Project 1: Plotting Coordinates and Projections

Source: Baxter, R., Sloan, J.L., Gutowski, M., Wherley, M., Pfeiffer, C., and DiBiase, D. (n.d.). Interactive Album of Map Projections.  Retrieved September 12, 2014, from http://projections.mgis.psu.edu

The map above is known as a Robinson map projection.  It was introduced in 1963 by Arthur H. Robinson (Egsc.usgs.gov, n.d.).  Robinson projections are Pseudocylindrical.  Distortions ellipses in the map are noted by the by the red circles.  “Distortion is very low along the Equator and the 45°of center.  Greatest near the poles.” (Egsc.usgs.gov, n.d.).  This map is a “compromise” between known map distortion properties, as it seeks to minimize distortion as much as possible (DiBiase,Ch.2, p29).  Since the Earth isn’t a perfect sphere, one can more associate the Earth to an ellipsoid. Most maps are subject to these distortion properties under four main spatial properties.  

These properties are: Area, Distance, Shape, and Direction. The Robinson map used above preserves Distance well along the Equator and other parallels.  Direction is true along all parallels and the central meridian.  Scale is true along 38° North and South. It is constant along any given parallel and the same along North and South parallels from the equator (Egsc.usgs.gov. (n.d.).  

The map has been drawn with an extent of 40° North, 30° South, -120° West, and -100° East.

Geographic Coordinates
The place name shown on the map above represents the location of my hometown, Los Alamos, New Mexico.  The geographic coordinates of my home town are:

Latitude: 35° 53' 17" N, Longitude: -106° 18' 25" W

The Geographic Coordinate System is a three-dimensional spherical system used to navigate along earth’s surface utilizing a degree system based of measurement.  Longitude is a function of moving between positions East and West on the globe from 0° to 180°and -90° and -180°.  Latitude is a function of moving North and South along the globe between ranges of 90° at the North Pole and -90° at the South Pole.  Coordinates are usually represented in degrees, minutes, and seconds based on the 360° dimensions of a sphere. “A line of latitude is known as a parallel.” (DiBiase, Ch.2, p.11).  Imagine a grid of intersecting lines running north and south.  The lines running north and south are meridians.  The lines running east and west are known as parallels.  The coordinate system utilizes control points known as datums.  The horizontal datums on earth’s surface are define the geometric relationship between a coordinate system grid and the Earth surface (DiBiase, Ch2, p13).

UTM Coordinates

The UTM coordinates (NAD83 or NAD27) of my hometown (Los Alamos, NM) are:

Easting: 376,075.305 meters, Northing: 3,957,906.025 meters, Zone&Hemisphere: 13N

Source: DiBiase, D. and others 2014, Ch. 2, p.23, Figure 2.23.2. Retrieved September 27, 2014, from https://www.e-education.psu.edu/natureofgeoinfo/c2_p23.html

The Universal Transverse Mercator (UTM) coordinate system is based off the Transverse Mercator Projection.  It is comprised of a system of 60 zones divided along the earth’s surface, with  6°of longitude.  The zones are numbered from West to East with a starting point from 1 to 60.  They begin at 180° West longitude (DiBiase, D. and others 2014).  In the polar zones, latitudes of greater than 84° in the north and 80° in the South are excluded.  Each zone labels coordinates as Eastings and Northings, typically they are measured in units of meters measured from a horizontal datum.  Easting headings are distances east of the origin.  Northing headings are distances north of the origin.   The best way to describe these headings would be to assign an “x-coordinate” value to all Eastings measurements and a “y-coordinate” to all Northing measurements (Easting and Northing. n.d.).    The measurements are expressed in meters instead of degrees as each grid cell in a UTM projection represents 500,000 meters on each side of the origin.  The widest part (666,000 meters wide) is located at the equator.  Because earth surface is not perfect, relative sizes and shapes needed to be created as guide.   To get precise coordinates, transformations need to be calculated between different ellipsoids in the past and present (DiBiase, D. and others 2014).

National or Regional Coordinates

The State Plane coordinates (NAD83 or NAD27) of my hometown (Los Alamos, NM) are:

Easting: 494,858.946 meters, Northing: 542,094.502 meters, NAD83 Zone: 3002

The State Plane Coordinate System (SPC) consists of 124 zones which cover the United States.  It utilizes “Eastings” and “Northings” the in same manner as the UTM systems does.  SPC zones have been designed with three main objectives.  The first objective sets out to use plane coordinates for ease of use on flat grids.  The second objective seeks to have all known values positive.  “SPC Zone origins are defined so as to ensure that every easting and northing in every zone are positive numbers.” (DiBiase, Ch2_p27).  The third objective seeks to keep the maximum error in each zone to “1 part in 10,000 or better.”(DiBiase, Ch2_p26).  SPC zone are plotted via a Transverse Mercator or Lambert Conformal Conic map projections (DiBiase, Ch2, p26).  SPC zones cover smaller areas, which leads to fewer distortions errors over the map than the UTM system. These distortions are reduced by using two standard parallel lines.

The horizontal datum relates to the SPC coordinates though the NAD27 to NAD 83 datum.  The NAD27 datum was created in 1927 and was eventually replaced by a more geocentric ellipsoid called the GRS80.  When converting from old datums to new ones, some error or “datums shift” is observed in the new data transformations (DaBaise, Ch2, p19).  When converting from NAD27 to NAD83 in the NADCON conversion utility, a shift of 52.942 meters was recorded in my hometown of Los Alamos, NM (National Geodetic Survey, 2004).

Comparison

The coordinate systems Geographic, Universal Transverse Mercator (UTM), and State Plane Coordinate (SPC) all have unique properties and characteristics.  The Geographic system is based off a system in a spherical 360°degrees.  The Geographic Coordinate System uses a Degrees, Minutes, Seconds system to navigate between areas on a map (DiBiase, D. and others 2014).  Geographic Coordinate Systems are best used when viewing large areas.   The UTM and SPC projections utilize measurements of meters.  SPC zones tend to be projected on a Lambert Conic Conformal or Transverse Mercator map, which have parameters like standard lines and central meridians which are optimized for each zone (DiBiase, Ch2_p26).     Geographical coordinates are not projected due to the earth almost spherical like shape.  The UTM system is projected via a Transverse Mercator containing 60 zones; whereas, SPC has 124 zones.  The SPC system tends to be more accurate as it covers a smaller area (DaBaise, D. and others 2014).  UTM has a much better representation of measuring distance and area than the Geographical Coordinate System does; however, UTM measurements can become cumbersome when trying to measure outside of each zone.  The NAD (North American Datum) 27 and NAD83 datums are both horizontal datums.  The NAD27 is based off the Clarke 1866 ellipsoid.  The NAD83 datum was founded off the GRS80 ellipsoid.  NAD27 and NAD83 differ only in that are based off different ellipsoids (DiBiase, D. and others 2014).

In Summary, the three different coordinate systems vary in shapes and sizes depending on the type of map projection desired.  Depending on the scale and detail of the map, some projections work better than others.  Some maps preserve fewer distortions near standard lines and some exaggerate distortions near the poles.  One can choose from many datums available to utilize the best ellipsoid required for the map desired or needed to show data correctly.

References:

Baxter, R., Sloan, J.L., Gutowski, M., Wherley, M., Pfeiffer, C., and DiBiase, D. (n.d.). Interactive Album of Map Projections.  Retrieved September 12, 2014, from http://projections.mgis.psu.edu

DiBiase, D. and others (2014). Nature of Geographic Information. The Pennsylvania State University. Retrieved September 12, 2014 from https://www.e-education.psu.edu/natureofgeoinfo/.

Easting and Northing. (n.d.).  In Wikipedia. Retrieved September 30, 2014, from http://en.wikipedia.org/wiki/Easting_and_northing

Egsc.usgs.gov. (n.d.).  Map Projections Poster.  Retrieved September 28, 2014 from http://egsc.usgs.gov/isb//pubs/MapProjections/projections.html#robinson

National Geodetic Survey (2004) NADCON – North American Datum Conversion Utility.  Retrieved September 12, 2014 from http://www.ngs.noaa.gov/cgi-bin/nadcon.prl

National Geodetic Survey (2004a).  SPC Utilities.  Retrieved September 12, 2014, from http://www.ngs.noaa.gov/TOOLS/spc.html

National Geodetic Survey (2004b).  UTM Utilities.  Retrieved September 14, 2014, from http://www.ngs.noaa.gov/TOOLS/utm.html

United States Geological Survey (2006a). Geographic Names Information System.  Retrieved September 12, 2014, from http://geonames.usgs.gov

United States Geological Survey (2006b). Map Projections Poster. Retrieved September 12, 2014, from http://www.scribd.com/doc/92268542/Map-Projections-Poster-USGS

X-Ray Vision for Robots: Seeing Through Walls with Only WiFi

X-Ray Vision for Robots: Seeing Through Walls with Only WiFi

Project Information In the News Related Publications Key Features Potential Applications Setup Summary Sample Imaging Results

X-Ray Vision for Robots with Only WiFi In the News: NSF (Science360), BBC Interview, Engadget, Gizmag, Daily Mail, Gizmodo, IDG (PC World, IT World, Computer World) , International Business Times (Yahoo News), Headline and Global News, SD Times, I-Programmer, Investors Business Daily, The Verge, Ubergizmo, Outer Places, UCSB press release, and other outlets, Aug. 2014 Imagine unmanned vehicles arriving behind thick concrete walls. They have no prior knowledge of the area behind these walls. But they are able to see every square inch of the invisible area through the walls, fully discovering what is on the other side with high accuracy. The objects on the other side do not even have to move to be detected. Now, imagine robots doing all these with only WiFi signals and no other sensors. In this project, we have shown how to do this. Watch the video for more details and results.

Project Information

• Project Duration: 2008-present
• Current Team Members:
  • PI: Yasamin Mostofi
    
  • Graduate Students: Saandeep Depatla , Lucas Buckland
    
• Related Awards:
  • Presidential Early Career Award for Scientists and Engineers (PECASE) from President Obama, October 2011
    
  • IEEE 2012 Outstanding Engineer Award of Region 6 (all western US), Sept. 2012
    
• US Patent # 8,712,679
• Supporting Grant: This project is one part of the NSF CAREER award "Compressive Cooperative Sensing and Navigation in Mobile Networks."
  

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Related Publications

• A. Gonzalez-Ruiz, A Ghaffarkhah, and Y. Mostofi, "An Integrated Framework for Obstacle Mapping with See-Through Capabilities using Laser and Wireless Channel Measurements," IEEE Sensors Journal volume 14, issue 1, Jan. 2014.[pdf][bibtex]
  
• A. Gonzalez-Ruiz and Y. Mostofi, "Cooperative Robotic Structure Mapping Using Wireless Measurements - A Comparison of Random and Coordinated Sampling Patterns," IEEE Sensors Journal, volume 13, issue 7, April 2013.[pdf][bibtex]
  
• Y. Mostofi, "Cooperative Wireless-Based Obstacle/Object Mapping and See-Through Capabilities in Robotic Networks," in IEEE Transactions on Mobile Computing, Jan. 2012.[pdf][bibtex]
  
• Ph.D. Thesis: A. Gonzalez-Ruiz, "Compressive Cooperative Obstacle Mapping with See-Through Capabilities in Mobile Networks," Nov. 2012.[pdf]
  
• Y. Mostofi, "Compressive Cooperative Sensing and Mapping in Mobile Networks," IEEE Transactions on Mobile Computing, vol. 10, no. 12, pp. 1770-1785, December 2011.[pdf][bibtex]
  
• Y. Mostofi and A. Gonzalez-Ruiz, "Compressive Cooperative Obstacle Mapping in Mobile Networks," invited paper, IEEE Military Communications Conference (Milcom), Oct. 2010. [pdf][bibtex]
  
• Y. Mostofi and P. Sen, "Compressive Cooperative Mapping in Mobile Networks," American Control Conference (ACC), 2009. [pdf][bibtex]
  

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Setup Summary

Our proposed approach enables seeing a completely unknown area behind thick walls, only based on wireless measurements using WLAN cards. The figure below shows an example of the considered problem. The superimposed red volume marks the area that is completely unknown to an outside node (such as an unmanned vehicle or a WiFi-enabled smart node) and needs to be seen with details, based on only WiFi measurements. Note that most area is blocked by the first wall, which is concrete and thus highly attenuating. The two unmanned vehicles are interested in fully seeing what is inside at the targeted resolution of 2cm. Note that they know nothing about this area and have not made any prior measurements here.

This figure is generated for illustrative purposes. For a true snapshot of the robots in operation, see our Video and the Sample Imaging Results Section. Note that in the video, any marker on the floor is only for our evaluation purposes and are not used by the robots for positioning, navigation or imaging.

Challenges: This is an extremely challenging multi-disciplinary problem, which involves wireless communications, signal processing, and robotics. Consider the figure above for instance. A horizontal cut of the area of interest is 5.26m x 5.26m. Based on our targeted resolution of 2cm, this amounts to 69,169 unknown variables just for a horizontal cut, resulting in a considerably under-determined system since making that many wireless measurements would simply be prohibitive for the robots. Furthermore, there will be several propagation phenomena that the robots may not be able to include in their modeling. Finally, the robot positioning is also prone to error.
Our Approach: One robot measures the wireless transmissions of the other robot that is in the broadcast mode. Each wireless transmission passes through the unknown area and the objects attenuate the signal depending on their material properties and locations. By devising a framework based on proper wave propagation modeling and sparse signal processing, we have shown that it is indeed possible for the two unmanned vehicles to image the entire area, with a high targeted resolution, and see through highly-attenuating walls. More specifically, we formulate an approximated wave propagation model. Then, we exploit the sparsity of the map in wavelet, total variations, or space domain in order to solve this severely under-determined system. We have also taken advantage of directional antennas (see the figure above) in order to increase the imaging resolution. See our Video and Related Publications where we introduce our framework, show the underlying tradeoffs of different sparsity/imaging approaches, discuss the impact of different motion patterns of the robots, and present a number of experimental results.
Note that the same approach can be used for imaging on a handheld WiFi-enabled node or on a fixed WiFi network.
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Sample Imaging Results

Here, we show a few sample results where two unmanned vehicles see a 2D cut of a completely unknown area at the targeted resolution of 2cm. A similar concept can be extended to full 3D imaging. Note that any marker on the ground is only used by us for assessing the accuracy of the operation and is not used by the robots for positioning or imaging. In the imaging results, the quoted percentage measurements denote the percentage of the number of gathered wireless measurements as compared to the total number of unknown pixels that need to be seen. This ratio shows how under-determined the considered problem is. Sample dimensions and their imaged versions are also provided on the figures in blue.

The left figure above shows the area of interest that is completely unknown, while the middle figure shows a horizontal cut of it. The white areas indicate that there is an object while the black areas denote that there is nothing in those spots. Two unmanned vehicles can see through the walls and also see the walls (right figure) based on only WiFi measurements.

The left figure above shows the area of interest that is completely unknown, while the middle figure shows a horizontal cut of it. The white areas indicate that there is an object while the black areas denote that there is nothing in those spots. Two unmanned vehicles can see through the walls (as shown in the right figure) based on only WiFi measurements. Note: the method that enabled this imaging result is in a submitted paper.

The left figure above shows the area of interest that is completely unknown and needs to be imaged, while the middle figure shows a horizontal cut of it (it is 2.56mx2.56m). The white areas indicate that there is an object while the black areas denote that there is nothing in those spots. Two unmanned vehicles can image this area (as shown in the right figure) based on only WiFi measurements.

Integration with a Laser Scanner: The figure above shows our proposed integrated framework where both laser scanner and WiFi measurements are used. The first row shows the area of interest that is completely unknown and needs to be imaged, while the first figure of the second row shows a horizontal cut of it (it is 7.67mx7.67m). The white areas indicate that there is an object while the black areas denote that there is nothing in those spots. Two unmanned vehicles then move outside of the area of interest to image a horizontal cut. The second figure of the second row presents the case that only a laser scanner is used. As can be seen, the occluded parts of the structure behind the walls can not be seen, as expected. The two right figures of the second row then show the performance of our proposed integrated framework based on both WiFi measurements and laser scanner data. It can be seen that the details can be clearly identified.

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Summary of KEY FEATURES of our framework

• Needed hardware for imaging: Only WLAN card. We have also utilized directional antennas to increase imaging resolution.
  
• Capabilities: Our approach enables seeing a completely-unknown area (with details) through thick walls by using only WiFi signals. This technology can be implemented on any WiFi-enabled gadget. We have furthermore shown how to use this in a robotic setting to give see-through vision to robots. In a typical unmanned vehicle setting, the robots can use laser scanners to see what is in front of them. Clearly, a laser scanner can not see through walls. Here, we have shown that by using only the WiFi measurements, the unmanned vehicles can not only image through walls but can also image the wall itself without any laser scanner. We can additionally integrate our framework with a laser scanner for further capabilities, as is demonstrated in our Sample Imaging Results.
  
• Imaging Resolution: In several of our results, the imaged location of an object (such as its center) is off from its true location by less than 5cm. Sample numbers are provided in our results. Note that we are not just locating a single object but imaging every inch of the unknown space.
  
• Needed Coordination for Taking Measurements in Each Route: None in our latest setup, which allows for faster collection of measurements. The two robots decide on which route to take. Once starting a route, there will be no coordination between the two robots. One robot simply measures its WiFi receptions periodically. The WLAN card of the other robot is in broadcast mode. Each robot keeps estimating its own position and the position of the other robot based on the set speed. Also, each robot traverses each route autonomously in our latest setup. An experiment may consist of a few routes. Once a route is finished, we currently manually move the robots to the start of a new route to save time. This part can be automated as well.
  
• Motion Patterns: We have proposed two different motion patterns for the unmanned vehicles. In what we call "random", the robots (or a robot) have no specific motion pattern and simply walk outside of the area of interest, while measuring the wireless receptions. Note that this does not mean that a random pattern is taken. It simply means no specific pattern is needed. This case is suitable if there are navigational barriers outside of the area, limiting the movements of the robots. In what we call "coordinated", the two robots move in a coordinated (semi-parallel) fashion outside of the area, similar to how CT-scan is done. In this case, the two robots simply decide on which routes to travel before starting to traverse them. Note that they do not have to coordinate their positions (or anything else) as they travel a route and will just set their speeds the same. Each robot then locally estimates its own position and the position of the other robot as it travels its route.
  
• Computational Complexity of Imaging: This depends on the size of the unknown area, number of gathered wireless measurements and the targeted accuracy. Our experience so far has shown less than 100 seconds for processing all the data and getting the image for our biggest structure, on an Intel core i7-3770 at 3.4 GHz.
  
• Onboard Positioning of Each Vehicle: Each unmanned vehicle only has a gyroscope and a wheel encoder for positioning, which are very common parts of unmanned vehicles. This allows it to estimate how much it has travelled in each route and put a position stamp on the wireless measurements it is collecting periodically in that route.
  
• Sources of Errors: Extracting the image information, especially the occluded parts, solely from wireless measurements and with unmanned vehicles is a challenging task due to several sources of errors. For instance, the modeling of the wireless link can not capture all the propagation effects, the problem is severely under-determined, and the onboard positioning of the robot (as well as its prediction of where the other node is) is prone to error. We are thus working on constantly improving our framework to enable the vehicles to image more complex areas.
  

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Potential Applications

• Search and Rescue, and Surveillance: Imagine a search and rescue operation after an earthquake. The ability to see through walls would allow the outside nodes/humans to assess the situation inside the building before entering it. Furthermore, the automation through utilizing robots would allow the operation to take place in areas hazardous to humans. For instance, consider the nuclear accident after the 2011 Tohoku earthquake and tsunami in Japan. The ability to send unmanned vehicles that can see through blocking objects can tremendously expedite the evaluation of the site from outside.
  
• Occupancy Detection: Our approach can be extended to detect the level of occupancy of an area. This is valuable information for the optimization of several services that depend on how crowded an area is.
  
• Classification of Object Materials Behind the Wall: Our approach can learn the material properties of the objects on the other side of the wall. Thus, it has the potential to classify what kind of objects (human, metal, wood, etc) are present on the other side (in addition to their location and geometry).
• Archeological Sites: Having a non-invasive approach to see details through blocking objects, without a need to dig, can be very useful in archeological exploration.
  
• Robotic Networks: The vision of a team of unmanned vehicles deployed in our society to help us with different tasks is closer than ever. These nodes need to constantly build an understanding of their environment (e.g., obstacle mapping) for path planning and navigation. The proposed wireless see-through capability would allow the nodes to cooperatively map areas that have several occluded parts and better plan their trajectories and mission.
  
• Localization for Smart Environments: The proposed see-through wall imaging approach can be deployed on a fixed wireless network or on smart WiFi-enabled gadgets to image hidden objects in an environment. This can increase the capabilities of several location-aware services in future smart homes and malls. Detecting home intruders before entering your house or elderly movement monitoring are a few examples of the possibilities.
  

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Other Acknowledgements

• Graduated Ph.D. Students: Alejandro Gonzalez-Ruiz and Alireza Ghaffarkhah
• Students who have helped during running of our experiments: Yuan Yan, Zhengli Zhao, Herbert Cai, Yanglei Li, Joshua Kay
• Dept. of ECE at UCSB, College of Engineering at UCSB for facilitating the experiments

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