NLOS Mitigation in TOA-based Indoor Localization by Nonlinear Filtering under Skew t-distributed Measurement Noise

Wireless localization by time-of-arrival (TOA) measurements is typically corrupted by non-line-of-sight (NLOS) conditions, causing biased range measurements that can degrade the overall positioning performance of the system. In this article, we propose a localization algorithm that is able to mitigate the impact of NLOS observations by employing a heavy-tailed noise statistical model. Modeling the observation noise by a skew t-distribution allows us to, on the one hand, employ a computationally light sigma-point Kalman filtering method while, on the other hand, be able to effectively characterize the positive skewed non-Gaussian nature of TOA observations under LOS/NLOS conditions. Numerical results show the enhanced performance of such approach

Uncertainty Exchange Through Multiple Quadrature Kalman Filtering

One of the major challenges in Bayesian filtering is the curse of dimensionality. The quadrature Kalman filter (QKF) is the method of choice in many real-life Gaussian problems, but its computational complexity increases exponentially with the dimension of the state. As a promising solution to overcome the filter limitations in such scenarios, we further explore the multiple state-partitioning approach, which considers the partition of the original space into several subspaces, with the goal to apply a low-dimensional filter at each partition. In this contribution, the key idea is to take advantage of the estimation uncertainty provided by the QKF to improve the interaction among filters and avoid the point estimate approximation performed in the original Multiple QKF (MQKF). The new filter formulation, named Improved MQKF, considers Gauss-Hermite quadrature rules to propagate the subspaces of interest, together with cubature rules for marginalization purposes. The nested quadrature-cubature approximation provides robustness and improves the filter performance. Simulation results for a multiple target tracking scenario are provided to support the discussion

Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

This paper proposes a novel strong tracking filter (STF), which is suitable for dealing with the filtering problem of nonlinear systems when the following cases occur: that is, the constructed model does not match the actual system, the measurements have the one-step random delay, and the process and measurement noises are correlated at the same epoch. Firstly, a framework of decoupling filter (DF) based on equivalent model transformation is derived. Further, according to the framework of DF, a new extended Kalman filtering (EKF) algorithm via using first-order linearization approximation is developed. Secondly, the computational process of the suboptimal fading factor is derived on the basis of the extended orthogonality principle (EOP). Thirdly, the ultimate form of the proposed STF is obtained by introducing the suboptimal fading factor into the above EKF algorithm. The proposed STF can automatically tune the suboptimal fading factor on the basis of the residuals between available and predicted measurements and further the gain matrices of the proposed STF tune online to improve the filtering performance. Finally, the effectiveness of the proposed STF has been proved through numerical simulation experiments

NLOS mitigation in indoor localization by marginalized Monte Carlo Gaussian smoothing

One of the main challenges in indoor time-of-arrival (TOA)-based wireless localization systems is to mitigate non-line-of-sight (NLOS) propagation conditions, which degrade the overall positioning performance. The positive skewed non-Gaussian nature of TOA observations under LOS/NLOS conditions can be modeled as a heavy-tailed skew t-distributed measurement noise. The main goal of this article is to provide a robust Bayesian inference framework to deal with target localization under NLOS conditions. A key point is to take advantage of the conditionally Gaussian formulation of the skew t-distribution, thus being able to use computationally light Gaussian filtering and smoothing methods as the core of the new approach. The unknown non-Gaussian noise latent variables are marginalized using Monte Carlo sampling. Numerical results are provided to show the performance improvement of the proposed approach

Vacancy state detector oriented to convolutional neural network, background subtraction and embedded systems

Dupla diplomação com a UTFPR - Universidade Tecnológica Federal do ParanáMuch has been discussed recently related to population ascension, the reasons for this event, and, in particular, the aspects of society affected. Over the years, the city governments realized a higher level of growth, mainly in terms of urban scale, technology, and individuals numbers. It comprises improvements and investments in their structure and policies, motivated by improving conditions in population live quality and reduce environmental, energy, fuel, time, and money resources, besides population living costs, including the increasing demand for parking structures accessible to the general or private-public, and a waste of substantial daily time and fuel, disturbing the population routinely. Therefore, one way to achieve that challenge is focused on reducing energy, money, and time costs to travel to work or travel to another substantial location. That work presents a robust, and low computational power Smart Parking system adaptive to several environments changes to detect and report vacancy states in a parking space oriented to Deep Learning, and Embedded Systems. This project consists of determining the parking vacancy status through statistical and image processing methods, creates a robust image data set, and the Convolutional Neural Network model focused on predict three final classes. In order to save computational power, this approach uses the Background Subtraction based on the Mixture of Gaussian method, only updating parking space status, in which large levels of motion are detected. The proposed model presents 94 percent of precision at the designed domain.Muito se discutiu recentemente sobre a ascensão populacional, as razões deste evento e, em particular, os aspectos da sociedade afetados. Ao longo dos anos, os governos perceberam um grande nível de crescimento, principalmente em termos de escala urbana, tecnologia e número de indivíduos. Este fato deve-se a melhorias e investimentos na estrutura urbana e políticas motivados por melhorar as condições de qualidade de vida da população e reduzir a utilização de recursos ambientais, energéticos, combustíveis, temporais e monetários, além dos custos de vida da população, incluindo a crescente demanda por estruturas de estacionamento acessíveis ao público em geral ou público-privado. Portanto, uma maneira de alcançar esse desafio é manter a atenção na redução de custos de energia, dinheiro e tempo para viajar para o trabalho ou para outro local substancial. Esse trabalho apresenta um sistema robusto de Smart Parking, com baixo consumo computacional, adaptável a diversas mudanças no ambiente observado para detectar e relatar os estados das vagas de estacionamento, orientado por Deep Learning e Embedded Systems. Este projeto consiste em determinar o status da vaga de estacionamento por meio de métodos estatísticos e de processamento de imagem, criando um conjunto robusto de dados e um modelo de Rede Neuronal Convolucional com foco na previsão de três classes finais. A fim de reduzir consumo computacional, essa abordagem usa o método de Background Subtraction, somente atualizando o status do espaço de estacionamento em que grandes níveis de movimento são detectados. O modelo proposto apresenta 94 porcento da precisão no domínio projetado

Bayesian Filtering for Dynamic Systems with Applications to Tracking

This M.Sc. thesis intends to evaluate various algorithms based on Bayesian statistical theory and validates with both synthetic data as well as experimental data. The focus is given in comparing the performance of new kind of sequential Monte Carlo filter, called cost reference particle filter, with other Kalman based filters as well as the standard particle filter. Different filtering algorithms based on Kalman filters and those based on sequential Monte Carlo technique are implemented in Matlab. For all linear Gaussian system models, Kalman filter gives the optimal solution. Hence only the cases which do not have linear-Gaussian probabilistic model are analyzed in this thesis. The results of various simulations show that, for those non-linear system models whose probability model can fairly be assumed Gaussian, either Kalman like filters or the sequential Monte Carlo based particle filters can be used. The choice among these filters depends upon various factors such as degree of nonlinearity, order of system state, required accuracy, etc. There is always a tradeoff between the required accuracy and the computational cost. It is found that whenever the probabilistic model of the system cannot be approximated as Gaussian, which is the case in many real world applications like Econometrics, Genetics, etc., the above discussed statistical reference filters degrade in performance. To tackle with this problem, the recently proposed cost reference particle filter is implemented and tested in scenarios where the system model is not Gaussian. The new filter shows good robustness in such scenarios as it does not make any assumption of probabilistic model. The thesis work also includes implementation of the above discussed prediction algorithms into a real world application, where location of a moving robot is tracked using measurements from wireless sensor networks. The flexibility of the cost reference particle filter to adapt to specific applications is explored and is found to perform better than the other filters in tracking of the robot. The results obtained from various experiments show that cost reference particle filter is the best choice whenever there is high uncertainty of the probabilistic model and when these models are not Gaussian. It can also be concluded that,contrary to the general perception, the estimation techniques based on ad-hoc references can actually be more efficient than those based on the usual statistical reference

Sequential estimation of neural models by Bayesian filtering

Un dels reptes més difícils de la neurociència és el d'entendre la connectivitat del cervell. Aquest problema es pot tractar des de diverses perspectives, aquí ens centrem en els fenòmens locals que ocorren en una sola neurona. L'objectiu final és, doncs, entendre la dinàmica de les neurones i com la interconnexió amb altres neurones afecta al seu estat. Les observacions de traces del potencial de membrana constitueixen la principal font d'informació per a derivar models matemàtics d'una neurona, amb cert sentit biofísic. En particular, la dinàmica de les variables auxiliars i els paràmetres del model són estimats a partir d'aquestes traces de voltatge. El procés és en general costós i típicament implica una gran varietat de blocatges químics de canals iònics, així com una certa incertesa en els valors dels paràmetres a causa del soroll de mesura. D'altra banda, les traces de potencial de membrana també són útils per obtenir informació valuosa sobre l'entrada sinàptica, un problema invers sense solució satisfactòria a hores d'ara. En aquesta Tesi, estem interessats en mètodes d'estimació seqüencial, que permetin evitar la necessitat de repeticions que podrien ser contaminades per la variabilitat neuronal. En particular, ens concentrem en mètodes per extreure l'activitat intrínseca dels canals iònics, és a dir, les probabilitats d'obertura i tancament de canals iònics, i la contribució de les conductàncies sinàptiques. Hem dissenyat un mètode basat en la teoria Bayesiana de filtrat per inferir seqüencialment aquestes quantitats a partir d'una única traça de voltatge, potencialment sorollosa. El mètode d'estimació proposat està basat en la suposició d'un model de neurona conegut. Això és cert fins a cert punt, però la majoria dels paràmetres en el model han de ser estimats per endavant (això és valid per a qualsevol model). Per tant, el mètode s'ha millorat pel cas de models amb paràmetres desconeguts, incloent-hi un procediment per estimar conjuntament els paràmetres i les variables dinàmiques. Hem validat els mètodes d'inferència proposats mitjançant simulacions realistes. Les prestacions en termes d'error d'estimació s'han comparat amb el límit teòric, que s'ha derivat també en el marc d'aquesta Tesi

Bayesian inference for dynamic pose estimation using directional statistics

The dynamic pose of an object, where the object can represent a spacecraft, aircraft, or mobile robot, among other possibilities, is defined to be the position, velocity, attitude, and angular velocity of the object. A new method to perform dynamic pose estimation is developed that leverages directional statistics and operates under the Bayesian estimation framework, as opposed to the minimum mean square error (MMSE) framework that conventional methods employ. No small attitude uncertainty assumption is necessary using this method, and, therefore, a more accurate estimate of the state can be obtained when the attitude uncertainty is large. Two new state densities, termed the Gauss-Bingham and Bingham-Gauss mixture (BGM) densities, are developed that probabilistically represent a state vector comprised of an attitude quaternion and other Euclidean states on their natural manifold, the unit hypercylinder. When the Euclidean states consist of position, velocity, and angular velocity, the state vector represents the dynamic pose. An uncertainty propagation scheme is developed for a Gauss-Bingham-distributed state vector, and two demonstrations of this uncertainty propagation scheme are presented that show its applicability to quantify the uncertainty in dynamic pose, especially when the attitude uncertainty becomes large. The BGM filter is developed, which is an approximate Bayesian filter in which the true temporal and measurement evolution of the BGM density, as quantified by the Chapman-Kolmogorov equation and Bayes\u27 rule, are approximated by a BGM density. The parameters of the approximating BGM density are found via integral approximation on a component-wise basis, which is shown to be the Kullback-Leibler divergence optimal parameters of each component. The BGM filter is then applied to three simulations in order to compare its performance to a multiplicative Kalman filter and demonstrate its efficacy in estimating dynamic pose. The BGM filter is shown to be more statistically consistent than the multiplicative Kalman filter when the attitude uncertainty is large --Abstract, page iii

Algorithms for Positioning with Nonlinear Measurement Models and Heavy-tailed and Asymmetric Distributed Additive Noise

Determining the unknown position of a user equipment using measurements obtained from transmitters with known locations generally results in a nonlinear measurement function. The measurement errors can have a heavy-tailed and/ or skewed distribution, and the likelihood function can be multimodal.A positioning problem with a nonlinear measurement function is often solved by a nonlinear least squares (NLS) method or, when filtering is desired, by an extended Kalman filter (EKF). However, these methods are unable to capture multiple peaks of the likelihood function and do not address heavy-tailedness or skewness. Approximating the likelihood by a Gaussian mixture (GM) and using a GM filter (GMF) solves the problem. The drawback is that the approximation requires a large number of components in the GM for a precise approximation, which makes it unsuitable for real-time positioning on small mobile devices.This thesis studies a generalised version of Gaussian mixtures, which is called GGM, to capture multiple peaks. It relaxes the GM’s restriction to non-negative component weights. The analysis shows that the GGM allows a significant reduction of the number of required Gaussian components when applied for approximating the measurement likelihood of a transmitter with an isotropic antenna, compared with the GM. Therefore, the GGM facilitates real-time positioning in small mobile devices. In tests for a cellular telephone network and for an ultra-wideband network the GGM and its filter provide significantly better positioning accuracy than the NLS and the EKF.For positioning with nonlinear measurement models, and heavytailed and skewed distributed measurement errors, an Expectation Maximisation (EM) algorithm is studied. The EM algorithm is compared with a standard NLS algorithm in simulations and tests with realistic emulated data from a long term evolution network. The EM algorithm is more robust to measurement outliers. If the errors in training and positioning data are similar distributed, then the EM algorithm yields significantly better position estimates than the NLS method. The improvement in accuracy and precision comes at the cost of moderately higher computational demand and higher vulnerability to changing patterns in the error distribution (of training and positioning data). This vulnerability is caused by the fact that the skew-t distribution (used in EM) has 4 parameters while the normal distribution (used in NLS) has only 2. Hence the skew-t yields a closer fit than the normal distribution of the pattern in the training data. However, on the downside if patterns in training and positioning data vary than the skew-t fit is not necessarily a better fit than the normal fit, which weakens the EM algorithm’s positioning accuracy and precision. This concept of reduced generalisability due to overfitting is a basic rule of machine learning.This thesis additionally shows how parameters of heavy-tailed and skewed error distributions can be fitted to training data. It furthermore gives an overview on other parametric methods for solving the positioning method, how training data is handled and summarised for them, how positioning is done by them, and how they compare with nonparametric methods. These methods are analysed by extensive tests in a wireless area network, which shows the strength and weaknesses of each method

Semi-Physical Real-Time Models with State and Parameter Estimation for Diesel Engines

Increasing requirements for the reduction of fuel consumption (CO2) and emissions require a precise electronic management of combustion engines. Engine-related measures to meet these requirements lead to an increase in variability and system complexity. To cope with increasing system complexity, model-based development methodology has proven effective. In this context, virtual development with real-time models plays an increasingly important role. The corresponding models can either be derived theoretically on the basis of known physical laws (white-box models) or obtained experimentally on the test bench by mathematically modeling the measured input and output behavior (black-box models). Both types of modeling have their advantages and disadvantages. A semi-physical modeling methodology is presented that combines the advantages of theoretical and experimental modeling and overcomes their disadvantages. The goal is to find suitable, simplified equation structures and to determine their unknown parameters experimentally by real-time capable, recursive parameter estimation methods. This leads to physically interpretable real-time models that are able to adapt their parameters according to the current engine operating behavior and thus offer good transferability to other engines. The semi-physical modeling methodology is applied to the air system and combustion of a common rail diesel engine with a variable exhaust gas turbocharger and high- and low-pressure exhaust gas recirculation. The focus lies on the derivation of semi-physical real-time model for the combustion and its underlying processes inside the cylinder. A semi-physical model approach for modeling the dynamics of combustion chamber processes is developed and combined with state and parameter estimation methods. This model approach enables crank angle-resolved calculation of the in-cylinder gas states and the determination of the characteristic combustion components of diesel combustion (premixed, diffusive combustion and burn-out). The technical implementation is realized close to the pressure indication system of the engine test bench, enabling a crankshaft-resolved model adaptation based on measured in-cylinder pressure. Model identification is performed using combined state and parameter estimation in steady-state engine operation. Model parameters are estimated perpetually for each duty cycle and converge to a constant value within 30-60 engine duty cycles. Final estimation results are stored as functions of engine operating point using experimental modeling. In this way, semi-physical real-time models are created directly online during the measurement. The treated method is considered as an extension of the functionality of conventional pressure indication systems. Furthermore, the derived semi-physical models are used for real-time engine simulation in the context of hardware-in-the-loop testing of ECUs. The research project (Project No. 1231) was financially and advisory supported by the Research Association for Combustion Engines (FVV) e.V. (Frankfurt am Main, Germany)