High Accuracy Time of Flight Measurement Using Digital Signal Processing Techniques for Subsea Applications

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iers followed by low pass filters introduces some delay.

Different digital signal processing algorithms have al-

ready been reported, which eliminate the delay [6].

The Hilbert Transform technique has been used in this

paper and the steps needed are as follows:

1) Obtained the Fourier transf orm of the sampled echo

using a complex FFTutility,

2) Set all negative frequency components to zero and

double the positive frequency components

3) Magnitude of the inverse FFT yields the envelope.

The function “x(k)” of the basic digital signal process-

ing algorithms are:

1

L1 norm: N

i

kekir

i (6)

2

1

L2 norm: N

i

kekiri

(7)

1

Correlation: N

i

kekir

i (8)

The delay value (T0) where the greatest similarity be-

tween the reference and delayed echo signal is found

corresponds to the index “K0” which makes “x(k)” mini-

mum in Equations (6)-(7) and maximum in (8).

3. Simulation Results for the Basic

Algorithms

The simulation is done using 6-KHz underwater acoustic

transducer that acts both as a transmitter and receiver,

converting an electrical signal into an acoustical one and

vice versa. Signals received from the transducer are fil-

tered by a bandpass amplifier whose centre frequency is

synchronous with the transducer operating frequency. The

results of the simulations are shown a nd di scussed bel o w.

3.1. Results of Correlation, L1 Norm and

L2 Norm

The Figure 2(a) shows the reference signal, the delayed

echo signal and the processed correlation, L1 Norm and

L2 Norm directly without envelope extraction. The de-

layed echo signal is delayed by 88 samples, sampling

rate is 60,000 samples/sec with a phase difference of

2400 (1.1111e–005 sec) which present a T.o.F equal to

0.001477 sec and corresponding distance from the target

is equal to 1.1083 meters. It can be seen that the proc-

essed output which is maximum of the correlation and

minimum of both L1 and L2 Norms show a delay of

87samples. There is an error of one sampling interval

added to phase shift. That is due to the phase difference

of the delayed echo signal with respect to the reference

signal. Actual distance from the target is 1.1083 meters

and that calculated by using DSP algorithms is 1.0875

meters. There is an error of 20.83 mm by processing the

actual echo signals.

The extracted envelopes of the reference and the de-

layed echo signals are shown in Figure 2(b). The lower

three plots are the outputs of the correlation, L1 Norm

and L2 Norm algorithms performed on the extracted en-

velopes. It can be seen that the processed output which is

maximum of the correlation and minimum of both L1

and L2 Norms show a delay of 88 samples.

There is an error of only a phase shift. That is due to the

phase difference of the delayed echo signal with respect to

the reference signal. Actual distance from the target is

1.1083 meters and that calculated by using DSP algori-

thms is 1.100 met ers which gives an error of 8.33 m m .

3.2. Sampling Frequency

The normalized sampling frequency is the ratio of the

sampling rate with respect to the signal frequency. It

presents number of samples taken for each cycle. The

effect of this parameter without envelope extraction is

shown in Figure 3(a). For L1 and L2 algorithms the er-

ror reduces monotonically but non-linearly. In case of

correlation the error reduces linearly and for the meas-

urement using delay of the maximum values of reference

and delayed echo (MVRE) signals the error is non-linear

and do not reduce monotonically.

In Figure 3(b) the simulation is shown with the same

reference and delayed echoes but the processing includes

envelope extraction also. It can be seen that for L1 and

L2 algorithms, the error remains rather constant if the

ratio Fs/F becomes higher. In case of correlation the error

is very high when the ratio Fs/F is less than 3 and it then

reduces for the higher values. For MVRE signal there is

very small variation in the error.

3.3. Noise

The performance of different DSP algorithms is shown in

Figure 4(a) without envelope extraction. L1 and L2

norms show large error at low signal to noise ratio (S/N).

The error due to correlation is almost constant. The

MVRE algorithms show very s mall error and the change

in error is also very small.

The performance of different DSP algorithms is shown

in Figure 4(b) with envelope extraction. L1 norms show

increase in error at higher signal to noise ratio (S/N).

There is a small variation in the error due to correlation

and L2 norm. The MVRE algorithms show very small

error till S/N ratio is less than 0.5 and the error becomes

more than 2.5 meters for less values of S/N ratio.

3.4. Computing Time

It is clear from the Figure 5 shown below that the compu-

tational ti me rises with the increase in number of samples.

The L1 and L2 norm and correlation algorithm require

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