Enhancing Positioning Accuracy in Urban Terrain by Fusing Data from a GPS Receiver, Inertial Sensors, Stereo-Camera and Digital Maps for Pedestrian Navigation

The paper presents an algorithm for estimating a pedestrian location in an urban environment. The algorithm is based on the particle filter and uses different data sources: a GPS receiver, inertial sensors, probability maps and a stereo camera. Inertial sensors are used to estimate a relative displacement of a pedestrian. A gyroscope estimates a change in the heading direction. An accelerometer is used to count a pedestrian’s steps and their lengths. The so-called probability maps help to limit GPS inaccuracy by imposing constraints on pedestrian kinematics, e.g., it is assumed that a pedestrian cannot cross buildings, fences etc. This limits position inaccuracy to ca. 10 m. Incorporation of depth estimates derived from a stereo camera that are compared to the 3D model of an environment has enabled further reduction of positioning errors. As a result, for 90% of the time, the algorithm is able to estimate a pedestrian location with an error smaller than 2 m, compared to an error of 6.5 m for a navigation based solely on GPS

Computational Effective Fault Detection by Means of Signature Functions

<div><p>The paper presents a computationally effective method for fault detection. A system’s responses are measured under healthy and ill conditions. These signals are used to calculate so-called signature functions that create a signal space. The current system’s response is projected into this space. The signal location in this space easily allows to determine the fault. No classifier such as a neural network, hidden Markov models, etc. is required. The advantage of this proposed method is its efficiency, as computing projections amount to calculating dot products. Therefore, this method is suitable for real-time embedded systems due to its simplicity and undemanding processing capabilities which permit the use of low-cost hardware and allow rapid implementation. The approach performs well for systems that can be considered linear and stationary. The communication presents an application, whereby an industrial process of moulding is supervised. The machine is composed of forms (dies) whose alignment must be precisely set and maintained during the work. Typically, the process is stopped periodically to manually control the alignment. The applied algorithm allows on-line monitoring of the device by analysing the acceleration signal from a sensor mounted on a die. This enables to detect failures at an early stage thus prolonging the machine’s life.</p></div

A sketch showing an exaggerated situation of misaligned forms.

<p>A sketch showing an exaggerated situation of misaligned forms.</p

Illustration of overfitting.

<p>Blue bullets—training data; red circles “unseen” (verification) data; continuous blue line—polynomial fitted accurately to 7 training points; red dashed lined—polynomial of optimal order fitted to the training data.</p

Projection of points <i>P</i>_<i>o</i>(<i>f</i>_{<i>v</i>, <i>i</i>}(<i>t</i>)) for functions from the verification set <b>f</b>_<i>v</i>(<i>t</i>) on 3 planes.

<p>Big green spheres—projections of points <i>P</i>_<i>o</i>(<i>a</i>_{<i>v</i>, <i>i</i>}(<i>t</i>)); red cubes—projections of <i>P</i>_<i>o</i>(<i>b</i>_{<i>v</i>, <i>i</i>}(<i>t</i>)); small blue spheres—projections of <i>P</i>_<i>o</i>(<i>c</i>_{<i>v</i>, <i>i</i>}(<i>t</i>)).</p

A simplified diagram of a moulding process being monitored.

<p>“A” stands for an accelerometer, “PC” for personal computer where the signals from the measurement card were stored and analysed.</p

Plots of signature functions.

<p>a) under healthy conditions—; b) under the first type of fault—; c) under the second type of fault—.</p

An example of projecting a signal <i>h</i>(<i>t</i>) on the two-dimensional space spanned by two signals and .

<p>The projection of <i>h</i>(<i>t</i>) reads . The coordinates of the head of this vector are denoted by <i>P</i>.</p

Standard deviations of <i>c</i>_<i>a</i>, <i>c</i>_<i>b</i> and <i>c</i>_<i>c</i> (for the verification set <b>f</b>_<i>v</i>(<i>t</i>)) are calculated as <i>σ</i>_<i>a</i>, <i>σ</i>_<i>b</i> and <i>σ</i>_<i>c</i>—see Eqs (54 and 55).

<p>Standard deviations of <i>c</i>_<i>a</i>, <i>c</i>_<i>b</i> and <i>c</i>_<i>c</i> (for the verification set <b>f</b>_<i>v</i>(<i>t</i>)) are calculated as <i>σ</i>_<i>a</i>, <i>σ</i>_<i>b</i> and <i>σ</i>_<i>c</i>—see Eqs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150787#pone.0150787.e085" target="_blank">54</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150787#pone.0150787.e086" target="_blank">55</a>).</p