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250
An Introduction to the Kalman Filter
 UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
, 1995
"... In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area o ..."
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Cited by 1132 (15 self)
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In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation.
The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown.
The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.
Robust Monte Carlo Localization for Mobile Robots
, 2001
"... Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilistic localization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), whi ..."
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Cited by 829 (88 self)
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Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilistic localization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), which approximate the posterior under a common Bayesian formulation of the localization problem. Building on the basic MCL algorithm, this article develops a more robust algorithm called MixtureMCL, which integrates two complimentary ways of generating samples in the estimation. To apply this algorithm to mobile robots equipped with range finders, a kernel density tree is learned that permits fast sampling. Systematic empirical results illustrate the robustness and computational efficiency of the approach.
A New Extension of the Kalman Filter to Nonlinear Systems
, 1997
"... The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which ..."
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Cited by 747 (6 self)
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The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearises all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterise mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet general...
Monte Carlo Localization: Efficient Position Estimation for Mobile Robots
 IN PROC. OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI
, 1999
"... This paper presents a new algorithm for mobile robot localization, called Monte Carlo Localization (MCL). MCL is a version of Markov localization, a family of probabilistic approaches that have recently been applied with great practical success. However, previous approaches were either computational ..."
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Cited by 344 (49 self)
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This paper presents a new algorithm for mobile robot localization, called Monte Carlo Localization (MCL). MCL is a version of Markov localization, a family of probabilistic approaches that have recently been applied with great practical success. However, previous approaches were either computationally cumbersome (such as gridbased approaches that represent the state space by highresolution 3D grids), or had to resort to extremely coarsegrained resolutions. Our approach is computationally efficient while retaining the ability to represent (almost) arbitrary distributions. MCL applies samplingbased methods for approximating probability distributions, in a way that places computation " where needed." The number of samples is adapted online, thereby invoking large sample sets only when necessary. Empirical results illustrate that MCL yields improved accuracy while requiring an order of magnitude less computation when compared to previous approaches. It is also much easier to implement...
Kalman Filterbased Algorithms for Estimating Depth from Image Sequences
, 1989
"... Using known camera motion to estimate depth from image sequences is an important problem in robot vision. Many applications of depthfrommotion, including navigation and manipulation, require algorithms that can estimate depth in an online, incremental fashion. This requires a representation that ..."
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Cited by 258 (27 self)
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Using known camera motion to estimate depth from image sequences is an important problem in robot vision. Many applications of depthfrommotion, including navigation and manipulation, require algorithms that can estimate depth in an online, incremental fashion. This requires a representation that records the uncertainty in depth estimates and a mechanism that integrates new measurements with existing depth estimates to reduce the uncertainty over time. Kalman filtering provides this mechanism. Previous applications of Kalman filtering to depthfrommotion have been limited to estimating depth at the location of a sparse set of features. In this paper, we introduce a new, pixelbased (iconic) algorithm that estimates depth and depth uncertainty at each pixel and incrementally refines these estimates over time. We describe the algorithm and contrast its formulation and performance to that of a featurebased Kalman filtering algorithm. We compare the performance of the two approaches by analyzing their theoretical convergence rates, by conducting quantitative experiments with images of a flat poster, and by conducting qualitative experiments with images of a realistic outdoorscene model. The results show that the new method is an effective way to extract depth from lateral camera translations. This approach can be extended to incorporate general motion and to integrate other sources of information, such as stereo. The algorithms we have developed, which combine Kalman filtering with iconic descriptions of depth, therefore can serve as a useful and general framework for lowlevel dynamic vision.
A General Method for Approximating Nonlinear Transformations of Probability Distributions
, 1996
"... In this paper we describe a new approach for generalised nonlinear filtering. We show that the technique is more accurate, more stable, and far easier to implement than an extended Kalman filter. Several examples are provided, including the application of the new filter to problems involving discont ..."
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Cited by 170 (3 self)
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In this paper we describe a new approach for generalised nonlinear filtering. We show that the technique is more accurate, more stable, and far easier to implement than an extended Kalman filter. Several examples are provided, including the application of the new filter to problems involving discontinuous functions. 1 Introduction Possibly the most important problem arising in tracking and control applications is the representation and maintenance of uncertainty. The state of a system, whether measured or estimated, is rarely known perfectly because (a) measuring instruments and processes have limited precision, and/or (b) estimates of evolving systems are based on process models that fail to include all governing parameters. The uncertainty associated with a state estimate can be represented most generally by a probability distribution incorporating all knowledge about the state. Because the amount of knowledge about the state is inherently finite, a complete parameterisation of the ...
SCAAT: Incremental Tracking with Incomplete Information
, 1997
"... We present a promising new mathematical method for tracking a user's pose (position and orientation) for interactive computer graphics. The method, which is applicable to a wide variety of both commercial and experimental systems, improves accuracy by properly assimilating sequential observatio ..."
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Cited by 160 (15 self)
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We present a promising new mathematical method for tracking a user's pose (position and orientation) for interactive computer graphics. The method, which is applicable to a wide variety of both commercial and experimental systems, improves accuracy by properly assimilating sequential observations, filtering sensor measurements, and by concurrently autocalibrating source and sensor devices. It facilitates user motion prediction, multisensor data fusion, and higher report rates with lower latency than previous methods. Tracking systems determine the user's pose by measuring signals from lowlevel hardware sensors. For reasons of physics and economics, most systems make multiple sequential measurements which are then combined to produce a single tracker report. For example, commercial magnetic trackers using the SPASYN ( Space Synchro) system sequentially measure three magnetic vectors and then combine them mathematically to produce a report of the sensor pose. Our new approach produces tracker reports as each new lowlevel sensor measurement is made rather than waiting to form a complete collection of observations. Because single observations underconstrain the mathematical solution, we refer to our approach as singleconstraintatatime or SCAAT tracking. The key is that the single observations provide some information about the user's state, and thus can be used to incrementally improve a previous estimate. We recursively apply this principle, incorporating new sensor data as soon as it is measured. With this approach we are able to generate estimates more frequently, with less latency, and with improved accuracy. We present results from both an actual implementation, and from extensive simulations.
The scaled unscented transformation
 in Proc. IEEE Amer. Control Conf
, 2002
"... Abstract — This paper describes a generalisation of the unscented transformation (UT) which allows sigma points to be scaled to an arbitrary dimension. The UT is a method for predicting means and covariances in nonlinear systems. A set of samples are deterministically chosen which match the mean and ..."
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Cited by 145 (2 self)
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Abstract — This paper describes a generalisation of the unscented transformation (UT) which allows sigma points to be scaled to an arbitrary dimension. The UT is a method for predicting means and covariances in nonlinear systems. A set of samples are deterministically chosen which match the mean and covariance of a (not necessarily Gaussiandistributed) probability distribution. These samples can be scaled by an arbitrary constant. The method guarantees that the mean and covariance second order accuracy in mean and covariance, giving the same performance as a second order truncated filter but without the need to calculate any Jacobians or Hessians. The impacts of scaling issues are illustrated by considering conversions from polar to Cartesian coordinates with large angular uncertainties.
Ensemble Square Root Filters
, 2003
"... Ensemble data assimilation methods assimilate observations using statespace estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics ..."
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Cited by 116 (7 self)
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Ensemble data assimilation methods assimilate observations using statespace estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics. This transformation may be performed stochastically by treating observations as random variables, or deterministically by requiring that the updated analysis perturbations satisfy the Kalman filter analysis error covariance equation. Deterministic analysis ensemble updates are implementations of Kalman square root filters. The nonuniqueness of the deterministic transformation used in square root Kalman filters provides a framework to compare three recently proposed ensemble data assimilation methods.