STAP Fondé sur une Modélisation Autorégressive (AR) des Interférences

STAP Fondé sur une Modélisation Autorégressive (AR) des Interférences

Julien Petitjean Eric Grivel 

Thales systèmes aéroportés, Avenue Gustave Eiffel, F-33608 Pessac Cedex

Laboratoire IMS – Département LAPS, UMR 5218 CNRS, IPB ENSEIRB-MATMECA – Université de Bordeaux 1351, cours de la libération, F-33405 Talence

Page: 
203-229
|
DOI: 
https://doi.org/10.3166/TS.28.203-229
Received: 
N/A
|
Accepted: 
N/A
|
Published: 
31 March 2011
| Citation

OPEN ACCESS

Abstract: 

In the STAP domain, modeling the interferences as an autoregressive (AR) process with the detector called Parametric Adaptive Matched Filter (PAMF), provides an estimation of the clutter-rejection filter with few training data. The main difficulty of this approach is the estimation of the AR matrices by using the training data. Thus, we propose an on-line estimation based on the Kalman filter and its variants. A comparative study is carried out and illustrates the relevance of such approaches with data provided by the DGA.

Extended Abstract

The purpose of Radar (RAdio Detection And Ranging) is mainly to detect, to

locate and to track targets. When coherent-pulse radar is used, the target velocity can be also estimated. For surveillance mission, airborne radars are required to provide long-range detection of increasingly smaller targets. Unfortunately, two main problems occur. Firstly, the long-range detection may be difficult due to the decay of the reflected power. Secondly, the jammer, the thermal noise and the clutter which is due to the atmosphere, the rain, the ground or the sea can disturb the return of the slow-moving target.

To address the above problems, adaptive radar, the theory of which was proposed in various papers by Brennan, Mallett and Reed in the 70’s, can be considered. More particularly, when a phased array antenna system is used, space-time adaptive processing (STAP) consists in simultaneously combining the signals which are received by multiple elements of an antenna array and which result from multiple pulse repetition periods of a coherent processing interval. More specifically, STAP aims at maximizing the signal-to-interference-plus-noise ratio (SINR). Then, the filter output is used to define a test statistic that makes it possible to detect whether there is a target or not in the cell under test.

For a few years, several variants have been proposed to both reduce the computational cost, the number of training data and to make the detection more robust against interfering targets. Among them, the so-called “Partially” STAP approaches take into account the characteristics of the received data. When dealing with the subspace techniques, a projection into the interference-free subspace can be done. Another approach consists in modeling the interferences as an multichannel autoregressive (AR) process used with a specific detector called Parametric Adaptive Matched Filter (PAMF). This algrithm provides an estimation of the clutter-rejection filter with few training data. This estimation is also robust against interfering targets and the non-stationarity of the clutter. Nevertheless, the main difficulty of this approach is probably the estimation of the AR matrices by using the training data.

Therefore, in this paper, we propose to study two cases:

Firstly, if the interferences are only composed of a Gaussian clutter, well-known off-line estimation approaches such as the multichannel Yule-Walker, the Maximum Likelihood (ML) estimation or the Nuttall-Strand method can be considered. As an alternative, Kalman filter can be used as it is the minimum mean square error estimator of the AR matrices.

Secondly, if the interferences are composed of thermal noise and Gaussian clutter, the clutter is modeled as a multichannel AR process disturbed by a thermal noise. In that case, we focus our attention on the most disturbing interference, namely the clutter. However, the parameter estimation issue may be a hard task. Off-line noisecompensating algorithms have been proposed by Mahmoudi, Zheng, etc. in other fields than radar processing. In that case, the variance of the additive noise and the parameters are jointly estimated. Nevertheless, Zheng’s method is no longer reliable when the signal-to-noise ratio (SNR) becomes lower than 10 dB. Indeed, it may lead to a set of AR parameter matrix estimates corresponding to an unstable system. Errors-in Variables approaches can be also considered and provide both the variancesof the thermal noise, the AR matrices and the covariance matrix of the driving process. However, the computational cost is high. For the above reasons, we propose to study the relevance of on-line approaches based on Kalman filtering in this paper.In that case, the state space representation of this system comprises two equations,the update equation of which is not linear. To estimate the parameters, we first suggest using the extended Kalman filter. It is based on the 1st order Taylor expansion of the state space representation of the system around the last state vector estimate.Then,we study the Sigma Point Kalman Filters, which include two methods:

1/ the unscented Kalman filter, which is based on the unscented transformation

initially proposed by Julier,

2/ the central difference Kalman filter, which is based on the Stirling interpolation formula to derive another expression for the mean and the covariance matrix estimations of the posterior variable.

Then, a comparative study is carried out and illustrates the relevance of such approaches with eleven sets of real data provided by the DGA. To evaluate the performances of the correlation method, the EKF and the UKF, the SINR is estimated at the output of the PAMF. The PAMF combined with the UKF estimation gives the highest SINR for seven sets of data. In addition, this method requires only four range cells as training data and is quite robust against the non Gaussian assumptions of clutter. In addition, with its square-root form allowing its computational cost to be lower than the standard UKF, its use is relevant for embedded systems.

REMARK. – It is true that other variants of Kalman filtering such as Iterative Kalman filtering, 2nd order extended Kalman filtering and quadrature Kalman filtering could be considered. To reduce the computational cost, the so-called Sigma rho Kalman filter could be used. To relax the Gaussian assumptions, H∞ filter and its variants in the non-linear case such as the extended H∞ filtering or an Unscented H∞ filtering could be studied.

RÉSUMÉ

Dans le cadre du traitement STAP, une modélisation autorégressive (AR) des

interférences utilisée avec un détecteur appelé Parametric Adaptive Matched Filter (PAMF) donne lieu à un filtre de réjection du fouillis pour lequel le domaine d’entraînement est réduit.La principale difficulté de cette approche réside alors dans l’estimation des matrices AR à l’aide des données d’entraînement. Dans cette publication, les auteurs proposent une estimation récursive fondée sur un filtrage de Kalman et ses variantes. Une étude comparative des différentes méthodes est menée sur les données fournies par la DGA – Maîtrise de l’Information.

Keywords: 

multichannel autoregressive process, Parametric Adaptive Matched Filter (PAMF), Kalman filter, extended Kalman filter, sigma point Kalman filter, unscented Kalman filter, central difference Kalman filter.

MOTS-CLÉS

processus autorégressif vectoriel, Parametric Adaptive Matched Filter (PAMF), filtrage de Kalman, filtrage de Kalman étendu, filtrage de Kalman par sigma point, filtrage de Kalman non parfumé, filtrage de Kalman à différence centrale.

1. Introduction
2. Modélisation AR des Interférences, Détecteurs Paramétriques de Cibles Associés et Techniques d’Estimation des Matrices AR
3. Estimations Récursives des Matrices AR
4. Simulations
5. Conclusions et Perspectives
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