Sensor Data Fusion for Improving Traffic Mobility in Smart Cities

The ever-increasing urban population and vehicular traffic without a corresponding expansion of infrastructure have been a challenge to transportation facilities managers and commuters. While some parts of transportation infrastructure have big data available, so many other locations have sparse data. This has posed a challenge in traffic state estimation and prediction for efficient and effective infrastructure management and route guidance. This research focused on traffic prediction problems and aims to develop novel spatial-temporal and robust algorithms, that can provide high accuracy in the presence of both big data and sparse data in a large urban road network. Intelligent transportation systems require the knowledge of current traffic state and forecast for effective implementation. The actual traffic state has to be estimated as the existing sensors do not capture the needed state. Sensor measurements often contain missing or incomplete data as a result of communication issues, faulty sensors or cost leading to incomplete monitoring of the entire road network. This missing data pose challenges to traffic estimation approaches. In this work, a robust spatio-temporal traffic imputation approach capable of withstanding high missing data rate is presented. A particle-based approach with Kriging interpolation is proposed. The performance of the particle-based Kriging interpolation for different missing data ratios was investigated for a large road network. A particle-based framework for dealing with missing data is also proposed. An expression of the likelihood function is derived for the case when the missing value is calculated based on Kriging interpolation. With the Kriging interpolation, the missing values of the measurements are predicted, which are subsequently used in the computation of likelihood terms in the particle filter algorithm. In the commonly used Kriging approaches, the covariance function depends only on the separation distance irrespective of the traffic at the considered locations. A key limitation of such an approach is its inability to capture well the traffic dynamics and transitions between different states. This thesis proposes a Bayesian Kriging approach for the prediction of urban traffic. The approach can capture these dynamics and model changes via the covariance matrix. The main novelty consists in representing both stationary and non-stationary changes in traffic flows by a discriminative covariance function conditioned on the observation at each location. An advantage is that by considering the surrounding traffic information distinctively, the proposed method is very likely to represent congested regions and interactions in both upstream and downstream areas

Streaming Probabilistic PCA for Missing Data with Heteroscedastic Noise

Streaming principal component analysis (PCA) is an integral tool in large-scale machine learning for rapidly estimating low-dimensional subspaces of very high dimensional and high arrival-rate data with missing entries and corrupting noise. However, modern trends increasingly combine data from a variety of sources, meaning they may exhibit heterogeneous quality across samples. Since standard streaming PCA algorithms do not account for non-uniform noise, their subspace estimates can quickly degrade. On the other hand, the recently proposed Heteroscedastic Probabilistic PCA Technique (HePPCAT) addresses this heterogeneity, but it was not designed to handle missing entries and streaming data, nor does it adapt to non-stationary behavior in time series data. This paper proposes the Streaming HeteroscedASTic Algorithm for PCA (SHASTA-PCA) to bridge this divide. SHASTA-PCA employs a stochastic alternating expectation maximization approach that jointly learns the low-rank latent factors and the unknown noise variances from streaming data that may have missing entries and heteroscedastic noise, all while maintaining a low memory and computational footprint. Numerical experiments validate the superior subspace estimation of our method compared to state-of-the-art streaming PCA algorithms in the heteroscedastic setting. Finally, we illustrate SHASTA-PCA applied to highly-heterogeneous real data from astronomy.Comment: 19 pages, 6 figure

Computing missing values in time series

This work presents two algorithms to estimate missing values in time series. The first is the Kalman Filter, as developed by Kohn and Ansley (1986) and others. The second is the additive outlier approach, developed by Pefia, Ljung and Maravall. Both are exact and lead to the same results. However, the first is, in general, faster and the second more flexible

Combining information in statistical modelling

How to combine information from different sources is becoming an important statistical area of research under the name of Meta Analysis. This paper shows that the estimation of a parameter or the forecast of a random variable can also be seen as a process of combining information. It is shown that this approach can provide sorne useful insights on the robustness properties of sorne statistical procedures, and it also allows the comparison of statistical models within a common framework. Sorne general combining rules are illustrated using examples from ANOVA analysis, diagnostics in regression, time series forecasting, missing value estimation and recursive estimation using the Kalman Filter

Learning sparse representations of depth

This paper introduces a new method for learning and inferring sparse representations of depth (disparity) maps. The proposed algorithm relaxes the usual assumption of the stationary noise model in sparse coding. This enables learning from data corrupted with spatially varying noise or uncertainty, typically obtained by laser range scanners or structured light depth cameras. Sparse representations are learned from the Middlebury database disparity maps and then exploited in a two-layer graphical model for inferring depth from stereo, by including a sparsity prior on the learned features. Since they capture higher-order dependencies in the depth structure, these priors can complement smoothness priors commonly used in depth inference based on Markov Random Field (MRF) models. Inference on the proposed graph is achieved using an alternating iterative optimization technique, where the first layer is solved using an existing MRF-based stereo matching algorithm, then held fixed as the second layer is solved using the proposed non-stationary sparse coding algorithm. This leads to a general method for improving solutions of state of the art MRF-based depth estimation algorithms. Our experimental results first show that depth inference using learned representations leads to state of the art denoising of depth maps obtained from laser range scanners and a time of flight camera. Furthermore, we show that adding sparse priors improves the results of two depth estimation methods: the classical graph cut algorithm by Boykov et al. and the more recent algorithm of Woodford et al.Comment: 12 page

Missing observations and additive outliers in time series models

The paper deals with estimation of missing observations in possible nonstationary ARIMA models. First, the model is assumed known, and the structure of the interpolation filter is analyzed. Using the inverse or dual autocorrelation function it is seen how estimation of a missing observation is analogous to the removal of an outlier effect; both problems are closely related with the signal plus noise decomposition of the series. The results are extended to cover, first, the case of a missing observation near the two extremes of the series; then to the case of a sequence of missing observations, and finally to the general case of any number of sequences of any length of missing observations. The optimal estimator can always be expressed, in a compact way, in terms of the dual autocorrelation function or a truncation thereof; is mean squared error is equal to the inverse of the (appropriately chosen) dual autocovariance matrix. The last part of the paper illustrates a point of applied interest: When the model is unknown, the additive outlier approach may provide a convenient and efficient alternative to the standard Kalman filter-fixed point smoother approach for missing observations estimation