The optimum linear smoother as a combination of two optimum linear filters

Fraser, Donald C.; Potter, John

doi:10.1109/tac.1969.1099196

Cited by 331 publications

(178 citation statements)

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“…When the EM algorithm is applied to dual estimation in a linear system, the E-step is an optimal smoother such as forward-backward smoothing [8]. The M-step yields new parameter settings that can be computed from summary statistics of the E-step distributions [19], [20].…”

Section: B Simulated Resultsmentioning

confidence: 99%

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Maximum likelihood estimation of sensor and action model functions on a mobile robot

Stronger

Stone

2008

2008 IEEE International Conference on Robotics and Automation

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Abstract-In order for a mobile robot to accurately interpret its sensations and predict the effects of its actions, it must have accurate models of its sensors and actuators. These models are typically tuned manually, a brittle and laborious process. Autonomous model learning is a promising alternative to manual calibration, but previous work has assumed the presence of an accurate action or sensor model in order to train the other model. This paper presents an adaptation of the Expectation-Maximization (EM) algorithm to enable a mobile robot to learn both its action and sensor model functions, starting without an accurate version of either. The resulting algorithm is validated experimentally both on a Sony Aibo ERS-7 robot and in simulation.

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Section: B Simulated Resultsmentioning

confidence: 99%

“…In this paper, all state distributions are approximated as multivariate Gaussians. In linear systems, the E-step then amounts to an optimal smoother such as the forward-backward smoother [8]. In the nonlinear case, taking a first-order approximation results in an EKFS.…”

Section: Introductionmentioning

confidence: 99%

Maximum likelihood estimation of sensor and action model functions on a mobile robot

Stronger

Stone

2008

2008 IEEE International Conference on Robotics and Automation

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“…Since a target can generate a number of measurements in each step, the set of measurements associated with the target is denoted 50) where N j = |Y j | is the number of measurements associated with the target at time step j and y i j is the ith associated measurement at time step j. The measurements are assumed to be generated by independent and identically distributed processes.…”

Section: Extended Target Modelmentioning

confidence: 99%

Tracking of Animals Using Airborne Cameras

Veiback¹

2016

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The various elements of a modern target tracking framework are covered. Background theory on pre-processing, modelling and estimation is presented as well as some novel ideas on the topic by the author. In addition, a few applications are posed as target tracking problems for which solutions are gradually constructed as relevant theory is covered.Among considered problems are how to constrain targets to a region, use stateindependent measurements to improve estimation in jump Markov models and how to incorporate observations sampled at an uncertain time into a state-space model.A framework is developed for tracking dolphins constrained to a basin using an overhead camera that suffers from occlusions. In this scenario, conventional motion models would suffer from infeasible predictions outside the basin. A motion model is developed for the dolphins where collisions with nearby walls are avoided by turning. The basin is modelled as a polygon where each point along the edge influences the turn rate of the dolphin. The proposed model results in predictions inside the basin, increasing robustness against occlusions. An extension to a Gaussian mixture background model providing a degree of confidence for detections is used to improve tracking in the presence of shadows. A probabilistic data association filter is also modified to estimate the dolphin extension as an ellipse. The proposed framework is able to maintain tracks through occlusions and poor light conditions. A framework is developed for estimating takeoff times and directions of birds in circular cages using an overhead camera. A jump Markov model is used to model the stationary and flight behaviours of the birds. A proposed extension also incorporates state-independent measurements, such as blurriness, to improve mode estimation. Takeoff times and directions are estimated from mode transitions and results are compared to manually annotated data.The cameras are inaccessible in both applications, disallowing proper calibrations. As an alternative, a method is proposed to estimate stationary camera models from available data and known features in the scene. A map of the basin and the funnel dimensions are used respectively. The method estimates a homography and distortion parameters in an invertible mapping function.An extension to the linear Gaussian state-space models is proposed, incorporating an additional observation with an uncertain timestamp. The posterior distribution of the states is derived for the model, which is shown to be a mixture of Gaussians, as well as some estimators for the distribution. The effects of incorporating the observation with an uncertain timestamp into the model are analysed for a one-dimensional scenario. The model is also applied to improve the GPS position of an orienteering sprinter by using the control position as an observation with an uncertain timestamp. Populärvetenskaplig sammanfattningMålföljning (eng. target tracking) är ett moget forskningsområde med anor tillbaka till åtminstone 30-talet. Då tävlade en ha...

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“…Our interest in the smoothing problem was caused by the Mayne-Fraser twofilter formula [5,6], on which topic a large number of papers have been written [7][8][9][12][13][14][15][16][17] . In some of these papers the authors have encountered difficulties in motivating this formula, and the many attempts to justify it stochastically have, in our opinion , been less than convincing~ In our stochastic realization setting the two filters have a natural interpretation :…”

Section: Such a Representation Is Called A Stochastic Realization Of mentioning

confidence: 99%

“…where x~ and x~ are given by Fraser two-filter f ormuZ-a [5,6], which has received considerable attention in the literature [7][8][9][13][14][15][16][17] . Although this algorithm is easy to derive formally [9], its probabilistic justification has caused considerable difficulty, partly due to the fact that Q*(t) as t -~ T. The system (3.20) has usually been interpreted as a backward filter , and in [14][15][16][17] [14 , 15 , 17], in which papers the back ward estima te…”

Section: ~(mentioning

confidence: 99%