Kimanta Nisa da Matsayi a Tsarin Haske da ake iya Gani tare da LED na RGB: Nazarin CRLB da ML

Teburin Abubuwan Ciki

1. 1. Gabatarwa & Bayyani
2. 2. Tsarin Tsarin da Yanayi
   1. 2.1 Yanayi na 1: Tsarin Aiki Tare tare da Sanin Tsarin Tashoshi
   2. 2.2 Yanayi na 2: Tsarin Aiki Ba tare da Daidaitawa ba tare da Sanin Tsarin Tashoshi
   3. 2.3 Yanayi na 3: Tsarin Aiki Tare tare da Rashin Sanin Tsarin Tashoshi
3. 3. Iyakokin Daidaito na Ka'idar: Ƙaramin Iyaka na Cramér-Rao
4. 4. Masu Kimantawa na Aiki: Hanyar Mafi Yiwuwar Yiwuwa
5. 5. Sakamako da Nazarin Aiki
6. 6. Fahimtar Tsaki & Ra'ayi na Manazarta
7. 7. Cikakkun Bayanai na Fasaha & Tsarin Lissafi
8. 8. Tsarin Nazari: Nazarin Lamari na Ra'ayi
9. 9. Ayyukan Gaba & Hanyoyin Bincike
10. 10. Nassoshi

1. Gabatarwa & Bayyani

Wannan aikin yana bincika iyakokin daidaito na asali don kimanta nisa da matsayi a cikin Tsarin Tsayawar Haske da ake iya Gani (VLP) waɗanda ke amfani da Fitilun LED na Ja-Kore-Blu (RGB). Babbar gudummawar ita ce cikakken nazari na ka'idar da na aiki a cikin yanayi daban-daban guda uku na aiki, tare da kimanta aikin ta hanyar Ƙaramin Iyaka na Cramér-Rao (CRLB) da kuma samo masu kimantawa na Mafi Yiwuwar Yiwuwa (ML) da suka dace. Binciken ya ba da mahimman bayanai game da lokacin da yadda LED na RGB ke ba da fa'idodi fiye da LED mai launi ɗaya don gano wuri.

2. Tsarin Tsarin da Yanayi

An tsara nazarin ne a kusa da mahimman yanayi guda uku waɗanda ke wakiltar ƙayyadaddun aiki na yau da kullun a cikin aiwatar da VLP.

2.1 Yanayi na 1: Tsarin Aiki Tare tare da Sanin Tsarin Tashoshi

Yana ɗauka cewa akwai cikakkiyar daidaitawa tsakanin mai aikawa da mai karɓa, da kuma cikakken sanin dabarar raguwar tashoshi (misali, tsarin Lambertian). Wannan yana wakiltar mafi kyawun yanayi na ka'idar inda za a iya amfani da cikakken bayanin Lokacin Isowa (TOA) da Ƙarfin Siginar da aka Karɓa (RSS).

2.2 Yanayi na 2: Tsarin Aiki Ba tare da Daidaitawa ba tare da Sanin Tsarin Tashoshi

Babu daidaitawar da ke akwai tsakanin mai aikawa da mai karɓa. Dole ne mai karɓa ya dogara kacokan kan bayanin RSS don kimantawa, amma an san tsarin tashoshi. Wannan yanayi ne mafi aiki amma mai ƙalubale wanda ya zama ruwan dare a cikin aiwatarwa masu tsada.

2.3 Yanayi na 3: Tsarin Aiki Tare tare da Rashin Sanin Tsarin Tashoshi

Yayin da ake samun daidaitawa (wanda ke ba da damar amfani da TOA), ainihin halayen raguwar tashoshi ba a san su ga mai karɓa ba. Wannan yana ƙirƙira yanayin da ke da abubuwan muhalli da ba a iya faɗi ba ko kayan aikin da ba a daidaita su ba.

3. Iyakokin Daidaito na Ka'idar: Ƙaramin Iyaka na Cramér-Rao

CRLB yana ba da ƙaramin iyaka na asali akan bambance-bambancen kowane mai kimantawa mara son zuciya. Don vector na siga $\boldsymbol{\theta}$ (misali, nisa ko matsayi na 2D/3D), bisa la'akari da vector na lura $\mathbf{x}$, ana ba da CRLB ta hanyar juzu'in Matrix na Bayanin Kifi (FIM) $\mathbf{I}(\boldsymbol{\theta})$:

$\text{Var}(\hat{\theta}_i) \geq [\mathbf{I}^{-1}(\boldsymbol{\theta})]_{ii}, \quad \text{inda} \quad [\mathbf{I}(\boldsymbol{\theta})]_{ij} = -E\left[ \frac{\partial^2 \ln p(\mathbf{x}; \boldsymbol{\theta})}{\partial \theta_i \partial \theta_j} \right]$

Takardar ta samo bayyanannun maganganun CRLB don kimanta nisa da matsayi a kowane yanayi. Wani muhimmin binciken shine cewa CRLB don kimanta nisa a cikin Yanayi na 1 yana daidaitawa da juzu'in murabba'in ingantaccen bandwidth $\beta^2$ na siginar haske da aka aika: $\text{CRLB}(d) \propto 1/\beta^2$. Wannan yana nuna muhimmiyar rawar da ƙirar sigina ke takawa a cikin tsarin aiki tare.

4. Masu Kimantawa na Aiki: Hanyar Mafi Yiwuwar Yiwuwa

Ga kowane yanayi, ana samun mai kimantawa na ML da ya dace. Mai kimantawa na ML don nisan $d$ a cikin Yanayi na 1, ƙarƙashin zato na ƙara farar Gaussian mai hayaniya (AWGN), ya haɗa da warwarewa:

$\hat{d}_{\text{ML}} = \arg\min_d \sum_{k=1}^{K} \left( r_k - \alpha \frac{P_t}{d^2} s(t_k - \tau(d)) \right)^2$

inda $r_k$ samfuran da aka karɓa ne, $P_t$ ƙarfin watsawa ne, $\alpha$ ribar tashoshi ce, $s(\cdot)$ siginar da aka aika ce, kuma $\tau(d)$ TOA ne. Takardar ta nuna cewa waɗannan masu kimantawa na ML na iya kaiwa ga CRLB a ƙarƙashin yanayin babban sigina-zuwa-hayaniya (SNR).

5. Sakamako da Nazarin Aiki

Sakamakon ka'idar da na siminti sun nuna wasu mahimman alamu:

• Kwatanta Yanayi: Yanayi na 1 (aiki tare, sanannen tashoshi) yana ba da mafi kyawun daidaito, sannan Yanayi na 3 (aiki tare, tashoshi da ba a sani ba), tare da Yanayi na 2 (ba tare da daidaitawa ba) yana nuna mafi girman iyakokin kuskure, musamman a ƙananan bandwidth.
• Fa'idar LED na RGB: An nuna amfani da LED na RGB yana inganta daidaiton kimantawa. An bayyana wannan a hankali ta hanyar ribar bambance-bambance—siginoni masu zaman kansu daga tashoshin R, G, da B suna ba da lura da yawa, kaɗan marasa alaƙa na sigogi na geometric iri ɗaya (nisa/matsayi), yana daidaita hayaniya yadda ya kamata.
• Musayar Bandwidth da Ƙarfi: A cikin tsarin aiki tare, ƙara ingantaccen bandwidth $\beta$ na siginar yana rage CRLB sosai, sau da yawa ya fi tasiri fiye da kawai ƙara ƙarfin haske. Wannan yana da mahimman tasiri ga ƙirar tsarin, yana fifita ƙirar siginar da ta fi sauƙi akan ƙarfin ƙarfi.
• Aikin ML: An nuna masu kimantawa na ML da aka samo ta hanyar siminti suna kusantar CRLB ɗin su a isassun manyan ƙarfin haske na watsawa, suna tabbatar da ingancin su na aiki a cikin yankuna masu babban SNR.

6. Fahimtar Tsaki & Ra'ayi na Manazarta

Fahimtar Tsaki: Aikin Demirel da Gezici ba kawai wata takarda ta VLP ba ce; cikakken bincike ne na fa'idar LED na RGB a cikin gano wuri. Babbar fahimtar ita ce cewa amfanin RGB ya wuce launi ko watsa bayanai—wani nau'i ne na bambance-bambancen sarari a fakaice. Ta hanyar samar da tashoshi uku masu layi daya, waɗanda suke tare a zahiri amma sun bambanta ta fuskar bakan, LED na RGB yana ba da redundancy na lura sau 3x don sigogi na geometric, yana kai hari kai tsaye ga yanayin iyakacin hayaniya na ma'aunin RSS da TOA. Wannan yayi kama da amfani da eriya da yawa a cikin tsarin RF amma an cimma shi ta hanyar canjin kayan aiki mai arha, mai mayar da hankali kan haske.

Tsarin Hankali: Hankalin takardar yana da tsabta mara kyau. Ya fara ne ta hanyar ayyana fagen fama (yanayi uku na gaskiya), ya kafa iyakokin aiki na ƙarshe (CRLB) a matsayin ma'auni na zinariya, sannan ya gina sojoji na aiki (masu kimantawa na ML) don ganin yadda suka iya kusanta wannan iyaka. Kwatanta a duk faɗin yanayi yana da ƙarfi musamman. Yana nuna a ƙididdiga cewa daidaitawa ba ta da amfani a ƙasa da wani bakin kofa na bandwidth—ƙa'idar ƙira mai mahimmanci da yawa a manta a aikace. Idan ingantaccen bandwidth na siginar ku yana da ƙasa, zaku iya adana farashi da rikitarwa na daidaitawa kuma ku tsaya kan hanyoyin RSS marasa daidaitawa.

Ƙarfi & Kurakurai: Ƙarfinsa yana cikin hanyarsa ta asali, ta farko ta lissafi. Ba ya ba da shawarar hack na dabara; ya samo iyakoki na asali, yana sa sakamakonsa ya dace da duniya. Amfani da CRLB yana ba da ma'auni mara ƙalubale. Duk da haka, binciken yana da kuskuren al'ada na yawancin ayyukan ka'idar: yana dogaro sosai akan zato na AWGN da sanannun tsarin tashoshi kamar tsarin Lambertian. VLP na duniyar gaske yana fama da hanyoyi da yawa, inuwa, hasashe marasa Lambertian (daga saman mai sheki), da hayaniyar hasken yanayi—abubuwan da zasu iya lalata aiki sosai daga waɗannan iyakokin ka'idar, kamar yadda aka lura a cikin binciken gwaji kamar na Jami'ar California's Visible Light Communication Consortium. Takardar ta yarda da tsarin tashoshi da ba a sani ba a cikin Yanayi na 3 amma tana ɗaukarsa a matsayin rashin tabbas na siga. Ƙalubalen da ya fi rikitarwa shine tsarin tashoshi wanda ba na siga ba, mai motsi, wanda shine inda hanyoyin da ke da alaƙa da bayanai da na injin koyo, waɗanda aka yi wahayi zuwa gare su ta hanyar ayyuka kamar CycleGAN don daidaita yanki, ke tafiya yanzu.

Fahimta Mai Aiki: Ga masu zane-zane na tsarin, wannan takarda tana ba da umarni bayyananne: 1) Ba da fifiko ga Bandwidth: Idan kuna gina tsarin aiki tare, saka hannun jari a cikin manyan direbobin bandwidth da tsare-tsaren daidaitawa (misali, OFDM) kafin kunna ƙarfin haske. 2) Yi hujjar RGB: Yi amfani da hujjar bambance-bambance don ba da hujjar ɗan tsada na LED na RGB fiye da LED mai launi ɗaya don aikace-aikacen gano wuri masu daidaito. 3) Zaɓi Fagen Fadanku: Don manyan binciken cikin gida, mai arha (misali, kayan ajiya), tsarin da ya dogara da RSS mara daidaitawa tare da LED na RGB na iya ba da mafi kyawun ciniki-daidaito. Don jagorar robot na tiyata, je aiki tare kuma kada ku yi kasada akan bandwidth. 4) Gaba Gaba shine Ƙarfi: An fahimci iyakokin ka'idar yanzu. Sabon igiyar ƙirƙira, kamar yadda aka gani a cikin bugu na arXiv na baya-bayan nan da mujallolin IEEE, za ta mayar da hankali kan sanya waɗannan masu kimantawa ƙarfi ga gaskiyar rikitarwa na yaduwar cikin gida, mai yuwuwa haɗa hanyoyin tushen samfuri (kamar na wannan takarda) tare da dabarun tushen koyo don juriyar tashoshi.

7. Cikakkun Bayanai na Fasaha & Tsarin Lissafi

Ana ƙirƙira ƙarfin haske da aka karɓa $P_r$ daga LED ta hanyar dabarar Lambertian:

$P_r = \begin{cases} \frac{m+1}{2\pi d^2} A \cos^m(\phi) \cos(\psi) P_t, & 0 \le \psi \le \Psi_c \\ 0, & \psi > \Psi_c \end{cases}$

inda $d$ nisa ne, $A$ yanki na ganowa ne, $\phi$ kusurwar haske ne, $\psi$ kusurwar faɗuwa ce, $\Psi_c$ filin gani na mai karɓa ne, $m$ tsari na Lambertian ne, kuma $P_t$ ƙarfin watsawa ne. Ga LED na RGB, wannan samfurin ya shafi kowane tashar launi (R, G, B) da kansu, tare da yuwuwar $P_t$ daban-daban a kowane tashoshi.

Bayanin Kifi don nisan $d$ a cikin Yanayi na 1, la'akari da TOA da RSS, da tattara bayanai daga tashoshin launi $N_c$ (misali, 3 don RGB), ana iya bayyana shi kamar haka:

$I(d) = \sum_{c=1}^{N_c} \left( \frac{2 \beta_c^2 \text{SNR}_c}{c^2} + \frac{4 \text{SNR}_c}{d^2} \right)$

inda $\beta_c$ shine ingantaccen bandwidth na tashoshi $c$, $c$ saurin haske ne, kuma $\text{SNR}_c$ shine ma'aunin sigina-zuwa-hayaniya don wannan tashoshi. Kalmar farko a cikin taƙaitawa ta fito ne daga bayanin TOA kuma ya dogara da $\beta_c^2$. Kalma ta biyu ta fito ne daga bayanin RSS. Taƙaitawar ta nuna a fili ribar bambance-bambance daga amfani da tashoshi da yawa.

8. Tsarin Nazari: Nazarin Lamari na Ra'ayi

Yanayi: Zana tsarin VLP don kewayawar motar da aka sarrafa ta atomatik (AGV) a cikin masana'antar wayo.

Aiwatar da Tsarin:

1. Nazarin Bukatu: Daidaiton gano wuri < 10 cm a cikin 3D. Muhalli yana da manyan rufi (5m), injina yana haifar da rufe ido lokaci-lokaci, da hasken fitila na yanayi.
2. Zaɓin Yanayi: Bukatar babban daidaito yana tura zuwa tsarin aiki tare (Yanayi 1 ko 3). Duk da haka, bayanin rufewa da ba a sani ba da canzawa yana nuna cewa ba za a san tsarin tashoshi da kyau a kowane lokaci ba, yana ba da hujjar nazarin Yanayi na 3.
3. Zaɓin Fasaha: Yi amfani da LED na RGB don kayan aikin rufi. Nazarin daga wannan takarda ya ba da hujjar zaɓin: ribar bambance-bambance tana taimakawa wajen rage asarar daidaito lokacin da wani tashar launi ya toshe ko ya ragu sosai ta wani abu mai rufewa.
4. Ƙirar Siga: Don cimma daidaiton da aka samo daga CRLB, lissafta ingantaccen bandwidth $\beta$ da ake buƙata. Dabarun takardar sun nuna cewa tare da bambance-bambancen RGB, $\beta$ da ake buƙata (don haka farashin tsarin/rikitattun abubuwa) don takamaiman daidaito ya fi ƙasa fiye da na tsarin launi ɗaya.
5. Aiwatar da Mai Kimantawa: Aiwar da mai kimantawa na ML don Yanayi na 3. Yi amfani da lokacin daidaitawa don gina tsarin tashoshi na farko, amma ƙyale mai kimantawa ya daidaita ta hanyar ɗaukar wasu sigogi na tashoshi a matsayin ba a sani ba (dangane da tsarin takardar).
6. Tabbatarwa: Kwatanta kuskuren gano wurin AGV na duniyar gaske da CRLB da aka annabta don SNR da bandwidth na tsarin. Babban rata zai nuna tasirin da ba a ƙirƙira ba (misali, hanyoyi da yawa), yana sa ya motsa zuwa ga ingantattun hanyoyin tushen samfuri/bayanai.

9. Ayyukan Gaba & Hanyoyin Bincike

Aikin asali da aka gabatar ya buɗe kofofi zuwa aikace-aikace masu ci gaba da hanyoyin bincike da yawa:

• 6G Haɗaɗɗun Ganowa da Sadarwa (ISAC): VLP ɗan takara ne na halitta don ISAC a cikin hanyoyin sadarwa na gaba. LED na RGB na iya ba da haske, saurin watsa bayanai (Li-Fi), da daidaitaccen gano wuri a lokaci guda, kamar yadda aka bincika a cikin bincike daga cibiyoyi kamar PureLiFi da Jami'ar Edinburgh.
• Ƙara Gaskiya (AR) & Metaverse: Gano wuri na cikin gida na ƙasa-centimita yana da mahimmanci don ƙwarewar AR mara katsewa. Tsarin VLP na RGB da aka haɗa a cikin hasken ɗaki na iya ba da madaidaicin da ake buƙata don anga abubuwa da bin diddigin mai amfani ba tare da na'urori masu auna firikwensin waje ba.
• Robotics da Kewayawar Jirgi maras Matuki: A cikin wuraren da ba a yarda da GPS ba kamar ɗakunan ajiya, ma'adinai, ko gonakin cikin gida, VLP tare da LED na RGB yana ba da ingantaccen mafita na kewayawa mai dogaro da kayan aiki. Riba ta bambance-bambance tana da mahimmanci don magance canje-canjen daidaitawar robot/jirgi mara matuki.
• Binciken Lafiya da Kula da Lafiya: Bin diddigin marasa lafiya da kadarori a asibiti tare da babban dogaro da rashin tsangwama na RF.
• Hanyoyin Bincike:
  1. Koyon Injin don Gano Wuri mara Sanin Tashoshi: Haɓaka masu kimantawa na zurfin koyo (misali, ta amfani da hanyoyin sadarwar jijiyoyi a kan ƙirar siginar da aka karɓa) waɗanda suka ƙarfi ga tashoshi gaba ɗaya da ba a sani ba da masu motsi, suna motsawa fiye da samfurin da ba a sani ba na Yanayi na 3.
  2. Tsarin Haɗin RF-VLC: Haɗa VLP tare da gano wuri na UWB ko WiFi don rufe kowane makaho na fasaha, yana amfani da babban daidaito na VLP a cikin buɗaɗɗen wurare da ikon shiga na RF.
  3. Masu Karɓar VLP masu Tattara Makamashi: Zana masu karɓa waɗanda zasu iya yin gano wuri ta amfani da makamashin haske da aka tattara da kansa, yana ba da damar kullun na'urori na IoT.
  4. Daidaituwa: Turawa don ƙa'idodin masana'antu gabaɗaya akan daidaitawa, lambobi, da ka'idoji don VLP, kama da IEEE 802.15.7 don VLC, don tabbatar da aiki tare.

10. Nassoshi

1. Demirel, I., & Gezici, S. (2021). Kimanta Nisa da Matsayi a Tsarin Haske da ake iya Gani tare da LED na RGB. arXiv preprint arXiv:2106.00396.
2. Kahn, J. M., & Barry, J. R. (1997). Sadarwar infrared mara waya. Proceedings of the IEEE, 85(2), 265-298.
3. Zhuang, Y., Hua, L., Qi, L., Yang, J., Cao, P., Cao, Y., ... & Thompson, J. (2018). Binciken tsarin gano wuri ta amfani da fitilun LED masu iya gani. IEEE Communications Surveys & Tutorials, 20(3), 1963-1988.
4. Visible Light Communication Consortium (VLCC). (2023). Bincike akan Lalacewar VLP na Aiki. [Kan layi]. Ana samuwa: http://www.vlcc.net
5. Isola, P., Zhu, J. Y., Zhou, T., & Efros, A. A. (2017). Fassarar hoto-zuwa-hoto tare da hanyoyin sadarwa na gaba. Proceedings of the IEEE conference on computer vision and pattern recognition (shafi na 1125-1134). (Mai dacewa don hanyoyin daidaita tashoshi masu alaƙa da bayanai).
6. PureLiFi. (2023). Li-Fi don Haɗaɗɗun Ganowa da Sadarwa. [Takarda Fari].
7. Ma'auni na IEEE don Gida da Manyan Hanyoyin Sadarwa–Sashi na 15.7: Sadarwar Haske mara Waya ta Gajeren Zango ta Amfani da Haske da ake iya Gani. (2018). IEEE Std 802.15.7-2018.