The 'Doppler' principle of sound waves is described by considering the noise of a train whistle as the train passes an observer. While the train is approaching, the frequency of the whistle appears to be higher than it really is, and as the train moves away from the observer, the frequency appears lower. Radio waves can be said to behave in a similar fashion.
A signal from a radio broadcast transmitter moves away from the transmitter in all direction at the same constant speed. The radio waves itself leaves the aerial in the same form in all directions. However, if we consider a portion of the waveform generated from a moving transmitter, by the time the last part of the portion leaves the aerial, the aerial itself will have move relative to the first part. The portion of the wave will appear to have shortened in the direction of the aerial movement. A stationary receiver in the direction of the travel , will 'hear' more cycles per second , therefore a higher frequency than that transmitted. By the same analogy, it will appear to have lengthened in the opposite direction.
The same would apply if the receiver were moving and the transmitter was not, or if both were moving. The received frequency will change in relation to the relative speed between the transmitter and the receiver.
For normal pulse radar, this may not be considered a disadvantage, in that a moving target will reflect a frequency slightly different from that transmitted. It means the radar receiver must have a fairly broad bandwidth to accept a variety of reflected frequencies around the original. However, the principle can be used in other to expand the values of electromagnetic waves in navigation.
One benefit of a Doppler radar lies in its ability to transmit continuous wave (CW) signals rather than pulsed. Effective power is increased because the pulse width is not limited. In CW signals, the transmitted frequency is blanked out at the receiver, and only signals reflected from those targets which have relative movement towards or away from the radar unit, and which are returned at a different frequencies are processes.
A fixed Doppler radar can be detected any target which is moving towards or away from it by transmitting a constant frequency and comparing the frequency of the received, reflected signal. While it is transmitting, it cannot receive exactly same frequency, and so any target which is neither approaching nor receding will not be detected.. However this mean there is not 'ground clutter' or weather returns to interfere with the picture.
If the transmission is constant (CW), less power is needed for detection at the same range. A Doppler radar cannot indicate the range of the target, but if used in conjunction with a primary pulse radar, which can, it can filter out the signals which show no 'Doppler Shift'. As a result, a display fed from both system and indication only those targets which respond on both, will only show moving targets. The system has a 'Moving target indicator' or MTI.
The problem with a MTI is that a target which is moving at very slow speed such as a balloon, will be filtered out. Any target which is flying tangential to the receiver (at 90 deg to the track of the antenna) will also have no Doppler shift, and so will not be visible either.
Relative Speed Measurements
The actual 'Doppler shift' in the frequency from the transmission to reception of the waves can be used in a formula to discover the relative speed between the transmitter and the receiver.
V is the relative velocity between the transmitter and the receiver.
ℷ is the wavelength of the original signal
fd is the change in frequency due to the Doppler effect
However, when the effect is found in a radar, the target is moving relative to both transmitter and receiver, so the receiver frequency will be affected double by the Doppler effect. The formula for the radar signal then becomes
The Doppler principle has been available for a considerable time in an airborne (self-contained) navigation system, with the advantage that it does not depends on the serviceability or availability of the external navigation aids. It may still be used to provide information to a navigation computer.
In principle, the airborne Doppler equipment sends a continuous radar beam forwards of the aircraft, measuring the Doppler shift (frequency change) of the received signals, and computers the aircraft's ground speed from the Doppler formula. In practice four beams are used, pointer to an angle downwards to reach the ground, and from the received signal frequencies the computer calculated the drift as well as the ground speed.
For accuracy, the system should produce the maximum frequency change, so a beam should be as hear horizontal as possible. However, at small depression angle, much of the beam is reflected away from the receiver, so a larger depression angle is required, usually about 60 deg. The beam typically have a width if 1 deg to 5 deg. The actual doppler shift will be less than from a direct reflection, in fact it will also depend on the cosine of the depression angle.
It is unusual for an aircraft to fly at a constant altitude for long, so depression angle would continually change. To overcome such variations, a beam pointed backwards at the same depression is used, and that shift is also measure. The frequency received by the rear receiver would be less than that from the transmitter, where as that from the front would be more, although the actual numerical value would change would be same if it were not for the variation in depression angle. If the aircraft pitches nose up, the leefective depression angle of the front bean will decrease, and that of the rear beam increases.
Having measure both shifts, a positive shift from the front and a negative shift from the rear , the computer subtracts the rear shift from the front shift, producing a large positive shift. When the total shift is fed into the formula and divided by 2, it is as if the average depression angle were almost constant. This also compensates for minor frequency errors in the transmitter, and in addition takes account of rising or falling ground beneath the aircraft. This double beam system became known as a 'Janus array'.
An aircraft experiences drift, and moves along a track which is different from its heading. An error would occur in its calculated ground speed, as the equipment would only measure the speed along the heading. This can be prevented by fitting two beams pointed at an angle out from the heading, rather than one. The two shift can be added together and divided by two in order to produce an average shift along tracks. Again the formula has to be altered, not only to divide the total shift from the forward beams by two, but also to compensate for the angle out from the heading.
In simple practice four beams are used, two angled forwards and two angled rearwards, although only three are strictly necessary because the computer can make the calculations needed. The horizontal angle is typically about 10 deg.
The antenna system usually sends out its beams in a sequence of pairs from right and rear left together, then front left and rear right. The computer can determine the difference in shift, therefore speed, let and right of the heading, and by combining that with the ground speed a drift angle can be calculated. In fact most systems use the difference in shift to turn the aerial itself until there is no difference. The physical angle between the antenna system and the aircraft is the drift angle.
JAMUS BEAM SYSTEM
Characteristics of Airborne Doppler
The accuracy and reliability of the Doppler system depends on the quality of the reflected signals. That in turn depends on the surface which is reflecting the signal. A smooth surface, such as calm water, will reflect poorly, because most of the energy will be reflected away from the receiver. Vertical land features, or a rough surface such as sand with a grain size close to the wavelength of the signal, will reflect well Rolling pasture or swelling water will usually give a good signal.
There are two frequencies in use by commercially available systems. Both of these are, 8.8 GHz and 13.5 GHz, are in the SHF band to allow a narrow beam width and accurate calculations using the formula.
The four beam (Janus) system is regarded as having an accuracy of 0.1% of the true groundspeed, and 0.1 deg of drift. The ICAO standard for doppler systems is to demonstrate an accuracy of 0.5% of both indicated ground speed and indicated drift.
If the aerial is slightly misaligned with the aircraft axis, errors will occur.
If the reflecting surface, the sea, is it sleft moving, the relative speed will not be true ground speed. This is often called 'sea movement error'.
If the aircraft is climbing or descending, the system will detect movements, although the Janus array minimises this.
There is an error called 'sea bias'. On a flat surface, the closest part of these beams will reflect more strongly than the farthest part, because it has a greater depression angle. The calculated ground speed will then be less than true ground speed, because the formula assumed the depression angle of the centre of the beam. A land/sea switch is fitted, which when operated, increases the indicated groundspeed by 1%.
As an extension of sea bias, if the water us flat calm, not enough energy will return. A memory circuit maintains the movement of the indications at the previous rates (deduced reckoning or DR).
The drift can be measured accurately, but if the accuracy drift is applied to an inaccurate compass heading, the inaccuracy will be carried over to the calculated track.
Doppler derived Position
The raw Doppler information would normally be fed to a navigation computer to calculate the aircraft's position by adding drift and ground speed to a previously know position. As we have seen , ground speed errors are in the order of 0.1%, so along track errors are small.
However, compass system errors, or more commonly errors in actually flying the required heading, generate a much larger cumulative cross-track errors, even though the drift errors are small. the system errors in a Doppler derived position is accepted as being 1% of the total distance flown, and 1 deg of drift.