In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data 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.

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...

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 grid-based approaches that represent the state space by high-resolution 3D grids), or had to resort to extremely coarse-grained resolutions. Our approach is computationally efficient while retaining the ability to represent (almost) arbitrary distributions. MCL applies sampling-based methods for approximating probability distributions, in a way that places computation " where needed." The number of samples is adapted on-line, 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...

Using known camera motion to estimate depth from image sequences is an important problem in robot vision. Many applications of depth-from-motion, including navigation and manipulation, require algorithms that can estimate depth in an on-line, 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 depth-from-motion have been limited to estimating depth at the location of a sparse set of features. In this paper, we introduce a new, pixel-based (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 feature-based 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 outdoor-scene 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 low-level dynamic vision.

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 low-level 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 under-constrain the mathematical solution, we refer to our approach as single-constraint-at-a-time 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.

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 ...

The problem considered here involves the design and application of a recursive algorithm to a sequence of images of a moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be "smooth" in the sense that it can be modeled by retaining an arbitrary number of terms in the appropriate Taylor series expansions. Translational motion involves a standard rectilinear model, while rotational motion is described with quaternions. Neglected terms of the Taylor series are modeled as process noise. A state-space model is constructed, incorporating both kinematic and structural states, and recursive techniques are used to estimate the state vector as a function of time.

Our HiBall Tracking System generates over 2000 head-pose estimates per second with less than one millisecond of latency, and less than 0.5 millimeters and 0.02 degrees of position and orientation noise, everywhere in a 4.5 by 8.5 meter room. The system is remarkably responsive and robust, enabling VR applications and experiments that previously would have been difficult or even impossible. Previously we published descriptions of only the Kalman filter-based software approach that we call Single-Constraint-at-a-Time tracking. In this paper we describe the complete tracking system, including the novel optical, mechanical, electrical, and algorithmic aspects that enable the unparalleled performance. 1.1 Keywords virtual environments, tracking, calibration, autocalibration, delay, latency, sensor fusion, Kalman filter, optical sensor 2. INTRODUCTION In 1991 the University of North Carolina demonstrated a working scalable optoelectronic head-tracking system in the Tomorrow'...

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 Gaussian-distributed) 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.

This paper addresses the problem of estimation when the cross-correlation in the errors between different random variables are unknown. A new data fusion algorithm, the Covariance Intersection Algorithm (CI), is presented. It is proved that this algorithm yields consistent estimates irrespective of the actual correlations. This property is illustrated in an application of decentralised estimation where it is impossible to consistently use a Kalman filter.