Performance Analysis of Bearings-only Tracking Problems for Maneuvering Target and Heterogeneous Sensor Applications

State estimation, i.e. determining the trajectory, of a maneuvering target from noisy measurements collected by a single or multiple passive sensors (e.g. passive sonar and radar) has wide civil and military applications, for example underwater surveillance, air defence, wireless communications, and self-protection of military vehicles. These passive sensors are listening to target emitted signals without emitting signals themselves which give them concealing properties. Tactical scenarios exists where the own position shall not be revealed, e.g. for tracking submarines with passive sonar or tracking an aerial target by means of electro-optic image sensors like infrared sensors. This estimation process is widely known as bearings-only tracking. On the one hand, a challenge is the high degree of nonlinearity in the estimation process caused by the nonlinear relation of angular measurements to the Cartesian state. On the other hand, passive sensors cannot provide direct target location measurements, so bearings-only tracking suffers from poor target trajectory estimation accuracy due to marginal observability from sensor measurements. In order to achieve observability, that means to be able to estimate the complete target state, multiple passive sensor measurements must be fused. The measurements can be recorded spatially distributed by multiple dislocated sensor platforms or temporally distributed by a single, moving sensor platform. Furthermore, an extended case of bearings-only tracking is given if heterogeneous measurements from targets emitting different types of signals, are involved. With this, observability can also be achieved on a single, not necessarily moving platform. In this work, a performance bound for complex motion models, i.e. piecewisely maneuvering targets with unknown maneuver change times, by means of bearings-only measurements from a single, moving sensor platform is derived and an efficient estimator is implemented and analyzed. Furthermore, an observability analysis is carried out for targets emitting acoustic and electromagnetic signals. Here, the different signal propagation velocities can be exploited to ensure observability on a single, not necessarily moving platform. Based on the theoretical performance and observability analyses a distributed fusion system has been realized by means of heterogeneous sensors, which shall detect an event and localize a threat. This is performed by a microphone array to detect sound waves emitted by the threat as well as a radar detector that detects electromagnetic emissions from the threat. Since multiple platforms are involved to provide increased observability and also redundancy against possible breakdowns, a WiFi mobile ad hoc network is used for communications. In order to keep up the network in a breakdown OLSR (optimized link state routing) routing approach is employed

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Kwantowa metrologia z atomami i światłem

The primary objective of this dissertation is to propose methods of generating nonclassical states of matter or light and examine the possibility of using such states in precise measurements of physical quantities. The first part of this objective is realised by using quantum-mechanical formalism with an emphasis on the theory of ultra-cold atomic gases and cavity quantum electrodynamics, and the second part is realised with methods of the theory of estimation with the Fisher information playing the pivotal role. The fusion of these methods is generally known as quantum metrology. In recent years, a lot of theoretical and experimental effort was put in the field of quantum metrology since it not only promises to develop measurement techniques that give better precision than the same measurements performed in a classical framework but also can be used to study the most fundamental aspects of quantum theory, like quantum entanglement. The first method which we consider is based on the mechanism of creating spinsqueezed states known as the one-axis twisting, which can be realised, for instance, in a Bose-Einstein condensate trapped in a double-well potential forming effectively a two-mode system. We show that the spin-squeezed states are just a small family of entangled states that can be generated by one-axis twisting Hamiltonian. This vast family of twisted states includes even the highest entangled state known as the Schrödinger’s cat. We also show how to exploit this quantum resource in a measurement of an unknown parameter with imperfect atomic detectors and when the strength of the interaction between the atoms is not precisely known. The second scheme for creating non-classical states is based on the quantum non-demolition measurement. This method involves an atom passing through an optical cavity which entangles with the photons inside the cavity and a subsequent measurement on the atom that collapses the combined matter-light state to a nonclassical state of light. To take into account photon losses in the cavity, we harness the master equation in Lindblad form. We show how such non-classical states can be extracted from the cavity and used later in a Mach-Zehnder interferometer. Based on the Wigner function, we also explain what features of this kind of states give rise to a high sensitivity of an interferometer. Finally, we show how a system that exhibits chaotic properties can be studied from the metrological perspective with the help of quantum Fisher information. Classical chaotic systems are systems that are highly sensitive to initial conditions. However, quantum systems can never exhibit this type of dynamics since the Schrödinger’s equation is linear. Therefore, one often says about quantum signatures of chaos. First, we show a textbook example of classical chaos, which is a double-rod pendulum, and, subsequently, we show how quantum Fisher information can serve to investigate characteristic time-scales of chaotic systems and the transition from integrable to chaotic dynamics. This could open a new possibility to study the relationship between the classical and quantum chaos.Głównym celem tej dysertacji jest zaproponowanie metod tworzenia kwantowych stanów materii oraz ´swiatła i sprawdzenie mozliwo´sci wykorzystania tych stanów ˙ do precyzyjnych pomiarów wielko´sci fizycznych. Pierwsza cz ˛e´s´c tego celu realizowana jest przy pomocy formalizmu kwantowo-mechanicznego w kontek´scie teorii ultra-zimnych gazów atomowych oraz kwantowej elektrodynamiki we wn ˛ece, natomiast druga cz ˛e´s´c realizowana jest za pomoc ˛a metod teorii estymacji z informacj ˛a Fishera w roli głównej. Poł ˛aczenie powyzszych metod jest znane ogólnie pod poj ˛eciem ˙ kwantowej metrologii. W ostatnich latach wiele teoretycznego i eksperymentalnego wysiłku zostało włozonego w dziedzin ˛e kwantowej metrologii, poniewa ˙ z dzi ˛eki niej ˙ mozliwy b ˛edzie nie tylko rozwój technik pomiarowych daj ˛acych lepsz ˛a precyzj ˛e ni ˙ z˙ te same pomiary wykonane w ramach klasycznej teorii, ale takze mo ˙ ze by´c u ˙ zyta do ˙ badania fundamentalnych aspektów mechaniki kwantowej takich jak spl ˛atanie. Pierwsz ˛a metod ˛a, któr ˛a rozwazamy to mechanizm tworzenia tworzenia stanów ˙ spinowo-´sci´sni ˛etych znany jako one-axis twisting, który moze by´c zastosowany na ˙ przykład w kondensacie Bosego-Einsteina uwi ˛ezionego w podwójnej studni potencjału tworz ˛ac efektywnie kondensat dwu składnikowy. Pokazujemy, ze stany spinowo- ˙ ´sci´sni ˛ete stanowi ˛a tylko mał ˛a rodzin ˛e stanów spl ˛atanych, które mog ˛a by´c wytworzone przez Hamiltonian one-axis twisting. Ta duza rodzina stanów typu ˙ twisted zawiera nawet najbardziej spl ˛atany stan znany jako kot Schroödingera. Pokazujemy równiez jak wykorzysta´c te kwantowe zasoby w pomiarze nieznanego parametru, ˙ wykorzystuj ˛ac nieidealne detektory atomowe oraz w przypadku kiedy oddziaływanie pomi ˛edzy atomami nie jest dokładnie znane. Drugi schemat tworzenia kwantowo-skorelowanych stanów jest oparty na quantum non-demolition measurement. W metodzie tej atom przelatuj ˛acy przez wn ˛ek ˛e optyczn ˛a zostaje spl ˛atany z obecnymi w niej fotonami, a w wyniku pomiaru wykonanego na atomie nast ˛epuje kolaps funkcji falowej ł ˛acznego stanu materii i ´swiatła do nieklasycznego stanu ´swiatła. W celu uwzgl ˛ednienia strat fotonów we wn ˛ece uzywamy równania ˙ master w formie Lindblada. Pokazujemy jak takie nieklasyczne stany mog ˛a zosta´c wydobyte z wn ˛eki oraz uzyte pó ´zniej w interferometrze Macha- ˙ Zehndera. Bazuj ˛ac na funkcji Wignera wyja´sniamy równiez jakie cechy tego rodzaju ˙ stanów przyczyniaj ˛a si ˛e do niezwykle wysokiej czuło´sci interferometru. Na koniec pokazujemy, jak układ wykazuj ˛acy wła´sciwo´sci chaotyczne moze zo- ˙ sta´c badany z perspektywy metrologicznej za pomoc ˛a kwantowej informacji Fishera. Klasyczne układy chaotyczne to układy, które s ˛a bardzo czułe na warunki pocz ˛atkowe. Jednakze, kwantowe uk ˙ łady nie mog ˛a wykazywa´c takiego rodzaju dynamiki, poniewaz równanie Schrödingera jest liniowe w funkcji falowej. Mo ˙ zna jed- ˙ nak mówi´c o tak zwanych kwantowych sygnaturach chaosu. Na pocz ˛atku pokazujemy podr˛ecznikowy przykład klasycznego chaosu, jakim jest podwójne wahadło, a nast ˛epnie pokazujemy jak kwantowa informacja Fishera moze pos ˙ łuzy´c do badania ˙ charakterystycznych skal czasowych układów chaotycznych i przej´scia pomi ˛edzy porz ˛adkiem a chaosem. Takie podej´scie otwiera nowe mozliwo´sci badania zwi ˛azku ˙ pomi ˛edzy kwantowym chaosem a porz ˛adkiem

GLRT-based threshold detection-estimation performance improvement and application to uniform circular antenna arrays

©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder."The problem of estimating the number of independent Gaussian sources and their parameters impinging upon an antenna array is addressed for scenarios that are problematic for standard techniques, namely, under "threshold conditions" (where subspace techniques such as MUSIC experience an abrupt and dramatic performance breakdown). We propose an antenna geometry-invariant method that adopts the generalized-likelihood-ratio test (GLRT) methodology, supported by a maximum-likelihood-ratio lower-bound analysis that allows erroneous solutions ("outliers") to be found and rectified. Detection-estimation performance in both uniform circular and linear antenna arrays is shown to be significantly improved compared with conventional techniques but limited by the performance-breakdown phenomenon that is intrinsic to all such maximum-likelihood (ML) techniques.Yuri I. Abramovich, Nicholas K. Spencer, and Alexei Y. Gorokho

Modeling and Parameter Estimation of Sea Clutter Intensity in Thermal Noise

abstract: A critical problem for airborne, ship board, and land based radars operating in maritime or littoral environments is the detection, identification and tracking of targets against backscattering caused by the roughness of the sea surface. Statistical models, such as the compound K-distribution (CKD), were shown to accurately describe two separate structures of the sea clutter intensity fluctuations. The first structure is the texture that is associated with long sea waves and exhibits long temporal decorrelation period. The second structure is the speckle that accounts for reflections from multiple scatters and exhibits a short temporal decorrelation period from pulse to pulse. Existing methods for estimating the CKD model parameters do not include the thermal noise power, which is critical for real sea clutter processing. Estimation methods that include the noise power are either computationally intensive or require very large data records. This work proposes two new approaches for accurately estimating all three CKD model parameters, including noise power. The first method integrates, in an iterative fashion, the noise power estimation, using one-dimensional nonlinear curve fitting, with the estimation of the shape and scale parameters, using closed-form solutions in terms of the CKD intensity moments. The second method is similar to the first except it replaces integer-based intensity moments with fractional moments which have been shown to achieve more accurate estimates of the shape parameter. These new methods can be implemented in real time without requiring large data records. They can also achieve accurate estimation performance as demonstrated with simulated and real sea clutter observation datasets. The work also investigates the numerically computed Cram\'er-Rao lower bound (CRLB) of the variance of the shape parameter estimate using intensity observations in thermal noise with unknown power. Using the CRLB, the asymptotic estimation performance behavior of the new estimators is studied and compared to that of other estimators.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

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

An Information Fusion Perspective

A fundamental issue concerned the effectiveness of the Bayesian filter is raised.The observation-only (O2) inference is presented for dynamic state estimation.The "probability of filter benefit" is defined and quantitatively analyzed.Convincing simulations demonstrate that many filters can be easily ineffective. The general solution for dynamic state estimation is to model the system as a hidden Markov process and then employ a recursive estimator of the prediction-correction format (of which the best known is the Bayesian filter) to statistically fuse the time-series observations via models. The performance of the estimator greatly depends on the quality of the statistical mode assumed. In contrast, this paper presents a modeling-free solution, referred to as the observation-only (O2) inference, which infers the state directly from the observations. A Monte Carlo sampling approach is correspondingly proposed for unbiased nonlinear O2 inference. With faster computational speed, the performance of the O2 inference has identified a benchmark to assess the effectiveness of conventional recursive estimators where an estimator is defined as effective only when it outperforms on average the O2 inference (if applicable). It has been quantitatively demonstrated, from the perspective of information fusion, that a prior "biased" information (which inevitably accompanies inaccurate modelling) can be counterproductive for a filter, resulting in an ineffective estimator. Classic state space models have shown that a variety of Kalman filters and particle filters can easily be ineffective (inferior to the O2 inference) in certain situations, although this has been omitted somewhat in the literature

Structured least squares problems and robust estimators

Cataloged from PDF version of article.A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values