Augmented Physics-Based Models for High-Order Markov Filtering.

Hybrid physics-based data-driven models, namely, augmented physics-based models (APBMs), are capable of learning complex state dynamics while maintaining some level of model interpretability that can be controlled through appropriate regularizations of the data-driven component. In this article, we extend the APBM formulation for high-order Markov models, where the state space is further augmented with past states (AG-APBM). Typically, state augmentation is a powerful method for state estimation for a high-order Markov model, but it requires the exact knowledge of the system dynamics. The proposed approach, however, does not require full knowledge of dynamics, especially the Markovity order. To mitigate the extra computational burden of such augmentation we propose an approximated-state APBM (AP-APBM) implementation leveraging summaries from past time steps. We demonstrate the performance of AG- and AP-APBMs in an autoregressive model and a target-tracking scenario based on the trajectory of a controlled aircraft with delay-feedback control. The experiments showed that both proposed strategies outperformed the standard APBM approach in terms of estimation error and that the AP-APBM only degraded slightly when compared to AG-APBM. For example, the autoregressive (AR) model simulation in our settings showed that AG-APBM and AP-APBM reduced the estimate error by 31.1% and 26.7%. The time cost and memory usage were reduced by 37.5% and 20% by AP-APBM compared to AG-APBM.

Dynamical Hyperspectral Unmixing With Variational Recurrent Neural Networks.

Multitemporal hyperspectral unmixing (MTHU) is a fundamental tool in the analysis of hyperspectral image sequences. It reveals the dynamical evolution of the materials (endmembers) and of their proportions (abundances) in a given scene. However, adequately accounting for the spatial and temporal variability of the endmembers in MTHU is challenging, and has not been fully addressed so far in unsupervised frameworks. In this work, we propose an unsupervised MTHU algorithm based on variational recurrent neural networks. First, a stochastic model is proposed to represent both the dynamical evolution of the endmembers and their abundances, as well as the mixing process. Moreover, a new model based on a low-dimensional parametrization is used to represent spatial and temporal endmember variability, significantly reducing the amount of variables to be estimated. We propose to formulate MTHU as a Bayesian inference problem. However, the solution to this problem does not have an analytical solution due to the nonlinearity and non-Gaussianity of the model. Thus, we propose a solution based on deep variational inference, in which the posterior distribution of the estimated abundances and endmembers is represented by using a combination of recurrent neural networks and a physically motivated model. The parameters of the model are learned using stochastic backpropagation. Experimental results show that the proposed method outperforms state of the art MTHU algorithms.

Deep Learning of GNSS Acquisition.

Signal acquisition is a crucial step in Global Navigation Satellite System (GNSS) receivers, which is typically solved by maximizing the so-called Cross-Ambiguity Function (CAF) as a hypothesis testing problem. This article proposes to use deep learning models to perform such acquisition, whereby the CAF is fed to a data-driven classifier that outputs binary class posteriors. The class posteriors are used to compute a Bayesian hypothesis test to statistically decide the presence or absence of a GNSS signal. The versatility and computational affordability of the proposed method are addressed by splitting the CAF into smaller overlapping sections, which are fed to a bank of parallel classifiers whose probabilistic results are optimally fused to provide a so-called probability ratio map from which acquisition is decided. Additionally, the article shows how noncoherent integration schemes are enabled through optimal data fusion, with the goal of increasing the resulting classifier accuracy. The article provides simulation results showing that the proposed data-driven method outperforms current CAF maximization strategies, enabling enhanced acquisition at medium-to-high carrier-to-noise density ratios.

Delay-Tolerant Distributed Inference in Tracking Networks.

This paper discusses asynchronous distributed inference in object tracking. Unlike many studies, which assume that the delay in communication between partial estimators and the central station is negligible, our study focuses on the problem of asynchronous distributed inference in the presence of delays. We introduce an efficient data fusion method for combining the distributed estimates, where delay in communications is not negligible. To overcome the delay, predictions are made for the state of the system based on the most current available information from partial estimators. Simulation results show the efficacy of the methods proposed.

Cloud-Based Single-Frequency Snapshot RTK Positioning.

With great potential for being applied to Internet of Things (IoT) applications, the concept of cloud-based Snapshot Real Time Kinematics (SRTK) was proposed and its feasibility under zero-baseline configuration was confirmed recently by the authors. This article first introduces the general workflow of the SRTK engine, as well as a discussion on the challenges of achieving an SRTK fix using actual snapshot data. This work also describes a novel solution to ensure a nanosecond level absolute timing accuracy in order to compute highly precise satellite coordinates, which is required for SRTK. Parameters such as signal bandwidth, integration time and baseline distances have an impact on the SRTK performance. To characterize this impact, different combinations of these settings are analyzed through experimental tests. The results show that the use of higher signal bandwidths and longer integration times result in higher SRTK fix rates, while the more significant impact on the performance comes from the baseline distance. The results also show that the SRTK fix rate can reach more than 93% by using snapshots with a data size as small as 255 kB. The positioning accuracy is at centimeter level when phase ambiguities are resolved at a baseline distance less or equal to 15 km.

Low Complexity Robust Data Demodulation for GNSS.

In this article, we provide closed-form approximations of log-likelihood ratio (LLR) values for direct sequence spread spectrum (DS-SS) systems over three particular scenarios, which are commonly found in the Global Navigation Satellite System (GNSS) environment. Those scenarios are the open sky with smooth variation of the signal-to-noise ratio (SNR), the additive Gaussian interference, and pulsed jamming. In most of the current communications systems, block-wise estimators are considered. However, for some applications such as GNSSs, symbol-wise estimators are available due to the low data rate. Usually, the noise variance is considered either perfectly known or available through symbol-wise estimators, leading to possible mismatched demodulation, which could induce errors in the decoding process. In this contribution, we first derive two closed-form expressions for LLRs in additive white Gaussian and Laplacian noise channels, under noise uncertainty, based on conjugate priors. Then, assuming those cases where the statistical knowledge about the estimation error is characterized by a noise variance following an inverse log-normal distribution, we derive the corresponding closed-form LLR approximations. The relevance of the proposed expressions is investigated in the context of the GPS L1C signal where the clock and ephemeris data (CED) are encoded with low-density parity-check (LDPC) codes. Then, the CED is iteratively decoded based on the belief propagation (BP) algorithm. Simulation results show significant frame error rate (FER) improvement compared to classical approaches not accounting for such uncertainty.

Robust Filtering Techniques for RTK Positioning in Harsh Propagation Environments.

Global navigation satellite systems (GNSSs) play a key role in intelligent transportation systems such as autonomous driving or unmanned systems navigation. In such applications, it is fundamental to ensure a reliable precise positioning solution able to operate in harsh propagation conditions such as urban environments and under multipath and other disturbances. Exploiting carrier phase observations allows for precise positioning solutions at the complexity cost of resolving integer phase ambiguities, a procedure that is particularly affected by non-nominal conditions. This limits the applicability of conventional filtering techniques in challenging scenarios, and new robust solutions must be accounted for. This contribution deals with real-time kinematic (RTK) positioning and the design of robust filtering solutions for the associated mixed integer- and real-valued estimation problem. Families of Kalman filter (KF) approaches based on robust statistics and variational inference are explored, such as the generalized M-based KF or the variational-based KF, aiming to mitigate the impact of outliers or non-nominal measurement behaviors. The performance assessment under harsh propagation conditions is realized using a simulated scenario and real data from a measurement campaign. The proposed robust filtering solutions are shown to offer excellent resilience against outlying observations, with the variational-based KF showcasing the overall best performance in terms of Gaussian efficiency and robustness.

Robust Fusion of c-VEP and Gaze.

Brain computer interfaces (BCIs) are one of the developing technologies, serving as a communication interface for people with neuromuscular disorders. Electroencephalography (EEG) and gaze signals are among the commonly used inputs for the user intent classification problem arising in BCIs. Fusing different types of input modalities, i.e. EEG and gaze, is an obvious but effective solution for achieving high performance on this problem. Even though there are some simplistic approaches for fusing these two evidences, a more effective method is required for classification performances and speeds suitable for real-life scenarios. One of the main problems that is left unrecognized is highly noisy real-life data. In the context of the BCI framework utilized in this work, noisy data stem from user error in the form of tracking a nontarget stimuli, which in turn results in misleading EEG and gaze signals. We propose a method for fusing aforementioned evidences in a probabilistic manner that is highly robust against noisy data. We show the performance of the proposed method on real EEG and gaze data for different configurations of noise control variables. Compared to the regular fusion method, robust method achieves up to 15% higher classification accuracy.

Robust Statistics for GNSS Positioning under Harsh Conditions: A Useful Tool?

Navigation problems are generally solved applying least-squares (LS) adjustments. Techniques based on LS can be shown to perform optimally when the system noise is Gaussian distributed and the parametric model is accurately known. Unfortunately, real world problems usually contain unexpectedly large errors, so-called outliers, that violate the noise model assumption, leading to a spoiled solution estimation. In this work, the framework of robust statistics is explored to provide robust solutions to the global navigation satellite systems (GNSS) single point positioning (SPP) problem. Considering that GNSS observables may be contaminated by erroneous measurements, we survey the most popular approaches for robust regression (M-, S-, and MM-estimators) and how they can be adapted into a general methodology for robust GNSS positioning. We provide both theoretical insights and validation over experimental datasets, which serves in discussing the robust methods in detail.

Detection of Induced GNSS Spoofing Using S-Curve-Bias.

In Global Navigation Satellite System (GNSS), a spoofing attack consists of forged signals which possibly cause the attacked receivers to deduce a false position, a false clock, or both. In contrast to simplistic spoofing, the induced spoofing captures the victim tracking loops by gradually adjusting it's parameters, e.g., code phase and power. Then the victims smoothly deviates from the correct position or timing. Therefore, it is more difficult to detect the induced spoofing than the simplistic one. In this paper, by utilizing the dynamic nature of such gradual adjustment process, an induced spoofing detection method is proposed based on the S-curve-bias (SCB). Firstly, SCB in the inducing process is theoretically derived. Then, in order to detect the induced spoofing, a detection metric is defined. After that, a series of experiments using the Texas spoofing test battery (TEXBAT) are performed to demonstrate the effectiveness of the proposed algorithm.

Huber's Non-Linearity for GNSS Interference Mitigation †.

Satellite-based navigation is prevalent in both commercial applications and critical infrastructures, providing precise position and time referencing. As a consequence, interference to such systems can have repercussions on a plethora of fields. Additionally, Privacy Preserving Devices (PPD)—jamming devices—are relatively inexpensive and easy to obtain, potentially denying the service in a wide geographical area. Current jamming mitigation technology is based on interference cancellation approaches, requiring the detection and estimation of the interference waveform. Recently, the Robust Interference Mitigation (RIM) framework was proposed, which leverages results in robust statistics by treating the jamming signal as an outlier. It has the advantage of rejecting jamming signals without detecting or estimating its waveform. In this paper, we extend the framework to situations where the jammer is sparse in some transformed domain other than the time domain. Additionally, we analyse the use of Huber’s non-linearity within RIM and derive its loss of efficiency. We compare its performance to state-of-the-art techniques and to other RIM solutions, with both synthetic and real signals, showing remarkable results.

Sequential detection of influenza epidemics by the Kolmogorov-Smirnov test.

BACKGROUND: Influenza is a well known and common human respiratory infection, causing significant morbidity and mortality every year. Despite Influenza variability, fast and reliable outbreak detection is required for health resource planning. Clinical health records, as published by the Diagnosticat database in Catalonia, host useful data for probabilistic detection of influenza outbreaks. METHODS: This paper proposes a statistical method to detect influenza epidemic activity. Non-epidemic incidence rates are modeled against the exponential distribution, and the maximum likelihood estimate for the decaying factor λ is calculated. The sequential detection algorithm updates the parameter as new data becomes available. Binary epidemic detection of weekly incidence rates is assessed by Kolmogorov-Smirnov test on the absolute difference between the empirical and the cumulative density function of the estimated exponential distribution with significance level 0 ≤ α ≤ 1. RESULTS: The main advantage with respect to other approaches is the adoption of a statistically meaningful test, which provides an indicator of epidemic activity with an associated probability. The detection algorithm was initiated with parameter λ0 = 3.8617 estimated from the training sequence (corresponding to non-epidemic incidence rates of the 2008-2009 influenza season) and sequentially updated. Kolmogorov-Smirnov test detected the following weeks as epidemic for each influenza season: 50-10 (2008-2009 season), 38-50 (2009-2010 season), weeks 50-9 (2010-2011 season) and weeks 3 to 12 for the current 2011-2012 season. CONCLUSIONS: Real medical data was used to assess the validity of the approach, as well as to construct a realistic statistical model of weekly influenza incidence rates in non-epidemic periods. For the tested data, the results confirmed the ability of the algorithm to detect the start and the end of epidemic periods. In general, the proposed test could be applied to other data sets to quickly detect influenza outbreaks. The sequential structure of the test makes it suitable for implementation in many platforms at a low computational cost without requiring to store large data sets.