Observability and fisher information matrix in nonlinear regression

Jauffret, Claude

doi:10.1109/taes.2007.4285368

Cited by 67 publications

(42 citation statements)

References 6 publications

(4 reference statements)

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“…Jauffret [16] clearly articulates the link between the rank of the FIM and observability of the parameters being estimated. In the context of calibration, a singular FIM corresponds to some unobservable directions in the parameter space given the current set of observations.…”

Section: Truncated Svd and Qr Solutionsmentioning

confidence: 99%

Self-supervised calibration for robotic systems

Maye

Furgale

Siegwart

2013

2013 IEEE Intelligent Vehicles Symposium (IV)

111

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Abstract-We present a generic algorithm for self calibration of robotic systems that utilizes two key innovations. First, it uses information theoretic measures to automatically identify and store novel measurement sequences. This keeps the computation tractable by discarding redundant information and allows the system to build a sparse but complete calibration dataset from data collected at different times. Second, as the full observability of the calibration parameters may not be guaranteed for an arbitrary measurement sequence, the algorithm detects and locks unobservable directions in parameter space using a truncated QR decomposition of the Gauss-Newton system. The result is an algorithm that listens to an incoming sensor stream, builds a minimal set of data for estimating the calibration parameters, and updates parameters as they become observable, leaving the others locked at their initial guess.Through an extensive set of simulated and real-world experiments, we demonstrate that our method outperforms state-of-the-art algorithms in terms of stability, accuracy, and computational efficiency.

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Section: Truncated Svd and Qr Solutionsmentioning

confidence: 99%

Self-supervised calibration for robotic systems

Maye

Furgale

Siegwart

2013

2013 IEEE Intelligent Vehicles Symposium (IV)

111

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“…In this circumstance, some useful analytic conclusions can be obtained. Jauffret discovered the link between the invertibility of Fisher information matrix and the observability of a parameter estimated in a nonlinear problem (Jauffret, 2007), which builds the foundation of our research. Meanwhile, the implementation of observability analysis based on FIM has been dramatically extended.…”

Section: Introductionmentioning

confidence: 72%

On the observability of Mars entry navigation using radiometric measurements

Yu¹,

Cui²,

Zhu³

2014

Advances in Space Research

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“…When the SS equations which model the trilateration are unobservable, the estimated value does not converge to a meaningful solution due to lack of measurement information [16]. The observability of the equations can be investigated by using the Fisher information matrix [17,18]. According to our study the equations are unobservable, and it means that most conventional approaches such as the EKF cannot accurately estimate all of the original states and the biases.…”

Section: Introductionmentioning

confidence: 91%

“…Here, the FIM is denoted as F, and the covariance matrix of the measurement noise v(t) is written as R. For convenience, we abbreviate the time instant t such as z(t) = z and R(t) = R. The inverse of the FIM means the Cramér-Rao lower bound of any unbiased estimator [17]. Further if the FIM is singular, i.e.…”

Section: Observability Of Biased Distance Modelmentioning

confidence: 99%

Localization based on two-stage treatment for dealing with noisy and biased distance measurements

Cho

Lee

Kim

et al. 2012

EURASIP J. Adv. Signal Process.

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Localization can be performed by trilateration in which the coordinates of a target are calculated by using the coordinates of reference points and the distances between each reference point and the target. Because the distances are measured on the basis of the time-of-flight of various kinds of signals, they contain errors which are the noise and bias. The presence of bias can become a major problem because its magnitude is generally unknown. In this article, we propose an algorithm that combines the Kalman filter (KF) and the least square (LS) algorithm to treat noisy and biased distances measured by chirp spread spectrum ranging defined in IEEE 802.15.4a. By using the KF, we remove the noise in the measured distance; hence, the noise-eliminated distance, which still contains bias, is obtained. The next step consists of the calculation of the target coordinates by using the weighted LS algorithm. This algorithm uses the noise-eliminated distance obtained by using the KF, and the weighting parameters of the algorithm are determined to reduce the effects of bias. To confirm the accuracy of the proposed algorithm, we present the results of indoor localization experiments.

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Observability and fisher information matrix in nonlinear regression

Abstract: This paper is devoted to the link between the Fisher Information Matrix invertibility and the observability of a parameter to be estimated in a nonlinear regression problem.

Cited by 67 publications

References 6 publications

Self-supervised calibration for robotic systems

Self-supervised calibration for robotic systems

On the observability of Mars entry navigation using radiometric measurements

Localization based on two-stage treatment for dealing with noisy and biased distance measurements

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