<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2663-3981</journal-id>
<journal-title><![CDATA[Revista cartográfica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. cartogr.]]></abbrev-journal-title>
<issn>2663-3981</issn>
<publisher>
<publisher-name><![CDATA[Instituto Panamericano de Geografía e Historia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2663-39812020000200135</article-id>
<article-id pub-id-type="doi">10.35424/rcarto.i101.669</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Aplicação das normas L1 e L&#8734; em redes altimétricas: identificação de outliers e construção do modelo estocástico]]></article-title>
<article-title xml:lang="en"><![CDATA[L1 and L&#8734; norms adjustment in leveling networks: outlier identification and stochastic modeling]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Suraci]]></surname>
<given-names><![CDATA[Stefano Sampaio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Oliveira]]></surname>
<given-names><![CDATA[Leonardo Castro de]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Militar de Engenharia  ]]></institution>
<addr-line><![CDATA[ Río de Janeiro]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Instituto Militar de Engenharia  ]]></institution>
<addr-line><![CDATA[ Río de Janeiro]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<numero>101</numero>
<fpage>135</fpage>
<lpage>153</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2663-39812020000200135&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2663-39812020000200135&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2663-39812020000200135&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo: Nesse artigo, aplicações da minimização da norma L1 (ML1) e da norma L&#8734; (ML&#8734;) na estimação de redes altimétricas foram investigadas. Redes de nivelamento simuladas pela Técnica de Monte Carlo e dados reais da rede brasileira de nivelamento foram empregados nos experimentos. Na identificação de outliers pela ML1, foi verificado que o ajustamento com pesos unitários apresentou condições vantajosas em relação ao modelo estocástico usual dos pesos proporcionais ao inverso do comprimento das linhas de nivelamento. O Classificador VL1, que estipula um Valor de Corte para os resíduos do ajustamento pela ML1 a partir do qual a respectiva observação passa a ser classificada como outlier, foi proposto. A taxa de sucesso dele na identificação de outliers foi superior à do procedimento data snooping iterativo em cenários de geometria da rede deficiente. Já a aplicação da ML&#8734; investigada é posterior ao tratamento de outliers. Um modelo estocástico alternativo para ajustamento da rede pelo MMQ que aproveitou a característica de minimização do máximo resíduo absoluto da rede no ajustamento pela ML&#8734; foi analisado. Além dessa minimização, o ajustamento da rede pelo MMQ com o modelo alternativo gerou, na significativa maioria dos casos, resíduos e precisão desses e dos parâmetros estimados mais homogêneos, com menor desvio padrão, que aqueles com o modelo estocástico usual. Todos os resultados são especialmente relevantes para o caso de redes altimétricas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper, applications of L1 norm minimization (ML1) and of L&#8734; norm minimization (ML&#8734;) in the estimation of leveling networks were investigated. Leveling networks simulated by the Monte Carlo technique and real data from the Brazilian leveling network were employed in the experiments. In the identification of outliers by ML1, it was verified that the adjustment with unit weights presented advantageous conditions in relation to the usual stochastic model of weights of observations as proportional to the inverse of the length of the leveling lines. The Classificador VL1, which stipulates a cut-off value for the residuals of the adjustment by ML1 from which the respective observation is classified as outlier, was proposed. Its success rate in identifying outliers was higher than that of the iterative data snooping procedure in poor network geometry scenarios. The application investigated for ML&#8734; is after the treatment of outliers. An alternative stochastic model for network adjustment by Least Squares (LS) that took advantage of the characteristic of minimization of the maximum absolute residual of the network in the adjustment by ML&#8734; was analyzed. In addition to this minimization, the adjustment of the network by LS with the proposed model generated, in most cases, residuals and precision of these and of the estimated parameters more homogeneous, with lower standard deviation, than those with the usual stochastic model. All results are especially relevant for the case of altimetric networks.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[normas L1e L&#8734;]]></kwd>
<kwd lng="pt"><![CDATA[modelo estocástico]]></kwd>
<kwd lng="pt"><![CDATA[Monte Carlo]]></kwd>
<kwd lng="pt"><![CDATA[altimetria]]></kwd>
<kwd lng="en"><![CDATA[L1 and L&#8734; norms]]></kwd>
<kwd lng="en"><![CDATA[stochastic model]]></kwd>
<kwd lng="en"><![CDATA[Monte Carlo]]></kwd>
<kwd lng="en"><![CDATA[leveling networks]]></kwd>
</kwd-group>
</article-meta>
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