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    Simultaneous Localization and Map Building Perception happens locally, in the egocentric frame of reference of the robot.In order to ensure correspondence between the local representation of the environment built by the landmark extraction processes, and the global representation contained in a map, the robot must estimate its own position with respect to this map.34153
    The use of stochastic models for map building and localization in mobile
    robotics has gained much popularity in recent years [24, 38, 61]. Of particular
    interest is the use of predictive filters to estimate the robot position and
    uncertainty, and to update these estimates from sensor readings while at the
    same time building an incremental map of the environment [7, 16, 21, 31, 63,
    79, 83].
    One of the most critical limitations to the application of such estimationtheoretic
    approaches to map building and localization is the data association
    problem. Data association refers to the issue of matching observations with
    previously learned elements from the environment. Some techniques can be
    used to alleviate the data association problem, such as the tracking of landmarks
    from one robot position to the next, or by using efficient tests for sceneto-
    model landmark match hypothesis verification. Obviously there is always a
    compromise between the possibility of fully invariant landmark characterization
    and the difficulty to extract such characterizing features from raw sensor
    data.
    As we address issues such as viewpoint invariance and feature extraction
    from sensor data, it is overwhelming how undesired environment dynamics,
    occlusions, and sensor noise can still make data association a daunting task.
    One possibility to overcome the data association problem altogether is with
    the deployment of uniquely identifiable man-made beacons to aid in localization.
    Unfortunately, there exist multiple situations where this is not possible,
    and a map must still be constructed without environment contamination. An
    alternative approach explored in this work is the use of temporal and spatial
    landmark quality measures to validate observations.
    During the course of our research we have tested and implemented SLAM
    solutions for indoor mobile robots with a laser range scanner, based mainly
    on the algorithm described in this chapter, and with the extensions described
    in subsequent chapters along this book, such as full observability, temporal
    landmark quality, unscented vehicle transformations, etc. Figure 1.1 plots a
    series of snapshots of a test run of our SLAM algorithm with our mobile robot
    Marco from Figure 1.2. A 3d partial representation of the final map built is
    shown in Figure 1.3. In the plots the reader can see for example, localization
    variances as level curves around wall endpoints. These are the type of maps
    one could expect to obtain when using an EKF approach to SLAM, such as
    the one explained throgout this book.
    We start our discussion by reviewing in Section 1.1 the traditional full
    covariance extended Kalman filter approach to simultaneous localization and
    map building (EKF-SLAM in short), based primarily on the works by Smith
    and Cheeseman [79] and Dissanayake et al. [31]. In Section 1.2, explicit formulas
    for two mobile platforms are presented. First, we show the case of a
    simple linear one-dimensional mobile robot, the monobot. Then, we extend
    the analysis to the more realistic case of a planar mobile robot.
    Spatial landmark compatibility tests are needed to validate data association
    hypothesis in terms of the estimated localization error for each landmark.
    Their use is crucial for the solution of data association in SLAM [21, 70]. We
    have realized however, that in situations with moderate scene dynamics, spatial
    landmark compatibility may not suffice in the search for data association
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