. However, the derived doppler does not truly reflect the GPS signal doppler due to errors in inertial sensors. As the tracking loop bandwidth is reduced significantly in ultra-tightly integrated systems, any offsets in the aiding doppler creates undesired correlations in the tracking loop resulting in sub-optimal performance of the loop. The paper addresses this issue and also provides a mitigating mechanism to reduce the effects of incorrect estimates of the doppler. It is shown that doppler offsets resulting in a bias in the tracking loop can be appropriately modelled and removed. Mathematical algorithms pertaining to this are provided and the results are summarized. Simulations show that the bias due to aiding doppler offsets could be effectively addressed by appropriate modelling.

This paper is presented as a think piece and poses the introduction of a new type of high-speed craft to represent the growing number of fast manoeuvrable craft that could safely maintain their speed in heavy traffic areas. A method of defining such craft is introduced and a proposal made for a corresponding amendment to the COLREGS.