Parametric Estimation Techniques for Space-Time Adaptive Processing with Applications for Airborne Bistatic Radar Systems

This thesis considers parametric scenario based methods for Space-Time Adaptive Processing (STAP) in airborne bistatic radar systems. STAP is a multidimensional filtering technique used to mitigate the influence of interference and noise in a target detector. To be able to perform the mitigation, an accurate estimate is required of the associated space-time covariance matrix to the interference and noise distribution. In an airborne bistatic radar system geometry-induced effects due to the bistatic configuration introduces variations in the angle-Doppler domain over the range dimension. As a consequence of this, clutter observations of such systems may not follow the same distribution over the range dimension. This phenomena may affect the estimator of the space-time covariance matrix.\ua0In this thesis, we study a parametric scenario based approach to alleviate the geometry-induced effects. Thus, the considered framework is based on so called radar scenarios. A radar scenario is a description of the current state of the bistatic configuration, and is thus dependent on a few parameters connected to the two radar platforms which comprise the configuration. The scenario description can via a parametric model be used to represent the geometry-induced effects present in the system. In the first topic of this thesis, an investigation is conducted of the effects on scenario parameter residuals on the performance of a detector. Moreover, two methods are presented which estimate unknown scenario parameters from secondary observations. In the first estimation method, a maximum likelihood estimate is calculated for the scenario parameters using the most recent set of secondary data. In the second estimation method, a density is formed by combination of the likelihood associated with the most recent set of radar observations with a prior density obtained by propagation of previously considered scenario parameter estimates through a dynamical model of the scenario platforms motion over time. From the formed density a maximum a posteriori estimate of the scenario parameters can be derived. Thus, in the second estimation method, the radar scenario is tracked over time. Consequently, in the first topic of the thesis, the sensitivity between scenario parameters and detector performance is evaluated in various aspects, and two methods are investigated to estimate unknown scenario parameters from different radar scenarios.\ua0In the second part of the thesis, the scenario description is used to estimate a space-time covariance matrix and to derive a generalized likelihood ratio test for the airborne bistatic radar configuration. Consequently, for the covariance matrix estimate, the scenario description is used to derive a transformation matrix framework which aims to limit the non-stationary behavior of the secondary data observed by a bistatic radar system. Using the scenario based transformation framework, a set of non-stationary secondary data can be transformed to become more stationarily distributed after the transformation. A transformed set of secondary data can then be used in a conventional estimator to estimate the space-time covariance matrix. Furthermore, as the scenario description provides a representation of the geometry-induced effects in a bistatic configuration, the scenario description can be used to incorporate these effects into the design of a detector. Thus, a generalized likelihood ratio test is derived for an airborne bistatic radar configuration. Moreover, the presented detector is adaptive towards the strength of both the clutter interference and the thermal noise

On Spectral Estimation and Bistatic Clutter Suppression in Radar Systems

Target detection serve as one of the primary objectives in a radar system. From observations, contaminated by receiver thermal noise and interference, the processor needs to determine between target absence or target presence in the current measurements. To enable target detection, the observations are filtered by a series of signal processing algorithms. The algorithms aim to extract information used in subsequent calculations from the observations. In this thesis and the appended papers, we investigate two techniques used for radar signal processing; spectral estimation and space-time adaptive processing.\ua0In this thesis, spectral estimation is considered for signals that can be well represented by a parametric model. The considered problem aims to estimate frequency components and their corresponding amplitudes and damping factors from noisy measurements. In a radar system, the problem of gridless angle-Doppler-range estimation can be formulated in this way. The main contribution of our work includes an investigation of the connection between constraints on rank and matrix structure with the accuracy of the estimates.Space-time adaptive processing is a technique used to mitigate the influence of interference and receiver thermal noise in airborne radar systems. To obtain a proper mitigation, an accurate estimate of the space-time covariance matrix in the currently investigated cell under test is required. Such an estimate is based on secondary data from adjacent range bins to the cell under test. In this work, we consider airborne bistatic radar systems. Such systems obtains non-stationary secondary data due to geometry-induced range variations in the angle-Doppler domain. Thus, the secondary data will not follow the same distribution as the observed snapshot in the cell under test. In this work, we present a method which estimates the space-time covariance matrix based upon a parametric model of the current radar scenario. The parameters defining the scenario are derived as a maximum likelihood estimate using the available secondary data. If used in a detector, this approach approximately corresponds to a generalized likelihood ratio test, as unknowns are replaced with their maximum likelihood estimates based on secondary data

Mitigation of Ground Clutter in Airborne Bistatic Radar Systems

Space-Time Adaptive Processing is a commonly used technique to mitigate ground clutter reflections from an airborne radar system. It estimates a covariance matrix based on spatial and temporal information, and the estimate is thereafter used to suppress the ground clutter. In a side-looking monostatic radar system, the estimate is rather straight forward based on radar observations. However, in this paper, we consider bistatic systems where the power of adaptivity is limited due to nonstationarity of the ground clutter reflections over the range dimension. To overcome this, scenario dependent transformations are commonly used when forming the sample covariance matrix. In this contribution we instead investigate a detector where the clutter covariance matrix is determined from the geometry of the bistatic scenario. Using a Monte-Carlo simulation, we investigate how sensitive the detector is to errors in the assumed geometry, and compare this with state-of-the-art adaptive methods. The results indicates that a good clutter rejection is obtained for errors of order 103 m for assumed transmitter position and 100km/h for assumed transmitter velocity

AN IMPROVED METHOD FOR PARAMETRIC SPECTRAL ESTIMATION

One important class of problems within spectral estimation is when the signal can be well represented by a parametric model. These kind of problems can be found in many applications such as radar, sonar and wireless communication, and has therefore been extensively investigated. The main problem is to estimate frequencies and their corresponding amplitudes and damping factors from noisy measurements. One approach to this problem is to form a matrix of measurements, and then find an approximation to the range space of the matrix, with requirements that the approximation is of low rank and have a Hankel structure. From the approximation, the signal parameters can be extracted. In this work, we investigate three different methods which follows this methodology. The main contribution will be an illustration of how the problem formulation and rank constraint management affects the accuracy of the estimate. Numerical simulations indicates that a method which formulates a single convex envelope of a least squares fit to the measurement matrix and to the rank constraint jointly is more accurate than the other two investigated methods

A Parametric Approach to Space-Time Adaptive Processing in Bistatic Radar Systems

Space-time adaptive processing (STAP) is an important airborne radar technique used to improve target detection in environments of clutter and jammers. Effective STAP implementations are dependent on an accurate estimate of the space-time covariance matrix, which characterizes noise and interference in the radar signal. Inside-looking monostatic radar systems, the estimate based on secondary radar observations is rather straight forward as all the samples in secondary data can be argued to be from a single distribution, and the sample covariance can be used as an estimate of the space-time covariance matrix. However, in many other radar configurations, the vital underlying STAP training assumption that secondary data are identically distributed is violated, which implies that detection performance can be significantly degraded. This article develops a new method that can be used when secondary data do not share a common distribution due to geometry-induced range dependencies. This phenomenon is of particular concern in bistatic radar systems. We propose a model-based approach, where the distribution of noise and clutter for each range bin is parameterized by a set of scenario parameters. Using secondary data, the scenario parameters are estimated by maximizing the likelihood function. Based on the estimated scenario parameters, the STAP covariance estimate is formed for the cell under test. The presented method is compared with other state-of-the-art methods for bistatic radar STAP via numerical simulations. The simulations indicate that the presented method, with a proper initialization, yields an estimate of the STAP covariance matrix that significantly increases the signal-to-interference-plus-noise ratio compared to the other investigated methods

A Parametric Generalized Likelihood Ratio Test for Airborne Bistatic Radar Systems

One of the main objectives of a radar system is to provide target detections. That is, from observations contaminated by receiver noise and interference determine the presence or absence of targets in the current measurements. To enable target detections, the test statistics formed by the processor is dependent on an accurate estimate of the spacetime covariance matrix to characterize the influence of thermal noise and interference on the radar signal. In a side-looking monostatic configuration, the estimate is rather straight forward as the secondary data used in the estimate can be argued to be statistically identical and independently distributed as the observation in the cell under test. However, for many other radar configurations, secondary data may suffer from angleDoppler variations over the range dimension, which introduces a non-stationary behavior in the observations. If used in a detector, such secondary data may cause significantly degraded detection performance. In this work, we propose an approach which incorporates the non-stationarities of the secondary data into the generalized likelihood ratio test. Thus, we propose a scenario and range dependent parametric model of the observed data and formulate an adaptive detector based on the generalized likelihood ratio test. The presented approach is evaluated against other state-of-the-art methods for managing target detections in the presence of non-stationary secondary data in bistatic systems. The simulations indicates that the proposed approach of imposing scenario based structure on the generalized likelihood ratio test significantly contributes to an increased performance of the target detection scheme compared to the other investigated methods

Scenario Tracking for Airborne Bistatic Radar Systems

An effective space-time adaptive processing implementation provides an accurate estimate of the corresponding space-time covariance matrix of the distribution of the interference and the noise. Such an estimate is commonly calculated from secondary observations associated with the most recent coherent processing interval. In this paper, we derive the covariance matrix using a parametric model which depends on a few parameters describing the state of the radar scenario. With this formulation, it is sufficient to estimate the\ua0 scenario parameters to obtain the covariance matrix estimate. The scenario parameters represents the position and velocities of the platforms comprising the airborne bistatic configuration. Moreover, the framework of radar scenarios enables information from previously considered coherent processing intervals to contribute to the covariance matrix estimate. Consequently, as the scenario parameters denotes motion characteristics of a platform, the scenario parameters can be tracked over time by assuming a motion model. Thus, the estimator of this paper uses a combination of the likelihood density of the most recent set of radar observations, together with a dynamical model which enables the propagation of the scenario parameters dynamics through time. Hence, the density of the likelihood and the prior density from the propagation of previous scenario parameter estimates through time is combined to calculate a maximum a posteriori estimate of the scenario parameters. In numerical simulations, the maximum a posteriori estimate is compared with the corresponding scenario parameter estimate considering only a maximum likelihood estimate. The numerical simulations indicates that the maximum a posteriori estimate obtains a scenario parameter estimate which is closer to the true scenario parameters. Moreover, the maximum a posteriori estimate is more robust towards a low number of secondary data comprising the likelihood density compared to the maximum likelihood estimate

Scenario Based Transformations for Compensation of Non-Stationary Radar Clutter

Space-Time Adaptive Processing is an important technique for enhancing detection performance in airborne radar systems. The enhanced performance is obtained by mitigating the influence of interference and noise in the radar observations. To perform the mitigation, an accurate estimate of the corresponding space-time covariance matrix of the interference and noise distribution is required. Usually, such an estimate is obtained from secondary data collected from neighboring range bins around the currently investigated cell-under-test. However, in a bistatic radar configuration, the secondary data suffers from geometry-induced angle-Doppler variations along the range dimension. In such configurations, additional processing to handle the angle-Doppler variations is required to obtain a covariance matrix estimate of high accuracy. In this paper, we derive a transformation matrix framework to compensate for the variations over range in the secondary data. The framework is a combination of an incomplete scenario model and secondary data which are used together to obtain a space-time covariance matrix estimate. Thus, the incomplete scenario model is used to find the unitary transformation matrix which, in a Frobenius norm sense, minimizes the expected clutter response from the incomplete scenario model in each range bin towards the corresponding clutter response in a reference range bin. The unitary property of the transformation preserve the stationary behavior of the thermal noise under the transformation. Using such transformation, a set of non-stationary secondary data can be transformed to become more stationary distributed after the transformation. A sample covariance matrix estimator is applied on the transformed set of secondary data to obtain a space-time covariance matrix estimate. The outlined procedure is denoted as a Scenario Based Transformation (SBT) STAP. In numerical simulations, the SBT algorithm is compared with other state-of-the-art methods for the considered problem. The numerical simulations include evaluations on scenarios with a various degree of mismatch between the model generating observations and the model assumed by the investigated algorithms. The included model misspecifications are intrinsic clutter motion, antenna array calibration residuals and incorrect antenna gain patterns. In case of a model match, the simulations indicated that the SBT method yields an improved performance compared to the other investigated methods. For the simulations including model misspecifications, the results indicates that the level of misspecification influence the performance of the considered methods. For a low level of misspecifications, the SBT approach yields an accurate covariance estimate. However, for large misspecifications, the simulations indicates that a non-parametric approach leads to better results