Particle filtering and the laplace method for target tracking

Quang, Paul Bui; Musso, Christian; Gland, François Le

doi:10.1109/taes.2015.140419

Cited by 15 publications

(17 citation statements)

References 25 publications

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“…Many of the algorithms mentioned in previous sections can be reformulated with a particle filter-based integral approximation: the unscented particle filter [Mer+01], the sigmapoint particle filter [Mer04], the Gaussian mixture sigma-point particle filter [MW03], and a Laplace method-inspired particle filter [QML16].…”

Section: Dmentioning

confidence: 99%

A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding

Burkhart¹

2020

Preprint

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Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes’ rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein—von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant “T9” used the DKF to type out messages on a tablet PC. Nonstationarities, or changes to the statistical relationship between states and measurements that occur after model training, pose a significant challenge to effective filtering. In brain-computer interfaces, one common type of nonstationarity results from wonkiness or dropout of a single neuron. We show how a robust measurement model can be used within the DKF framework to effectively ignore large changes in the behavior of a single neuron. At BrainGate2, a successful online human neural decoding experiment validated this approach against the commonly-used Kalman filter.

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Section: Dmentioning

confidence: 99%

A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding

Burkhart¹

2020

Preprint

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“…Then, the determinant of FIM can be expressed as According to (11) and (13), when states at are fixed, determinant of FIM is only related to leading angle and step length, and it is an even function of leading angle. To illustrate the relationship between determinant of FIM and leading angle, define the normalized determinant of FIM as Figure 2, for a specified step length, there is an optimal leading angle within (0 ∘ , 90 ∘ ) which maximizes the normalized determinant of FIM.…”

Section: Optimal Observability Guidance Lawmentioning

confidence: 99%

“…To address the problem, target motion analysis (TMA) is generally employed to estimate range and time to go from noisecorrupted bearings measurements. To enhance estimation accuracy, different filters including extended Kalman filter (EKF) [9], particle filter (PF) [10,11], maximum likelihood estimation (MLE), [12] and pseudo-linear estimation [13] were successfully applied in bearings-only TMA. On the other hand, estimation accuracy also relies on state observability which is related to the missile-target relative geometry relation [14][15][16], so it can be improved via missile trajectory optimization.…”

Section: Introductionmentioning

confidence: 99%

Two-Phase Optimal Guidance Law considering Impact Angle Constraint with Bearings-Only Measurements

Wang

Tang

Guo

et al. 2017

International Journal of Aerospace Engineering

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The implementation of advanced guidance laws with bearings-only measurements requires estimation of the range information. To improve estimation accuracy and satisfy the impact angle constraint, this paper proposes a two-phase optimal guidance law consisting of an observing phase and an attacking phase. In the observing phase, the determinant of Fisher information matrix is maximized to achieve the optimal observability and a suboptimal solution expressed by leading angle is derived analytically. Then, a terminal sliding-mode guidance law is designed to track the desired leading angle. In the followed attacking phase, an optimal guidance law is integrated with a switching term to satisfy both the impact angle constraint and the field-of-view constraint. Finally, comparison studies of the proposed guidance law and a traditional optimal guidance law are conducted on stationary targets and maneuvering targets cases. Simulation results demonstrate that the proposed guidance law is able to improve the range observability and achieve better terminal performances including impact angle accuracy and miss distance.

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“…Before completing this introduction, we should also mention a work, which addresses an issue which is connex to our concern. In (Bui Quang et al, 2016), Musso, Bui Quang and Le Gland proposed to combine Laplace method and particle filtering in order to dynamically estimate a state from partial measures with small observation noise. Actually, a partial measure with small observation noise implies a conditionning of the law by an approximated constraint.…”

Section: Introductionmentioning

confidence: 99%

“…This is more or less the kind of problem we are dealing with. However, the approach proposed in (Bui Quang et al, 2016) is essentially unimodal, although it is possible to address some level of multimodality by a mixture of law (Musso et al, 2016). But for the moment this extension is far from meeting our requirements.…”

Section: Introductionmentioning

confidence: 99%

Simulating a Random Vector Conditionally to a Subvariety: A Generic Dichotomous Approach

Dambreville

2021

Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

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The problem of sampling a random vector conditionnaly to a subvariety within a box (actually, a small volume around the subvariety) is addressed. The approach is generic, in the sense that the subvariety may be defined by an isosurface related to any (computable) continuous function. Our approach is based on a dichotomous method. As a result, the sampling process is straightforward, accurate and avoids the use of MCMC methods. Our implementation relies on the evaluation of the matching with the subvariety at each dichotomy step. By using interval analysis techniques for evaluating the matching, our method has been applied up to the dimension 11. Perspectives are evoked for improving the sampling efficiency on higher dimensions. A concept and an example of application of this simulation technique to black-box function optimization are detailed.

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Particle filtering and the laplace method for target tracking

Cited by 15 publications

References 25 publications

A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding

A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding

Two-Phase Optimal Guidance Law considering Impact Angle Constraint with Bearings-Only Measurements

Simulating a Random Vector Conditionally to a Subvariety: A Generic Dichotomous Approach

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