Cognitive Radar Detection in Nonstationary Environments and Target Tracking

Target detection and tracking are the most fundamental and important problems in a wide variety of defense and civilian radar systems. In recent years, to cope with complex environments and stealthy targets, the concept of cognitive radars has been proposed to integrate intelligent modules into conventional radar systems. To achieve better performance, cognitive radars are designed to sense, learn from, and adapt to environments. In this dissertation, we introduce cognitive radars for target detection in nonstationary environments and cognitive radar networks for target tracking.For target detection, many algorithms in the literature assume a stationary environment (clutter). However, in practical scenarios, changes in the nonstationary environment can perturb the parameters of the clutter distribution or even alter the clutter distribution family, which can greatly deteriorate the target detection capability. To avoid such potential performance degradation, cognitive radar systems are envisioned which can rapidly recognize the nonstationarity, accurately learn the new characteristics of the environment, and adaptively update the detector. To achieve this cognition, we propose a unifying framework that integrates three functions: (i) change-point detection of clutter distributions by using a data-driven cumulative sum (CUSUM) algorithm and its extended version, (ii) learning/identification of clutter distribution by using kernel density estimation (KDE) methods and similarity measures (iii) adaptive target detection by automatically modifying the likelihood-ratio test and the corresponding detection threshold. We also conduct extensive numerical experiments to show the merits of the proposed method compared to a nonadaptive case, an adaptive matched filter (AMF) method, and the clairvoyant case.For target tracking, with remarkable advances in sensor techniques and deployable platforms, a sensing system has freedom to select a subset of available radars, plan their trajectories, and transmit designed waveforms. Accordingly, we propose a general framework for single target tracking in cognitive networks of radars, including joint consideration of waveform design, path planning, and radar selection. We formulate the tracking procedure using the theories of dynamic graphical models (DGM) and recursive Bayesian state estimation (RBSE). This procedure includes two iterative steps: (i) solving a combinatorial optimization problem to select the optimal subset of radars, waveforms, and locations for the next tracking instant, and (ii) acquiring the recursive Bayesian state estimation to accurately track the target. Further, we use an illustrative example to introduce a specific scenario in 2-D space. Simulation results based on this scenario demonstrate that the proposed framework can accurately track the target under the management of a network of radars

Nonlinear Filtering based on Log-homotopy Particle Flow : Methodological Clarification and Numerical Evaluation

The state estimation of dynamical systems based on measurements is an ubiquitous problem. This is relevant in applications like robotics, industrial manufacturing, computer vision, target tracking etc. Recursive Bayesian methodology can then be used to estimate the hidden states of a dynamical system. The procedure consists of two steps: a process update based on solving the equations modelling the state evolution, and a measurement update in which the prior knowledge about the system is improved based on the measurements. For most real world systems, both the evolution and the measurement models are nonlinear functions of the system states. Additionally, both models can also be perturbed by random noise sources, which could be non-Gaussian in their nature. Unlike linear Gaussian models, there does not exist any optimal estimation scheme for nonlinear/non-Gaussian scenarios. This thesis investigates a particular method for nonlinear and non-Gaussian data assimilation, termed as the log-homotopy based particle flow. Practical filters based on such flows have been known in the literature as Daum Huang filters (DHF), named after the developers. The key concept behind such filters is the gradual inclusion of measurements to counter a major drawback of single step update schemes like the particle filters i.e. namely the degeneracy. This could refer to a situation where the likelihood function has its probability mass well seperated from the prior density, and/or is peaked in comparison. Conventional sampling or grid based techniques do not perform well under such circumstances and in order to achieve a reasonable accuracy, could incur a high processing cost. DHF is a sampling based scheme, which provides a unique way to tackle this challenge thereby lowering the processing cost. This is achieved by dividing the single measurement update step into multiple sub steps, such that particles originating from their prior locations are graduated incrementally until they reach their final locations. The motion is controlled by a differential equation, which is numerically solved to yield the updated states. DH filters, even though not new in the literature, have not been fully explored in the detail yet. They lack the in-depth analysis that the other contemporary filters have gone through. Especially, the implementation details for the DHF are very application specific. In this work, we have pursued four main objectives. The first objective is the exploration of theoretical concepts behind DHF. Secondly, we build an understanding of the existing implementation framework and highlight its potential shortcomings. As a sub task to this, we carry out a detailed study of important factors that affect the performance of a DHF, and suggest possible improvements for each of those factors. The third objective is to use the improved implementation to derive new filtering algorithms. Finally, we have extended the DHF theory and derived new flow equations and filters to cater for more general scenarios. Improvements in the implementation architecture of a standard DHF is one of the key contributions of this thesis. The scope of the applicability of DHF is expanded by combining it with other schemes like the Sequential Markov chain Monte Carlo and the tensor decomposition based solution of the Fokker Planck equation, resulting in the development of new nonlinear filtering algorithms. The standard DHF, using improved implementation and the newly derived algorithms are tested in challenging simulated test scenarios. Detailed analysis have been carried out, together with the comparison against more established filtering schemes. Estimation error and the processing time are used as important performance parameters. We show that our new filtering algorithms exhibit marked performance improvements over the traditional schemes

Space-Time Parameter Estimation in Radar Array Processing

This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance

Space-Time Parameter Estimation in Radar Array Processing

This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance

Signal processing for airborne bistatic radar

The major problem encountered by an airborne bistatic radar is the suppression of bistatic clutter. Unlike clutter echoes for a sidelooking airborne monostatic radar, bistatic clutter echoes are range dependent. Using training data from nearby range gates will result in widening of the clutter notch of STAP (space-time adaptive processing) processor. This will cause target returns from slow relative velocity aircraft to be suppressed or even go undetected. Some means of Doppler compensation for mitigating the clutter range dependency must be carried out. This thesis investigates the nature of the clutter echoes with different radar configurations. A novel Doppler compensation method using Doppler interpolation in the angle-Doppler domain and power correction for a JDL (joint domain localized) processor is proposed. Performing Doppler compensation in the Doppler domain, allows several different Doppler compensations to be carried out at the same time, using separate Doppler bins compensation. When using a JDL processor, a 2-D Fourier transformation is required to transform space-time domain training data into angular-Doppler domain. Performing Doppler compensation in the spacetime domain requires Fourier transformations of the Doppler compensated training data to be carried out for every training range gate. The whole process is then repeated for every range gate under test. On the other hand, Fourier transformations of the training data are required only once for all range gates under test, when using Doppler interpolation. Before carrying out any Doppler compensation, the peak clutter Doppler frequency difference between the training range gate and the range gate under test, needs to be determined. A novel way of calculating the Doppler frequency difference that is robust to error in pre-known parameters is also proposed. Reducing the computational cost of the STAP processor has always been the desire of any reduced dimension processors such as the JDL processor. Two methods of further reducing the computational cost of the JDL processor are proposed. A tuned DFT algorithm allow the size of the clutter sample covariance matrix of the JDL processor to be reduced by a factor proportional to the number of array elements, without losses in processor performance. Using alternate Doppler bins selection allows computational cost reduction, but with performance loss outside the clutter notch region. Different systems parameters are also used to evaluate the performance of the Doppler interpolation process and the JDL processor. Both clutter range and Doppler ambiguity exist in radar systems operating in medium pulse repetitive frequency mode. When suppressing range ambiguous clutter echoes, performing Doppler compensation for the clutter echoes arriving from the nearest ambiguous range alone, appear to be sufficient. Clutter sample covariance matrix is estimated using training data from the range or time or both dimension. Investigations on the number of range and time training data required for the estimation process in both space-time and angular-Doppler domain are carried out. Due to error in the Doppler compensation process, a method of using the minimum amount of range training data is proposed. The number of training data required for different clutter sample covariance matrix sizes is also evaluated. For Doppler interpolation and power correction JDL processor, the number of Doppler bins used can be increased, to reduce the amount of training data required, while maintaining certain desirable processor performance characteristics

COMBAT SYSTEMS Volume 1. Sensor Elements Part I. Sensor Functional Characteristics

This document includes: CHAPTER 1. SIGNATURES, OBSERVABLES, & PROPAGATORS. CHAPTER 2. PROPAGATION OF ELECTROMAGNETIC RADIATION. I. – FUNDAMENTAL EFFECTS. CHAPTER 3. PROPAGATION OF ELECTROMAGNETIC RADIATION. II. – WEATHER EFFECTS. CHAPTER 4. PROPAGATION OF ELECTROMAGNETIC RADIATION. III. – REFRACTIVE EFFECTS. CHAPTER 5. PROPAGATION OF ELECTROMAGNETIC RADIATION IV. – OTHER ATMOSPHERIC AND UNDERWATER EFFECTS. CHAPTER 6. PROPAGATION OF ACOUSTIC RADIATION. CHAPTER 7. NUCLEAR RADIATION: ITS ORIGIN AND PROPAGATION. CHAPTER 8. RADIOMETRY, PHOTOMETRY, & RADIOMETRIC ANALYSIS. CHAPTER 9. SENSOR FUNCTIONS. CHAPTER 10. SEARCH. CHAPTER 11. DETECTION. CHAPTER 12. ESTIMATION. CHAPTER 13. MODULATION AND DEMODULATION. CHAPTER 14. IMAGING AND IMAGE-BASED PERCEPTION. CHAPTER 15. TRACKING. APPENDIX A. UNITS, PHYSICAL CONSTANTS, AND USEFUL CONVERSION FACTORS. APPENDIX B. FINITE DIFFERENCE AND FINITE ELEMENT TECHNIQUES. APPENDIX C. PROBABILITY AND STATISTICS. INDEX TO VOLUME 1. Note by author: Note: Boldface entries in the table of contents are not yet completed

Feature-based object tracking in maritime scenes.

A monitoring of presence, location and activity of various objects on the sea is essential for maritime navigation and collision avoidance. Mariners normally rely on two complementary methods of the monitoring: radar and satellite-based aids and human observation. Though radar aids are relatively accurate at long distances, their capability of detecting small, unmanned or non-metallic craft that generally do not reflect radar waves sufficiently enough, is limited. The mariners, therefore, rely in such cases on visual observations. The visual observation is often facilitated by using cameras overlooking the sea that can also provide intensified infra-red images. These systems or nevertheless merely enhance the image and the burden of the tedious and error-prone monitoring task still rests with the operator. This thesis addresses the drawbacks of both methods by presenting a framework consisting of a set of machine vision algorithms that facilitate the monitoring tasks in maritime environment. The framework detects and tracks objects in a sequence of images captured by a camera mounted either on a board of a vessel or on a static platform over-looking the sea. The detection of objects is independent of their appearance and conditions such as weather and time of the day. The output of the framework consists of locations and motions of all detected objects with respect to a fixed point in the scene. All values are estimated in real-world units, i. e. location is expressed in metres and velocity in knots. The consistency of the estimates is maintained by compensating for spurious effects such as vibration of the camera. In addition, the framework continuously checks for predefined events such as collision threats or area intrusions, raising an alarm when any such event occurs. The development and evaluation of the framework is based on sequences captured under conditions corresponding to a designated application. The independence of the detection and tracking on the appearance of the sceneand objects is confirmed by a final cross-validation of the framework on previously unused sequences. Potential applications of the framework in various areas of maritime environment including navigation, security, surveillance and others are outlined. Limitations to the presented framework are identified and possible solutions suggested. The thesis concludes with suggestions to further directions of the research presented

Advanced signal processing tools for ballistic missile defence and space situational awareness

The research presented in this Thesis deals with signal processing algorithms for the classification of sensitive targets for defence applications and with novel solutions for the detection of space objects. These novel tools include classification algorithms for Ballistic Targets (BTs) from both micro-Doppler (mD) and High Resolution Range Profiles (HRRPs) of a target, and a space-borne Passive Bistatic Radar (PBR) designed for exploiting the advantages guaranteed by the Forward Scattering (FS) configuration for the detection and identification of targets orbiting around the Earth.;Nowadays the challenge of the identification of Ballistic Missile (BM) warheads in a cloud of decoys and debris is essential in order to optimize the use of ammunition resources. In this Thesis, two different and efficient robust frameworks are presented. Both the frameworks exploit in different fashions the effect in the radar return of micro-motions exhibited by the target during its flight.;The first algorithm analyses the radar echo from the target in the time-frequency domain, with the aim to extract the mD information. Specifically, the Cadence Velocity Diagram (CVD) from the received signal is evaluated as mD profile of the target, where the mD components composing the radar echo and their repetition rates are shown.;Different feature extraction approaches are proposed based on the estimation of statistical indices from the 1-Dimensional (1D) Averaged CVD (ACVD), on the evaluation of pseudo-Zerike (pZ) and Krawtchouk (Kr) image moments and on the use of 2-Dimensional (2D) Gabor filter, considering the CVD as 2D image. The reliability of the proposed feature extraction approaches is tested on both simulated and real data, demonstrating the adaptivity of the framework to different radar scenarios and to different amount of available resources.;The real data are realized in laboratory, conducting an experiment for simulating the mD signature of a BT by using scaled replicas of the targets, a robotic manipulator for the micro-motions simulation and a Continuous Waveform (CW) radar for the radar measurements.;The second algorithm is based on the computation of the Inverse Radon Transform (IRT) of the target signature, represented by a HRRP frame acquired within an entire period of the main rotating motion of the target, which are precession for warheads and tumbling for decoys. Following, pZ moments of the resulting transformation are evaluated as final feature vector for the classifier. The features guarantee robustness against the target dimensions and the initial phase and the angular velocity of its motion.;The classification results on simulated data are shown for different polarization of the ElectroMagnetic (EM) radar waveform and for various operational conditions, confirming the the validity of the algorithm.The knowledge of space debris population is of fundamental importance for the safety of both the existing and new space missions. In this Thesis, a low budget solution to detect and possibly track space debris and satellites in Low Earth Orbit (LEO) is proposed.;The concept consists in a space-borne PBR installed on a CubeSaT flying at low altitude and detecting the occultations of radio signals coming from existing satellites flying at higher altitudes. The feasibility of such a PBR system is conducted, with key performance such as metrics the minimumsize of detectable objects, taking into account visibility and frequency constraints on existing radio sources, the receiver size and the compatibility with current CubeSaT's technology.;Different illuminator types and receiver altitudes are considered under the assumption that all illuminators and receivers are on circular orbits. Finally, the designed system can represent a possible solution to the the demand for Ballistic Missile Defence (BMD) systems able to provide early warning and classification and its potential has been assessed also for this purpose.The research presented in this Thesis deals with signal processing algorithms for the classification of sensitive targets for defence applications and with novel solutions for the detection of space objects. These novel tools include classification algorithms for Ballistic Targets (BTs) from both micro-Doppler (mD) and High Resolution Range Profiles (HRRPs) of a target, and a space-borne Passive Bistatic Radar (PBR) designed for exploiting the advantages guaranteed by the Forward Scattering (FS) configuration for the detection and identification of targets orbiting around the Earth.;Nowadays the challenge of the identification of Ballistic Missile (BM) warheads in a cloud of decoys and debris is essential in order to optimize the use of ammunition resources. In this Thesis, two different and efficient robust frameworks are presented. Both the frameworks exploit in different fashions the effect in the radar return of micro-motions exhibited by the target during its flight.;The first algorithm analyses the radar echo from the target in the time-frequency domain, with the aim to extract the mD information. Specifically, the Cadence Velocity Diagram (CVD) from the received signal is evaluated as mD profile of the target, where the mD components composing the radar echo and their repetition rates are shown.;Different feature extraction approaches are proposed based on the estimation of statistical indices from the 1-Dimensional (1D) Averaged CVD (ACVD), on the evaluation of pseudo-Zerike (pZ) and Krawtchouk (Kr) image moments and on the use of 2-Dimensional (2D) Gabor filter, considering the CVD as 2D image. The reliability of the proposed feature extraction approaches is tested on both simulated and real data, demonstrating the adaptivity of the framework to different radar scenarios and to different amount of available resources.;The real data are realized in laboratory, conducting an experiment for simulating the mD signature of a BT by using scaled replicas of the targets, a robotic manipulator for the micro-motions simulation and a Continuous Waveform (CW) radar for the radar measurements.;The second algorithm is based on the computation of the Inverse Radon Transform (IRT) of the target signature, represented by a HRRP frame acquired within an entire period of the main rotating motion of the target, which are precession for warheads and tumbling for decoys. Following, pZ moments of the resulting transformation are evaluated as final feature vector for the classifier. The features guarantee robustness against the target dimensions and the initial phase and the angular velocity of its motion.;The classification results on simulated data are shown for different polarization of the ElectroMagnetic (EM) radar waveform and for various operational conditions, confirming the the validity of the algorithm.The knowledge of space debris population is of fundamental importance for the safety of both the existing and new space missions. In this Thesis, a low budget solution to detect and possibly track space debris and satellites in Low Earth Orbit (LEO) is proposed.;The concept consists in a space-borne PBR installed on a CubeSaT flying at low altitude and detecting the occultations of radio signals coming from existing satellites flying at higher altitudes. The feasibility of such a PBR system is conducted, with key performance such as metrics the minimumsize of detectable objects, taking into account visibility and frequency constraints on existing radio sources, the receiver size and the compatibility with current CubeSaT's technology.;Different illuminator types and receiver altitudes are considered under the assumption that all illuminators and receivers are on circular orbits. Finally, the designed system can represent a possible solution to the the demand for Ballistic Missile Defence (BMD) systems able to provide early warning and classification and its potential has been assessed also for this purpose