Noise covariance estimation for Kalman filter tuning using Bayesian approach and Monte Carlo

Matisko, Peter; Havlena, Vladimı́r

doi:10.1002/acs.2369

Cited by 39 publications

(42 citation statements)

References 19 publications

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“…Its functional form, regression vector, and parameters generally differ for different output entries. This flexibility and the scalar-wise modelling of the uncertainty are the main gains of the factorised form (9). Analogically, the state evolution model factorises…”

Section: Preliminariesmentioning

confidence: 99%

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State and parameter estimation of state‐space model with entry‐wise correlated uniform noise

Pavelková

Kárný

2013

Adaptive Control & Signal

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Joint parameter and state estimation is proposed for linear state-space model with uniform, entry-wise correlated, state and output noises (LSU model for short). The adopted Bayesian modelling and approximate estimation produce an estimator that (a) provides the maximum a posteriori estimate enriched by information on its precision, (b) respects correlated noise entries without demanding the user to tune noise covariances, and (c) respects bounded nature of real-life variables.L. PAVELKOVÁ AND M. KÁRNÝ KF, however, faces significant, extensively counteracted, troubles with respect to both (b) and (c) as seen in the following representative samples of existing solutions.As for requirements (a) and (b), KF and its extensions work well when the noise covariances are well chosen. Then, they also provide adequate information on the estimate precision. The covariances are predominantly taken as design parameters of KF as their estimation represents a highly nonlinear problem [8,9]. The number of covariance entries grow quadratically with the state and output dimensions, which soon makes their experimental tuning infeasible. The number of opted entries can be decreased by a nontrivial parsimonious parametrisation [10] or made linearly growing in a factorised version of the state-space model [11,12], but the sensitivity to covariances choice persists, and neither (a) nor (b) are met.The requirement (c) can be fulfilled by a projection of the estimates onto the constraint surface via quadratic programming [13]. Another way is proposed by the probability density function (pdf) truncation approach [14] where the pdf of the state estimate is computed by the standard KF and then truncated at the constraint edges. The constrained state estimate is equal to the mean of the truncated pdf. The induced high-computational demands limit the degree of meeting (c). More importantly, techniques employing a projection or truncation in conjunction with the system model having unbounded support and light tails respect the constraints during estimation but not during modelling. Consequently, the posterior pdf forming the outcome of the Bayesian treatment is a worse estimator than necessary. Indeed, this pdf is a product of prior pdf on parameters and initial state, and likelihood function as a product of pdfs describing the state-space model with observed data inserted. The system model with the constrained states has a complex state and parameter-dependent normalising factor entering the likelihood. This factor is neglected by the discussed techniques.The complexity of the support and form of the exact posterior pdf corresponding to the adequate modelling of boundedness limits feasibility of the Bayesian estimation. Nevertheless, it is desirable to address it as there is a broad range of problems in which explicit inclusion of constraints into the system model significantly improves the estimation quality.The correct modelling of state boundedness and elaboration of the corresponding joint estimator providing both point estimates and info...

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Section: Preliminariesmentioning

confidence: 99%

“…Then, they also provide adequate information on the estimate precision. The covariances are predominantly taken as design parameters of KF as their estimation represents a highly nonlinear problem [8,9]. The number of covariance entries grow quadratically with the state and output dimensions, which soon makes their experimental tuning infeasible.…”

mentioning

confidence: 99%

State and parameter estimation of state‐space model with entry‐wise correlated uniform noise

Pavelková

Kárný

2013

Adaptive Control & Signal

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“…Four relevant methods briefed in his work are: Bayesian, maximum likelihood, correlation and covariance matching. Mehra's work has still been of important directive significance to various recent researches on VCME (Dunık and Šimandl 2008;Bavdekar, et al 2011;Bulut et al 2011;Matisko and Havlena 2013;etc. ).…”

Section: Introductionmentioning

confidence: 99%

A posteriori estimation of stochastic model for multi-sensor integrated inertial kinematic positioning and navigation on basis of variance component estimation

Qian

Wang

2016

J. Glob. Position. Syst.

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Improving a priori stochastic models of the process and measurement noise vectors in Kalman Filer (KF) has always been a challenge. As one preferable technique to address this challenge, the variance component estimation (VCE) applied on the Kalman Filter's process and measurement noise covariance matrix (Q & R) has been proved in plenty of applications. Unsurprisingly, VCE was expected to re-establish the stochastic model about the random errors in the IMU's measurements in a multisensor integrated positioning and navigation system applying Kalman Filter. However, in the conventional error states-based GPS aided inertial navigation system (GPS/INS), the stochastic model tuning is difficult for the IMU's measurements due to the amalgamation of the observables from inertial sensor and other aiding sensors. This paper proposes a generic method for the stochastic model tuning about the random errors in IMU measurements together with other sensors. The core of this novel approach is based on an innovative multisensor integration strategy which deploys upon the vehicle's generic kinematic model and takes the IMU's output as raw measurements in Kalman Filter (IMU/GNSS Kalman Filter). As a result, the statistical orthogonality between random error vectors of any two sensors enables the separate but parallel statistics collection of each individual random error source. Given these independent statistics corresponding to each error source, the VCE technique iteratively tunes all stochastic model of the process and measurement noise vectors. The success of the VCE algorithm is shown through a real dataset involving GPS and inertial sensors.

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“…The method provides an optimal measurement of the process-noise parameters [14]. A numerical characterisation of the method shows that for a given detector the method is reliable up to some limit momentum 1 This work has been performed under a number of assumptions/approximations.…”

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confidence: 99%

Calorimeter-less gamma-ray telescopes: Optimal measurement of charged particle momentum from multiple scattering by Bayesian analysis of Kalman filtering innovations.

Bernard¹,

Frosini²

2017

Proceedings of 7th International Fermi Symposium — PoS(IFS2017)

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Novel gamma-ray telescope schemes (silicon wafer stacks, emulsions, gas detectors) are being developed so as to bridge the sensitivity gap between Compton and pair-creation telescopes. The lower average density with respect to the tungsten/silicon active target of the Fermi-LAT makes large effectivearea telescopes voluminous objects, for which the photon energy measurement by conventional means (calorimeter, magnetic spectrometer, transition radiation detector) is a challenge for the mass budget of the space mission. We present an optimal measurement of track momentum by the multiple measurement of the angular deflections induced by multiple scattering in the active target itself, using a Bayesian analysis of the filtering innovations of a series of Kalman filters applied to the track. For a silicon-wafer-stack telescope, the method yields meaningful results up to a couple of GeV/c.

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Noise covariance estimation for Kalman filter tuning using Bayesian approach and Monte Carlo

Cited by 39 publications

References 19 publications

State and parameter estimation of state‐space model with entry‐wise correlated uniform noise

State and parameter estimation of state‐space model with entry‐wise correlated uniform noise

A posteriori estimation of stochastic model for multi-sensor integrated inertial kinematic positioning and navigation on basis of variance component estimation

Calorimeter-less gamma-ray telescopes: Optimal measurement of charged particle momentum from multiple scattering by Bayesian analysis of Kalman filtering innovations.

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