# Knowledge-Aided Multichannel Adaptive SAR/GMTI Processing: Algorithm and Experimental Results

- Di Wu
^{1}Email author, - Daiyin Zhu
^{1}and - Zhaoda Zhu
^{1}

**2010**:164187

https://doi.org/10.1155/2010/164187

© Di Wu et al. 2010

**Received: **30 May 2009

**Accepted: **18 January 2010

**Published: **11 March 2010

## Abstract

The multichannel synthetic aperture radar ground moving target indication (SAR/GMTI) technique is a simplified implementation of space-time adaptive processing (STAP), which has been proved to be feasible in the past decades. However, its detection performance will be degraded in heterogeneous environments due to the rapidly varying clutter characteristics. Knowledge-aided (KA) STAP provides an effective way to deal with the nonstationary problem in real-world clutter environment. Based on the KA STAP methods, this paper proposes a KA algorithm for adaptive SAR/GMTI processing in heterogeneous environments. It reduces sample support by its fast convergence properties and shows robust to non-stationary clutter distribution relative to the traditional adaptive SAR/GMTI scheme. Experimental clutter suppression results are employed to verify the virtue of this algorithm.

## 1. Introduction

Synthetic aperture radar (SAR) is an important sensor that can reconstruct the reflectivity image of the ground stationary scene. Ground moving target indication (GMTI) with SAR has been widely explored for both military and civilian task. Moving target detection in SAR image is a difficulty, because the slowly moving target may be totally submerged among the main-beam clutter in spatial, time, and frequency domain. Space-time adaptive processing (STAP) [1–3] is a leading technology candidate for improving detection performance of airborne and spaceborne radar in strong clutter and interference environments. A simple, but of most practical importance, SAR/STAP scheme is the well-known multichannel along-track interferometric (ATI) SAR which has been widely used in the past decades [4, 5]. It utilizes two or more receiving channels whose baseline lies along the flight direction, SAR images from different channels concerning the same scene are generated, and clutter suppression can be achieved by combining these complex images. Actually, the "combining" mentioned above can be seen as a beamforming process in image domain and the weights should be estimated adaptively from the secondary data due to the unknown characteristics of the interference (considered to be composed of clutter and thermal noise in this paper).

It has been indicated in many literatures (e.g., [6–8]) that STAP performance can be severely degraded in heterogeneous environments. As a simplified STAP, adaptive SAR/GMTI system is confronted with the same problem. Since the adaptive weights depend on two unknown quantities, that is, the clutter-plus-noise ( ) covariance matrix and the target steering vector, the precise estimation of the covariance matrix in heterogeneous environments presents to be a key for the detection tasks.

Knowledge-aided (KA) STAP such as colored loading and data prewhitening techniques has been proposed to mitigate the performance loss due to realistic environments with fast varying clutter characteristics [9–12]. It incorporates a priori knowledge in the traditional local training schemes (estimate the covariance matrix concerning the pixel under test by averaging over the adjacent range pixels) to obtain a more precise estimation of the characteristics of interference. Everything from digital terrain, elevation data, SAR images, even hyperspectral imagery can be exploited as a priori knowledge. It is intuitive to believe that the same KA scheme can also be introduced to the adaptive SAR/GMTI processing in heterogeneous environments.

In this paper, we focus our research on the use of a priori knowledge in SAR/GMTI detection processing. A parametric model of multichannel SAR covariance matrix is investigated at first, which can be employed as the prior form to be incorporated into the local training scheme. Based on that, a KA adaptive SAR/GMTI algorithm is proposed and verified by experimental results to be effective in real-world clutter environment.

The remainder of this paper is organized as follows. Section 2 briefly reviews the fundamental of a multichannel SAR detection processing and analyzes the impact of heterogeneous environments. In Section 3, a priori model of the covariance matrix is formulated, and a KA adaptive SAR/GMTI algorithm is proposed to operate in the real-world clutter environments. In Section 4, experimental clutter suppression results are provided to demonstrate the desirable improvement of the proposed KA method. At last, Section 5 provides a summary and conclusions. All the experimental results shown in this paper are obtained from the measured data collected by a three-channel ATI SAR system.

Vectors are denoted by boldface lowercase letters and matrices by boldface uppercase letters. We use superscripts , *, and , to denote the transpose, conjugate and transpose conjugate operation, respectively. The Frobenius matrix norm is denoted as and the expectation operator as .

## 2. Multichannel SAR/GMTI in Heterogeneous Environments

This section develops a brief review of moving target detection flaw for a multichannel SAR system. The optimal beamforming weight vector maximizing the output signal-to-interference-plus-noise ratio (SINR) and the impact of a non-stationary clutter distribution are investigated. We validate the performance loss due to heterogeneous environments using measured data taken from a three-channel SAR system.

### 2.1. Multichannel SAR/GMTI Detection Architecture

Consider a multichannel SAR system with receiving channels; the returns from each transmitted pulse are received by all the channels and undergo SAR processing to produce images. As we know, Many successful SAR imaging algorithms have been widely used [13], for example, the range-Doppler (RD), chirp scaling (CS), and omega-k algorithm, and so forth. In this paper, the polar format algorithm (PFA) [14, 15] is utilized for the images generation. Thus, for a certain image pixel, there are complex samples from different channels, which are represented by . The beamformer input and weight vector can be represented by the column vectors and , respectively. The well-known optimum weight vector maximizing the output SINR is [16]

where is an arbitrary constant, and and are the clutter-plus-noise ( ) covariance matrix and desired signal steering vector, respectively. In practice, due to the unknown statistics of the interference environment, the covariance matrix associated with a certain pixel is never known a priori. Thus for adaptive processing, it is common to replace with its maximum likelihood estimation (MLE) [1–3]:

In (2), is the sample vector from the range pixel close to the pixel under test which is also called the secondary data. An important assumption for (2) is that the samples are drawn from an independent and identically distributed (i.i.d) Gaussian stochastic process. Substituting (2) into (1) yields the weight vector

The literature commonly refers to the implementation in (3) as sample matrix inversion (SMI). With this weight vector, the beamformer's output can be represented as

After applying the aforementioned steps for every pixel, the weighted map mentioned above is formed for the next CFAR processing.

### 2.2. Performance Loss in Heterogeneous Environments

From (3) we note that since the inverted clutter-plus-noise covariance matrix is employed for weight training, the ability to accurately estimate is decisive to a successful detection. It is clear that real-world ground clutter model will not always observe the i.i.d assumption. Variations in the underlying terrain, the intrinsic clutter motion, and the target-like signals will contribute to stationary violations [6–10]. In SAR system with high resolution, clutter properties change rapidly over image pixels. Such effects lead to covariance matrix estimation errors, adaptive filter mismatch, and consequently, performance loss in GMTI processing.

Parameters of the three-channel ATI SAR system.

Parameter | Value |
---|---|

center frequency | X band |

antenna length | 1 m |

bandwidth | 200 MHz |

PRF | 1250 Hz |

number of pulses | 1024 |

distance between each antenna port phase center | 0.33 m |

platform speed | 110 m/s |

platform altitude | 5.0 km |

distance between antenna phase center and scene center | 24 km |

Given the impact of non-stationary clutter environments above, the traditional adaptive SAR/GMTI scheme based on the covariance matrix estimation in (2) is prone to be erroneous in heterogeneous clutter environments. It is inappropriate to consider a covariance matrix estimation method simply using (2). In the next section, a priori knowledge is introduce to construct the weight vectors, and the knowledge-aided adaptive SAR/GMTI algorithm is proposed to enhance the detection performance in heterogeneous environments.

## 3. Knowledge-Aided Adaptive SAR/GMTI

Knowledge-aided STAP such as colored loading and data prewhitening techniques has been proposed to enhance detection performance in heterogeneous environment [9–12]. It incorporates an initial guess of , let us say , formed via a priori knowledge in the estimation of . According to the theory of Bayesian estimation, the improved estimate is given by a linear combination of and [17]:

A method to choose adaptively so as to maximally whiten the observed interference data is provided in [9]. Recently, new approaches for selecting have been proposed in [11, 12], which enable us to obtain an automatic estimate of directly from the received data set via the principle of minimum mean-squared error (MSE).

Based on these KA STAP techniques, a KA adaptive SAR/GMTI algorithm for multichannel SAR system is proposed in the following discussion, which can be considered as an extension of the KA STAP schemes. However, it is in possession of many particular characteristics and can be conveniently implemented in practical SAR/GMTI processing.

### 3.1. A Priori Form of the Clutter-Plus-Noise Covariance Matrix

As the clutter-plus-noise covariance matrix is central to adaptive beamforming, we begin by building up a priori form of the multichannel SAR covariance matrix that helps motivate the KA SAR/GMTI algorithm.

Because of the two-dimensional high resolution, interference present at a certain image pixel can be seen as clutter echo received from a single clutter patch plus a sampled value of thermal noise. The interference vector received on the multichannel SAR system with *K* receiving elements can be represented by the
vector as

where , , are the complex amplitude, elevation, and azimuth angle concerning the clutter from a certain patch, is the Hadamard product, denotes the ideal clutter spatial steering vector without any modulation, is the angle dependent array error vector, and represents the vector of sampled thermal noise. in the parenthesis represents small unknown random modulations or errors on the clutter signal whose characteristics may vary with angle of arrival, terrain, and so forth, is a vector of ones, and is a zero-mean random vector with typically tiny variance [10, 18].

We now consider the model of covariance matrix for multichannel SAR system, assuming that the clutter and noise vector are uncorrelated:

where is the clutter covariance matrix, is the noise power on each channel and pixel, and is a identity matrix. Now consider with the clutter vector denoted by the first term in (6):

In (8), denotes the clutter power concerning the discussing patch, represents the matrix of ones, , and the results of covariance matrix taper (CMT) theory [2, 19] have been invoked. It is logical to recognize that the clutter covariance matrix is comprised of a deterministic component

and an unknown component

[10]. Thus, we can conclude from (7) and (8) that if the parameters, that is, , , , and , at least the estimates of them, can be obtained a priori, it is not unreasonable to select

as an initial guess of to be incorporated in the estimation of covariance matrix. Hence we concern ourselves with the problem of finding the proper values of those parameters in the following discussion.

For a -channel uniform linear array (ULA) with denoting the distance between each receiving phase center whose baseline lies along the flight direction, the spatial steering vector, as a depiction of the ULA response to a point source with direction of arrival (DoA) , takes the form

where is the radar wavelength. It is obvious that the values of and are totally known before flight, and the DOA for a certain clutter path is also available via reading the records of inertial navigation unit (INU). Thus we can obtain a relative accurate value of clutter steering vector if the values of these parameters are faithful.

denotes the mismatch between different receiving channels, whose value can be derived from the actual array manifold. However, in most cases, we can never know the perfectly accurate array manifold; several measures for exploiting the clutter signal itself to estimate have been proposed [18, 20].

As for the noise power , we can use the designed signal-to-noise ratio (SNR) of a receiver as an approximation or estimate it from the minimum eigenvalue in the eigenspectrum for a receiver test file. Besides, a simple estimation can be applied by averaging the clutter-free region in SAR image.

For estimating the clutter power , one can utilize knowledge source as digital terrain maps, land coverage data, or stationary scene SAR images as reference. Several works have been done for these estimations; for example, paper [9] provides a method by employing digital maps, and [21] focuses the estimation on using SAR images.

Accomplishing the replacement of all the parameters with their obtained values yields the prior form of to be used in the KA covariance matrix estimation as (5). However, the aforementioned value obtaining process for these parameters seems to be an inconvenient work in practical processing because ( ) we may not have any digital maps or SAR images before flight; the terrain information can only be acquired by the SAR images formed in the flight; ( ) the records of INU always present to be not accurate enough and lagging relative to the real values; ( ) since spatial steering vector and the array errors vary with azimuth and elevation, we need to calculate them every time when process a new pixel under test. These problems motivate us to find a simple model of the prior covariance matrix. As we can see in the next part, by reasonable calibrating and compensating the multichannel SAR raw data, the model of a priori clutter covariance matrix is simplified to be a matrix of ones with a scaling scalar tantamount to the local clutter power, based on which a KA adaptive SAR/GMTI algorithm is proposed for operating in real-world environments.

### 3.2. Knowledge-Aided Adaptive SAR/GMTI Algorithm

The first step involves the calibration of array errors. The mismatch between different receiving channels is equalized by exploiting the received data itself. Several methods have been proposed for calibrating various kinds of errors in different domains; (see [22, 23]). In our experiment, we adopt the approach mentioned in [23] to calibrate the array errors in two-dimension frequency domain and the prior form of covariance matrix corresponding to (11) as follows:

where denotes the residual array error vector that can be sorted to the unknown component in (8); hence can be rewritten as

As we know, since the phase lags induced by different along track positions of receiving antenna ports can be recognized as phase response mismatch between different receiving channels varying with DOA, they are also compensated in this step. Thus, the clutter steering vector for each pixel is reformatted to be a vector of ones, followed by the transformed covariance matrix which takes the form

In step 2, the calibrated data for each channel undergo the image formation procedure and correlated maps are obtained for the same scenario.

Step involves the construction of the prior covariance matrix for each pixel. As indicated by (15), this step can be accomplished by estimating the two parameters and . The noise floor can be estimated by choosing the minimum eigenvalue of a sample covariance matrix or averaging over the clutter-free region in SAR images. Both methods have been used for the three-channel SAR system and equivalent results are obtained. Since the receiver noise does not change over pixels, is estimated only once and applied to the entire image.

We consider the situation that no a priori terrain information such as digital maps and locations of man-made features is known before flight; the only knowledge source is the multichannel SAR images. Given the data compensated in the aforementioned steps, we then wish to estimate the clutter voltage of by minimizing the mean-squared error (MSE) as

where denotes the input date after calibration and compensation in step 1. One of the estimated solutions to (16) takes the form

followed by the estimation of clutter power calculated by . In (17), denotes the samples vector after calibration in step 1 and the sample number for this estimation. In order to achieve an estimation of the local clutter power with high fidelity, the samples are drawn from the closest region adjacent to the pixel under test (containing the pixel under test) and is chosen to be small. Considering the present of targets in the sample set disturbing the estimation, the pixels which may comprise target signal should be removed. For doing this, a difference image between two images from different channels is formed, and the image pixels whose power exceeding a predetermined threshold (20 dB above the noise floor) are censored.

After step 1 3, a priori form of covariance matrix has been generated for each pixel. Step is to concern the local training scheme, in which the sample covariance matrix for each pixel is estimated using (2) with the sample vectors chosen from the adjacent range pixels (including several guard cells to avoid the cancellation of moving target itself) around the pixel under test.

Since the prior and sample forms of covariance matrix are available after accomplishing the former steps, a linear combination of them is generated using (5) in step 5. We use the method proposed in [12] to estimate the coefficient as

where denotes the samples vector after calibration in step 1. Hence the beamformer weight vectors for each pixel can be computed as

followed by the formation of the modified map for target detection.

The last step contains CFAR processing, estimation of target's velocity, and target relocation. Many methods have been proposed for the estimation of moving target parameters, such as monopulse [24], adaptive monopulse [24], or maximum likelihood method [25]. Since this paper does not specifically address the problem of parameters estimation, detailed discussion is not provided herein. However, the experimental results of radial velocity estimation and reloaction of moving target using the maximum likelihood method are shown in the next section.

### 3.3. Improvement for Performance Loss

## 4. Experimental Results

*T*1

*T*5) with varied radial velocities show different azimuth displacements in the image, which are marked by the white arrows.

With SAR image generated from each receiving channel, the KA and local training SMI algorithm were applied for clutter suppression, respectively. To achieve a fair comparison, the data were also preprocessed using Ender's 2D calibration algorithm [23] with 1024 receiving pulses before SMI processing. We now examine how the algorithms performed against the real-world clutter environment. We first present the data as plots of output power residue (after adaptive processing) around the 5 control targets versus the range index. In each plot, a control target is at the central range gate and its return essentially extends to about 10–15 right and left adjacent gates. Thus the data from the pixel under test and its adjacent range pixels (guard cells) are not used for covariance matrix estimation when we adaptively process the data. The sample vectors are formed from the data vectors associated with the range cells to the immediate right and left of the right and left guard cells, respectively. We evaluate and plot the output residue in windows ( 100 range pixels) around the range pixels occupied by the 5 control targets.

## 5. Conclusions

An effective method was developed for clutter suppression of a multichannel SAR/GMTI system performs in heterogeneous environment in this paper. It arose from the knowledge-aided STAP schemes and named as KA adaptive SAR/GMTI algorithm. In this algorithm, the prior form of covariance matrix concerning each image pixel is reformed to be a matrix of ones multiplied by the local clutter power plus a identity matrix multiplied by the thermal noise power. The prior form is incorporated in the estimating of the covariance matrix to achieve an accurate estimate relative to the local training scheme. And then, clutter suppression beamforming is applied with the weight vector calculated by the KA covariance matrix. This new algorithm reduces sample support by its fast convergence properties and results in a clutter suppression performance that is more robust to nonstationary clutter distribution relative to the traditional scheme, which has been proved by the experimental clutter suppression results from a three-channel SAR system. These virtues make the algorithm to be an advisable choice for ground slowly moving targets detection in real-world clutter environments.

## Declarations

### Acknowledgments

This work was supported by a Grant from the Aeronautical Science Foundation (no. 20080152004) and the Ph.D. Programs Foundation of Ministry of Education of China (no. 20070280531).

## Authors’ Affiliations

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