A Kalman Filter Implementation for Precision Improvement in Low-Cost GPS Positioning of Tractors
Identifieur interne : 000574 ( Pmc/Curation ); précédent : 000573; suivant : 000575A Kalman Filter Implementation for Precision Improvement in Low-Cost GPS Positioning of Tractors
Auteurs : Jaime Gomez-Gil ; Ruben Ruiz-Gonzalez ; Sergio Alonso-Garcia ; Francisco Javier Gomez-GilSource :
- Sensors (Basel, Switzerland) [ 1424-8220 ] ; 2013.
Abstract
Low-cost GPS receivers provide geodetic positioning information using the NMEA protocol, usually with eight digits for latitude and nine digits for longitude. When these geodetic coordinates are converted into Cartesian coordinates, the positions fit in a quantization grid of some decimeters in size, the dimensions of which vary depending on the point of the terrestrial surface. The aim of this study is to reduce the quantization errors of some low-cost GPS receivers by using a Kalman filter. Kinematic tractor model equations were employed to particularize the filter, which was tuned by applying Monte Carlo techniques to eighteen straight trajectories, to select the covariance matrices that produced the lowest Root Mean Square Error in these trajectories. Filter performance was tested by using straight tractor paths, which were either simulated or real trajectories acquired by a GPS receiver. The results show that the filter can reduce the quantization error in distance by around 43%. Moreover, it reduces the standard deviation of the heading by 75%. Data suggest that the proposed filter can satisfactorily preprocess the low-cost GPS receiver data when used in an assistance guidance GPS system for tractors. It could also be useful to smooth tractor GPS trajectories that are sharpened when the tractor moves over rough terrain.
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DOI: 10.3390/s131115307
PubMed: 24217355
PubMed Central: 3871121
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">A Kalman Filter Implementation for Precision Improvement in Low-Cost GPS Positioning of Tractors</title><author><name sortKey="Gomez Gil, Jaime" sort="Gomez Gil, Jaime" uniqKey="Gomez Gil J" first="Jaime" last="Gomez-Gil">Jaime Gomez-Gil</name><affiliation><nlm:aff id="af1-sensors-13-15307"> Department of Signal Theory, Communications and Telematics Engineering, University of Valladolid, 47011 Valladolid, Spain; E-Mails:<email>rruigon@ribera.tel.uva.es</email> (R.R.-G.);<email>salonsog@ribera.tel.uva.es</email> (S.A.-G.)</nlm:aff></affiliation></author><author><name sortKey="Ruiz Gonzalez, Ruben" sort="Ruiz Gonzalez, Ruben" uniqKey="Ruiz Gonzalez R" first="Ruben" last="Ruiz-Gonzalez">Ruben Ruiz-Gonzalez</name><affiliation><nlm:aff id="af1-sensors-13-15307"> Department of Signal Theory, Communications and Telematics Engineering, University of Valladolid, 47011 Valladolid, Spain; E-Mails:<email>rruigon@ribera.tel.uva.es</email> (R.R.-G.);<email>salonsog@ribera.tel.uva.es</email> (S.A.-G.)</nlm:aff></affiliation></author><author><name sortKey="Alonso Garcia, Sergio" sort="Alonso Garcia, Sergio" uniqKey="Alonso Garcia S" first="Sergio" last="Alonso-Garcia">Sergio Alonso-Garcia</name><affiliation><nlm:aff id="af1-sensors-13-15307"> Department of Signal Theory, Communications and Telematics Engineering, University of Valladolid, 47011 Valladolid, Spain; E-Mails:<email>rruigon@ribera.tel.uva.es</email> (R.R.-G.);<email>salonsog@ribera.tel.uva.es</email> (S.A.-G.)</nlm:aff></affiliation></author><author><name sortKey="Gomez Gil, Francisco Javier" sort="Gomez Gil, Francisco Javier" uniqKey="Gomez Gil F" first="Francisco Javier" last="Gomez-Gil">Francisco Javier Gomez-Gil</name><affiliation><nlm:aff id="af2-sensors-13-15307"> Department of Electromechanical Engineering, University of Burgos, 09006 Burgos, Spain; E-Mail:<email>fjggil@ubu.es</email></nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">24217355</idno><idno type="pmc">3871121</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3871121</idno><idno type="RBID">PMC:3871121</idno><idno type="doi">10.3390/s131115307</idno><date when="2013">2013</date><idno type="wicri:Area/Pmc/Corpus">000574</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000574</idno><idno type="wicri:Area/Pmc/Curation">000574</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">000574</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">A Kalman Filter Implementation for Precision Improvement in Low-Cost GPS Positioning of Tractors</title><author><name sortKey="Gomez Gil, Jaime" sort="Gomez Gil, Jaime" uniqKey="Gomez Gil J" first="Jaime" last="Gomez-Gil">Jaime Gomez-Gil</name><affiliation><nlm:aff id="af1-sensors-13-15307"> Department of Signal Theory, Communications and Telematics Engineering, University of Valladolid, 47011 Valladolid, Spain; E-Mails:<email>rruigon@ribera.tel.uva.es</email> (R.R.-G.);<email>salonsog@ribera.tel.uva.es</email> (S.A.-G.)</nlm:aff></affiliation></author><author><name sortKey="Ruiz Gonzalez, Ruben" sort="Ruiz Gonzalez, Ruben" uniqKey="Ruiz Gonzalez R" first="Ruben" last="Ruiz-Gonzalez">Ruben Ruiz-Gonzalez</name><affiliation><nlm:aff id="af1-sensors-13-15307"> Department of Signal Theory, Communications and Telematics Engineering, University of Valladolid, 47011 Valladolid, Spain; E-Mails:<email>rruigon@ribera.tel.uva.es</email> (R.R.-G.);<email>salonsog@ribera.tel.uva.es</email> (S.A.-G.)</nlm:aff></affiliation></author><author><name sortKey="Alonso Garcia, Sergio" sort="Alonso Garcia, Sergio" uniqKey="Alonso Garcia S" first="Sergio" last="Alonso-Garcia">Sergio Alonso-Garcia</name><affiliation><nlm:aff id="af1-sensors-13-15307"> Department of Signal Theory, Communications and Telematics Engineering, University of Valladolid, 47011 Valladolid, Spain; E-Mails:<email>rruigon@ribera.tel.uva.es</email> (R.R.-G.);<email>salonsog@ribera.tel.uva.es</email> (S.A.-G.)</nlm:aff></affiliation></author><author><name sortKey="Gomez Gil, Francisco Javier" sort="Gomez Gil, Francisco Javier" uniqKey="Gomez Gil F" first="Francisco Javier" last="Gomez-Gil">Francisco Javier Gomez-Gil</name><affiliation><nlm:aff id="af2-sensors-13-15307"> Department of Electromechanical Engineering, University of Burgos, 09006 Burgos, Spain; E-Mail:<email>fjggil@ubu.es</email></nlm:aff></affiliation></author></analytic><series><title level="j">Sensors (Basel, Switzerland)</title><idno type="eISSN">1424-8220</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Low-cost GPS receivers provide geodetic positioning information using the NMEA protocol, usually with eight digits for latitude and nine digits for longitude. When these geodetic coordinates are converted into Cartesian coordinates, the positions fit in a quantization grid of some decimeters in size, the dimensions of which vary depending on the point of the terrestrial surface. The aim of this study is to reduce the quantization errors of some low-cost GPS receivers by using a Kalman filter. Kinematic tractor model equations were employed to particularize the filter, which was tuned by applying Monte Carlo techniques to eighteen straight trajectories, to select the covariance matrices that produced the lowest Root Mean Square Error in these trajectories. Filter performance was tested by using straight tractor paths, which were either simulated or real trajectories acquired by a GPS receiver. The results show that the filter can reduce the quantization error in distance by around 43%. Moreover, it reduces the standard deviation of the heading by 75%. Data suggest that the proposed filter can satisfactorily preprocess the low-cost GPS receiver data when used in an assistance guidance GPS system for tractors. It could also be useful to smooth tractor GPS trajectories that are sharpened when the tractor moves over rough terrain.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Slaughter, D C" uniqKey="Slaughter D">D.C. Slaughter</name></author><author><name sortKey="Giles, D K" uniqKey="Giles D">D.K. Giles</name></author><author><name sortKey="Downey, D" uniqKey="Downey D">D. Downey</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhang, N" uniqKey="Zhang N">N. Zhang</name></author><author><name sortKey="Wang, M" uniqKey="Wang M">M. Wang</name></author><author><name sortKey="Wang, N" uniqKey="Wang N">N. Wang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Auernhammer, H" uniqKey="Auernhammer H">H. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Sensors (Basel)</journal-id><journal-id journal-id-type="iso-abbrev">Sensors (Basel)</journal-id><journal-title-group><journal-title>Sensors (Basel, Switzerland)</journal-title></journal-title-group><issn pub-type="epub">1424-8220</issn><publisher><publisher-name>Molecular Diversity Preservation International (MDPI)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">24217355</article-id><article-id pub-id-type="pmc">3871121</article-id><article-id pub-id-type="doi">10.3390/s131115307</article-id><article-id pub-id-type="publisher-id">sensors-13-15307</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>A Kalman Filter Implementation for Precision Improvement in Low-Cost GPS Positioning of Tractors</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Gomez-Gil</surname><given-names>Jaime</given-names></name><xref ref-type="aff" rid="af1-sensors-13-15307"><sup>1</sup></xref><xref rid="c1-sensors-13-15307" ref-type="corresp"><sup>*</sup></xref></contrib><contrib contrib-type="author"><name><surname>Ruiz-Gonzalez</surname><given-names>Ruben</given-names></name><xref ref-type="aff" rid="af1-sensors-13-15307"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Alonso-Garcia</surname><given-names>Sergio</given-names></name><xref ref-type="aff" rid="af1-sensors-13-15307"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Gomez-Gil</surname><given-names>Francisco Javier</given-names></name><xref ref-type="aff" rid="af2-sensors-13-15307"><sup>2</sup></xref></contrib></contrib-group><aff id="af1-sensors-13-15307"><label>1</label> Department of Signal Theory, Communications and Telematics Engineering, University of Valladolid, 47011 Valladolid, Spain; E-Mails:<email>rruigon@ribera.tel.uva.es</email> (R.R.-G.);<email>salonsog@ribera.tel.uva.es</email> (S.A.-G.)</aff><aff id="af2-sensors-13-15307"><label>2</label> Department of Electromechanical Engineering, University of Burgos, 09006 Burgos, Spain; E-Mail:<email>fjggil@ubu.es</email></aff><author-notes><corresp id="c1-sensors-13-15307"><label>*</label> Author to whom correspondence should be addressed; E-Mail: <email>jgomez@tel.uva.es</email>; Tel.: +34-6175-07469; Fax: +34-9834-23667.</corresp></author-notes><pub-date pub-type="collection"><month>11</month><year>2013</year></pub-date><pub-date pub-type="epub"><day>08</day><month>11</month><year>2013</year></pub-date><volume>13</volume><issue>11</issue><fpage>15307</fpage><lpage>15323</lpage><history><date date-type="received"><day>03</day><month>9</month><year>2013</year></date><date date-type="rev-recd"><day>03</day><month>11</month><year>2013</year></date><date date-type="accepted"><day>04</day><month>11</month><year>2013</year></date></history><permissions><copyright-statement>© 2013 by the authors; licensee MDPI, Basel, Switzerland.</copyright-statement><copyright-year>2013</copyright-year><license><license-p>This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link>).</license-p></license></permissions><abstract><p>Low-cost GPS receivers provide geodetic positioning information using the NMEA protocol, usually with eight digits for latitude and nine digits for longitude. When these geodetic coordinates are converted into Cartesian coordinates, the positions fit in a quantization grid of some decimeters in size, the dimensions of which vary depending on the point of the terrestrial surface. The aim of this study is to reduce the quantization errors of some low-cost GPS receivers by using a Kalman filter. Kinematic tractor model equations were employed to particularize the filter, which was tuned by applying Monte Carlo techniques to eighteen straight trajectories, to select the covariance matrices that produced the lowest Root Mean Square Error in these trajectories. Filter performance was tested by using straight tractor paths, which were either simulated or real trajectories acquired by a GPS receiver. The results show that the filter can reduce the quantization error in distance by around 43%. Moreover, it reduces the standard deviation of the heading by 75%. Data suggest that the proposed filter can satisfactorily preprocess the low-cost GPS receiver data when used in an assistance guidance GPS system for tractors. It could also be useful to smooth tractor GPS trajectories that are sharpened when the tractor moves over rough terrain.</p></abstract><kwd-group><kwd>Kalman filter</kwd><kwd>agricultural vehicle</kwd><kwd>Global Positioning System (GPS)</kwd><kwd>vehicle guidance</kwd><kwd>sensor data fusion</kwd><kwd>autonomous navigation</kwd></kwd-group></article-meta></front><floats-group><fig id="f1-sensors-13-15307" position="float"><label>Figure 1.</label><caption><p>Graphic illustration of precision and accuracy concepts.</p></caption><graphic xlink:href="sensors-13-15307f1"></graphic></fig><fig id="f2-sensors-13-15307" position="float"><label>Figure 2.</label><caption><p>RMC Sentences acquired from two different GPS receivers. The yellow-highlighted numbers represent the latitude and longitude geodetic coordinates. It can be observed that the high end <italic>Trimble R4</italic> provides 12 digits for latitude and 13 for longitude while the low-cost <italic>Navilock NL-402U</italic> provides only eight digits for latitude and nine for longitude.</p></caption><graphic xlink:href="sensors-13-15307f2"></graphic></fig><fig id="f3-sensors-13-15307" position="float"><label>Figure 3.</label><caption><p>Illustration of the quantization effect on the positions supplied by a GPS receiver, showing that quantified trajectories register (i) position errors; and (ii) speed errors, as shown by the variable distances between the blue rectangles; and (iii) heading error, which are higher in trajectories nearby, but different from, the direction of any coordinate axis.</p></caption><graphic xlink:href="sensors-13-15307f3"></graphic></fig><fig id="f4-sensors-13-15307" position="float"><label>Figure 4.</label><caption><p>Tractor schematic and description of variables.</p></caption><graphic xlink:href="sensors-13-15307f4"></graphic></fig><fig id="f5-sensors-13-15307" position="float"><label>Figure 5.</label><caption><p>Stage diagram of the Kalman filtering loop.</p></caption><graphic xlink:href="sensors-13-15307f5"></graphic></fig><fig id="f6-sensors-13-15307" position="float"><label>Figure 6.</label><caption><p>Black box diagram of the system implementation.</p></caption><graphic xlink:href="sensors-13-15307f6"></graphic></fig><fig id="f7-sensors-13-15307" position="float"><label>Figure 7.</label><caption><p>(<bold>a</bold>) Paths used in the tuning process and distance performance evaluation; (<bold>b</bold>) Flow charts of Kalman filter evaluation with artificial data and with onboard GPS real data.</p></caption><graphic xlink:href="sensors-13-15307f7"></graphic></fig><fig id="f8-sensors-13-15307" position="float"><label>Figure 8.</label><caption><p>Illustration of the quantization and Kalman filter process conducted over an ideal sample trajectory. The RMSE is defined, according <xref rid="FD13" ref-type="disp-formula">Equation (13)</xref>, as the square root of the average of all the distances squared with respect to the real reference path position.</p></caption><graphic xlink:href="sensors-13-15307f8"></graphic></fig><fig id="f9-sensors-13-15307" position="float"><label>Figure 9.</label><caption><p>(<bold>a</bold>) One of the trajectories of the tests with one stake and the cord; (<bold>b</bold>) Low-cost GPS receiver placed over the tractor cab; (<bold>c</bold>) Laptop inside the tractor cab.</p></caption><graphic xlink:href="sensors-13-15307f9"></graphic></fig><fig id="f10-sensors-13-15307" position="float"><label>Figure 10.</label><caption><p>Results of positioning improvement at a 5 Hz update rate, constant speed of 5 km/h (3.1 mph) and 60° heading angle along a straight path (<bold>a</bold>) in a simulation with artificial data; and (<bold>b</bold>) in tests, processing data from a real onboard <italic>Navilock NL-402U</italic> GPS receiver. The purple line joins two corresponding points, before and after the filtering, to qualitatively show the negligible magnitude of the delay.</p></caption><graphic xlink:href="sensors-13-15307f10"></graphic></fig><fig id="f11-sensors-13-15307" position="float"><label>Figure 11.</label><caption><p>Histogram of distance errors, with 5 Hz update rate, using the simulations along the 18 straight lines shown in <xref rid="f7-sensors-13-15307" ref-type="fig">Figure 7a</xref>. (<bold>a</bold>) before applying the Kalman filter; (<bold>b</bold>) after applying the Kalman filter. The histogram has been normalized so that it has a unitary area, representing an approximation to the probability density function (<italic>pdf</italic>) of the distance errors statistical random variable.</p></caption><graphic xlink:href="sensors-13-15307f11"></graphic></fig><fig id="f12-sensors-13-15307" position="float"><label>Figure 12.</label><caption><p>Heading angle (<italic>θ</italic>) histogram, (<bold>a</bold>) of the real ideal path; (<bold>b</bold>) of the grid-quantized path; and (<bold>c</bold>) of the recovered path after applying the proposed Kalman filter. Simulated data were obtained for a straight path with a 60° heading angle and at varying speeds of between 5 and 10 km/h. The histogram has been normalized to have a unitary area, representing an approximation to the probability density function (<italic>pdf</italic>) of the heading angle statistical random variable.</p></caption><graphic xlink:href="sensors-13-15307f12"></graphic></fig><fig id="f13-sensors-13-15307" position="float"><label>Figure 13.</label><caption><p>Heading angle (<italic>θ</italic>) histogram (<bold>a</bold>) of the estimated reference path; (<bold>b</bold>) of the raw GPS data; and (<bold>c</bold>) of the filtered data using the proposed Kalman filter. Data were obtained from a real onboard <italic>Navilock NL-402U</italic> GPS receiver, along a straight path with a 60° heading angle and at a constant speed of 5 km/h. The histogram has been normalized to have a unitary area, representing an approximation to the probability density function (<italic>pdf</italic>) of the heading angle statistical random variable.</p></caption><graphic xlink:href="sensors-13-15307f13"></graphic></fig><table-wrap id="t1-sensors-13-15307" position="float"><label>Table 1.</label><caption><p>Statistical parameters of the distribution of errors, before and after applying the proposed Kalman filter, along the 18 simulated straight paths (<xref rid="f7-sensors-13-15307" ref-type="fig">Figure 7a</xref>).</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="center" valign="middle" rowspan="1" colspan="1"></th><th align="center" valign="middle" rowspan="1" colspan="1"><bold>Before Filtering</bold></th><th align="center" valign="middle" rowspan="1" colspan="1"><bold>After Filtering</bold></th></tr></thead><tbody><tr><td align="center" valign="top" rowspan="1" colspan="1">Distances Root-Mean Square Error (RMSE) (cm)</td><td align="center" valign="top" rowspan="1" colspan="1">6.56</td><td align="center" valign="top" rowspan="1" colspan="1">3.74</td></tr><tr><td align="center" valign="top" rowspan="1" colspan="1">Distances 95<italic>th</italic>-percentile (cm)</td><td align="center" valign="top" rowspan="1" colspan="1">8.48</td><td align="center" valign="top" rowspan="1" colspan="1">4.31</td></tr></tbody></table></table-wrap><table-wrap id="t2-sensors-13-15307" position="float"><label>Table 2.</label><caption><p>Statistical parameters of the heading angle distributions, before and after applying the proposed Kalman filter, along a straight path with a 60° heading angle, in simulations with artificial data.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="center" valign="middle" rowspan="1" colspan="1"></th><th align="center" valign="middle" rowspan="1" colspan="1"><bold>Before Filtering</bold></th><th align="center" valign="middle" rowspan="1" colspan="1"><bold>After Filtering</bold></th></tr></thead><tbody><tr><td align="center" valign="top" rowspan="1" colspan="1">Standard deviation (°)</td><td align="center" valign="top" rowspan="1" colspan="1">6.9362</td><td align="center" valign="top" rowspan="1" colspan="1">1.8301</td></tr><tr><td align="center" valign="top" rowspan="1" colspan="1">95<italic>th</italic>-percentile range (centered on real heading angle) (°)</td><td align="center" valign="top" rowspan="1" colspan="1">29.0661</td><td align="center" valign="top" rowspan="1" colspan="1">7.2651</td></tr></tbody></table></table-wrap><table-wrap id="t3-sensors-13-15307" position="float"><label>Table 3.</label><caption><p>Statistical parameters of the heading angle distribution, before and after applying the proposed Kalman filter, along a straight path with a 60° heading angle, in real field tests.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="center" valign="middle" rowspan="1" colspan="1"></th><th align="center" valign="middle" rowspan="1" colspan="1"><bold>Before Filtering</bold></th><th align="center" valign="middle" rowspan="1" colspan="1"><bold>After Filtering</bold></th></tr></thead><tbody><tr><td align="center" valign="top" rowspan="1" colspan="1">Standard deviation (°)</td><td align="center" valign="top" rowspan="1" colspan="1">16.5594</td><td align="center" valign="top" rowspan="1" colspan="1">4.1326</td></tr><tr><td align="center" valign="top" rowspan="1" colspan="1">95<italic>th</italic>-percentile range (centered on reference heading angle) (°)</td><td align="center" valign="top" rowspan="1" colspan="1">55.1185</td><td align="center" valign="top" rowspan="1" colspan="1">14.7193</td></tr></tbody></table></table-wrap></floats-group></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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