Hyperbolic Navigation System Research Articles

Method for determining of statistical characteristics of evaluated distance obtained from measurements of Doppler frequency offsets

This paper presents a technique for obtaining of the main statistical characteristics of the distance estimation between the flying object and a hyperbolic navigation system using two Doppler frequency shifts of the navigation signal. This problem arises when the guidance of the object at a target point along a hyperbola using a bistatic hyperbolic navigation system is considered. Despite the fact that the object guidance loop is closed according to the time difference of arrival information, it is necessary to enter the distance between the object and the center of the navigation system into the algorithm for generating control commands in order to stabilize the frequency response of the control loop and eliminate dynamic errors. This article discusses the statistical characteristics of the estimated range based on the measurements of three values of the object’s speed: its own speed and two projections of this speed on the lines connecting the object with the navigation positions.

Method for determining of the distance to the object in the hyperbolic navigation system via doppler frequency offsets

In this paper, a method for estimating the distance to the object guided along a hyperbola to a target using a bistatic hyperbolic navigation system on a plane is given. At the same time, to solve the guidance problem, the number of required navigation positions is reduced by one in comparison with the classical method of hyperbolic navigation. However, in the guidance algorithms, it is still required to estimate the distance of the targeted object from the center of the base, the methods of obtaining which are considered in the work.

High Performance, Low Cost Loran-C Cycle Identification and ECD Estimation

A Loran-C system is a hyperbolic navigation system which works based on time difference of arrival (TDOA). Cycle identification is the task of finding time of arrival of the incoming signal. Finding time of arrival of the signal needs choosing a reference point which is defined to be the third zero crossing of the signal. ECD is the varied Loran-C signal’s envelope from the original pulse. Cycle identification and ECD estimation accuracies have considerable effects on the Loran-C system receivers’ localization accuracy and the error in cycle identification or ECD estimation has direct effect on each other so it is important to estimate the reference point and ECD as precise as possible. In this paper, algorithms for cycle identification and ECD estimation are proposed.Furthermore, this paper addresses the problem of the reference points existence between two samples and proposes two algorithms to estimate the reference points time of arrival between two samples which leads to reach high accuracy using low sampling frequency. The simulation results show that the proposed methods for cycle identification and ECD estimation are robust in noisy conditions and intersample cycle identification algorithms give accurate estimate of the reference points between two samples.

Integrated navigation complex based on hyperbolic and satellite navigation systems

The problem of integrated navigation complex structure is discussed. The hyperbolicand satellite navigation systems are proposed to be the consisting parts of such a complex. Theproblem of their integration is solved

Disturbances of decca waves near a huge bridge

A hyperbolic navigation system using a radio wave in the 100-kHz band is installed in the ocean surrounding Japan. This system is used widely by the fishing industry because the reproducibility of the measured location is high. Recently, near the land, several huge structures such as the Seto Bridge have been erected on the water which causes significant error in determining the location of a ship. This paper studies the disturbances of Decca waves of the Kita-Kyushu Decca chain due to the Minami-Bisan Seo-Ohashi Bridge. It was found that, with respect to the disturbance of Decca waves, the two main towers of the suspension bridge could be considered as vertical electric dipoles. In the measurement of the electrical field strength at four frequencies of the Decca station, the standing wave of the electrical field strength appeared more conspicuously with a higher frequency at the locations away from the bridge by more than 0.18 wavelength except near the bridge on the west side. It is assumed that the secondary waves from two main towers considered as vertical electric dipoles are superposed on the primary wave. Then the numerical results are carried out from the theoretical equation of the received electric field, and the measured results are explained. Also, it is found that the static capacitance of the vertical electric dipoles is 0.1 to 0.2 μF. Hence, it was possible to establish a macroscopic model of the bridge for which the main towers are considered as vertical electric dipoles.

Operating LORAN-C Position Fix with Nonhyperbolic Position Lines

Hyperbolic navigation systems ( LORAN-C, DECCA Navigator and OMEGA ) represent a widely used class of position fixingsyst.ems.Most of their incorporated traditional receivers display position fihyperbolic position lines and geometrical factors relevant to these lines. Avionics applications as well as automatic vehicle location systems entails low-cost receivers which operate wholly or largely automatically and which display position measurements in geographical coordinates (latitude -longitude) or as headings and distances to given waypoints and/or integrated with readings from dead-reckoning sensors.Solution issues to some of these problems have been addressed in two published papers by the authors.The underlying idea is to involve modifications in the processing algorithms of on-board receivers.In essence ,that modification was based on generating non-hyperbolic position lines :circles and/or ellipses out of the originally designed hyperbolic systems. Theoretical evaluation of that proposal was the subject of one the authors papers. In the present paper ,the proposed modification is applied to a real ON--EARTH LORAN-C station to confirm the obtained results. Moreover,an algorithm as well as an implementation proposals are presented .The case of short base-length as in the DECCA chains is presented with its algorithm and the proposal for implementation is highlighted.

Loran-C Chains: Determination of Extent of Cover

A mainly theoretical study has been undertaken to demonstrate how the extent of cover from a hyperbolic navigation system chain can be evaluated. The impetus for the study was the need to assess how Loran-C could be extended over Western Europe, particularly in the South western Approaches, North Sea, English Channel and Bay of Biscay sea areas.The technique described in this article leads to an accurate determination of the electric field strength at a distance from each transmitting site and takes into account the complexities of the ground-wave propagation path. This field-strength contour is combined with the geometric effects of station siting (expansion factors) to yield a constant S/N contour (–10 dB) which defines the ¼n.m. error and hence the limit of cover for the hyperbolic chain under study.In order to exercise the analytical methods a hypothetical Loran-C chain was studied comprising a master station at Lessay (France), with secondary stations at Soustons (also in France), at Sylt (dual rated; off the North Sea coast of Germany, near the Danish border) and at a fourth station located in north-west Britain on the Hebridean island of Barra. The study indicated that such a hypothetical chain would significantly improve Loran-C cover over much of western Europe.

Errors of algorithms for position determination from hyperbolic navigation systems

Abstract Formulas for errors of algorithms for conversion of hyperbolic to geographic coordinates are derived in this article. It has been proved that the noniterative algorithm has errors caused by simplifications necessary to obtain a noniterative solution, errors not present in the iterative algorithm. A method of analysis of additional errors is presented which makes it possible to adjust the accuracy of geodetic formulas to the required accuracy of the conversion algorithm and to the accuracy of the navigation system.

On Some Aspects of Omega Windfinding

A generalized hyperbolic navigation system using Omega signals is defined. For three stations this system is shown to be equivalent to the ordinary hyperbolic navigation system. It is shown that the velocity and position determination are independent of the station selected to be the common station. Furthermore, a formula is given to combine several estimates of the wind vector into a single optimum estimate. The efficiency of using three frequencies instead of a single frequency to derive the wind vector is derived.

The Transformation of Hyperbolic to Geographical Coordinates by a Gradient Method

Position fixing with the Omega hyperbolic navigation system requires the use of charts or tables unless the receiver itself is able to display the geographical coordinates directly. Plotting position lines on Omega charts is a simple operation but owing to their small scale (1 : 2, 187, 400 for the Mediterranean area) it is impossible to obtain a satisfactory accuracy of fix, while the use of Omega tables becomes particularly laborious when frequent fixes are required.

The Velocity Field: A New Concept in Navigation

The practical navigator relies on his ability to perform two fundamentally distinct operations: fixing his position and determining the course to steer. Guidance, in the sense that he receives (or generates within his craft) signals which continually define a vector coincident with his desired track, is not normally available to him.Certain radio aids, notably the hyperbolic navigation systems, have however, frequently been used in the guidance role where the direction in which the signals can be particularly easily interpreted happens to coincide with the course to be steered. Thus, flying down a Decca lane is an acceptable operational technique which corresponds to making the aircraft follow the locus of constant range-difference to two points at known locations. It is not in principle necessary for the craft to perform the conversion from hyperbolic to Earth coordinates in order to do this.

Current Developments in Loran-D

Loran-D is a highly accurate pulsed hyperbolic navigation system similar to and compatible with Loran-C, but designed for military tactical use. The helicopter—transportable—transmitter stations have quickly erectable antennas using new tower technology. A signal range over half that of Loran-C is achieved by the fortunate propagation characteristics of 100 KHz waves, by a modified compatible signal format and by improved transmitter solid state technology. Deployments of the stations in the U.S. and Europe are described. The potential uses of Loran-D include: gap filler in Loran-C coverage, a transportable survey system, and long range navigation coverage for many civilian applications.

Position determination from hyperbolic navigation systems

A method based on Sodano's inverse solution of geodesics for determining geodetic positions from hyperbolic navigation time differences is derived to an accuracy of 0.005 sec of arc. The inverse problem is also solved. Hyperbolic coordinates can be transformed directly to universal transverse Mercator coordinates by proper application of the universal transverse Mercator scale factor.

Derivation of Circular Fixes in Hyperbolic Navigation Systems

Relationships between positions determined by the intersections of hyperbolae defined by the differences in the times of arrival of pulses from three fixed transmitters and those determined by the intersections of circles centered at two of the transmitters provides the means of estimating the systematic errors in the radii of the circles due to clock bias errors. The radii are determined from a clock located at the fix point which is not synchronized with the clock used to establish the sequence of pulses from the transmitters. This clock is assumed to indicate a known function of the transmitter clock time having stationary but unknown coefficients. These coefficients are estimated by least squares methods from a sequence of hyperbolic fixes outside of the exterior base line regions. After the clock synchronization errors are reduced the random time measurement errors of the hyperbolic and circular systems will become comparable. The spacial errors of the circular fixes will be less than those of the hyperbolic fixes. This is due to the greater spacial displacement of a hyperbolic line of position with a time difference error than that of a circle due to a corresponding error in the time of transmission over the radius.

Loran-Inertial Navigation Systems for Long-Range Use

Loran C, a long-range hyperbolic navigation system, is currently used in transoceanic aircraft only to provide periodic position up-dating of primary self-contained navigation systems. The successful development and flight testing of an automatic coordinate converter has recently shown that the potential of the Loran system of navigation is vastly greater than past utilization has indicated. This paper briefly discusses the advantages of combining an increased capability Loran sub-system and an unsophisticated inertial sub-system within the framework provided by a heavy logistics support aircraft.

Ear‐to‐ground

DECCA‐GENERAL PRECISION EQUIPMENT TIE‐UP. A new Company, General Precision Decca Systems Incorporated, has been formed jointly by The Decca Navigator Co. Ltd. and General Precision Equipment Corporation of Terrytown, New York. The new Company will be licensed under all patents and related know‐how of the The Dccca Navigator Co. Ltd. and will engage in the design, production and marketing of electronic navigation equipment for commercial and military aerospace applications and military marine requirements. Products will include hyperbolic navigation systems, position fixing systems for survey, airborne computers and pictorial displays. The Dccca system is currently being used by the U.S.A.F., U.S. Army and U.S. Navy and by New York Airways for their helicopter operations and in addition the U.S. Coast Guard has recently approved the New York transmitting chain for use by ships. There is little doubt that this joint undertaking between Dccca and General Precision represents a major step forward in the fight for acceptance of the Dccca area coverage navigation system in the United States and throughout the world.

Service Area Calibration of Hyperbolic Navigation Systems

It is well known that in low-frequency hyperbolic navigational systems the phase differences measured by the receiver do not correspond precisely to the hyperbolas on the plotting chart. This is largely because of variations in the terrain over which the waves are propagated. The system service area may be sampled so that the curve distortions can be ascertained at selected points. This article discusses how the whole service area can be calibrated, given a knowledge of the grid distortions at a sample of points. The mathematical treatment takes into account the correlation between the grid distortions at adjacent sampling points by using autocorrelation theory.The degree to which fixing accuracy is improved by the proposed method of calibration is assessed against the background of an actual set of field measurements.Mr. Sullivan is Head of the Applied Research Group of the Navigation and Guidance Laboratory at the Institute of Science and Technology. Dr. Porter is Assistant Professor of Electrical Engineering at The University of Michigan, and Head, Analytical Research Group of Navigation and Guidance Laboratory at the Institute of Science and Technology.In low-frequency ground-wave navigation systems such as Loran-C and Decca, position information is determined from measurements of time and/or phase differences in signals received from several separately located transmitter stations. A pair of stations generates a family of hyperbolic lines which are the loci of points of constant time/phase difference. Two station pairs provide a grid of hyperbolas. By measurement of the time/phase difference between the signals from two transmitters, the receiver is located on a hyperbolic line. The same receiver is located on a second line by similar measurement which uses another pair of stations; the receiver is thus fixed specifically at the intersection of the two lines.

Multiple Pulse and Phase Code Modulation in the Loran-C System

Transmission of a group of closely spaced pulses increases the duty cycle and consequently the range of the Loran-C (formerly called Cytac) 100-kc pulsed hyperbolic radio navigation system while retaining the advantages of time sharing. Phase coding by carrier phase reversal, coupled with synchronous detection, facilitates automatic master and slave identification and search, and prevents multihop skywave interference. Instrumentation for simple and complex pulse patterns is considered. The phase codes used are characterized by lack of spurious responses associated with other bipolar codes.