Keywords. DECCA, OMEGA, VOR, INS, Integrated systems

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1 Keywords. DECCA, OMEGA, VOR, INS, Integrated systems 7.4 DECCA Decca is also a position-fixing hyperbolic navigation system which uses continuous waves and phase measurements to determine hyperbolic lines-of position. The basic principle here is that when two stations at a distance from each other transmit synchronised continuous wave signals, a receiver placed somewhere between them can relate its position to the phase difference between the two signals, i.e., there is a change in phase difference as the receiver changes position (see Fig.7.6). The transmitted signal frequency is between 70 to 130 KHz with range approximately 200 km. Four stations, a master and three slaves, form a chain. They transmit at frequencies which are multiples of a base frequency f (which is about 14 KHz). At the receiver the master signals are frequency multiplied to produce references which are phase compared with the appropriately multiplied slave signals (Fig.7.7). The phase difference serves as the measure of the range difference and is represented in the form of hyperbola-like iso-phase lines between the two stations (Fig.7.8).The region between two iso-phase lines representing zero degree phase difference is called a lane. On the base-line between stations a complete phase cycle of 360 degrees at the comparison frequencies represents a distance of 750m m (which is the wavelength). Hence, measuring phase to an accuracy of 5 degrees gives a resolution of about 10-15m. However, the resulting position is ambiguous since the same phase measurement repeats every cycle or every wavelength. Special facilities, essentially performing phase comparisons at synthetically produced lower frequencies have to be introduced into the system to resolve this ambiguity. Due to the low frequency operation of Decca, it is subject to skywave contamination (i.e., contamination if signal due to reflection from the iono- 131

2 Figure 7.6: The phase difference in Decca sphere). This is the reason for its low operating range. 7.5 OMEGA Omega is a system which works on the same principle as Decca. But its operating frequency is very low (VLF). Essentially ground based transmitters are employed to transmit in four fixed frequencies KHz, KHz, KHz and KHz. Using VLF enables full worldwide coverage with only eight transmitters placed at stations in Norway, Liberia, Hawaii, North 132

3 Figure 7.7: The phase comparator in Decca Dakota, La Reunion Islands, Argentina, Australia and Japan. To give station identification the stations transmit the various frequencies at set times in a common 10 sec sequence. The low operating frequency of Omega causes quite large inaccuracies in position identification, but it has the advantage that submarine vehicles can receive its signals at appreciable depths underwater. Though Omega was developed for maritime use, it has been widely adopted as a navigational aid on the transoceanic air routes. It was also used by the British quite extensively in the Falklands war, even though one of the transmitters was located in Argentina! 133

4 Figure 7.8: The iso-phase lines in Decca 7.6 VERY HIGH FREQUENCY OMNI-DIRECTIONAL RANGE (VOR) Range and bearing are the basis for most modern position fixing systems. The range and.or bearings to a number of points whose position is known are obtained and used to calculate the position of the observer. Hence, the bearings to any existing radio transmission stations of known location could be used for navigation purposes. Usually radio transmission is done at low and medium frequencies to get wide coverage but when such signals are used 134

5 for bearing measurement, ionospheric and atmospheric conditions cause large errors. To avoid this, one may use high frequency stations, but they have the problem of limited range. To overcome some of these difficulties associated with simple direction finding techniques a number of systems were developed using dedicated transmitters. These provide specially modulated radio beams so that when the signal is received by the aircraft the modulation obtained depends on its position in the beam, thus providing navigational information. One such system, which is widely used, is the VOR system. In the VOR, a series of aerials, situated in a circle around a central reference aerial at the ground station, transmit a constant amplitude VHF carrier frequency ( MHz) which is switched between them to simulate a rotating cardioid (heart-shaped) beam. At a receiver this gives a frequency (which is usually 30 Hz). A reference signal at the rotation frequency amplitude modulates a carrier which is transmitted from the omni-directional reference aerial. The timing of this reference is adjusted so that for a receiver situated at the magnetic North of the VOR station, the frequency modulation from the rotating cardioid beam is in phase with the amplitude modulation from the reference aerial. The phase angle between the two types of modulation obtained at any other location is then the same as the angle from North from the station to the receiver. The VOR system is shown in Fig INERTIAL NAVIGATION SYSTEM (INS) An automatic navigation system which would be undetectable, unjammable and operate anywhere in the world at any time in any weather conditions would seem ideal for military use. Dead-reckoning would appear to meet these requirements, but these systems use doppler speed sensors which radiate signals and therefore are detectable. Inertial navigation, which are 135

6 Figure 7.9: The VOR system essentially dead-reckoning systems, avoid the detection problem by measuring the acceleration of the vehicle using internal sensors and then calculating its velocity by integration. The position of the vehicle can then be computed by a second integration, given the initial position and velocity. Accelerometers are used for measuring accelerations. Signals from gyroscopes are used to prevent the accelerometers from tilting as the vehicle rotates in space. We shall skip the details here. A major drawback of inertial navigation is that the errors in measurement are monotonically increasing functions of time. Hence, one would require very 136

7 accurate (and so very expensive!) accelerometers and gyros in applications where the navigation is done by dead-reckoning over long periods of time. To improve the accuracy of such systems, Strapped down systems were designed which are attached to the body of the vehicle (rather than a gimbal arrangement which decouples the vehicle movement). 7.8 INTEGRATED NAVIGATION SYSTEMS Where several sensors or navigational aids providing separate outputs are available, it is possible to feed all of these outputs into one or more computers, which then provide a single output to the pilot or the autopilot. One reason for integration is to improve reliability. Another is to increase accuracy. The need for greater accuracy than that attainable by individual navigational aids must be weighed against the added cost and complexity of the integrated system. Such an integrated navigation system uses both dead-reckoning and positionfixing, each assisting the other to give a solution better than either can give alone. The dead-reckoning system provides a continuous position and velocity indication and another version of position is obtained from a position fixing system. The two versions are compared and the difference is ascribed as an error in either or both inputs. The estimate of the dead-reckoning error is then used to correct the dead-reckoning system over the next period of operation. Position-fixing information is usually noisy and Kalman filter algorithm is used nowadays to process these noisy signals. PROBLEMS AND EXERCISES 1. Consider an aircraft flying over the surface of the earth and measuring its own velocity using a doppler radar transmitting at 100 MHz. The radar 137

8 transmits along beams A and B shown in the figure given below. The doppler shift in the signal along A is +100 Hz and along B is +150 Hz. Find the velocity of the aircraft in terms of v and θ. Figure 7.10: 2. A vehicle moves on a two-dimensional plane starting from a known initial position (0,0). A dead-reckoning navigation system provides the direction and speed of movement every 10 minutes. A separate position-fixing navigation system also provides an accurate position fix every 10 minutes. These are tabulated below. 138

9 < DEAD RECKONING > POSITION-FIXING t(min) θ(deg) v(km/hr) (x,y) in km (0,0) (6,7) (13,12) (23,13) (a) If the dead-reckoning computations are done using only the initial position fix (0,0) then what is the error at each intermediate point? Plot these intermediate points on a graph sheet. (b) If the intermediate position fix information are also used, then find the amount by which the position-fix information corrects the dead reckoning computation at each intermediate point. Plot these points on the same graph sheet. (c) What is the computed position (by dead reckoning) of the vehicle at t = 40 mins, when (i) no position fix information is used? (ii) when position fix information is used? (iii) What is the error between the two? Plot these points on the same graph sheet. 3. Consider a LORAN master-slave pair placed D kms apart (see figure below). Derive the equation of the line-of-position passing through a point on the base-line d kms apart from the master. Plot the lines of position when D = 40 km and d = 0, 10, 20, 50 kms. 4. In the above system let D = 100km. The slave receives the signal from the master and transmits it after a coding delay of 10 msec. Derive the equation for the line-of-position corresponding to a time difference of 10.5 msec between the master signal and the slave signal. Where does this line of position intersect the base line? 139

10 Figure 7.11: The iso-phase lines in Decca 140

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