## 1. Introduction

The background of this research is the multi-death crash of Concorde Air France in 2000, which was caused by a piece of debris on the taxiway and evinces the need to detect Foreign Object Debris (FOD) on runways. FODs may lacerate aircraft tires or wear engines [

1] during taking off and landing. According to statistics from Insight SRIT, the authoritative analysis company in UK, over 66% of airport emergencies are related to FOD [

2]. It has become the second most common threat to aviation security after bird hit.

The International Civil Aviation Organization stipulates explicitly that at least four-time inspections per day must be ensured to the runway. While manual inspection can only guarantee safety for 1% of the flights, the automated FOD detection systems could provide nearly 100% effective inspections for all flights [

3].

In existing systems [

4,

5,

6,

7], the radar and Electro-Optical (EO) hybrid devices are most commonly utilized. But EO sensors will be greatly weakened in inclement weathers [

8,

9]. In comparison, radars can provide all-time and all-weather inspection to runways [

10]. Wide band millimeter-wave radars have high enough resolutions to detect small pieces of metal, stones, concrete or even plastics on runways. For instance, COBRBA-220 [

11], the ultra-wide-band system, could reach a resolution of 1.8 cm. The 77 GHz FOD detection radar [

12] developed under the cooperation between Japan and France showed signal attenuation less than 0.18 dB as well as high sensitivity to −20 dBsm objects. In recent years, performances of some other radars working around 70 GHz [

13], 76.5 GHz [

14], 78 GHz [

15,

16], 96 GHz [

17], even 110 GHz [

18] have been successively validated by test data in controlled conditions (e.g., wave form, polarization, and antenna gain).

Although stationary FOD detections have been well developed by Constant False Alarm Rate (CFAR) algorithms [

19,

20,

21,

22], the radar-based FOD surveillance is still challenged by finding debris in different motion states (e.g., rolling small screws, wind-driven plastic bags [

23,

24] and invading wildlife [

1] (p. 1), especially in clutter conditions [

3].

Space-time Adaptive Processing (STAP) [

25,

26] has been maturely utilized in Synthetic Aperture Radar (SAR) to suppress ground clutter and indicate motive targets [

27]. The same technique can potentially be utilized to design space-time filters to detect motive FOD in strong clutter, if exact clutter covariance estimation is obtained. STAP requires that the number of training samples [

28] must have more than double Degrees of Freedom (DOFs) and be Independent Identically Distributed (IID) with the detected samples. However, these requirements are rarely satisfied in practice, which makes the STAP performance limited [

29].

A series of methods have been proposed to release the IID constraint, and thus to accelerate computation and convergence. The most representative and widely used are the reduced-dimension and the reduced-rank STAPs [

30,

31,

32], which operate on the basis of matrix transformations. The Sparse-Recovery (SR) STAP technique [

33,

34] has attracted great attention because it can reduce computation significantly in the case of insufficient training samples by making utilization of clutter sparsity in the space-time plane. By employing environment knowledge, Knowledge Aided- (KA-) STAPs are proposed with significant superiority, prominent value, and wide prospect to radar intellectualization. By utilizing prior information in algorithms directly, Bayesian filtering [

35,

36] and data pre-whitening STAPs [

37,

38] are investigated but the performance is influenced by the mismatch between prior knowledge and time-varying environment. Some other ideas have concerned environment sensing for intelligent sample selection [

39,

40] to analyze rather than estimate the clutter covariance by samples. But these STAPs demand exact backscattering coefficients and high resolution cells, with the support of real scene topography [

41,

42], digital elevation model data [

43], hyper-spectral remote sensing images [

44] and so on.

Based on the above analysis, we propose a clutter-analysis-based STAP for motive FOD detection in a familiar environment, which decouple from IID training samples to estimate clutter covariance. The prior knowledge could be easily obtained from the SAR observations, the high-resolution visible spectrum images, or the airport construction drawings [

45] (pp. 4–7).

The rest of this paper is organized as follows: in

Section 2, the radar coverage is divided into scattering cells based on the geometric model in

xOy coordinates. In

Section 3, the space-time clutter is deduced and addressed according to the parameter-modified scattering model.

Section 4 concerns the filter design in the space-time domain. Experiments and discussions are overviewed in

Section 5 that support the conclusions drawn in

Section 6.

## 4. Clutter-Analysis-Based STAP

Clutter is required to be suppressed in the space-time domain by effective filtering. Traditional STAPs perform well under homogeneous clutter background by estimating clutter covariance from real echo directly. Notice that clutter echo from some range gates, which contains only one isotropic scattering surface (as

Figure 2 depicts), is considered homogeneous, thus enough IID training samples could be gathered. Scattering cell division is not required considering the increasing computation. As for those range gates involving both lawn and concrete runways, we utilize the presented STAP to achieve exact

${\widehat{\mathbf{R}}}_{\mathbf{c}}$ for effective filter weight solution, considering the limited performance of some previous methods. Two approaches could be selected according to practical clutter cases, combining the characteristics and advantages of them.

According to all discussion above, the flow chart shows the processing steps involving the proposed STAP as well as traditional method for FOD detection:

See

Figure 6, the clutter properties (homogeneous or not) could be known according to the corresponding range gates. To the homogeneous clutter echo, generated by lawn surface only, we employ traditional STAPs to estimate clutter covariance matrix from real IID samples directly (indicated by the green blocks in the flow diagram). Aided by the scene knowledge and a parameter-modified scattering model, we utilize the clutter-estimation-based STAP for effective suppression to the non-homogeneous clutter at those range gates involving runways and lawns, through scene-knowledge-aided division of scattering cells in

xOy coordinates, transformation to polar coordinates (illustrated by pink), back-scattering coefficient acquirement based on the known grazing angles, and clutter echo deduction with the antenna pattern

G, and

${\widehat{\mathbf{R}}}_{\mathbf{c}}$ estimation, as depicted by the blue blocks. Note that the dotted arrow in the figure implies the proposed STAP is real-clutter-decoupling.

Before solving the filter weight, the space-time coupled echoes of FOD items are first deduced. For general analysis, we consider all possible targets as one or more scattering points. Taking a point target moving at

${v}_{FOD}$ in radial direction in the cell at

$\left({x}_{t},{y}_{t}\right)$ as the example, the space frequency and Doppler are written as

${\mathbf{v}}_{\mathrm{st}}$ and

${\mathbf{v}}_{\mathrm{dt}}$ in space and time domains are expressed as [

49]

Thus, the target echo is as the following equation shows [

49]

in the condition that the scattering intensity

${\xi}_{t}$ and the amplitude

${\rho}_{t}$ satisfies

${\rho}_{t}=\sqrt{{\xi}_{t}}$. The optimal weight vector obeying Linearly Constrained Minimum Variance (LCMV) is:

which is known as the Wiener solution where

$\mu $ =

${({\mathbf{v}}_{\mathrm{t}}{}^{\mathbf{H}}{\mathbf{R}}_{\mathbf{x}}{}^{-1}{\mathbf{v}}_{\mathrm{t}})}^{-1}$ [

50].

${\mathbf{R}}_{\mathbf{x}}{}^{\prime}={\mathbf{R}}_{\mathbf{x}}-{\mathbf{R}}_{\mathbf{s}}$ is preferable than

${\mathbf{R}}_{\mathbf{x}}$ in practice to avoid signal cancellation [

49] (pp. 22,23). Thus, the target Doppler and azimuth are both acquired according to

$\widehat{{\mathbf{w}}_{opt}=}\mu {({\mathbf{R}}_{\mathbf{s}}+{\widehat{\mathbf{R}}}_{\mathbf{c}}+{\mathbf{R}}_{\mathbf{n}})}^{-1}({\mathbf{v}}_{\mathrm{st}}\otimes {\mathbf{v}}_{\mathrm{dt}})$.

## 6. Conclusions

STAP methods for moving FOD detection deserves more attention for many compelling advantages such as lower cost, more flexibility and higher resolution. However, the performance of the conventional statistical STAP meets great degradation under nonhomogeneous samples or environment. This paper proposed a clutter-analysis-based Space-time Adaptive Processing (STAP) method in order to obtain effective clutter suppression and moving FOD indication, under inhomogeneous clutter background. We first divided the radar coverage into equal scattering cells in the rectangular coordinates system rather than the polar ones. We then measured normalized RCSs within the X-band and employed the acquired results to modify the parameters of traditional models. Finally, we described the clutter expressions as responses of the scattering cells in the space and time domain to obtain the theoretical clutter covariance. Experimental results at 10 GHz indicated that FODs with a reflection higher than −30 dBsm could be effectively detected by a LCMV filter in azimuth when the noise was −60 dBm. It was also validated to indicate a −40 dBsm target in Doppler. The approach could obtain effective clutter suppression 60 dB deeper than the training-sample-coupled STAP under the same conditions.

Nevertheless, key problems confronted in real-world applications are presented for this STAP technique, which include false alarm effect, influence of spatial errors, and huge computational cost with exact cell division. Moreover, we also plan to investigate its performance under non-ideal conditions such as the presence of SAR yaw, steering vector mismatch, and complex terrains. Therefore, it is of great value to develop robust algorithms. We also realize that thinner item detection disturbed by strong interferences is the most difficult task in meeting practical demands. Future work will include testing on an airport runway to measure practicability and accuracy.