1,162 research outputs found
Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing
The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances
Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing
The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances
Iterative Unbiased FIR State Estimation: A Review of Algorithms
In this paper, we develop in part and review various iterative unbiased finite impulse response (UFIR) algorithms (both direct and two-stage) for the filtering, smoothing, and prediction of time-varying and time-invariant discrete state-space models in white Gaussian noise environments. The distinctive property of UFIR algorithms is that noise statistics are completely ignored. Instead, an optimal window size is required for optimal performance. We show that the optimal window size can be determined via measurements with no reference. UFIR algorithms are computationally more demanding than Kalman filters, but this extra computational effort can be alleviated with parallel computing, and the extra memory that is required is not a problem for modern computers. Under real-world operating conditions with uncertainties, non-Gaussian noise, and unknown noise statistics, the UFIR estimator generally demonstrates better robustness than the Kalman filter, even with suboptimal window size. In applications requiring large window size, the UFIR estimator is also superior to the best previously known optimal FIR estimators
A kepstrum approach to filtering, smoothing and prediction
The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization
where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new
approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to
adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the
type or order of the signal generating model. And unlike other approaches - with the exception of spectral
subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to
stationary signal and additive white noise
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
How to efficiently identify multiple-input multiple-output (MIMO) linear
parameter-varying (LPV) discrete-time state-space (SS) models with affine
dependence on the scheduling variable still remains an open question, as
identification methods proposed in the literature suffer heavily from the curse
of dimensionality and/or depend on over-restrictive approximations of the
measured signal behaviors. However, obtaining an SS model of the targeted
system is crucial for many LPV control synthesis methods, as these synthesis
tools are almost exclusively formulated for the aforementioned representation
of the system dynamics. Therefore, in this paper, we tackle the problem by
combining state-of-the-art LPV input-output (IO) identification methods with an
LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step.
The resulting modular LPV-SS identification approach achieves statical
efficiency with a relatively low computational load. The method contains the
following three steps: 1) estimation of the Markov coefficient sequence of the
underlying system using correlation analysis or Bayesian impulse response
estimation, then 2) LPV-SS realization of the estimated coefficients by using a
basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate
from a maximum-likelihood point of view by a gradient-based or an
expectation-maximization optimization methodology. The effectiveness of the
full identification scheme is demonstrated by a Monte Carlo study where our
proposed method is compared to existing schemes for identifying a MIMO LPV
system
Cohort aggregation modelling for complex forest stands: Spruce-aspen mixtures in British Columbia
Mixed-species growth models are needed as a synthesis of ecological knowledge
and for guiding forest management. Individual-tree models have been commonly
used, but the difficulties of reliably scaling from the individual to the stand
level are often underestimated. Emergent properties and statistical issues
limit their effectiveness. A more holistic modelling of aggregates at the whole
stand level is a potentially attractive alternative. This work explores
methodology for developing biologically consistent dynamic mixture models where
the state is described by aggregate stand-level variables for species or
age/size cohorts. The methods are demonstrated and tested with a two-cohort
model for spruce-aspen mixtures named SAM. The models combine single-species
submodels and submodels for resource partitioning among the cohorts. The
partitioning allows for differences in competitive strength among species and
size classes, and for complementarity effects. Height growth reduction in
suppressed cohorts is also modelled. SAM fits well the available data, and
exhibits behaviors consistent with current ecological knowledge. The general
framework can be applied to any number of cohorts, and should be useful as a
basis for modelling other mixed-species or uneven-aged stands.Comment: Accepted manuscript, to appear in Ecological Modellin
Recursive and non-recursive filters for sequential smoothing and prediction with instantaneous phase and frequency estimation applications (extended version)
A simple procedure for the design of recursive digital filters with an
infinite impulse response (IIR) and non-recursive digital filters with a finite
impulse response (FIR) is described. The fixed-lag smoothing filters are
designed to track an approximately polynomial signal of specified degree
without bias at steady state, while minimizing the gain of high-frequency
(coloured) noise with a specified power spectral density. For the IIR variant,
the procedure determines the optimal lag (i.e. the passband group delay)
yielding a recursive low-complexity smoother of low order, with a specified
bandwidth, and excellent passband phase linearity. The filters are applied to
the problem of instantaneous frequency estimation, e.g. for Doppler-shift
measurement, for a complex exponential with polynomial phase progression in
additive white noise. For this classical problem, simulations show that the
incorporation of a prediction filter (with a one-sample lead) reduces the
incidence of (phase or frequency) angle unwrapping errors, particularly for
signals with high rates of angle change, which are known to limit the
performance of standard FIR estimators at low SNR. This improvement allows the
instantaneous phase of low-frequency signals to be estimated, e.g. for
time-delay measurement, and/or the instantaneous frequency of
frequency-modulated signals, down to a lower SNR. In the absence of unwrapping
errors, the error variance of the IIR estimators (with the optimal phase lag)
reaches the FIR lower bound, at a significantly lower computational cost.
Guidelines for configuring and tuning both FIR and IIR filters are provided.Comment: Reduced page count from 80 down to 50 by removing page breaks between
figures and reducing figure size. Added page numbers. Added (extended
version) to titl
Modelling bid-ask spreads in competitive dealership markets
pricing;estimation;asset valuation
New Results on LMVDR Estimators for LDSS Models
In the context of linear discrete state-space (LDSS) models, we generalize a result lately introduced in the restricted case of invertible state matrices, namely that the linear minimum variance distortionless response (LMVDR) filter shares exactly the same recursion as the linear least mean squares (LLMS) filter, aka the Kalman filter (KF), except for the initialization. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. This result is particularly noteworthy given the fact that, although LMVDR estimators are sub-optimal in mean-squared error sense, they are infinite impulse response distortionless estimators which do not depend on the prior knowledge on the mean and covariance matrix of the initial state. Thus the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. Seen from this perspective, we also show that the LMVDR filter can be regarded as a generalization of the information filter form of the KF. On another note, LMVDR estimators may also allow to derive unexpected results, as highlighted with the LMVDR fixed-point smoother
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