# Research on micro-feature extraction algorithm of target based on terahertz radar

- Zhengwu Xu
^{1}Email author, - Jian Tu
^{1}, - Jin Li
^{1}and - Yiming Pi
^{1}

**2013**:77

**DOI: **10.1186/1687-1499-2013-77

© Xu et al.; licensee Springer. 2013

**Received: **4 December 2012

**Accepted: **3 February 2013

**Published: **19 March 2013

## Abstract

Micro-Doppler motion of a target is an important characteristic in high-resolution radar observation. The target feature extraction of micro motion has already been applied to many aspects of radar research. In this article, general model is established for the echo signal of a target with micro-motion. Combination of time-frequency analysis method, a method using Radon transformation to detect the parameters of lines and sinusoidal curves to estimate motion parameters of target is proposed, and the estimation of reflection coefficients of scatterers is completed through nonlinear least squares and CLEAN algorithm. The simulation result shows that this method of Radon transformation has the advantages of high precision and strong anti-noise and can extract the parameters well. The model of echo signal and method of parameter estimation are useful for radar target detection and identification.

### Keywords

Micro-Doppler Time-frequency analysis Feature extraction Radon transformation NLS algorithm## 1. Introduction

Mechanical vibration or rotation of structures in a target may induce frequency modulation on returned signals and generate sidebands about the center frequency of the target’s Doppler frequency [1]. The modulation due to vibrations and rotations is called micro-Doppler phenomenon. Micro-Doppler phenomenon is very common in nature, such as the human heartbeat, vibration, or spin of missile warheads, etc.… while in terahertz band micro-Doppler phenomenon is particularly significant. The micro-Doppler effect enables us to determine the dynamic properties of the target and it offers a new approach for the analysis of target signatures. Micro-Doppler features serve as additional target features that are complementary to those made available by existing methods. The micro-Doppler effect can be used to identify specific types of vehicles, and determine their movement and the speed of their engines.

In this article, considering the micro-motion of target in the terahertz band, the echo model is established [2], time-frequency transformation and Radon transformation are applied to extract the micro characteristic parameters [3–6], Radon transformation is generally used to detect straight, based on Radon transformation, we propose a method using Radon transformation to detect the parameters of lines and sinusoidal curves to estimate the motion parameters of target. And the estimation of reflection coefficient of scatterers is completed through nonlinear least squares (NLS) and the CLEAN algorithm [2, 7]. These are very helpful for radar target detection and identification [8].

## 2. Target echo modeling

*t*or the infinite series of

*t*. Weierstrass quantitative shows that arbitrary radial rule of motion may be a finite polynomial of

*t*approximation

*n*is the number of finite polynomial, micro objectives of the target can be approximated as vibration or rotation movement, its rule of motion is

*A*is the vibration amplitude,

*B*is the frequency of vibration,

*φ*is the initial rotation angle, when

*t*=

*t*, the distance between target and the radar is?

where *σ*_{
i
} is the scattering coefficient of the *i* th scatterer, *f*_{0} is the radar carrier frequency, *c* denotes the speed of light. Here, we only consider the condition of *j* = 1 and *j* = 2.

*j*= 2, and the body of target is doing a uniformly accelerated motion, that is $\sum}_{j=0}^{n}{a}_{j}{t}^{j}={v}_{0}t+a{t}^{2$, then the rule of target’s motion can be approximated as

*λ*denotes radar wavelength, according to the definition of micro-Doppler, the micro-Doppler frequency of target equal to the derivative of phase with respect to time, then the instantaneous frequency of the signal can be expressed as

*f*

_{0}= 340 GHz, sampling frequency

*f*

_{s}= 4096 Hz, sampling points

*N*= 512, and observation time

*t*= 6 s. Assume that there are four scatterers, and

*v*

_{0}= 0.03 m/s

^{2},

*a*= 0.01 m/s

^{2},

*σ*

_{1}= 1,

*σ*

_{2}= 0.9,

*σ*

_{3}= 1,

*σ*

_{4}= 1,

*A*

_{1}=

*B*

_{1}=

*φ*

_{1}= 0,

*A*

_{2}=

*A*

_{4}= 0.1,

*A*

_{4}= 0.2,

*B*

_{2}= 3 rad/s,

*B*

_{3}= 2 rad/s,

*B*

_{4}= 1 rad/s,

*φ*

_{2}=

*φ*

_{3}=

*φ*

_{4}= 0.6 rad.

## 3. Parameter estimation

### 3.1. Micro-feature extraction based on Radon transformation

Previously, we established the echo model of target with micro-motion, and time-frequency transformation of the echoed signal is applied to gain the time-varying micro-Doppler frequency features of target. This section is to estimate the motion parameters of target with micro-motion, namely to extract the curves of target’s motion from the time-varying micro-Doppler frequency image.

We assume that the set of parameters to be estimated is θ = *v*_{0}, *a*, *A*, *B*, *φ*, as the straight line in Figure 1 is only related to parameters (*v*_{0}, *a*), we can divide it into a two-dimensional matrix and three-dimensional matrix to estimate, respectively, which can greatly reduce the calculation. First we will estimate (*v*_{0}, *a*) as shown in Figure 1.

*f*(

*x*,

*y*) is a linear integral in a certain direction. In general, the Radon transformation of

*f*(

*x*,

*y*) is defined as the linear integral of

*f*along a line. In two-dimensional space, Radon transformation can be defined by Equation (8)

where *D* is the entire image plane of *x*–*y*, *f*(*x*, *y*) is the gradation of point (*x*, *y*) in the image, *ρ* is the distance between the origin of coordinates and the line, *θ* is the angle between the line and *x*-axis, *δ* is a unit pulse function.

Radon transformation can be seen as the projection of the image in the *ρ* – *θ* space, of which each point corresponds to a straight line in the image space. And Radon transformation is the integral of the image pixels on each straight line, then each straight line in the image will become a bright spot in the *ρ* – *θ* space, which turn the line detection into detecting highlights in Radon domain.

From Figure 2b, it is easy to determine peaks’ position, which is interpreted by *ρ* and *θ*. After detecting the value of *ρ* and *θ*, we can detect the straight lines on image domain. The result is showed in Figure 2c.

*m*= 45.5,

*c*= 68.2 (

*m*is the slope,

*c*is the intercept), respectively. Taking

*m*= 4

*a*/

*λ*and

*c*= 2

*v*

_{0}/

*λ*into consideration we have ${\stackrel{\u2322}{\mathit{v}}}_{0}=0.03,\stackrel{\u2322}{a}=0.01$. Estimate the parameters of the curve after estimating the parameters of the line. As the linear parameters have been estimated, while all the scatterers of target have the same macro velocity and acceleration, then the amplitude, vibration frequency, initial phase of the curve in the figure only related to parameters

*A*,

*B*,

*φ*. Compensate the phase to correct the curve in the figure to a sinusoidal curve?

There are a few methods for micro-Doppler feature extraction such as *W*–*V* peak detection method [9] and the normalized first moment method [10] that are all based on time-frequency analysis methods. Here, Radon transformation detection method is chosen.

The basic idea of Radon transformation detecting curve is to do a linear integral along a specific path in a plane.

*B*. Now we let

Then the amplitude, frequency, initial phase of the sinusoidal curve in Figure 3 is determined by the three space coordinates *x*, *y*, *z*, respectively.

- 1.
Set the range of

*x*,*y*,*z*, and establish a discrete parameter space. - 2.
Establish a three-dimensional accumulator array

*P*(*X*,*Y*,*Z*), and initialize all elements of*P*(*X*,*Y*,*Z*) to zero. - 3.
Calculate the value of

*p*for each point in the parameter space*x*,*y*,*z*according to Equation (10) at*t*. - 4.
Take over all values of t to calculate the linear integral $\sum}_{t}g\left(t,p\right)$ of the time-varying micro-Doppler frequency image along the curve

*p*(*t*). - 5.
Find the local peak of the accumulator to obtain the spatial coordinate position of (

*X*,*Y*,*Z*).

After Radon transformation, each curve in the time-varying micro-Doppler frequency image will generate a corresponding peak in the parameter domain, the parameters of each scatterer can be estimated by detecting the position of peaks in the parameter domain.

As seen from Figure 4, in the image domain, the scatterers’ echo curve entangled with each other, but in the parameter domain, there are four distinct peaks corresponded to the curves. There may be a certain deviation between the true value and the parameter value extracted from the parameter domain after Radon transformation, in order to improve the accuracy of the estimated parameter, we let the estimated value to be the initial value, and search again with a small step in its nearby space, then the accurate estimated value of the parameter can be obtained.

The coordinates of the parameters corresponded to the four scatterers are (0,0,0), (0.1,3,0.6), (0.2,2,0.6), (0.1,1,0.6), then *A*_{1} = *x*_{1} = 0, *A*_{2} = *x*_{2} = 0.1, *A*_{3} = *x*_{3} = 0.2, *A*_{4} = *x*_{4} = 0.1, *B*_{1} = *y*_{1} = 0, *B*_{2} = *y*_{2} = 3, *B*_{3} = *y*_{3} = 2, *B*_{4} = *y*_{4} = 0, *C*_{1} = *z*_{1} = 0, *C*_{2} = *C*_{3} = *C*_{4} = 0.6. And (0, 0, 0) represents the sinusoidal line with amplitude, frequency, and initial phase are zero, which is equivalent to a straight line.

As can be seen from the above results, the Radon transformation detection method has the advantages of high precision and strong anti-noise. Its detection accuracy is determined by the size of the space grid of the three-dimensional accumulator, if the grid is small, the accuracy will be high, but the computational complexity of the algorithm grows rapidly as well.

*W*–

*V*peak detection method and the normalized first moment method are shown in Figure 6.

From the figure, we can know that in the condition of single scatterer without noise, the three methods can all extract micro-Doppler information very accurately.

*W*–

*V*peak detection method and the normalized first moment method have been unable to accurately estimate the parameters of target micro-Doppler.

*W*–

*V*peak detection method is close to the target micro-Doppler frequency, but still cannot make accurate estimates. While the Radon transformation detection method proposed in the article can maintain high accuracy even in the condition of multiple scatterers with strong noise.

### 3.2. Scattering coefficient estimating based on NLS

*i*th iteration of NLS may be expressed as

*S*

_{i−1}(

*t*) is the residual echo with the echo of (

*i*− 1)th scatterer estimated and removed. For

*i*= 1,

*S*

_{0}(

*t*) =

*S*(

*t*) and

*S*

_{ i }(

*t*;

*θ*) denote the radar echo of

*i*th scatterer. To solve Equation (12), set the derivative of $I\left(\stackrel{\u2322}{\sigma}\right)$ with respect to the parameter $\stackrel{\u2322}{\sigma}$ to zero, i.e.,

*S*

_{ i }*(

*t*;

*θ*) denotes the conjugate of

*S*

_{ i }(

*t*;

*θ*), then the estimation of the reflection coefficient of that scatterer can be given by

where *N* represents the number of scatterers, here, *N* = 4, *σ* represents the real reflection coefficient of the scatterers, $\stackrel{\u2322}{\sigma}$ denotes the estimated value.

From Equations (16) and (17), it can be calculated that the maximum relative error is 1.98%, and the mean quare error is 2.48 × 10^{–4}, this shows that the algorithm can be used to extract the parameters of scattering coefficient well.

**The estimated parameters of all scatterers**

${\stackrel{\u2322}{\mathit{v}}}_{\mathbf{0}}$ | $\stackrel{\u2322}{\mathit{a}}$ | $\stackrel{\u2322}{\mathit{A}}$ | $\stackrel{\u2322}{\mathit{B}}$ | $\stackrel{\u2322}{\phi}$ | $\stackrel{\u2322}{\sigma}$ | |
---|---|---|---|---|---|---|

Scatterer 1 | 0.03 | 0.010 | 0 | 0 | 0 | 1.0180 |

Scatterer 2 | 0.03 | 0.010 | 0.1 | 3 | 0.6 | 0.8822 |

Scatterer 3 | 0.03 | 0.010 | 0.2 | 2 | 0.6 | 1.0174 |

Scatterer 4 | 0.03 | 0.010 | 0.1 | 1 | 0.6 | 1.0070 |

If *j* in Equation (4) is *j* = 1, use the above method to estimate the parameters and establish the detection model of target.

## 4. Conclusion

This article establishes a novel echo model of target with micro-motion to analyze the characteristics of micro motion and investigates methods for motion parameter estimation and micro-Doppler signature extraction from target. Estimation of micro-motion parameters is completed through time-frequency transformation of the echoed signal and Radon transformation in terahertz band, and NLS and the CLEAN algorithm are utilized to estimate the scattering coefficients of each scatterer. This simulation result proves that Radon transformation detection method has high precision and good anti-noise performance which can accurately extract the micro-parameters. By adopting this estimate method, exact parameters are obtained for given signals. Thus, greatly precise the steps of target detection and identification.

## Declarations

### Acknowledgement

This study was supported by the National Natural Science Foundation of China under Projects 61271287 and the Fundamental Research Funds for the Central Universities under Projects ZYGX2012J029.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.