Moving Horizon Estimation with Dynamic Programming

Moving Horizon Estimation(MHE) is a optimization based strategy to state estimation. It involves computation of arrival cost, a penalty term, based on the MHE cost function. Minimization of this arrival cost is done through various methods. All these methods use nonlinear programming optimization technique which gives the estimate. The main idea of MHE revolves around minimizing the estimation cost function. The cost function is dependent on prediction error computation from data and arrival cost summarization. The major issue that hampers the MHE is choosing the arrival cost for ensuring stability of the overall estimation and computational time. In order to attain this stability, this thesis incorporates dynamic programming algorithm to estimate MHE cost function. Dynamic programming is an algorithm for solving complex problems. The MHE cost function algorithm has been modied based on dynamic programming algorithm in order to ensure stability of the overall estimation. In order to apply this algorithm, a specic non-linear lter, particle lter is used for the initialization of MHE. The reason of using particle lter for initialization of MHE is due to fact that dynamic programming algorithm works on principle of samples and particle lter provides the samples. A comparison of mean squared error(MSE) using the nonlinear programming optimization and dynamic programming optimization is veried for the proposed theory of using dynamic programming algorithm in estimation of cost functio

Unscented Kalman Filters for Vision-Based Relative Dynamics Estimation between Cooperating Spacecraft

Con questa tesi si è discussa la stima autonoma della dinamica relativa tra satelliti in volo in prossimità, concentrandosi sulle prestazioni dell'algoritmo di stima basato su filtri di Kalman. Lo scopo è stato quello di proporre nuove alternative per migliorare queste prestazioni sfruttando i filtri di Kalman Unscented che sono versioni più evolute e precise dei filtri di Kalman standard. In definitiva, le nuove soluzioni proposte risultano essere delle valide alternative

Moving Horizon Estimation with Dynamic Programming

Moving Horizon Estimation(MHE) is a optimization based strategy to state estimation. It involves computation of arrival cost, a penalty term, based on the MHE cost function. Minimization of this arrival cost is done through various methods. All these methods use nonlinear programming optimization technique which gives the estimate. The main idea of MHE revolves around minimizing the estimation cost function. The cost function is dependent on prediction error computation from data and arrival cost summarization. The major issue that hampers the MHE is choosing the arrival cost for ensuring stability of the overall estimation and computational time. In order to attain this stability, this thesis incorporates dynamic programming algorithm to estimate MHE cost function. Dynamic programming is an algorithm for solving complex problems. The MHE cost function algorithm has been modied based on dynamic programming algorithm in order to ensure stability of the overall estimation. In order to apply this algorithm, a specic non-linear lter, particle lter is used for the initialization of MHE. The reason of using particle lter for initialization of MHE is due to fact that dynamic programming algorithm works on principle of samples and particle lter provides the samples. A comparison of mean squared error(MSE) using the nonlinear programming optimization and dynamic programming optimization is veried for the proposed theory of using dynamic programming algorithm in estimation of cost functio

False data injection attack detection in smart grid

Smart grid is a distributed and autonomous energy delivery infrastructure that constantly monitors the operational state of its overall network using smart techniques and state estimation. State estimation is a powerful technique that is used to determine the overall operational state of the system based on a limited set of measurements collected through metering systems. Cyber-attacks pose serious risks to a smart grid state estimation that can cause disruptions and power outages resulting in huge economical losses and are therefore a big concern to a reliable national grid operation. False data injection attacks (FDIAs), engineered on the basis of the knowledge of the network configuration, are difficult to detect using the traditional data detection mechanisms. These detection schemes have been found vulnerable and failed to detect these FDIAs. FDIAs specifically target the state data and can manipulate the state measurements in such a way that these false measurements appear real to the main control systems. This research work explores the possibility of FDIA detection using state estimation in a distributed and partitioned smart grid. In order to detect FDIAs we use measurements for residual-based testing which creates an objective function; and the probability of erroneous data is determined from this residual test. In this test, a preset threshold is determined based on the prior history of the state data. FDIA cases are simulated within a smart grid considering that the Chi-square detection state estimator fails in identifying such attacks. We compute the objective function using the standard weighted least problem and then test the objective function against the value in the Chi-square table. The gain matrix and the Jacobian matrix are computed. The state variables are computed in the form of a voltage magnitude. The state variables are computed after the inception of an attack to assess these state magnitude results. Different sizes of partitioning are used to improve the overall sensitivity of the Chi-square results. Our additional estimator is based on a Kalman estimation that consists of the state prediction and state correction steps. In the first step, it obtains the state and matrix covariance prediction, and in the second step, it calculates the Kalman gain and the state and matrix covariance update steps. The set of points is created for the state vector x at a time instant t. The initial vector and covariance matrix are based on a priori knowledge of the historical estimates. A set of sigma points is estimated by the state update function. Sigma points refer to the minimal set of sampling points that are selected and transformed using nonlinear function, and the new mean and the covariance are formed out of these transformed points. The idea behind this is that it is easier to compute a Gaussian distribution than an arbitrary nonlinear function. The filter gain, the mean and the covariance are used to estimate the next state. Our simulation results show that the combination of Kalman estimation and distributed state estimation improves the overall stability index and vulnerability assessment score of the smart grid. We built a stability index table for a smart grid based on the state estimates value after the inception of an FDIA. The vulnerability assessment score of the smart grid is based on common vulnerability scoring system (CVSS) and state estimates under the influence of an FDIA. The simulations are conducted in the MATPOWER program and different electrical bus systems such as IEEE 14, 30, 39, 118 and 300 are tested. All the contributions have been published in reputable journals and conferences.Doctor of Philosoph

Optimal slip control for tractors with feedback of drive torque

Traction efficiency of tractors barely reaches 50 % in field operations. On the other hand, modern trends in agriculture show growth of the global tractor markets and at the same time increased demands for greenhouse gas emission reduction as well as energy efficiency due to increasing fuel costs. Engine power of farm tractors is growing at 1.8 kW per year reaching today about 500 kW for the highest traction class machines. The problem of effective use of energy has become crucial. Existing slip control approaches for tractors do not fulfil this requirement due to fixed reference set-point. The present work suggests an optimal control scheme based on set-point optimization and on assessment of soil conditions, namely, wheel-ground parameter identification using fuzzy-logic-assisted adaptive unscented Kalman filter.:List of figures VIII List of tables IX Keywords XI List of abbreviations XII List of mathematical symbols XIII Indices XV 1 Introduction 1 1.1 Problem description and challenges 1 1.1.1 Development of agricultural industry 1 1.1.2 Power flows and energy efficiency of a farm tractor 2 1.2 Motivation 9 1.3 Purpose and approach 12 1.3.1 Purpose and goals 12 1.3.2 Brief description of methodology 14 1.3.2.1 Drive torque feedback 14 1.3.2.2 Measurement signals 15 1.3.2.3 Identification of traction parameters 15 1.3.2.4 Definition of optimal slip 15 1.4 Outline 16 2 State of the art in traction management and parameter estimation 17 2.1 Slip control for farm tractors 17 2.2 Acquisition of drive torque feedback 23 2.3 Tire-ground parameter estimation 25 2.3.1 Kalman filter 25 2.3.2 Extended Kalman filter 27 2.3.3 Unscented Kalman filter 27 2.3.4 Adaptation algorithms for Kalman filter 29 3 Modelling vehicle dynamics for traction control 31 3.1 Tire-soil interaction 31 3.1.1 Forces in wheel-ground contact 32 3.1.1.1 Vertical force 32 3.1.1.2 Tire-ground surface geometry 34 3.1.2 Longitudinal force 36 3.1.3 Zero-slip condition 37 3.1.3.1 Soil shear stress 38 3.1.3.2 Rolling resistance 39 3.2 Vehicle body and wheels 40 3.2.1 Short description of Multi-Body-Simulation 40 3.2.2 Vehicle body and wheel models 42 3.2.3 Wheel structure 43 3.3 Stochastic input signals 45 3.3.1 Influence of trend and low-frequency components 47 3.3.2 Modelling stochastic signals 49 3.4 Further components and general view of tractor model 53 3.4.1 Generator, intermediate circuit, electrical motors and braking resistor 53 3.4.2 Diesel engine 55 4 Identification of traction parameters 56 4.1 Description of identification approaches 56 4.2 Vehicle model 58 4.2.1 Vehicle longitudinal dynamics 58 4.2.2 Wheel rotational dynamics 59 4.2.3 Tire dynamic rolling radius and inner rolling resistance coefficient 60 4.2.4 Whole model 61 4.3 Static methods of parameter identification 63 4.4 Adaptation mechanism of the unscented Kalman filter 63 4.5 Fuzzy supervisor for the adaptive unscented Kalman filter 66 4.5.1 Structure of the fuzzy supervisor 67 4.5.2 Stability analysis of the adaptive unscented Kalman filter with the fuzzy supervisor 69 5 Optimal slip control 73 5.1 Approaches for slip control by means of traction control system 73 5.1.1 Feedback compensation law 73 5.1.2 Sliding mode control 74 5.1.3 Funnel control 77 5.1.4 Lyapunov-Candidate-Function-based control, other approaches and choice of algorithm 78 5.2 General description of optimal slip control algorithm 79 5.3 Estimation of traction force characteristic curves 82 5.4 Optimal slip set-point computation 85 6 Verification of identification and optimal slip control systems 91 6.1 Simulation results 91 6.1.1 Identification of traction parameters 91 6.1.1.1 Comparison of extended Kalman filter and unscented Kalman filter 92 6.1.1.2 Comparison of ordinary and adaptive unscented Kalman filters 96 6.1.1.3 Comparison of the adaptive unscented Kalman filter with the fuzzy supervisor and static methods 99 6.1.1.4 Description of soil conditions 100 6.1.1.5 Identification of traction parameters under changing soil conditions 101 6.1.2 Approximation of characteristic curves 102 6.1.3 Slip control with reference of 10% 103 6.1.4 Comparison of operating with fixed and optimal slip reference 104 6.2 Experimental verification 108 6.2.1 Setup and description of the experiments 108 6.2.2 Virtual slip control without load machine 109 6.2.3 Virtual slip control with load machine 113 7 Summary, conclusions and future challenges 122 7.1 Summary of results and discussion 122 7.2 Contributions of the dissertation 123 7.3 Future challenges 123 Bibliography 125 A Measurement systems 137 A.1 Measurement of vehicle velocity 137 A.2 Measurement of wheel speed 138 A.3 Measurement or estimation of wheel vertical load 139 A.4 Measurement of draft force 140 A.5 Further possible measurement systems 141 B Basic probability theoretical notions 142 B.1 Brief description of the theory of stochastic processes 142 B.2 Properties of stochastic signals 144 B.3 Bayesian filtering 145 C Modelling stochastic draft force and field microprofile 147 D Approximation of kappa-curves 152 E Simulation parameters 15

CES-515 Towards Localization and Mapping of Autonomous Underwater Vehicles: A Survey

Autonomous Underwater Vehicles (AUVs) have been used for a huge number of tasks ranging from commercial, military and research areas etc, while the fundamental function of a successful AUV is its localization and mapping ability. This report aims to review the relevant elements of localization and mapping for AUVs. First, a brief introduction of the concept and the historical development of AUVs is given; then a relatively detailed description of the sensor system used for AUV navigation is provided. As the main part of the report, a comprehensive investigation of the simultaneous localization and mapping (SLAM) for AUVs are conducted, including its application examples. Finally a brief conclusion is summarized

Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting approach is proposed to construct the Likelihood Probability Density Function (Li-PDF) by using a comparably small number of so-called fulcrums. The likelihood of particles is thereby analytically inferred, explicitly or implicitly, based on the Li-PDF instead of directly computed by utilizing the observation, which can significantly reduce the computation and enables real time filtering. The proposed approach guarantees the estimation quality when an appropriate fitting function and properly distributed fulcrums are used. The details for construction of the fitting function and fulcrums are addressed respectively in detail. In particular, to deal with multivariate fitting, the nonparametric kernel density estimator is presented which is flexible and convenient for implicit Li-PDF implementation. Simulation comparison with a variety of existing approaches on a benchmark 1-dimensional model and multi-dimensional robot localization and visual tracking demonstrate the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a draft/preprint of one paper submitted to the IEEE Transaction

Highly computationally efficient state filter based on the delta operator

The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm