Phase Approach

8/6/2019 Phase Approach

1/47

objective

To find the range, azimuth and elevationangle of a UUV from a reference platform.


2/47

Point A is assigned as the coordinate origin in the measurement. Assuming at t


3/47

underwater positioning using phasemeasurement

This method conducts positioning via continuous phase measurementbetween a reference signal and the acoustic signal transmitted by the target tothe reference platform. It is named the Positioning-based-on-PHase-Measurement method orPPHM method in short.

Every 2 change in the phase difference between these two signalscorresponds to a one wavelength range increment along the radial directionfrom the targets initial position to its new position.

If a receiver array is used, with at least two hydrophones, the targets bearinginformation can be also calculated by measuring the phases of the outputsignals from each of the array hydrophones.


4/47

certain important features :

The proposed method is based on continuous phase monitoringof acoustic signals.

The PPHM method measures the relative range increment

between the reference platform and the target, instead of thetargets absolute coordinates. The PPHM method can track the trajectory of a moving target

continuously in real-time.


5/47

Assume there is a receiver at Point A and a transmitter at Point B. The distance between Aand B is r0. A sinusoidal signal given is sent out from B to A.where fo is the signalfrequency. The received signal is given at A is given bywhereis the phase delay caused by

ro and c is the velocity of the signals in water.


6/47

The range increment r=AB1 -AB will cause a phase shift (or (t) if the targetsspeed is not constant) in the received signal at A as below:whereany range increment rinduces the phase shift in the received signal. To estimate r , firstly an estimate of thephase shift, , is obtained using a phase detector, and then converted into ras:whereis the number of 2 phase flips in r


7/47

Received signals from B (dash line)and B1 (dot-dash line) with referencesignal ( solid line). Only two periods ofthe signals are shown forrepresentation.


8/47

An UUV (sender) emits an acoustic ping from thebow (front) end or from the stern (rear) end. Thesepings constitute one sending event.

Given is the set-up of the receiver hydrophones. The spacing between the hydrophonesis called as d. The pole of the co-ordinate frame lies at the center of the line joining thetwo points and the polar axis passes through this and is perpendicular to the line


9/47


10/47

range measurement

The received signal contains the acoustic signal from the target andthe noise, as shown belowwhere n(t) is the noise. is recoveredusing a phase detector, then converted into the estimate of the slantrange increment r . The targets new position in terms of range willbe


11/47

Phase AmbiguityConventional phase detectors usually require the inverse tangentcomputation to get . The inverse tangent function is a many-to-one function. All valuesof outside the interval (- , ) will be mapped back into this interval. However, as r

increases, will go beyond (- , ) . The phase obtained from the phase detectorcannot correctly reflect the range increment.Resolving Phase AmbiguityTo resolve it, one straightforward solution is to monitor continuously to detect any jumps bigger than 2. It requires a sufficiently high samplingrate. These jumps are then corrected by adding a factor of 2 to all subsequent terms inthe sequence. This procedure is called phase unwrapping. The unwrapped phase is:wheren is the number of phase jumps.


12/47

Block Diagram for tracking a Moving Target.


13/47

doa measurement

Att=t1, the target signal hits Receiver

A1 and at

t=t2 it hits Receiver

A2. From thegeometry of the receive array shown, the difference in signals arrival times,t=t1-

t2, is related to aswhere 1 and 2 are the phases of the signals receivedat ReceiverA1 andA2 as compared to the reference signal, respectively


14/47

The estimated azimuth angle is obtained as:


15/47

Block Diagram for Azimuth Angle Measurement.


16/47

elevation angle

The same concept can be used to measure the elevationangle . For this purpose, another receiver array with at leasttwo receivers is need. This array should be perpendicular to

the array for azimuth angle measurement


17/47


18/47


19/47

envelope extraction

To remove the negative frequency components , the real-valuedsignals analytic representation is needed. The analyticalrepresentation of the sinusoidal signal s1(t) is written as:The phaseofs1(t) will then be retrieved as:


20/47


21/47

Phase Detection Using Envelope Extraction.


22/47

phase unwrapping

In practice, the phase will be wrapped between and . In a discrete-timesampled data system the received data can expressed asWhen r> > 2, thephase difference can be registered only modulo 2. The technique for phaseunwrapping is to search the phase sequentially for jumps in phase greater than ,the assumption being that the phase changes at a rate slower than radians persample. These jumps are then corrected by adding a factor of 2 to all

subsequent terms in the sequence. If phase n is wrapped and phase n isunwrapped, we have:


23/47

simulation of an amplitude modulated single tone signal withvarying modulating index

Modulating signal: bs = Am * cos(2 * pi * fm * t);Modulated signal: Ac*(1 + a* bs) cos(2 * pi * fc * t);Am = 1; Ac = 10; Modulating Index, a = .5;Carrier Frequency, Fc = 100 Hz;Frequency of modulating signal, Fm = 10Hz.


24/47

Modulating Index, a = .5;Carrier Frequency, Fc = 500 Hz;Frequency of modulating signal, Fm = 10Hz.


25/47



26/47



27/47

observations

On increasing modulating index (< 1), size of envelopes inthe extraction increases ie energy inside envelopeincreases.

On increasing carrier frequency, oscillations within oneperiod of any envelope increases which makes envelopes

smoother. When modulating index is greater than 1, both envelopes

crosses each other at their zero crossings, which led tophase reversal of modulating signal at those points.


28/47

simulation of an fm signal with a single tone sinusoidal modulatingsignal.

RED: FREQUENCY MODULATED SIGNAL BLUE: MODULATING SIGNALCarrier Frequency = 1000HzFrequency of modulating signal = 50HzKf = 0.1; Am = 10


29/47

Frequency Spectrum of the earlier modulated signal.Bandwidth : 1100 Hz


30/47

noise : gaussian random process

The Autocorrelation function The time axis is not adjusted according to the timereference. But we can see its qualitative nature.


31/47


32/47

noise, z = x2 + y2, where x and y are gaussian distributed real-valued randomvariables with unit variance and zero mean.

The probability distribution function of the above distribution.


33/47


34/47



35/47



36/47

Modulating Index, a = 1.2;Carrier Frequency, Fc = 500 Hz;Frequency of modulating signal, Fm = 10Hz.


37/47

Modulating Index, a = 2;Carrier Frequency, Fc = 500 Hz;Frequency of modulating signal, Fm = 10Hz.


38/47


39/47

under-modulated signal


40/47

envelope detectors output of under-modulatedsignal


41/47

fm signal


42/47

distorted message signal after envelope detection


43/47

in the plot, the snr is infinite. the sampling rate used is 1000 and the center frequencyof the signal is 200. i have used three different delays (delay = 2, 4, 8). the plots ofthese delays are shown.

The arrows at the intersections is to show the ambiguity as increases. In short, while the resolution increases with , sodoes the ambiguity.


44/47

now, if we look at the phase and frequency output for the same signalwith a snr of 2db over the full bandwidth, following are the results


45/47

frequency


46/47

some interesting features arise when the frequency we are trying tomeasure is related to the angles pi/4, pi/2, pi etc. because forvarious can give us a number that is either close to or exactly pi, 2pi,

0 etc. the issue with a number close to 0 or 2pi is the fact that themeasured phase will jump between 0 and 2pi with noise. this will alsoruin our frequency measurement.


47/47

In the above two figures, the SNR is still 2dB but the frequency is now 240. The angular frequencyfor f = 240 is (240*2pi/1000). For delay of 4, 2pi. With noise, this value of will jump rapidlybetween 0 and 2pi as noticed in subplot 2 above. Also, for delay of 8, 4pi. Again, this value willjump between 0 and 2pi as shown in subplot 3 above. If you look at the frequency output now, it isquite noisy. A way to alleviate this problem is to unwrap the phase measurements

Documents

Phase Approach