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

Data Assimilation Based on Sequential Monte Carlo Methods for Dynamic Data Driven Simulation

Simulation models are widely used for studying and predicting dynamic behaviors of complex systems. Inaccurate simulation results are often inevitable due to imperfect model and inaccurate inputs. With the advances of sensor technology, it is possible to collect large amount of real time observation data from real systems during simulations. This gives rise to a new paradigm of Dynamic Data Driven Simulation (DDDS) where a simulation system dynamically assimilates real time observation data into a running model to improve simulation results. Data assimilation for DDDS is a challenging task because sophisticated simulation models often have: 1) nonlinear non-Gaussian behavior 2) non-analytical expressions of involved probability density functions 3) high dimensional state space 4) high computation cost. Due to these properties, most existing data assimilation methods fail to effectively support data assimilation for DDDS in one way or another. This work develops algorithms and software to perform data assimilation for dynamic data driven simulation through non-parametric statistic inference based on sequential Monte Carlo (SMC) methods (also called particle filters). A bootstrap particle filter based data assimilation framework is firstly developed, where the proposal distribution is constructed from simulation models and statistical cores of noises. The bootstrap particle filter-based framework is relatively easy to implement. However, it is ineffective when the uncertainty of simulation models is much larger than the observation model (i.e. peaked likelihood) or when rare events happen. To improve the effectiveness of data assimilation, a new data assimilation framework, named as the SenSim framework, is then proposed, which has a more advanced proposal distribution that uses knowledge from both simulation models and sensor readings. Both the bootstrap particle filter-based framework and the SenSim framework are applied and evaluated in two case studies: wildfire spread simulation, and lane-based traffic simulation. Experimental results demonstrate the effectiveness of the proposed data assimilation methods. A software package is also created to encapsulate the different components of SMC methods for supporting data assimilation of general simulation models

Development of Robust Control Schemes with New Estimation Algorithms for Shunt Active Power Filter

The widespread use of power electronics in industrial, commercial and even residential electrical equipments causes deterioration of the quality of the electric power supply with distortion of the supply voltage. This has led to the development of more stringent requirements regarding harmonic current generation, as are found in standards such as IEEE-519. Power Quality is generally meant to measure of an ideal power supply system. Shunt active power filter (SAPF) is a viable solution for Power Quality enhancement, in order to comply with the standard recommendations. The dynamic performance of SAPF is mainly dependent on how quickly and how accurately the harmonic components are extracted from the load current. Therefore, a fast and accurate estimation algorithm for the detection of reference current signal along with an effective current control technique is needed in order for a SAPF to perform the harmonic elimination successfully. Several control strategies of SAPF have been proposed and implemented. But, still there is a lot of scope on designing new estimation algorithms to achieve fast and accurate generation of reference current signal in SAPF. Further, there is a need of development of efficient robust control algorithms that can be robust in face parametric uncertainties in the power system yielding improvement in power quality more effectively in terms of tracking error reduction and efficient current harmonics mitigation. The work described in the thesis involves development of a number of new current control techniques along with new reference current generation schemes in SAPF. Two current control techniques namely a hysteresis current control (HCC) and sliding mode control (SMC) implemented with a new reference current generation scheme are proposed. This reference generation approach involves a Proportional Integral (PI) controller loop and exploits the estimation of the in phase fundamental components of distorted point of common coupling (PCC) voltages by using Kalman Filter (KF) algorithm. The KF-HCC based SAPF is found to be very simple in realization and performs well even under grid perturbations. But the slow convergence rate of KF leads towards an ineffective reference generation and hence harmonics cancellation is not perfect. Therefore, a SMC based SAPF is implemented with a faster reference scheme based on the proposed Robust Extended Complex Kalman Filter (RECKF) algorithm and the efficacy of this RECKF-SMC is compared with other variants of Kalman Filter such as KF, Extended Kalman Filter (EKF) and Extended Complex Kalman Filter (ECKF) employing simulations as well as real-time simulations using an Opal-RT Real-Time digital Simulator. The RECKF-SMC based SAPF is found to be more effective as compared to the KF-HCC, KF-SMC, EKF-SMC and ECKF-SMC. Subsequently, predictive control techniques namely Dead Beat Control (DBC) and Model Predictive Control (MPC) are proposed in SAPF along with an improved reference current generation scheme based on the proposed RECKF. This reference scheme is devoid of PI controller loop and can self-regulate the dc-link voltage. Both RECKF-DBC and RECKF-MPC approaches use a model of the SAPF system to predict its future behavior and select the most appropriate control action based on an optimality criterion. However, RECKF-DBC is more sensitive to load uncertainties. Also, a better compensation performance of RECKF-MPC is observed from the simulation as well as real-time simulation results. Moreover, to study the efficacy of this RECKF-MPC over PI-MPC, a comparative assessment has been performed using both steady state as well as transient state conditions. From the simulation and real-time simulation results, it is observed that the proposed RECKF-MPC outperforms PI-MPC. The thesis also proposed an optimal Linear Quadratic Regulator (LQR) with an advanced reference current generation strategy based on RECKF. This RECKF-LQR based SAPF has better tracking and disturbance rejection capability and hence RECKF-LQR is found to be more efficient as compared to RECKF-SMC, RECKF-DBC and RECKF-MPC approaches. Subsequently, two robust control approaches namely Linear Quadratic Gaussian (LQG) servo control and H∞ control are proposed in SAPF with highly improved reference generation schemes based on RECKF. These control strategies are designed with the purpose of achieving stability, high disturbance rejection and high level of harmonics cancellation. From simulation results, they are not only found to be robust against different load parameters, but also satisfactory THD results have been achieved in SAPF. A prototype experimental set up has been developed in the Laboratory with a dSPACE-1104 computing platform to verify their robustness. From both the simulation and experimentation, it is observed that the proposed RECKF-H∞ control approach to design a SAPF is found to be more robust as compared to the RECKF-LQG servo control approach in face parametric uncertainties due to load perturbations yielding improvement in power quality in terms of tracking error reduction and efficient current harmonics mitigation. Further, there is no involvement of any voltage sensor in this realization of RECKF-H∞ based SAPF resulting a more reliable and inexpensive SAPF system. Therefore, superiority of proposed RECKF-H∞ is proved amongst all the proposed control strategies of SAPF

Analysing Large-scale Surveillance Video

Analysing large-scale surveillance video has drawn signi cant attention because drone technology and high-resolution sensors are rapidly improving. The mobility of drones makes it possible to monitor a broad range of the environment, but it introduces a more di cult problem of identifying the objects of interest. This thesis aims to detect the moving objects (mostly vehicles) using the idea of background subtraction. Building a decent background is the key to success during the process. We consider two categories of surveillance videos in this thesis: when the scene is at and when pronounced parallax exists. After reviewing several global motion estimation approaches, we propose a novel cost function, the log-likelihood of the student t-distribution, to estimate the background motion between two frames. The proposed idea enables the estimation process to be e cient and robust with auto-generated parameters. Since the particle lter is useful in various subjects, it is investigated in this thesis. An improvement to particle lters, combining near-optimal proposal and Rao-Blackwellisation, is discussed to increase the e ciency when dealing with non-linear problems. Such improvement is used to solve visual simultaneous localisation and mapping (SLAM) problems and we call it RB2-PF. Its superiority is evident in both simulations of 2D SLAM and real datasets of visual odometry problems. Finally, RB2-PF based visual odometry is the key component to detect moving objects from surveillance videos with pronounced parallax. The idea is to consider multiple planes in the scene to improve the background motion estimation. Experiments have shown that false alarms signi cantly reduced. With the landmark information, a ground plane can be worked out. A near-constant velocity model can be applied after mapping the detections on the ground plane regardless of the position and orientation of the camera. All the detection results are nally processed by a multi-target tracker, the Gaussian mixture probabilistic hypothesis density (GM-PHD) lter, to generate tracks

Enhancements of online Bayesian filtering algorithms for efficient monitoring and improved uncertainty quantification in complex nonlinear dynamical systems

Recent years have seen a concurrent development of new sensor technologies and high-fidelity modeling capabilities. At the junction of these two topics lies an interesting opportunity for real-time system monitoring and damage assessment of structures. During monitoring, measurements from a structure are used to learn the parameters and equations characterizing a physics-based model of the system; thus enabling damage identification. Since monitored quantities are physical, these methods offer precious insight into the damage state of the structure (localization, type of damage and its extent). Furthermore, one obtains a model of the structure in its current condition, an essential element in predicting the future behavior of the structure and enabling adequate decision-making procedures. This dissertation focuses more specifically on solving some of the challenges associated with the use of online Bayesian learning algorithms, also called sequential filtering algorithms, for damage detection and characterization in nonlinear structural systems. A major challenge regarding online Bayesian filtering algorithms lies in achieving good accuracy for large dimensional systems and complex nonlinear non-Gaussian systems, where non-Gaussianity can arise for instance in systems which are not globally identifiable. In the first part of this dissertation, we show that one can derive algorithmic enhancements of filtering techniques, mainly based on innovative ways to reduce the dimensionality of the problem at hand, and thus obtain a good trade-off between accuracy and computational complexity of the learning algorithms. For instance, for particle filtering techniques (sampling-based algorithms) subjected to the so-called curse of dimensionality, the concept of Rao-Blackwellisation can be used to greatly reduce the dimension of the sampling space. On the other hand, one can also build upon nonlinear Kalman filtering techniques, which are very computationally efficient, and expand their capabilities to non-Gaussian distributions. Another challenge associated with structural health monitoring is the amount of uncertainties and variabilities inherently present in the system, measurements and/or inputs. The second part of this dissertation aims at demonstrating that online Bayesian filtering algorithms are very well-suited for SHM applications due to their ability to accurately quantify and take into account these uncertainties in the learning process. First, these algorithms are well-suited to address ill-conditioned problems, where not all parameters can be learnt from the available noisy data, a problem which frequently arises when considering large dimensional nonlinear systems. Then, in the case of unknown stochastic inputs, a method is derived to take into account in this sequential filtering framework unmeasured stationary excitations whose spectral properties are known but uncertain

Random media and processes estimation using non-linear filtering techniques: application to ensemble weather forecast and aircraft trajectories

L'erreur de prédiction d'une trajectoire avion peut être expliquée par différents facteurs. Les incertitudes associées à la prévision météorologique sont l'un d'entre-eux. Qui plus est, l'erreur de prévision de vent a un effet non négligeable sur l'erreur de prédiction de la position d'un avion. En regardant le problème sous un autre angle, il s'avère que les avions peuvent être utilisés comme des capteurs locaux pour estimer l'erreur de prévision de vent. Dans ce travail nous décrivons ce problème d'estimation à l'aide de plusieurs processus d'acquisition d'un même champ aléatoire. Quand ce champ est homogène, nous montrons que le problème est équivalent à plusieurs processus aléatoires évoluant dans un même environnement aléatoire pour lequel nous donnons un modèle de Feynman-Kac. Nous en dérivons une approximation particulaire et fournissons pour les estimateurs obtenus des résultats de convergence. Quand le champ n'est pas homogène mais qu'une décomposition en sous-domaine homogène est possible, nous proposons un modèle différent basé sur le couplage de plusieurs processus d'acquisition. Nous en déduisons un modèle de Feynman-Kac et suggérons une approximation particulaire du flot de mesure. Par ailleurs, pour pouvoir traiter un trafic aérien, nous développons un modèle de prédiction de trajectoire avion. Finalement nous démontrons dans le cadre de simulations que nos algorithmes peuvent estimer les erreurs de prévisions de vent en utilisant les observations délivrées par les avions le long de leur trajectoire.Aircraft trajectory prediction error can be explained by different factors. One of them is the weather forecast uncertainties. For example, the wind forecast error has a non negligible impact on the along track accuracy for the predicted aircraft position. From a different perspective, that means that aircrafts can be used as local sensors to estimate the weather forecast error. In this work we describe the estimation problem as several acquisition processes of a same random field. When the field is homogeneous, we prove that they are equivalent to random processes evolving in a random media for which a Feynman-Kac formulation is done. Then we give a particle-based approximation and provide convergence results of the ensuing estimators. When the random field is not homogeneous but can be decomposed in homogeneous sub-domains, a different model is proposed based on the coupling of different acquisition processes. From there, a Feynman-Kac formulation is derived and its particle-based approximation is suggested. Furthermore, we develop an aircraft trajectory prediction model. Finally we demonstrate on a simulation set-up that our algorithms can estimate the wind forecast errors using the aircraft observations delivered along their trajectory

Particle Filtering With Dependent Noise Processes

Modeling physical systems often leads to discrete time state-space models with dependent process and measurement noises. For linear Gaussian models, the Kalman filter handles this case, as is well described in literature. However, for nonlinear or non-Gaussian models, the particle filter as described in literature provides a general solution only for the case of independent noise. Here, we present an extended theory of the particle filter for dependent noises with the following key contributions: i) The optimal proposal distribution is derived; ii) the special case of Gaussian noise in nonlinear models is treated in detail, leading to a concrete algorithm that is as easy to implement as the corresponding Kalman filter; iii) the marginalized (Rao-Blackwellized) particle filter, handling linear Gaussian substructures in the model in an efficient way, is extended to dependent noise; and, finally, iv) the parameters of a joint Gaussian distribution of the noise processes are estimated jointly with the state in a recursive way.CADIC