CLC number: TB52

On-line Access: 2014-01-27

Received: 2013-08-07

Revision Accepted: 2013-11-20

Crosschecked: 2014-01-14

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Lin-wei Tao, Ying-min Wang. Target localization based on joint measurement of amplitude and frequency in a LOFAR field[J]. Journal of Zhejiang University Science A, 2014, 15(2): 130-137.

@article{title="Target localization based on joint measurement of amplitude and frequency in a LOFAR field",

author="Lin-wei Tao, Ying-min Wang",

journal="Journal of Zhejiang University Science A",

volume="15",

number="2",

pages="130-137",

year="2014",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.A1300263"

}

%0 Journal Article

%T Target localization based on joint measurement of amplitude and frequency in a LOFAR field

%A Lin-wei Tao

%A Ying-min Wang

%J Journal of Zhejiang University SCIENCE A

%V 15

%N 2

%P 130-137

%@ 1673-565X

%D 2014

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.A1300263

TY - JOUR

T1 - Target localization based on joint measurement of amplitude and frequency in a LOFAR field

A1 - Lin-wei Tao

A1 - Ying-min Wang

J0 - Journal of Zhejiang University Science A

VL - 15

IS - 2

SP - 130

EP - 137

%@ 1673-565X

Y1 - 2014

PB - Zhejiang University Press & Springer

ER -

DOI - 10.1631/jzus.A1300263

**Abstract: **To estimate the motion parameters of a moving target before its passing by the closest point of approach (CPA) point in a low frequency analyzing and recording (LOFAR) field, an error-free theoretical method based on the joint measurement of target radiated noise’s amplitude and frequency was presented. First, the error-free theoretical equations for target characteristic frequency, absolute velocity, the CPA, and amplitude of the radiation noise were derived by three equal interval measured values of the target amplitude and frequency. Then, the method to improve the calculation accuracy was given. Finally, the simulation and experiments were conducted in the air and showed the correctness of this method. By using one single piece of LOFAR, this method can calculate four target parameters and the relative error of each estimated parameter is less than 10%.

**
**

1. Introduction

Methods with single pieces of LOFAR for target parameter estimation are as follows. The classical algorithm for LOFAR, namely algorithm of Doppler-closest point of approach (CPA) was proposed in (Tao

Target localization with joint multiple LOFAR is another active direction, such as the classical LOFAR FIX (LOFIX) principle and analysis of localization accuracy in (Hu et al.,

This paper focuses on using a single piece of LOFAR. The radiated noise’s amplitude of the target at any time (not restricted to passing by the CPA necessarily) is collected by three types of equal intervals. The error-free calculation formulas for the four types of status information consisted of absolute velocity of the target, characteristic frequency of the target, the closest distance, and the absolute amplitude, are then derived.

2. Measurement model

By the Doppler shift equation, the line-spectrum frequency of the detected target by using LOFAR is (Tao and Wang,

Regarding the target as a point source, according to the spherical wave theory of sound propagation, the transmission loss is

The empirical formula of the low frequency band absorption coefficient which is derived from Liu and Lei (

The absorption coefficient is 0.000279–0.12 in the frequency band of 10–2000 Hz. If the distance is 10 km, the extended loss will be 80 dB, and the maximum absorption loss is 1.2 dB. Therefore, the absorption loss can be ignored when the frequency is in the low band.

Assuming that there are only extended loss and expansion of spherical waves, the amplitude data of the target noise which is received by LOFAR are (Liu and Lei,

The measurement of amplitude is

3. Calculation of the target’s parameters

Substituting Eq. (

Because

The velocity

4. Algorithm improvement

5. Computer simulation

We set the target speed of 5 m/s, characteristic line spectrum of 1000 Hz, radiation sound source level of 134 dB, and the equivalent voltage of 1 m away from the target

LOFAR is located in the origin of the coordinates, and the closest distance

The calculated results of the simulation model and sample data without errors are shown in Table

Because this algorithm is theoretically accurate and error-free, the calculation error depends entirely on the error of the calculation process. Matlab acted as the numerical simulation software due to its high calculation accuracy. In the actual process, the error of each calculated result can reach 10

Actual closest distance (m) | Calculated results |
|||

Frequency (Hz) | Velocity (m/s) | Closest distance (m) | Absolute amplitude (V) | |

100.00 | 999.99 | 5.00 | 100.00 | 501.90 |

1000.00 | 1000.00 | 4.99 | 999.99 | 501.90 |

10000.00 | 1000.00 | 4.99 | 9999.99 | 501.90 |

At present, the detection of the frequency is mainly using an adaptive line spectrum enhancer, which can greatly improve the frequency measurement under the colored noise. Its measurement accuracy can reach 0.1 Hz, which is given by

Eqs. (

Actual closest distance (m) | Calculated results |
|||

Frequency (Hz) | Velocity (m/s) | Closest distance (m) | Absolute amplitude (V) | |

100.00 | 1000.97 (0.10%) | 5.02 (0.40%) | 101.77 (1.77%) | 495.89 (1.22%) |

1000.00 | 998.96 (0.10%) | 5.20 (4.00%) | 970.82 (2.91%) | 483.26 (7.12%) |

10000.00 | 1003.32 (0.33%) | 6.33 (26.60%) | 8505.25 (14.95%) | 590.25 (17.58%) |

As shown in Table

The error increases dramatically at far distance, e.g., in the case of 10000.00 m, the calculated error of the velocity is up to 26.60%. The main reason is that the variation of the target’s frequency and amplitude is reduced with the increasing distance, and the variation is almost the same as that of the amplitude of the noise. Therefore, the calculated error is very large, and may even result in a singular matrix which cannot be calculated.

6. Experiment in the air

In the experiment (Fig.

The experiment content was mainly to change the different distances of the CPA (

Some typical processed results are shown in Fig.

The turning points at the frequency curve indicate the time when the target passed by the CPA point. It can be seen that the change rate of the CPA point is greater when the speed of the vehicle is higher.

There are totally 13 times valid processes in the entire experiment. The frequency and the amplitude of the signal are handled on the computer. The results are shown in Table

Serial No. | Actual distance (m) | Actual frequency (Hz) | Actual velocity (km/h) | Actual amplitude of the signal (V_{RMS}) |
Calculated distance (m) | Calculated frequency (Hz) | Calculated velocity (km/h) | Calculated amplitude (V_{RMS}) |

1 | 7.0 | 1000 | 80 | 15.55 | 7.03 | 1002.98 | 78.04 | 15.54 |

2 | 7.0 | 1000 | 60 | 15.55 | 6.87 | 1001.25 | 62.68 | 15.20 |

3 | 7.0 | 1000 | 40 | 15.55 | 6.95 | 999.50 | 41.91 | 15.98 |

4 | 11.6 | 1000 | 20 | 15.55 | 11.01 | 996.25 | 20.04 | 16.01 |

5 | 11.6 | 1000 | 40 | 15.55 | 11.46 | 1002.05 | 38.13 | 15.67 |

6 | 11.6 | 1000 | 60 | 15.55 | 10.24 | 997.43 | 57.43 | 14.28 |

7 | 11.6 | 1000 | 80 | 15.55 | 11.50 | 1001.24 | 79.29 | 15.64 |

8 | 15.0 | 1000 | 80 | 15.55 | 15.57 | 995.63 | 77.68 | 16.06 |

9 | 15.0 | 1000 | 60 | 15.55 | 16.05 | 1001.45 | 58.36 | 14.90 |

10 | 15.0 | 1000 | 40 | 15.55 | 15.33 | 1002.54 | 38.46 | 15.90 |

11 | 20.0 | 1000 | 60 | 15.55 | 21.98 | 1001.20 | 58.03 | 15.99 |

12 | 20.0 | 1000 | 40 | 15.55 | 18.74 | 999.35 | 39.79 | 16.58 |

13 | 20.0 | 1000 | 80 | 15.55 | 18.38 | 998.59 | 77.22 | 14.04 |

The experiment has achieved good results (Table

According to the analysis of the experiment results, the closest distance has the greatest impact on the calculation error, which is consistent with the results of the computer simulation. The greater the distance is, the larger the calculation error will be. The most accurate estimated parameter is frequency, due to the frequency being stronger in anti-interference ability than other parameters. At the same time, there is no error propagation in the calculation process, when this method is directly used to measure the frequency. The estimation accuracy of velocity is higher than that of the distance and absolute amplitude, because the velocity is directly due to the Doppler frequency shift. The accuracy of the velocity will decrease, if the accuracy of the frequency is lower. The estimation accuracy of the closest distance and the absolute amplitude is the worst one. The distance calculation depends on the change of the frequency. When the distance is far, the relative velocity is reduced, and the change rate of the frequency decreases, which is equal to the reduction of the signal noise ratio (SNR). Therefore, the accuracy of the calculated results is reduced. Moreover, for the amplitude of the signal, the external interference is added directly to the amplitude information, leading to poor estimation accuracy. For example, in the experiment of No. 6, a heavy truck passed by, so some strong broadband interference was introduced in the vicinity of the low frequency band of 300–500 Hz at the time of 0.075 s–0.18 s. The strong interference, shown in Fig.

7. Conclusions

The method does not need to overcome the disadvantages of the previous methods. The calculation is completed without the requirement of the CPA point. It improves the calculation speed and efficiency of the LOFAR, and makes the tactics more flexible. Moreover, it is an error-free method in theory, and has important theoretical significance in the algorithm research of the LOFAR fields.

The simulation and experimental results in air show the validity of the method. Relative error of each estimated parameter is less than 10%. Moreover, this method only uses one single piece of LOFAR, with the accurate estimation of the target distance, speed, frequency, and amplitude at close range. Hence, it has a very good application prospects for many engineering fields, such as road speed measurement, namely using a single microphone to measure the speed of a vehicle and amplitude level of the noise. Further research will focus on the case of how to improve the estimation accuracy of the target parameter over a long distance.

* Project supported by the National Natural Science Foundation of China (No. 51209173)

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