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Riccati Equation and EM Algorithm Convergence for Inertial Navigation Alignment
This correspondence investigates the convergence of a Kalman filter-based expectation-maximization (EM) algorithm for estimating variances. It is shown that if the variance estimates and the error covariances are initialized appropriately, the underlying Riccati equation solution and the sequence of...
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| Published in: | IEEE transactions on signal processing 2009-01, Vol.57 (1), p.370-375 |
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| Main Authors: | , , , |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c383t-1813e3e7c518b3dfa256ea0d519eeb309b151b59f3958aec18466769e2943a3a3 |
| container_end_page | 375 |
| container_issue | 1 |
| container_start_page | 370 |
| container_title | IEEE transactions on signal processing |
| container_volume | 57 |
| creator | Einicke, G.A. Malos, J.T. Reid, D.C. Hainsworth, D.W. |
| description | This correspondence investigates the convergence of a Kalman filter-based expectation-maximization (EM) algorithm for estimating variances. It is shown that if the variance estimates and the error covariances are initialized appropriately, the underlying Riccati equation solution and the sequence of iterations will be monotonically nonincreasing. Further, the process noise variance estimates converge to the actual values when the measurement noise becomes negligibly small. Conversely, when the process noise variance becomes negligible, the measurement noise variance estimates asymptotically approach the true values. An inertial navigation application is discussed in which performance depends on accurately estimating the process variances. |
| doi_str_mv | 10.1109/TSP.2008.2007090 |
| format | article |
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It is shown that if the variance estimates and the error covariances are initialized appropriately, the underlying Riccati equation solution and the sequence of iterations will be monotonically nonincreasing. Further, the process noise variance estimates converge to the actual values when the measurement noise becomes negligibly small. Conversely, when the process noise variance becomes negligible, the measurement noise variance estimates asymptotically approach the true values. An inertial navigation application is discussed in which performance depends on accurately estimating the process variances.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/TSP.2008.2007090</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algorithms ; Applied sciences ; Asymptotic properties ; Convergence ; Detection, estimation, filtering, equalization, prediction ; Estimates ; Exact sciences and technology ; Filtering ; Inertial navigation ; Information, signal and communications theory ; Iterative algorithms ; Kalman filtering ; Kalman filters ; Miscellaneous ; Noise ; Noise measurement ; Parameter estimation ; Riccati equation ; Riccati equations ; Signal and communications theory ; Signal processing ; Signal, noise ; State estimation ; stationary alignment ; Telecommunications and information theory ; Trajectory ; Variance</subject><ispartof>IEEE transactions on signal processing, 2009-01, Vol.57 (1), p.370-375</ispartof><rights>2009 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c383t-1813e3e7c518b3dfa256ea0d519eeb309b151b59f3958aec18466769e2943a3a3</citedby><cites>FETCH-LOGICAL-c383t-1813e3e7c518b3dfa256ea0d519eeb309b151b59f3958aec18466769e2943a3a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4663891$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,4024,27923,27924,27925,54796</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21020806$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Einicke, G.A.</creatorcontrib><creatorcontrib>Malos, J.T.</creatorcontrib><creatorcontrib>Reid, D.C.</creatorcontrib><creatorcontrib>Hainsworth, D.W.</creatorcontrib><title>Riccati Equation and EM Algorithm Convergence for Inertial Navigation Alignment</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>This correspondence investigates the convergence of a Kalman filter-based expectation-maximization (EM) algorithm for estimating variances. It is shown that if the variance estimates and the error covariances are initialized appropriately, the underlying Riccati equation solution and the sequence of iterations will be monotonically nonincreasing. Further, the process noise variance estimates converge to the actual values when the measurement noise becomes negligibly small. Conversely, when the process noise variance becomes negligible, the measurement noise variance estimates asymptotically approach the true values. An inertial navigation application is discussed in which performance depends on accurately estimating the process variances.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Asymptotic properties</subject><subject>Convergence</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Estimates</subject><subject>Exact sciences and technology</subject><subject>Filtering</subject><subject>Inertial navigation</subject><subject>Information, signal and communications theory</subject><subject>Iterative algorithms</subject><subject>Kalman filtering</subject><subject>Kalman filters</subject><subject>Miscellaneous</subject><subject>Noise</subject><subject>Noise measurement</subject><subject>Parameter estimation</subject><subject>Riccati equation</subject><subject>Riccati equations</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Signal, noise</subject><subject>State estimation</subject><subject>stationary alignment</subject><subject>Telecommunications and information theory</subject><subject>Trajectory</subject><subject>Variance</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9kctLAzEQxhdR8HkXvCyCelqd2SS7ybGU-gBf-ABvIU1na2Sb1WQr-N-b2uLBgwzMDMzv-2D4smwf4RQR1NnT4_1pCSAXrQYFa9kWKo4F8LpaTzsIVghZv2xm2zG-ASDnqtrK7h6ctaZ3-ehjnkbnc-Mn-egmH7TTLrj-dZYPO_9JYUreUt50Ib_yFHpn2vzWfLrpUjRo3dTPyPe72UZj2kh7q7mTPZ-PnoaXxfXdxdVwcF1YJllfoERGjGorUI7ZpDGlqMjARKAiGjNQYxQ4FqphSkhDFiWvqrpSVCrOTKqd7GTp-x66jznFXs9ctNS2xlM3j1rWAjgwVSby-F-ScYXIGE_g4R_wrZsHn77QskpIWUKVIFhCNnQxBmr0e3AzE740gl4EoVMQehGEXgWRJEcrXxOtaZtgvHXxV1cilCB_rA-WnCOi33P6m0mF7Bunho9I</recordid><startdate>200901</startdate><enddate>200901</enddate><creator>Einicke, G.A.</creator><creator>Malos, J.T.</creator><creator>Reid, D.C.</creator><creator>Hainsworth, D.W.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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It is shown that if the variance estimates and the error covariances are initialized appropriately, the underlying Riccati equation solution and the sequence of iterations will be monotonically nonincreasing. Further, the process noise variance estimates converge to the actual values when the measurement noise becomes negligibly small. Conversely, when the process noise variance becomes negligible, the measurement noise variance estimates asymptotically approach the true values. An inertial navigation application is discussed in which performance depends on accurately estimating the process variances.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2008.2007090</doi><tpages>6</tpages></addata></record> |
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| ispartof | IEEE transactions on signal processing, 2009-01, Vol.57 (1), p.370-375 |
| issn | 1053-587X 1941-0476 |
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| subjects | Algorithms Applied sciences Asymptotic properties Convergence Detection, estimation, filtering, equalization, prediction Estimates Exact sciences and technology Filtering Inertial navigation Information, signal and communications theory Iterative algorithms Kalman filtering Kalman filters Miscellaneous Noise Noise measurement Parameter estimation Riccati equation Riccati equations Signal and communications theory Signal processing Signal, noise State estimation stationary alignment Telecommunications and information theory Trajectory Variance |
| title | Riccati Equation and EM Algorithm Convergence for Inertial Navigation Alignment |
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