RcppArmadillo : accelerating R with high-performance C++ linear algebra

The R statistical environment and language has demonstrated particular strengths for interactive development of statistical algorithms, as well as data modelling and visualisation. Its current implementation has an interpreter at its core which may result in a performance penalty in comparison to directly executing user algorithms in the native machine code of the host CPU. In contrast, the C++ language has no built-in visualisation capabilities, handling of linear algebra or even basic statistical algorithms; however, user programs are converted to high-performance machine code, ahead of execution. A new method avoids possible speed penalties in R by using the Rcpp extension package in conjunction with the Armadillo C++ matrix library. In addition to the inherent performance advantages of compiled code, Armadillo provides an easy-to-use template-based meta-programming framework, allowing the automatic pooling of several linear algebra operations into one, which in turn can lead to further speedups. With the aid of Rcpp and Armadillo, conversion of linear algebra centered algorithms from R to C++ becomes straightforward. The algorithms retains the overall structure as well as readability, all while maintaining a bidirectional link with the host R environment. Empirical timing comparisons of R and C++ implementations of a Kalman filtering algorithm indicate a speedup of several orders of magnitude.

Aircraft dynamic navigation for unmanned aerial vehicles

This thesis describes the investigation of an Aircraft Dynamic Navigation (ADN) approach, which incorporates an Aircraft Dynamic Model (ADM) directly into the navigation filter of a fixed-wing aircraft or UAV. The result is a novel approach that offers both performance improvements and increased reliability during short-term GPS outages. This is important in allowing future UAVs to achieve routine, unconstrained, and safe operations in commercial environments. The primary contribution of this research is the formulation Unscented Kalman Filter (UKF) which incorporates a complex, non-linear, laterally and longitudinally coupled, ADM, and sensor suite consisting of a Global Positioning System (GPS) receiver, Inertial Measurement Unit (IMU), Electronic Compass (EC), and Air Data (AD) Pitot Static System.

Recursive actuator fault detection and diagnosis for emergency landing of UASs

This paper presents a practical recursive fault detection and diagnosis (FDD) scheme for online identification of actuator faults for unmanned aerial systems (UASs) based on the unscented Kalman filtering (UKF) method. The proposed FDD algorithm aims to monitor health status of actuators and provide indication of actuator faults with reliability, offering necessary information for the design of fault-tolerant flight control systems to compensate for side-effects and improve fail-safe capability when actuator faults occur. The fault detection is conducted by designing separate UKFs to detect aileron and elevator faults using a nonlinear six degree-of-freedom (DOF) UAS model. The fault diagnosis is achieved by isolating true faults by using the Bayesian Classifier (BC) method together with a decision criterion to avoid false alarms. High-fidelity simulations with and without measurement noise are conducted with practical constraints considered for typical actuator fault scenarios, and the proposed FDD exhibits consistent effectiveness in identifying occurrence of actuator faults, verifying its suitability for integration into the design of fault-tolerant flight control systems for emergency landing of UASs.

Real-time kinematic positioning over long baselines using triple-frequency BeiDou signals

The BeiDou system is the first global navigation satellite system in which all satellites transmit triple-frequency signals that can provide the positioning, navigation, and timing independently. A benefit of triple-frequency signals is that more useful combinations can be formed, including some extrawide-lane combinations whose ambiguities can generally be instantaneously fixed without distance restriction, although the narrow-lane ambiguity resolution (NL AR) still depends on the interreceiver distance or requires a long time to achieve. In this paper, we synthetically study decimeter and centimeter kinematic positioning using BeiDou triple-frequency signals. It starts with AR of two extrawide-lane signals based on the ionosphere-free or ionosphere-reduced geometry-free model. For decimeter positioning, one can immediately use two ambiguity-fixed extrawide-lane observations without pursuing NL AR. To achieve higher accuracy, NL AR is the necessary next step. Despite the fact that long-baseline NL AR is still challenging, some NL ambiguities can indeed be fixed with high reliability. Partial AR for NL signals is acceptable, because as long as some ambiguities for NL signals are fixed, positioning accuracy will be certainly improved.With accumulation of observations, more and more NL ambiguities are fixed and the positioning accuracy continues to improve. An efficient Kalman-filtering system is established to implement the whole process. The formulated system is flexible, since the additional constraints can be easily applied to enhance the model's strength. Numerical results from a set of real triple-frequency BeiDou data on a 50 km baseline show that decimeter positioning is achievable instantaneously.With only five data epochs, 84% of NL ambiguities can be fixed so that the real-time kinematic accuracies are 4.5, 2.5, and 16 cm for north, east, and height components (respectively), while with 10 data epochs more than 90% of NL ambiguities are fixed, and the rea- -time kinematic solutions are improved to centimeter level for all three coordinate components.

Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

Many problems of state estimation in structural dynamics permit a partitioning of system states into nonlinear and conditionally linear substructures. This enables a part of the problem to be solved exactly, using the Kalman filter, and the remainder using Monte Carlo simulations. The present study develops an algorithm that combines sequential importance sampling based particle filtering with Kalman filtering to a fairly general form of process equations and demonstrates the application of a substructuring scheme to problems of hidden state estimation in structures with local nonlinearities, response sensitivity model updating in nonlinear systems, and characterization of residual displacements in instrumented inelastic structures. The paper also theoretically demonstrates that the sampling variance associated with the substructuring scheme used does not exceed the sampling variance corresponding to the Monte Carlo filtering without substructuring. (C) 2012 Elsevier Ltd. All rights reserved.

Dynamic state estimation for identifying earthquake support motions in instrumented structures

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

Joint Approximately Sparse Channel Estimation and Data Detection in OFDM Systems Using Sparse Bayesian Learning

It is well known that the impulse response of a wide-band wireless channel is approximately sparse, in the sense that it has a small number of significant components relative to the channel delay spread. In this paper, we consider the estimation of the unknown channel coefficients and its support in OFDM systems using a sparse Bayesian learning (SBL) framework for exact inference. In a quasi-static, block-fading scenario, we employ the SBL algorithm for channel estimation and propose a joint SBL (J-SBL) and a low-complexity recursive J-SBL algorithm for joint channel estimation and data detection. In a time-varying scenario, we use a first-order autoregressive model for the wireless channel and propose a novel, recursive, low-complexity Kalman filtering-based SBL (KSBL) algorithm for channel estimation. We generalize the KSBL algorithm to obtain the recursive joint KSBL algorithm that performs joint channel estimation and data detection. Our algorithms can efficiently recover a group of approximately sparse vectors even when the measurement matrix is partially unknown due to the presence of unknown data symbols. Moreover, the algorithms can fully exploit the correlation structure in the multiple measurements. Monte Carlo simulations illustrate the efficacy of the proposed techniques in terms of the mean-square error and bit error rate performance.

MULTI-PITCH TRACKING USING GAUSSIAN MIXTURE MODEL WITH TIME VARYING PARAMETERS AND GRATING COMPRESSION TRANSFORM

Grating Compression Transform (GCT) is a two-dimensional analysis of speech signal which has been shown to be effective in multi-pitch tracking in speech mixtures. Multi-pitch tracking methods using GCT apply Kalman filter framework to obtain pitch tracks which requires training of the filter parameters using true pitch tracks. We propose an unsupervised method for obtaining multiple pitch tracks. In the proposed method, multiple pitch tracks are modeled using time-varying means of a Gaussian mixture model (GMM), referred to as TVGMM. The TVGMM parameters are estimated using multiple pitch values at each frame in a given utterance obtained from different patches of the spectrogram using GCT. We evaluate the performance of the proposed method on all voiced speech mixtures as well as random speech mixtures having well separated and close pitch tracks. TVGMM achieves multi-pitch tracking with 51% and 53% multi-pitch estimates having error <= 20% for random mixtures and all-voiced mixtures respectively. TVGMM also results in lower root mean squared error in pitch track estimation compared to that by Kalman filtering.

NESTED SPARSE BAYESIAN LEARNING FOR BLOCK-SPARSE SIGNALS WITH INTRA-BLOCK CORRELATION

In this work, we address the recovery of block sparse vectors with intra-block correlation, i.e., the recovery of vectors in which the correlated nonzero entries are constrained to lie in a few clusters, from noisy underdetermined linear measurements. Among Bayesian sparse recovery techniques, the cluster Sparse Bayesian Learning (SBL) is an efficient tool for block-sparse vector recovery, with intra-block correlation. However, this technique uses a heuristic method to estimate the intra-block correlation. In this paper, we propose the Nested SBL (NSBL) algorithm, which we derive using a novel Bayesian formulation that facilitates the use of the monotonically convergent nested Expectation Maximization (EM) and a Kalman filtering based learning framework. Unlike the cluster-SBL algorithm, this formulation leads to closed-form EMupdates for estimating the correlation coefficient. We demonstrate the efficacy of the proposed NSBL algorithm using Monte Carlo simulations.

Joint Channel Estimation and Data Detection in MIMO-OFDM Systems: A Sparse Bayesian Learning Approach

The impulse response of wireless channels between the N-t transmit and N-r receive antennas of a MIMO-OFDM system are group approximately sparse (ga-sparse), i.e., NtNt the channels have a small number of significant paths relative to the channel delay spread and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wireless channels are also group approximately cluster-sparse (gac-sparse), i.e., every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this paper, we cast the problem of estimating the ga-sparse and gac-sparse block-fading and time-varying channels in the sparse Bayesian learning (SBL) framework and propose a bouquet of novel algorithms for pilot-based channel estimation, and joint channel estimation and data detection, in MIMO-OFDM systems. The proposed algorithms are capable of estimating the sparse wireless channels even when the measurement matrix is only partially known. Further, we employ a first-order autoregressive modeling of the temporal variation of the ga-sparse and gac-sparse channels and propose a recursive Kalman filtering and smoothing (KFS) technique for joint channel estimation, tracking, and data detection. We also propose novel, parallel-implementation based, low-complexity techniques for estimating gac-sparse channels. Monte Carlo simulations illustrate the benefit of exploiting the gac-sparse structure in the wireless channel in terms of the mean square error (MSE) and coded bit error rate (BER) performance.

Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

Minimum sensor duty cycle with guaranteed estimator performance

In this paper, we consider Kalman filtering over a network and construct the optimal sensor data scheduling schemes which minimize the sensor duty cycle and guarantee a bounded error or a bounded average error at the remote estimator. Depending on the computation capability of the sensor, we can either give a closed-form expression of the minimum sensor duty cycle or provide tight lower and upper bounds of it. Examples are provided throughout the paper to demonstrate the results. © 2012 IEEE.

基于UKF滤波的自主移动机器人锂电池SOC估计

准确估计剩余电量(state of charge,SOC)关系到自主移动机器人(AMR)的生存与安全,是AMR研究中所面临的主要挑战之一。针对广义卡尔曼滤波估计SOC的不足,本文给出基于无色卡尔曼滤波(UKF)估计AMR锂电池SOC的新方法。通过试验对UKF和EKF进行了比较。试验验证了同样条件下,UKF比EKF具有更好的滤波估计精度。

Target Detection and Tracking With Heterogeneous Sensors

We present a multimodal detection and tracking algorithm for sensors composed of a camera mounted between two microphones. Target localization is performed on color-based change detection in the video modality and on time difference of arrival (TDOA) estimation between the two microphones in the audio modality. The TDOA is computed by multiband generalized cross correlation (GCC) analysis. The estimated directions of arrival are then postprocessed using a Riccati Kalman filter. The visual and audio estimates are finally integrated, at the likelihood level, into a particle filter (PF) that uses a zero-order motion model, and a weighted probabilistic data association (WPDA) scheme. We demonstrate that the Kalman filtering (KF) improves the accuracy of the audio source localization and that the WPDA helps to enhance the tracking performance of sensor fusion in reverberant scenarios. The combination of multiband GCC, KF, and WPDA within the particle filtering framework improves the performance of the algorithm in noisy scenarios. We also show how the proposed audiovisual tracker summarizes the observed scene by generating metadata that can be transmitted to other network nodes instead of transmitting the raw images and can be used for very low bit rate communication. Moreover, the generated metadata can also be used to detect and monitor events of interest.