1,545 research outputs found
Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting
We present a continuous time state estimation framework that unifies
traditionally individual tasks of smoothing, tracking, and forecasting (STF),
for a class of targets subject to smooth motion processes, e.g., the target
moves with nearly constant acceleration or affected by insignificant noises.
Fundamentally different from the conventional Markov transition formulation,
the state process is modeled by a continuous trajectory function of time (FoT)
and the STF problem is formulated as an online data fitting problem with the
goal of finding the trajectory FoT that best fits the observations in a sliding
time-window. Then, the state of the target, whether the past (namely,
smoothing), the current (filtering) or the near-future (forecasting), can be
inferred from the FoT. Our framework releases stringent statistical modeling of
the target motion in real time, and is applicable to a broad range of real
world targets of significance such as passenger aircraft and ships which move
on scheduled, (segmented) smooth paths but little statistical knowledge is
given about their real time movement and even about the sensors. In addition,
the proposed STF framework inherits the advantages of data fitting for
accommodating arbitrary sensor revisit time, target maneuvering and missed
detection. The proposed method is compared with state of the art estimators in
scenarios of either maneuvering or non-maneuvering target.Comment: 16 pages, 8 figures, 5 tables, 80 references; Codes availabl
Bayesian inference of time varying parameters in autoregressive processes
In the autoregressive process of first order AR(1), a homogeneous correlated
time series is recursively constructed as , using random Gaussian deviates and fixed values for
the correlation coefficient and for the noise amplitude . To model
temporally heterogeneous time series, the coefficients and can
be regarded as time-dependend variables by themselves, leading to the
time-varying autoregressive processes TVAR(1). We assume here that the time
series is known and attempt to infer the temporal evolution of the
'superstatistical' parameters and . We present a sequential
Bayesian method of inference, which is conceptually related to the Hidden
Markov model, but takes into account the direct statistical dependence of
successively measured variables . The method requires almost no prior
knowledge about the temporal dynamics of and and can handle
gradual and abrupt changes of these superparameters simultaneously. We compare
our method with a Maximum Likelihood estimate based on a sliding window and
show that it is superior for a wide range of window sizes
Combining Generative and Discriminative Models for Hybrid Inference
A graphical model is a structured representation of the data generating
process. The traditional method to reason over random variables is to perform
inference in this graphical model. However, in many cases the generating
process is only a poor approximation of the much more complex true data
generating process, leading to suboptimal estimation. The subtleties of the
generative process are however captured in the data itself and we can `learn to
infer', that is, learn a direct mapping from observations to explanatory latent
variables. In this work we propose a hybrid model that combines graphical
inference with a learned inverse model, which we structure as in a graph neural
network, while the iterative algorithm as a whole is formulated as a recurrent
neural network. By using cross-validation we can automatically balance the
amount of work performed by graphical inference versus learned inference. We
apply our ideas to the Kalman filter, a Gaussian hidden Markov model for time
sequences, and show, among other things, that our model can estimate the
trajectory of a noisy chaotic Lorenz Attractor much more accurately than either
the learned or graphical inference run in isolation
Learning Hidden Markov Models for Linear Gaussian Systems with Applications to Event-based State Estimation
This work attempts to approximate a linear Gaussian system with a
finite-state hidden Markov model (HMM), which is found useful in solving
sophisticated event-based state estimation problems. An indirect modeling
approach is developed, wherein a state space model (SSM) is firstly identified
for a Gaussian system and the SSM is then used as an emulator for learning an
HMM. In the proposed method, the training data for the HMM are obtained from
the data generated by the SSM through building a quantization mapping.
Parameter learning algorithms are designed to learn the parameters of the HMM,
through exploiting the periodical structural characteristics of the HMM. The
convergence and asymptotic properties of the proposed algorithms are analyzed.
The HMM learned using the proposed algorithms is applied to event-triggered
state estimation, and numerical results on model learning and state estimation
demonstrate the validity of the proposed algorithms.Comment: The manuscript is under review by a journa
Dynamic Filtering of Time-Varying Sparse Signals via l1 Minimization
Despite the importance of sparsity signal models and the increasing
prevalence of high-dimensional streaming data, there are relatively few
algorithms for dynamic filtering of time-varying sparse signals. Of the
existing algorithms, fewer still provide strong performance guarantees. This
paper examines two algorithms for dynamic filtering of sparse signals that are
based on efficient l1 optimization methods. We first present an analysis for
one simple algorithm (BPDN-DF) that works well when the system dynamics are
known exactly. We then introduce a novel second algorithm (RWL1-DF) that is
more computationally complex than BPDN-DF but performs better in practice,
especially in the case where the system dynamics model is inaccurate.
Robustness to model inaccuracy is achieved by using a hierarchical
probabilistic data model and propagating higher-order statistics from the
previous estimate (akin to Kalman filtering) in the sparse inference process.
We demonstrate the properties of these algorithms on both simulated data as
well as natural video sequences. Taken together, the algorithms presented in
this paper represent the first strong performance analysis of dynamic filtering
algorithms for time-varying sparse signals as well as state-of-the-art
performance in this emerging application.Comment: 26 pages, 8 figures. arXiv admin note: substantial text overlap with
arXiv:1208.032
Supervised and Unsupervised Speech Enhancement Using Nonnegative Matrix Factorization
Reducing the interference noise in a monaural noisy speech signal has been a
challenging task for many years. Compared to traditional unsupervised speech
enhancement methods, e.g., Wiener filtering, supervised approaches, such as
algorithms based on hidden Markov models (HMM), lead to higher-quality enhanced
speech signals. However, the main practical difficulty of these approaches is
that for each noise type a model is required to be trained a priori. In this
paper, we investigate a new class of supervised speech denoising algorithms
using nonnegative matrix factorization (NMF). We propose a novel speech
enhancement method that is based on a Bayesian formulation of NMF (BNMF). To
circumvent the mismatch problem between the training and testing stages, we
propose two solutions. First, we use an HMM in combination with BNMF (BNMF-HMM)
to derive a minimum mean square error (MMSE) estimator for the speech signal
with no information about the underlying noise type. Second, we suggest a
scheme to learn the required noise BNMF model online, which is then used to
develop an unsupervised speech enhancement system. Extensive experiments are
carried out to investigate the performance of the proposed methods under
different conditions. Moreover, we compare the performance of the developed
algorithms with state-of-the-art speech enhancement schemes using various
objective measures. Our simulations show that the proposed BNMF-based methods
outperform the competing algorithms substantially
Earthquake Forecasting Based on Data Assimilation: Sequential Monte Carlo Methods for Renewal Processes
In meteorology, engineering and computer sciences, data assimilation is
routinely employed as the optimal way to combine noisy observations with prior
model information for obtaining better estimates of a state, and thus better
forecasts, than can be achieved by ignoring data uncertainties. Earthquake
forecasting, too, suffers from measurement errors and partial model information
and may thus gain significantly from data assimilation. We present perhaps the
first fully implementable data assimilation method for earthquake forecasts
generated by a point-process model of seismicity. We test the method on a
synthetic and pedagogical example of a renewal process observed in noise, which
is relevant to the seismic gap hypothesis, models of characteristic earthquakes
and to recurrence statistics of large quakes inferred from paleoseismic data
records. To address the non-Gaussian statistics of earthquakes, we use
sequential Monte Carlo methods, a set of flexible simulation-based methods for
recursively estimating arbitrary posterior distributions. We perform extensive
numerical simulations to demonstrate the feasibility and benefits of
forecasting earthquakes based on data assimilation. In particular, we show that
the forecasts based on the Optimal Sampling Importance Resampling (OSIR)
particle filter are significantly better than those of a benchmark forecast
that ignores uncertainties in the observed event times. We use the marginal
data likelihood, a measure of the explanatory power of a model in the presence
of data errors, to estimate parameters and compare models.Comment: 55 pages, 15 figure
Kalman filter with impulse noised outliers : A robust sequential algorithm to filter data with a large number of outliers
Impulsed noise outliers are data points that differs significantly from other
observations.They are generally removed from the data set through local
regression or Kalman filter algorithm.However, these methods, or their
generalizations, are not well suited when the number of outliers is ofthe same
order as the number of low-noise data. In this article, we propose a new model
for impulsenoised outliers based on simple latent linear Gaussian processes as
in the Kalman Filter. We present a fastforward-backward algorithm to filter and
smooth sequential data and which also detect these outliers.We compare the
robustness and efficiency of this algorithm with classical methods. Finally, we
applythis method on a real data set from a Walk Over Weighing system admitting
around 60% of outliers. Forthis application, we further develop an (explicit)
EM algorithm to calibrate some algorithm parameters
Partially Linear Estimation with Application to Sparse Signal Recovery From Measurement Pairs
We address the problem of estimating a random vector X from two sets of
measurements Y and Z, such that the estimator is linear in Y. We show that the
partially linear minimum mean squared error (PLMMSE) estimator does not require
knowing the joint distribution of X and Y in full, but rather only its
second-order moments. This renders it of potential interest in various
applications. We further show that the PLMMSE method is minimax-optimal among
all estimators that solely depend on the second-order statistics of X and Y. We
demonstrate our approach in the context of recovering a signal, which is sparse
in a unitary dictionary, from noisy observations of it and of a filtered
version of it. We show that in this setting PLMMSE estimation has a clear
computational advantage, while its performance is comparable to
state-of-the-art algorithms. We apply our approach both in static and dynamic
estimation applications. In the former category, we treat the problem of image
enhancement from blurred/noisy image pairs, where we show that PLMMSE
estimation performs only slightly worse than state-of-the art algorithms, while
running an order of magnitude faster. In the dynamic setting, we provide a
recursive implementation of the estimator and demonstrate its utility in the
context of tracking maneuvering targets from position and acceleration
measurements.Comment: 13 pages, 5 figure
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