Recursive joint Cramér‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

Joint Cramér-Rao lower bound (JCRLB) is very useful for the performance evaluation of joint state and parameter estimation (JSPE) of non-linear systems, in which the current measurement only depends on the current state. However, in reality, the non-linear systems with two-adjacent-states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non-linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross-correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems

THEORETICAL ASPECTS AND REAL ISSUES IN AN INTEGRATED MULTIRADAR SYSTEM

In the last few years Homeland Security (HS) has gained a considerable interest in the research community. From a scientific point of view, it is a difficult task to provide a definition of this research area and to exactly draw up its boundaries. In fact, when we talk about the security and the surveillance, several problems and aspects must be considered. In particular, the following factors play a crucial role and define the complexity level of the considered application field: the number of potential threats can be high and uncertain; the threat detection and identification can be made more complicated by the use of camouflaging techniques; the monitored area is typically wide and it requires a large and heterogeneous sensor network; the surveillance operation is strongly related to the operational scenario, so that it is not possible to define a unique approach to solve the problem [1]. Information Technology (IT) can provide an important support to HS in preventing, detecting and early warning of threats. Even though the link between IT and HS is relatively recent, sensor integration and collaboration is a widely applied technique aimed to aggregate data from multiple sources, to yield timely information on potential threats and to improve the accuracy in monitoring events [2]. A large number of sensors have already been developed to support surveillance operations. Parallel to this technological effort in developing new powerful and dedicated sensors, interest in integrating a set of stand-alone sensors into an integrated multi-sensor system has been increasing. In fact, rather than to develop new sensors to achieve more accurate tracking and surveillance systems, it is more useful to integrate existing stand-alone sensors into a single system in order to obtain performance improvements In this dissertation, a notional integrated multi-sensor system acting in a maritime border control scenario for HS is considered. In general, a border surveillance system is composed of multiple land based and moving platforms carrying different types of sensors [1]. In a typical scenario, described in [1], the integrated system is composed of a land based platform, located on the coast, and an airborne platform moving in front of the coast line. In this dissertation, we handle two different fundamental aspects. In Part I, we focus on a single sensor in the system, i.e. the airborne radar. We analyze the tracking performance of such a kind of sensor in the presence of two different atmospheric problems: the turbulence (in Chapter 1) and the tropospheric refraction (in Chapter 2). In particular, in Chapter 1, the losses in tracking accuracy of a turbulence-ignorant tracking filter (i.e. a filter that does not take into account the effects of the atmospheric turbulences) acting in a turbulent scenario, is quantified. In Chapter 2, we focus our attention on the tropospheric propagation effects on the radar electromagnetic (em) signals and their correction for airborne radar tracking. It is well known that the troposphere is characterized by a refractive index that varies with the altitude and with the local weather. This variability of the refractive index causes an error in the radar measurements. First, a mathematical model to describe and calculate the em radar signal ray path in the troposphere is discussed. Using this mathematical model, the errors due to the tropospheric propagation are evaluated and the corrupted radar measurements are then numerically generated. Second, a tracking algorithm, based on the Kalman Filter, that is able to mitigate the tropospheric errors during the tracking procedure, is proposed. In Part II, we consider the integrated system in its wholeness to investigate a fundamental prerequisite of any data fusion process: the sensor registration process. The problem of sensor registration (also termed, for naval system, the grid-locking problem) arises when a set of data coming from two or more sensors must be combined. This problem involves a coordinate transformation and the reciprocal alignment among the various sensors: streams of data from different sensors must be converted into a common coordinate system (or frame) and aligned before they could be used in a tracking or surveillance system. If not corrected, registration errors can seriously degrade the global system performance by increasing tracking errors and even introducing ghost tracks. A first basic distinction is usually made between relative grid-locking and absolute grid-locking. The relative grid-locking process aligns remote data to local data under the assumption that the local data are bias free and that all biases reside with the remote sensor. The problem is that, actually, also the local sensor is affected by bias. Chapter 3 of this dissertation is dedicated to the solution of the relative grid-locking problem. Two different estimation algorithms are proposed: a linear Least Squares (LS) algorithm and an Expectation-Maximization-based (EM) algorithm. The linear LS algorithm is a simple and fast algorithm, but numerical results have shown that the LS estimator is not efficient for most of the registration bias errors. Such non-efficiency could be caused by the linearization implied by the linear LS algorithm. Then, in order to obtain a more efficient estimation algorithm, an Expectation-Maximization algorithm is derived. In Chapter 4 we generalize our findings to the absolute grid-locking problem. Part III of this dissertation is devoted to a more theoretical aspect of fundamental importance in a lot of practical applications: the estimate of the disturbance covariance matrix. Due to its relevance, in literature it can be found a huge quantity of works on this topic. Recently, a new geometrical concept has been applied to this estimation problem: the Riemann (or intrinsic) geometry. In Chapter 5, we give an overview on the state of the art of the application of the Riemann geometry for the covariance matrix estimation in radar problems. Particular attention is given for the detection problem in additive clutter. Some covariance matrix estimators and a new decision rule based on the Riemann geometry are analyzed and their performance are compared with the classical ones. [1] Sofia Giompapa, “Analysis, modeling, and simulation of an integrated multi-sensor system for maritime border control”, PhD dissertation, University of Pisa, April 2008. [2] H. Chen, F. Y. Wang, and D. Zeng, “Intelligence and security informatics for Homeland Security: information, communication and transportation,” Intelligent Transportation Systems, IEEE Transactions on, vol. 5, no. 4, pp. 329-341, December 2004

Exact Feature Extraction Using Finite Rate of Innovation Principles With an Application to Image Super-Resolution

The accurate registration of multiview images is of central importance in many advanced image processing applications. Image super-resolution, for example, is a typical application where the quality of the super-resolved image is degrading as registration errors increase. Popular registration methods are often based on features extracted from the acquired images. The accuracy of the registration is in this case directly related to the number of extracted features and to the precision at which the features are located: images are best registered when many features are found with a good precision. However, in low-resolution images, only a few features can be extracted and often with a poor precision. By taking a sampling perspective, we propose in this paper new methods for extracting features in low-resolution images in order to develop efficient registration techniques. We consider, in particular, the sampling theory of signals with finite rate of innovation and show that some features of interest for registration can be retrieved perfectly in this framework, thus allowing an exact registration. We also demonstrate through simulations that the sampling model which enables the use of finite rate of innovation principles is well suited for modeling the acquisition of images by a camera. Simulations of image registration and image super-resolution of artificially sampled images are first presented, analyzed and compared to traditional techniques. We finally present favorable experimental results of super-resolution of real images acquired by a digital camera available on the market

Statistical modelling of algorithms for signal processing in systems based on environment perception

One cornerstone for realising automated driving systems is an appropriate handling of uncertainties in the environment perception and situation interpretation. Uncertainties arise due to noisy sensor measurements or the unknown future evolution of a traffic situation. This work contributes to the understanding of these uncertainties by modelling and propagating them with parametric probability distributions

Precision of pose estimation using corner detection.

The aim of this research was to develop a method for recording ground truth with performance comparable to motion capture, in order to produce high-quality outdoor visual odometry datasets. A novel fiducial marker system was developed, featuring a smooth pattern which is used in an optimisation process to produce refined estimates. On average, precision was increased by 27 % compared to traditional fiducial markers. To investigate the limit of the increase in pose estimation precision possible with this method, the marker was modelled as a dense grid of checkerboard corners and the Cramér-Rao lower bound of the corresponding estimator was derived symbolically. This gave a lower bound for the variance of a pose estimated from a given image. The model was validated in simulation and using real images. The distribution of the error for a common checkerboard corner detector was evaluated to determine whether modelling it using independent and identically distributed Gaussian random variables was valid. In a series of experiments where images were collected from a tripod, a robot arm, and a slider-type electric actuator, it was determined that the error is usually normally distributed but its variance depends on the amount of lens blur in the image, and that any amount of motion blur can produce correlated results. Furthermore, in images with little blur (less than approximately one pixel) the estimates are biased, and both the bias and the variance are dependent on the location of the corner within a pixel. In real images, the standard deviation of the noise was around 80 % larger at the pixel edges than at the centre. The intensity noise from the image sensor was also found not to be identically distributed: in one camera, the standard deviation of the intensity noise varied by a factor of approximately four within the region around a checkerboard corner. This research suggests that it is possible to significantly increase fiducial marker pose estimation precision, presents a novel approach for predicting and evaluating pose estimation precision, and highlights sources of error not considered in prior work

A lateral nanoflow assay reveals nanoplastic fluorescence heterogeneity

Colloidal nanoplastics present technological opportunities, environmental concerns, and measurement challenges. To meet these challenges, we develop a lateral nanoflow assay from sample-in to answer-out. Our measurement system integrates complex nanofluidic replicas, super-resolution optical microscopy, and comprehensive statistical analyses to measure polystyrene nanoparticles that sorb and carry hydrophobic fluorophores. An elegant scaling of surface forces within our silicone devices hydrodynamically automates the advection and dominates the diffusion of the nanoparticles. Through steric interaction with the replica structure, the particle size distribution reciprocally probes the unknown limits of replica function. Multiple innovations in the integration and calibration of device and microscope improve the accuracy of identifying single nanoparticles and quantifying their diameters and fluorescence intensities. A statistical model of the measurement approaches the information limit of the system, discriminates size exclusion from surface adsorption, and reduces nonideal data to return the particle size distribution with nanometer resolution. A Bayesian statistical analysis of the dimensional and optical properties of single nanoparticles reveals their fundamental structure-property relationship. Fluorescence intensity shows a super-volumetric dependence, scaling with nanoparticle diameter to nearly the fourth power and confounding basic concepts of chemical sorption. Distributions of fluorescivity - the product of the number density, absorption cross section, and quantum yield of an ensemble of fluorophores - are ultrabroad and asymmetric, limiting ensemble analysis and dimensional or chemical inference from fluorescence intensity. These results reset expectations for optimizing nanoplastic products, understanding nanoplastic byproducts, and applying nanoplastic standards

Very High Resolution Tomographic SAR Inversion for Urban Infrastructure Monitoring — A Sparse and Nonlinear Tour

The topic of this thesis is very high resolution (VHR) tomographic SAR inversion for urban infrastructure monitoring. To this end, SAR tomography and differential SAR tomography are demonstrated using TerraSAR-X spotlight data for providing 3-D and 4-D (spatial-temporal) maps of an entire high rise city area including layover separation and estimation of deformation of the buildings. A compressive sensing based estimator (SL1MMER) tailored to VHR SAR data is developed for tomographic SAR inversion by exploiting the sparsity of the signal. A systematic performance assessment of the algorithm is performed regarding elevation estimation accuracy, super-resolution and robustness. A generalized time warp method is proposed which enables differential SAR tomography to estimate multi-component nonlinear motion. All developed methods are validated with both simulated and extensive processing of large volumes of real data from TerraSAR-X

Generic Multisensor Integration Strategy and Innovative Error Analysis for Integrated Navigation

A modern multisensor integrated navigation system applied in most of civilian applications typically consists of GNSS (Global Navigation Satellite System) receivers, IMUs (Inertial Measurement Unit), and/or other sensors, e.g., odometers and cameras. With the increasing availabilities of low-cost sensors, more research and development activities aim to build a cost-effective system without sacrificing navigational performance. Three principal contributions of this dissertation are as follows: i) A multisensor kinematic positioning and navigation system built on Linux Operating System (OS) with Real Time Application Interface (RTAI), York University Multisensor Integrated System (YUMIS), was designed and realized to integrate GNSS receivers, IMUs, and cameras. YUMIS sets a good example of a low-cost yet high-performance multisensor inertial navigation system and lays the ground work in a practical and economic way for the personnel training in following academic researches. ii) A generic multisensor integration strategy (GMIS) was proposed, which features a) the core system model is developed upon the kinematics of a rigid body; b) all sensor measurements are taken as raw measurement in Kalman filter without differentiation. The essential competitive advantages of GMIS over the conventional error-state based strategies are: 1) the influences of the IMU measurement noises on the final navigation solutions are effectively mitigated because of the increased measurement redundancy upon the angular rate and acceleration of a rigid body; 2) The state and measurement vectors in the estimator with GMIS can be easily expanded to fuse multiple inertial sensors and all other types of measurements, e.g., delta positions; 3) one can directly perform error analysis upon both raw sensor data (measurement noise analysis) and virtual zero-mean process noise measurements (process noise analysis) through the corresponding measurement residuals of the individual measurements and the process noise measurements. iii) The a posteriori variance component estimation (VCE) was innovatively accomplished as an advanced analytical tool in the extended Kalman Filter employed by the GMIS, which makes possible the error analysis of the raw IMU measurements for the very first time, together with the individual independent components in the process noise vector

Multistatic radar optimization for radar sensor network applications

The design of radar sensor networks (RSN) has undergone great advancements in recent years. In fact, this kind of system is characterized by a high degree of design flexibility due to the multiplicity of radar nodes and data fusion approaches. This thesis focuses on the development and analysis of RSN architectures to optimize target detection and positioning performances. A special focus is placed upon distributed (statistical) multiple-input multipleoutput (MIMO) RSN systems, where spatial diversity could be leveraged to enhance radar target detection capabilities. In the first part of this thesis, the spatial diversity is leveraged in conjunction with cognitive waveform selection and design techniques to quickly adapt to target scene variations in real time. In the second part, we investigate the impact of RSN geometry, particularly the placement of multistatic radar receivers, on target positioning accuracy. We develop a framework based on cognitive waveform selection in conjunction with adaptive receiver placement strategy to cope with time-varying target scattering characteristics and clutter distribution parameters in the dynamic radar scene. The proposed approach yields better target detection performance and positioning accuracy as compared with conventional methods based on static transmission or stationary multistatic radar topology. The third part of this thesis examines joint radar and communication systems coexistence and operation via two possible architectures. In the first one, several communication nodes in a network operate separately in frequency. Each node leverages the multi-look diversity of the distributed system by activating radar processing on multiple received bistatic streams at each node level in addition to the pre-existing monostatic processing. This architecture is based on the fact that the communication signal, such as the Orthogonal Frequency Division Multiplexing (OFDM) waveform, could be well-suited for radar tasks if the proper waveform parameters are chosen so as to simultaneously perform communication and radar tasks. The advantage of using a joint waveform for both applications is a permanent availability of radar and communication functions via a better use of the occupied spectrum inside the same joint hardware platform. We then examine the second main architecture, which is more complex and deals with separate radar and communication entities with a partial or total spectrum sharing constraint. We investigate the optimum placement of radar receivers for better target positioning accuracy while reducing the radar measurement errors by minimizing the interference caused by simultaneous operation of the communication system. Better performance in terms of communication interference handling and suppression at the radar level, were obtained with the proposed placement approach of radar receivers compared to the geometric dilution of precision (GDOP)-only minimization metric