We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

On robust estimation of the location parameter

https://www.alaakhamis.org/teaching/MCT200/reading/Information%20Fusion.pdf

Multisensor data fusion: A review of the state-of-the-art

Remaining Useful Life (RUL) of a component or a system is defined as the length from the current time to the end of the useful life. Accurate RUL estimation plays a critical role in Prognostics and Health Management(PHM). Data driven approaches for RUL estimation use sensor data and operational data to estimate RUL. Traditional regression based approaches and recent Convolutional Neural Network (CNN) approach use features created from sliding windows to build models. However, sequence information is not fully considered in these approaches. Sequence learning models such as Hidden Markov Models (HMMs) and Recurrent Neural Networks (RNNs) have flaws when modeling sequence information. HMMs are limited to discrete hidden states and are known to have issues when modeling long-term dependencies in the data. RNNs also have issues with long-term dependencies. In this work, we propose a Long Short-Term Memory (LSTM) approach for RUL estimation, which can make full use of the sensor sequence information and expose hidden patterns within sensor data with multiple operating conditions, fault and degradation models. Extensive experiments using three widely adopted Prognostics and Health Management data sets show that LSTM for RUL estimation significantly outperforms traditional approaches for RUL estimation as well as Convolutional Neural Network (CNN).

Long Short-Term Memory Network for Remaining Useful Life estimation

Brief paper: Optimal Kalman filtering fusion with cross-correlated sensor noises

When there exists the limitation of communication bandwidth between sensors and a fusion center, one needs to optimally precompress sensor outputs-sensor observations or estimates before the sensors' transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion, or when an allowed performance loss constraint exists, one needs to design the minimum dimension of sensor data. This paper will answer the above questions by using the matrix decomposition, pseudo-inverse, and eigenvalue techniques.

Optimal dimensionality reduction of sensor data in multisensor estimation fusion

This paper proposes a new distributed Kalman filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.

/pdf/globally-optimal-multisensor-distributed-random-parameter-3j1hhx8w5f.pdf

Globally Optimal Multisensor Distributed Random Parameter Matrices Kalman Filtering Fusion with Applications

Under the assumption of independent observation noises across sensors, Bar-Shalom and Campo proposed a distributed fusion formula for two-sensor systems, whose main calculation is the inverse of submatrices of the error covariance of two local estimates instead of the inverse of the error covariance itself. However, the corresponding simple estimation fusion formula is absent in a general distributed multisensor system. In this paper, an efficient iterative algorithm for distributed multisensor estimation fusion without any restrictive assumption on the noise covariance (i.e., the assumption of independent observation noises across sensors and the two-sensor system, and the direct computation of the Moore-Penrose generalized inverse of the joint error covariance of local estimates are not necessary) is presented. At each iteration, only the inverse or generalized inverse of a matrix having the same dimension as the error covariance of a single-sensor estimate is required. In fact, the proposed algorithm is a generalization of Bar-Shalom and Campo's fusion formula and reduces the computational complexity significantly since the number of iterative steps is less than the number of sensors. An example of a three-sensor system shows how to implement the specific iterative steps and reduce the computational complexities

An efficient algorithm for optimal linear estimation fusion in distributed multisensor systems

In this paper, the robust estimation fusion problem in multisensor systems with norm-bounded uncertainties concerning the error covariance matrix between local estimates is addressed. A robust fusion method by minimizing the worst-case fused mean-squared error (MSE) for all feasible error covariance matrices of local estimates is proposed. The minimax robust fusion weighting matrices can be explicitly formulated as a function of solution of a semidefinite programming (SDP). Some numerical examples demonstrate that when the error covariance matrix suffers disturbance, the proposed fusion method is more robust than the nominal fusion method which ignores the uncertainties, and can improve the performance when the disturbance is considerably large.

Jie Zhou

Papers

Brief paper: Optimal Kalman filtering fusion with cross-correlated sensor noises

Optimal dimensionality reduction of sensor data in multisensor estimation fusion

Globally Optimal Multisensor Distributed Random Parameter Matrices Kalman Filtering Fusion with Applications

An efficient algorithm for optimal linear estimation fusion in distributed multisensor systems

Minimax Robust Optimal Estimation Fusion in Distributed Multisensor Systems With Uncertainties