Status of CR-like lower bounds for nonlinear filtering

Kerr, T. H.

doi:10.1109/7.42076

Cited by 66 publications

(19 citation statements)

References 70 publications

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“…Some properties of the PCRB are summarized in Section II. Several lower bounds for nonlinear dynamical systems have appeared in the literature; see the overview in [6]. However, the continuous-time case has received heavy emphasis but not the discrete-time case, which is of greater practical importance.…”

Section: Introductionmentioning

confidence: 99%

“…Both of these bounds were obtained by comparing the information matrix of the original system with an information matrix of a suitable Gaussian system. The bound in [3] is already quite general, but it still has some limitations (see the discussion in [6]), i.e., the assumption that the dimension of the system and measurements are identical. Recently, the approach by Galdos has been generalized for nonlinear th-order autoregressive processes driven by additive Gaussian noise with state-dependent gain [4].…”

Section: Introductionmentioning

confidence: 99%

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Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

Tichavský

Muravchik

Nehorai

1998

IEEE Trans. Signal Process.

1,207

750

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Abstract-A mean-square error lower bound for the discretetime nonlinear filtering problem is derived based on the Van Trees (posterior) version of the Cramér-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

Tichavský

Muravchik

Nehorai

1998

IEEE Trans. Signal Process.

1,207

750

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“…In contrast to this, the parametric crlb framework sees the true state trajectory as known and deterministic. The papers [74,123] gives a good insight in early work done on estimation bounds for nonlinear filtering, including parametric crlb, while [10,124] presents more recent work with focus on posterior crlb.…”

Section: Crlb For Dynamic Systemsmentioning

confidence: 99%

On Pose Estimation in Room-Scaled Environments

Nyqvist¹

2016

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Systra mi, du är bäst! Ikväll ska vi tokdansa med Ronny och Ragge på bordet tills byxorna spricker så att mamma får dåndimpen och pappa ramlar ur soffan. AbstractPose (position and orientation) tracking in room-scaled environments is an enabling technique for many applications. Today, virtual reality (vr) and augmented reality (ar) are two examples of such applications, receiving high interest both from the public and the research community. Accurate pose tracking of the vr or ar equipment, often a camera or a headset, or of different body parts is crucial to trick the human brain and make the virtual experience realistic. Pose tracking in room-scaled environments is also needed for reference tracking and metrology. This thesis focuses on an application to metrology. In this application, photometric models of a photo studio are needed to perform realistic scene reconstruction and image synthesis. Pose tracking of a dedicated sensor enables creation of these photometric models. The demands on the tracking system used in this application is high. It must be able to provide sub-centimeter and sub-degree accuracy and at same time be easy to move and install in new photo studios.The focus of this thesis is to investigate and develop methods for a pose tracking system that satisfies the requirements of the intended metrology application. The Bayesian filtering framework is suggested because of its firm theoretical foundation in informatics and because it enables straightforward fusion of measurements from several sensors. Sensor fusion is in this thesis seen as a way to exploit complementary characteristics of different sensors to increase tracking accuracy and robustness. Four different types of measurements are considered; inertialmeasurements, images from a camera, range (time-of-flight) measurements from ultra wide band (uwb) radio signals, and range and velocity measurements from echoes of transmitted acoustic signals.A simulation study and a study of the Cramér-Rao lower filtering bound (crlb) show that an inertial-camera system has the potential to reach the required tracking accuracy. It is however assumed that known fiducial markers, that can be detected and recognized in images, are deployed in the environment. The study shows that many markers are required. This makes the solution more of a stationary solution and the mobility requirement is not fulfilled. A simultaneous localization and mapping (slam) solution, where naturally occurring features are used instead of known markers, are suggested solve this problem. Evaluation using real data shows that the provided inertial-camera slam filter suffers from drift but that support from uwb range measurements eliminates this drift. The slam solution is then only dependent on knowing the position of very few stationary uwb transmitters compared to a large number of known fiducial markers. As a last step, to increase the accuracy of the slam filter, it is investigated if and how range measurements can be complemented with velocity measurement obtained as a resu...

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“…From (8) and (11), the task is clear: We must characterize problems for which [see (13)], regardless of the number of observations of the time index . We thus examine (12) and rewrite it as Taking the gradient with respect to of the logarithm, we get (17) in which…”

Section: Some Sufficient Conditions For a Multiplicative Crlbmentioning

confidence: 99%

Matrix CRLB scaling due to measurements of uncertain origin

Niu

Willett

Bar‐Shalom

2001

IEEE Trans. Signal Process.

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Abstract-In many estimation situations, measurements are of uncertain origin. This is best exemplified by the target-tracking situation in which at each scan (of a radar, sonar, or electro-optical sensor), a number of measurements are obtained, and it is not known which, if any, of these is target originated. The source of extraneous measurements can be false alarms-especially in low-SNR situations that force the detector at the end of the signal processing chain to operate with a reduced threshold-or spurious targets. In several earlier papers, the surprising observation was made that the Cramér-Rao lower bound (CRLB) for the estimation of a fixed parameter vector (e.g., initial position and velocity) that characterizes the target motion, for the special case of multidimensional measurements in the presence of additive white Gaussian noise, is simply a multiple of that for the case with no uncertainty. That is, there is a scalar information-reduction factor; this is particularly useful as it allows comparison in terms of a scalar. In this paper, we explore this result to determine how wide the class of such problems is. It turns out to include many non-Gaussian situations. Simulations corroborate the analysis.

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Status of CR-like lower bounds for nonlinear filtering

Cited by 66 publications

References 70 publications

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

On Pose Estimation in Room-Scaled Environments

Matrix CRLB scaling due to measurements of uncertain origin

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