The Ensemble Kalman Filter: A Signal Processing Perspective

The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review paper is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma-point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general

Non-linear Kalman filters for calibration in radio interferometry

We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. We show using simulations that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly cheap algorithm that we believe to be robust, especially in low signal-to-noise regime. Potentially the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that the effects corrupting visibilities are understood and analytically stable. Recursive algorithms are particularly well adapted for pre-calibration and sky model estimate in a streaming way. This may be useful for the SKA-type instruments that produce huge amounts of data that have to be calibrated before being averaged

Kernel-based fault diagnosis of inertial sensors using analytical redundancy

Kernel methods are able to exploit high-dimensional spaces for representational advantage, while only operating implicitly in such spaces, thus incurring none of the computational cost of doing so. They appear to have the potential to advance the state of the art in control and signal processing applications and are increasingly seeing adoption across these domains. Applications of kernel methods to fault detection and isolation (FDI) have been reported, but few in aerospace research, though they offer a promising way to perform or enhance fault detection. It is mostly in process monitoring, in the chemical processing industry for example, that these techniques have found broader application. This research work explores the use of kernel-based solutions in model-based fault diagnosis for aerospace systems. Specifically, it investigates the application of these techniques to the detection and isolation of IMU/INS sensor faults – a canonical open problem in the aerospace field. Kernel PCA, a kernelised non-linear extension of the well-known principal component analysis (PCA) algorithm, is implemented to tackle IMU fault monitoring. An isolation scheme is extrapolated based on the strong duality known to exist between probably the most widely practiced method of FDI in the aerospace domain – the parity space technique – and linear principal component analysis. The algorithm, termed partial kernel PCA, benefits from the isolation properties of the parity space method as well as the non-linear approximation ability of kernel PCA. Further, a number of unscented non-linear filters for FDI are implemented, equipped with data-driven transition models based on Gaussian processes - a non-parametric Bayesian kernel method. A distributed estimation architecture is proposed, which besides fault diagnosis can contemporaneously perform sensor fusion. It also allows for decoupling faulty sensors from the navigation solution

A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks

Multisensor fusion and consensus filtering are two fascinating subjects in the research of sensor networks. In this survey, we will cover both classic results and recent advances developed in these two topics. First, we recall some important results in the development ofmultisensor fusion technology. Particularly, we pay great attention to the fusion with unknown correlations, which ubiquitously exist in most of distributed filtering problems. Next, we give a systematic review on several widely used consensus filtering approaches. Furthermore, some latest progress on multisensor fusion and consensus filtering is also presented. Finally, conclusions are drawn and several potential future research directions are outlined.the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61374039, 61304010, 11301118, and 61573246, the Hujiang Foundation of China under Grants C14002 and D15009, the Alexander von Humboldt Foundation of Germany, and the Innovation Fund Project for Graduate Student of Shanghai under Grant JWCXSL140

Computationally efficient solutions for tracking people with a mobile robot: an experimental evaluation of Bayesian filters

Modern service robots will soon become an essential part of modern society. As they have to move and act in human environments, it is essential for them to be provided with a fast and reliable tracking system that localizes people in the neighbourhood. It is therefore important to select the most appropriate filter to estimate the position of these persons. This paper presents three efficient implementations of multisensor-human tracking based on different Bayesian estimators: Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Sampling Importance Resampling (SIR) particle filter. The system implemented on a mobile robot is explained, introducing the methods used to detect and estimate the position of multiple people. Then, the solutions based on the three filters are discussed in detail. Several real experiments are conducted to evaluate their performance, which is compared in terms of accuracy, robustness and execution time of the estimation. The results show that a solution based on the UKF can perform as good as particle filters and can be often a better choice when computational efficiency is a key issue

A bank of unscented Kalman filters for multimodal human perception with mobile service robots

A new generation of mobile service robots could be ready soon to operate in human environments if they can robustly estimate position and identity of surrounding people. Researchers in this field face a number of challenging problems, among which sensor uncertainties and real-time constraints. In this paper, we propose a novel and efficient solution for simultaneous tracking and recognition of people within the observation range of a mobile robot. Multisensor techniques for legs and face detection are fused in a robust probabilistic framework to height, clothes and face recognition algorithms. The system is based on an efficient bank of Unscented Kalman Filters that keeps a multi-hypothesis estimate of the person being tracked, including the case where the latter is unknown to the robot. Several experiments with real mobile robots are presented to validate the proposed approach. They show that our solutions can improve the robot's perception and recognition of humans, providing a useful contribution for the future application of service robotics