Research Article  Open Access
J.F. Degurse, L. Savy, S. Marcos, J.Ph. Molinié, "Deterministic Aided STAP for Target Detection in Heterogeneous Situations", International Journal of Antennas and Propagation, vol. 2013, Article ID 826935, 10 pages, 2013. https://doi.org/10.1155/2013/826935
Deterministic Aided STAP for Target Detection in Heterogeneous Situations
Abstract
Classical spacetime adaptive processing (STAP) detectors are strongly limited when facing highly heterogeneous environments. Indeed, in this case, representative target free data are no longer available. Single dataset algorithms, such as the MLED algorithm, have proved their efficiency in overcoming this problem by only working on primary data. These methods are based on the APES algorithm which removes the useful signal from the covariance matrix. However, a small part of the clutter signal is also removed from the covariance matrix in this operation. Consequently, a degradation of clutter rejection performance is observed. We propose two algorithms that use deterministic aided STAP to overcome this issue of the single dataset APES method. The results on realistic simulated data and real data show that these methods outperform traditional single dataset methods in detection and in clutter rejection.
1. Introduction
In the context of radar signal processing, the purpose of spacetime adaptive processing (STAP) is to remove ground clutter returns, in order to enhance slow moving target detection. STAP performs twodimensional space and time adaptive filtering where different space channels are combined at different times [1]. Filter’s weights are adaptively computed from training data in the neighborhood of the range cell of interest, called cell under test (CUT). The estimation of these weights is always deducted, more or less directly, from an estimation of the covariance matrix of the received signal, which is the key quantity in the process of adaptation [2]. Any implementation of STAP processing must remain absolutely consistent with the strategy of radar processing whose purpose is to obtain a high probability of detection while keeping a very low probability of false alarm.
Classical spacetime adaptive processing (STAP) detectors are strongly limited when facing a severe nonstationary environment such as heterogeneous clutter. Indeed, in these cases, representative training data are no longer available. The Maximum Likelihood Estimation Detector (MLED) [3] is a single dataset detector among others [4]. It only operates with the data from the cell under test, hence its performance is not impacted by nonstationarity. Of course, no environment is purely heterogeneous or homogeneous and the problem can be addressed by combining primary and secondary data [5]. We will here consider the environment to be heterogeneous enough to only use primary data. To make the primary data targetfree, the MLED detector removes a thin part of the signal of the Doppler cell under test from the covariance matrix. A slight part of the clutter is removed along the target signal which implies a degradation of clutter rejection, especially if the number of Doppler cells is low. The less Doppler cells, the more the clutter removed from the covariance matrix and the worse the estimation of the covariance matrix. The bad estimation of the matrix can be addressed by using subspace methods [6] but the removal of some clutter is inherent to the APES method.
In this paper, we will show how we can overcome this problem by the use of deterministic aided STAP. Moreover, we will extend this method to the StopBand APES which greatly reduces the computational workload of the MLED detector.
Section 2 is devoted to the data model, and Section 3 summarizes the principle of the MLED APESbased detector and the StopBand APES algorithm. A deterministic based nonadaptive approach of spacetime processing is presented in Section 4. In Section 5, we describe two different approaches for deterministic aided STAP and finally, in Section 6, simulations are given to show that the proposed methods outperform the MLED and StopBand algorithms.
2. Data Model
Consider a radar antenna made of sensors that acquires pulse snapshots for each range gate . We will only use the primary data so we will forget the range gate dimension, also called fasttime dimension. Then, the processing algorithm works independently in each range cell. We adopt the following two hypothesis models where and mean that no target or a target is present, respectively: where the received data have been arranged into an matrix with being the number of training data pulse snapshots, being the number of pulses of the spatiotemporal vector, and being the complex amplitude of the target. is the spatiotemporal steering vector (length ), is the temporal steering vector (length ), and is the interference (clutter plus noise) matrix.
We make use of a temporal sliding window to work on the temporal dimension; consequently, the estimated covariance matrix is obtained from as follows: One classical STAP detector taken as reference uses the Adaptive Matched Filter (AMF) [1, 2]. The filter is Detection is achieved by comparing the output SNIR power of the matched filter to a threshold as follows: In case where a strong target is present at this range gate, contains the target covariance matrix. Consequently, the target is removed with the clutter and it can no longer be detected by (4). This happens when many targets are moving at the same speed but are at different distances (roads, highways, convoys, etc.). Another problem with this detector is that the ground clutter has to be homogeneous on the range domain. Otherwise, the clutter used to estimate the covariance matrix will not be representative of the clutter that has to be canceled, leading to a bad clutter rejection.
3. APESBased STAP Detectors
3.1. The Maximum Likelihood Estimation Detector
To overcome the previous issues of signal suppression or the none representativeness of secondary data, the MLED detector [7] based on the APES [8] algorithm removes the signal of interest from the covariance matrix. The problem is stated as follows: The obtained solution is where Detection is achieved using the output power normalized by the Adaptive Power Residue (APR = ) as follows: To avoid strong signal loss due to covariance matrix estimation errors [9], one may use in addition diagonal loading [10] or subspace methods [11].
3.2. Extension to StopBand APES
Because the MLED algorithm is a highresolution method, it requires an oversampling in Doppler frequency, typically by a factor four, to correctly work. Indeed, combining (5) and (6), it follows where is the projector into the target signal subspace: The problem (5) can then be recognized as a minimization of the interferenceplusnoise energy outside the subspace spanned by the target as follows: The solution is still but with the more general form for : This latest formulation not only shows the hyperresolution property along the frequency domain but also allows overcoming one major drawback of the MLED method for our application. The MLED has indeed a highfrequency resolution due to the sharpness of the projection with (dash curve, Figure 1). This is a problem because it requires a strong oversampling to be sure to remove the signal of interest from the covariance matrix and so it leads to an important increase of the computing load. In order to avoid this problem, we propose a new detector called StopBand APES. The minimization is using a projector on an extended subspace around the Doppler frequency under test. For instance, two adjacent halfcells can be added into the space spanned by with The sharpness and effectiveness of the cancellation around the target signal are characterized by the frequency response of the projector, which is, for a signal at frequency (), as follows: Figure 1 shows that building a projector with two adjacent halfcells is enough to correctly remove the signal in the cell under test. Nevertheless, compared to the MLED, the StopBand APES does not require oversampling of the Doppler resolution for the calculation and the application of the STAP filter. A zeropadding by a factor of 2 will still be required to access the signal that has to be evaluated every halfresolution cells for the creation of the projector [12, 13].
3.3. Limitations of the MLED and StopBand APES
In order to explore the use of subspacebased methods, we have to go deeper in the formulation of the MLED detector. Indeed, these methods will only work if the clutter subspace of the covariance matrix remains very close to the clutter subspace of the targetfree covariance matrix . For a given distance cell, if there is no target at this range, the covariance matrix only contains interference, that is, clutter and possibly jamming signal and noise, according to (2) as follows:
We can demonstrate [11] that the matrix is, without approximation:
The matrix is the interferenceplusnoise estimated covariance matrix, whereas is the scalar product of interferenceplusnoise vectors with their projection on . It follows from (16) that the modified covariance matrix used for MLED in (8) does no longer contain the target contribution and that the target will not be removed contrarily to the clutter by the MLED STAP filter (6).
The residual clutterplusnoise covariance matrix is slightly different from the actual covariance matrix (Figure 2). The term represents the part of the clutter that is removed from the covariance matrix. The number of Doppler cells being usually high, the projector is consequently very sharp; that, the term is small and both MLED and StopBand APES, which removes a wider part of the clutter from the covariance matrix , are all working. This effect can be seen on Figure 2 in a situation with and without target in the Doppler cell tested.
However, in a situation where the number of Doppler cells is low, we will observe a degradation of the clutter rejection performance of the MLED detector, and this degradation will be even worse for the StopBand APES algorithm. This effect is due to the partitioning which is done only in time domain. If spatiotemporal partitioning is employed, only a single bin of the angleDoppler plane is removed but the computational cost would hugely increase because of the angleDoppler scanning. We will present in the next section a deterministic processing and, in Section 5, a new method that makes use of deterministic processing to solve this problem.
4. Deterministic SpaceTime Processing
We will here briefly describe a nonadaptive spacetime processing which is the basis of the deterministic aided STAP processing we will introduce in the following section. For a sidemounted antenna, the clutter occupies a onedimension position in the twodimensional Dopplerangle domain. The clutter Doppler frequency is a function of the receiving angle as follows: with being the Doppler frequency of the clutter, being the receiving angle, being the platform speed, and being the wavelength of the radar frequency. Knowing this relation, we can build a filter that will remove all the signal that is in the 1Ddomain driven by (17). The general form of the filter, which will be referred in the following to nonadaptive or deterministic processing, has the same form as AMF in (3) as follows: but with where is the true noise covariance matrix (identity matrix in our case), is the number of mainlobe clutter patches, and is the spacetime steering vector of angle and frequency obtained with (17). In the same formulation of the filter as MLED and StopBand APES in (6), the matrix for each Doppler cell can be written as follows: where the vector is the predicted steering vector of the clutter. In this case, to process one Doppler cell, the steering vector of the Doppler cell under test and the two steering vectors from the adjacent Doppler cells are sufficient to correctly remove the clutter. However, the performance of this nonadaptive approach is very limited in practical situations because of the heterogeneity of the clutter (e.g urban or mountainous areas) and because of antenna/receivers calibration errors which make the real steering vector of the antenna slightly different from the actual steering vector used to build the covariance matrix.
To illustrate this effect, we compare the nonadaptive processing (18) to the classic adaptive processing on two sets of data. The first data are the simulated data that we build using the true spatial steering vector and the second set of data is made of realistic data simulated by a STAP simulator that emulates phases errors on the receiving channels and randomly adds impulsive echoes in the clutter. In both cases, clutter is Gaussian, homogeneous, and set to 40 dB. No target is present in these data. A sidelooking antenna with four uniformly spaced subarrays is used. Aircraft speed is set to ms^{−1}, radar frequency is GHz, and the pulse frequency (PRF) is kHz. The nonadaptive processing is only applied in the positive speed domain, that is to say that the negative speeds show the sum channel. The adaptive processing is applied on all the Doppler (speed) domains.
As we can see from Figures 3 and 4, nonadaptive processing works well on the errorfree simulated data. The cluttertonoise ratio (CNR) is close to 0 dB, like in the adaptive processing as shown on Figure 5, which implies an attenuation of 40 dB. On the realistic simulated data, the nonadaptive processing is not performing well, as it fails to suppress the clutter. Indeed, as we can see on Figure 6, the residual CNR is near 15 dB in the main lobe; the clutter attenuation is limited to 25 dB, implying many false alarms. The full rangeDoppler maps also point out this effect in Figures 7 and 8. From these results, we deduce that we cannot use a nonadaptive spacetime processing in real situations but we may use the deterministic of the clutter Dopplerangle relation together with adaptive processing to achieve better performance.
5. Deterministic Aided STAP
5.1. Deterministic Aided GMTI STAP
In GMTI operation, there are two main concerns about heterogeneous environments: clutter heterogeneity (land relief, urban environments) and highdensity target area (roads, highways). In many cases, few training data are available and the use of single data set methods is a very helpful alternative (see Section 3.1 and Section 3.2). To overcome the problem of these methods pointed out in Section 3.3, we propose a new method that includes some aspects of the nonadaptive processing. We saw in (16) that the term in (7) removes the interest signal (if any) and also a small part of the clutter. The idea here is to try to readd this clutter into the covariance matrix. The covariance matrix is then as follows: where is the projection of on the clutter steering vector as follows: with We can demonstrate that the covariance matrix of (16) can now be written as follows: If the clutter follows the theoretical Dopplerangle relation of (17), then the projection of the signal on the angleDoppler steering vector will be close to the clutter signal that has been removed from the matrix (), and the covariance matrix will be close to Note that we do not need to set an arbitrary clutter power value because the energy of the clutter is included in (cf. (22)).
In the case of StopBand APES, where the signal notch is wider, we use an extended projector as follows: with
5.2. Deterministic Aided STAP Processing for AirtoAir Mode
In airtoair situations, the problem is different. The spectral occupation of the mainlobe clutter is much smaller than that of GMTI, whereas clutter sidelobes are much more powerful and have to be cancelled. Moreover, target density is very low, compared to GMTI. As we do not have access to a Dopplerangle relation of the mainlobe clutter, we propose another approach to readd this clutter which is partially removed in the APESbased methods. In airtoair mode, the mainlobe clutter is pretty homogeneous in the range domain.
We will exploit this property to estimate the matrix on the range gates domain. For each Doppler cell, the covariance matrix is defined by However, the matrix which was equal to in (21) is now estimated as follows for each Doppler cells: with being the vector of the range cell and being the total number of range cells. If the clutter is homogeneous, then we can make the following approximation: This assumption implies that only the homogeneous component of the clutter will be readded in the covariance matrix. The density of the target has to remain low, otherwise useful signal will be nonnegligible in the matrix and SNR of targets will be attenuated. In the case of StopBand APES, (12) becomes with the data of the range cell under test, the data of the range cell , and the total number of range cells.
6. Results
6.1. GMTI Simulations
We test the GMTI deterministic aided STAP described in Section 5.1 on real airborne data. These data were obtained using the ONERA RAMSES radar system [14], which is a 4channel ULA antenna. The aircraft speed is , pulse repetition frequency is , the number of range gates is 300, the number of time taps used to form the spacetime data is , and the total number of time snapshots (radar pulses) is 64. Three targets are present in the scene (see Table 1).

The Dopplerrange of the sum channel (Figure 9) clearly emphasizes the heterogeneous clutter. The next figures present the results for the classical STAP (estimation on 10 range gates with 2 guard cells), MLED STAP, StopBand STAP, and deterministic aided StopBand STAP (estimation on 3 range gates with no guard cells for all processing). No oversampling is used for the STAP processors (although a 2x zeropadding is needed to access the data of the halfresolution Doppler cells in the case of StopBand) except for the MLED detector, which uses a 4xoversampling.
The classical STAP processing fails to correctly remove the heterogeneous clutter (Figure 10). The MLED STAP whose signal notch is very sharp also fails to completely remove the clutter. Due to its property of high resolution, the target Doppler extent is very thin and it is difficult to distinguish the targets on the rangeDoppler map (Figure 11). As predicted, the StopBland STAP processing allows even more clutter to be present as shown in Figure 12, whereas the deterministic aided StopBand (DAStopBand) effectively cancels the clutter (Figure 13). This is done without any attenuation on target 1 which lies in the clutter. Figure 14 points out the increased clutter attenuation of DAStopBand over classical StopBand for range gate number 149, where target 3 is present. Figure 15 shows the superiority of DAStopBand over classical STAP in clutter rejection for range gate 279, an area where the clutter is particularly powerful.
6.2. AirtoAir Simulations
The airtoair deterministic aided STAP (see Section 5.2) is tested on realistic synthetic data simulating an airtoair MTI scenario. A frontlooking AMSARlike antenna [15] is used for the simulations. The aircraft speed is , pulse repetition frequency is kHz, and the number of range gates is 100, corresponding to a physical range of 52.5 km to 59.5 km. The number of time taps used to form of spacetime data is and the total number of time snapshot (radar pulses) is 128. Five targets are present in the scene (see Table 2).

The sum channel (Figure 16) clearly shows that the mainlobe clutter (speeds from 230 to 280 m/s) and the sidelobes clutter occupy a wide part of the rangeDoppler map. Only two targets on the leftupper part of the map are detectable without STAP processing. On Figure 17, we can see that the classical STAP processing successfully removes the homogeneous main lobe clutter and does not removes the heterogeneous sidelobes clutter. Classical StopBand processing cancels almost all the sidelobes clutter but does not suppress all the mainlobe clutter (see Figure 18), whereas DAStopBand (Figure 19) totally removes it.
On Figure 20, the effect on clutter attenuation of the DAStopBand is visible through a comparison with classical StopBand. We can also observe that both types of StopBand processings do not completely remove the sidelobes clutter; this issue can be overcome by using subspacebased algorithms instead of matrix inversion [11].
7. Conclusion
In this paper, we propose two deterministic aided algorithms both based on the APES method. The first algorithm which relies on the deterministic Dopplerangle relation of the clutter is particularly adapted for GMTI detectors. The results on real data show that it outperforms both classical STAP and APESbased algorithms. The second algorithm, which aims to remove the continuous component of the interference, is on the other hand well adapted to airtoair modes. In this case, the continuous interference is the main lobe clutter. On realistic simulated data, it totally cancels the mainlobe clutter, whereas classical STAP and traditional APESbased algorithms fail, causing many false alarms.
Acknowledgment
The authors would like to thank the DGA from the French Ministry of Defense for their support and funding.
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Copyright
Copyright © 2013 J.F. Degurse et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.