Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model
A very simple Gaussian model is used to illustrate an interesting fitting result: a linear growth of the resolution with the number <i>N</i> of detecting layers. This rule is well beyond the well-known rule proportional to <inline-formula><math xmlns="http://www.w3.org/1998...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Instruments |
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| Online Access: | https://www.mdpi.com/2410-390X/6/1/10 |
| _version_ | 1797470591173787648 |
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| author | Gregorio Landi Giovanni E. Landi |
| author_facet | Gregorio Landi Giovanni E. Landi |
| author_sort | Gregorio Landi |
| collection | DOAJ |
| description | A very simple Gaussian model is used to illustrate an interesting fitting result: a linear growth of the resolution with the number <i>N</i> of detecting layers. This rule is well beyond the well-known rule proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula> for the resolution of the usual fits. The effect is obtained with the appropriate form of the variance for each hit (observation). The model reconstructs straight tracks with <i>N</i> parallel detecting layers, the track direction is the selected parameter to test the resolution. The results of the Gaussian model are compared with realistic simulations of silicon micro-strip detectors. These realistic simulations suggest an easy method to select the essential weights for the fit: the lucky model. Preliminary results of the lucky model show an excellent reproduction of the linear growth of the resolution, very similar to that given by realistic simulations. The maximum likelihood evaluations complete this exploration of the growth in resolution. |
| first_indexed | 2024-03-09T19:38:37Z |
| format | Article |
| id | doaj.art-24ef221377ac485ba0ce3bb4a2a7a3e2 |
| institution | Directory Open Access Journal |
| issn | 2410-390X |
| language | English |
| last_indexed | 2024-03-09T19:38:37Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Instruments |
| spelling | doaj.art-24ef221377ac485ba0ce3bb4a2a7a3e22023-11-24T01:44:35ZengMDPI AGInstruments2410-390X2022-01-01611010.3390/instruments6010010Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky ModelGregorio Landi0Giovanni E. Landi1Dipartimento di Fisica e Astronomia, Universita’ di Firenze and INFN Largo E. Fermi 2 (Arcetri), 50125 Firenze, ItalyArchonVR S.a.g.l., Via Cisieri 3, 6900 Lugano, SwitzerlandA very simple Gaussian model is used to illustrate an interesting fitting result: a linear growth of the resolution with the number <i>N</i> of detecting layers. This rule is well beyond the well-known rule proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula> for the resolution of the usual fits. The effect is obtained with the appropriate form of the variance for each hit (observation). The model reconstructs straight tracks with <i>N</i> parallel detecting layers, the track direction is the selected parameter to test the resolution. The results of the Gaussian model are compared with realistic simulations of silicon micro-strip detectors. These realistic simulations suggest an easy method to select the essential weights for the fit: the lucky model. Preliminary results of the lucky model show an excellent reproduction of the linear growth of the resolution, very similar to that given by realistic simulations. The maximum likelihood evaluations complete this exploration of the growth in resolution.https://www.mdpi.com/2410-390X/6/1/10least squares methodresolutionposition reconstructioncenter of gravitysilicon micro-strip detectorslucky model |
| spellingShingle | Gregorio Landi Giovanni E. Landi Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model Instruments least squares method resolution position reconstruction center of gravity silicon micro-strip detectors lucky model |
| title | Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model |
| title_full | Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model |
| title_fullStr | Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model |
| title_full_unstemmed | Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model |
| title_short | Beyond the <inline-formula><math display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula>-Limit of the Least Squares Resolution and the Lucky Model |
| title_sort | beyond the inline formula math display inline semantics msqrt mi n mi msqrt semantics math inline formula limit of the least squares resolution and the lucky model |
| topic | least squares method resolution position reconstruction center of gravity silicon micro-strip detectors lucky model |
| url | https://www.mdpi.com/2410-390X/6/1/10 |
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