Lock Detectors - Revision history

Filipe.Pelica: Included editor logo.

2014-09-18T16:36:26Z

Included editor logo.

← Older revision		Revision as of 16:36, 18 September 2014
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	\|YearOfPublication=2011		\|YearOfPublication=2011
			\|Logo=GMV
	\|Title={{PAGENAME}}		\|Title={{PAGENAME}}
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Carlos.Lopez at 11:01, 23 February 2012

2012-02-23T11:01:34Z

← Older revision		Revision as of 11:01, 23 February 2012
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	{{Article Infobox2		{{Article Infobox2
	\|Category=Receivers		\|Category=Receivers
	\|Editors=GMV ~~A.D.~~		\|Editors=GMV
	\|Level=Advanced		\|Level=Advanced
	\|YearOfPublication=2011		\|YearOfPublication=2011

Carlos.Lopez at 10:34, 23 February 2012

2012-02-23T10:34:52Z

← Older revision		Revision as of 10:34, 23 February 2012
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	{{Article Infobox2		{{Article Infobox2
	\|Category=Receivers		\|Category=Receivers
	\|~~Title={{PAGENAME}}~~		\|Editors=GMV A.D.
	~~\|Authors~~=GMV
	\|Level=Advanced		\|Level=Advanced
	\|YearOfPublication=2011		\|YearOfPublication=2011
	\|~~Logo~~=~~GMV~~		\|Title={{PAGENAME}}
	}}		}}
	In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the [[Tracking Loops\|tracking loops]]. The receiver must therefore ensure that the tracking loops are correctly following the incoming signal, and that they have not diverged away from the solution. This is the purpose of the lock detectors, which produce quality factors to assess how well the signal is being tracked.		In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the [[Tracking Loops\|tracking loops]]. The receiver must therefore ensure that the tracking loops are correctly following the incoming signal, and that they have not diverged away from the solution. This is the purpose of the lock detectors, which produce quality factors to assess how well the signal is being tracked.

Rui.Pereira: moved Work in Progress:Lock Detectors to Lock Detectors over redirect

2011-05-27T15:54:17Z

moved Work in Progress:Lock Detectors to Lock Detectors over redirect

← Older revision	Revision as of 15:54, 27 May 2011
(No difference)

Rui.Pereira: moved Lock Detectors to Work in Progress:Lock Detectors

2011-05-11T13:39:46Z

moved Lock Detectors to Work in Progress:Lock Detectors

← Older revision	Revision as of 13:39, 11 May 2011
(No difference)

Rui.Sarnadas at 14:05, 6 May 2011

2011-05-06T14:05:57Z

← Older revision		Revision as of 14:05, 6 May 2011
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	\|Logo=GMV		\|Logo=GMV
	}}		}}
	In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the tracking loops. The receiver must therefore ensure that the tracking loops are following ~~correctly~~ the incoming signal and that they have not diverged away from the solution. This is the purpose of the lock detectors ~~that~~ produce quality factors to assess how well the signal is being tracked.		In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the [[Tracking Loops\|tracking loops]]. The receiver must therefore ensure that the tracking loops are correctly following the incoming signal, and that they have not diverged away from the solution. This is the purpose of the lock detectors, which produce quality factors to assess how well the signal is being tracked.

	==Concept==		==Concept==
	The ~~objective~~ of the lock detectors is to assess whether the incoming signal is being correctly tracked at channel level or not. For that purpose, the GNSS receiver evaluates pre-defined quality parameters in order to assess:		The purpose of the '''lock detectors''' is to assess whether the incoming signal is being correctly tracked at channel level or not. For that purpose, the GNSS receiver evaluates pre-defined quality parameters in order to assess:
	*Code lock of the [[Delay Lock Loop (DLL)\|DLL]]
	*Phase lock of the [[Phase Lock Loop (PLL)\|PLL]]
	*Frequency lock of the [[Frequency Lock Loop (FLL)\|FLL]]

	~~These quality parameters may be obtained from~~ the ~~correlators’ outputs or cross-checking~~ of ~~internal information, as detailed hereafter.~~		*'''Code lock''' of the [[Delay Lock Loop (DLL)\|DLL]];
			*'''Phase lock''' of the [[Phase Lock Loop (PLL)\|PLL]];
			*'''Frequency lock''' of the [[Frequency Lock Loop (FLL)\|FLL]];

	~~After computing these~~ quality parameters~~, the receiver checks their values against pre-defined thresholds, which~~ may ~~depend on the application. As an example, if the receiver is targeting high accuracy, these thresholds might~~ be ~~more restrictive, whereas if~~ the ~~priority is solution availability~~, ~~then these thresholds are more likely to be relaxed.~~		These quality parameters may be obtained from the correlator outputs, or cross-checking of internal information, as detailed hereafter.
	Once loss of lock is declared, the receiver may react in different ways. If only one of the loops loses lock (e.g. the PLL), then the receiver may decide to keep the other loops closed and to restart only this loop. Conversely, the receiver may decide that this loss of ~~lock is unrecoverable and switch back to acquisition~~, ~~see also [[Receiver Operations\|Receiver Operations]]~~.

	These decisions are closely related to the receiver design ~~and~~ they are often the result of all the performance trade-offs tailored to the target application.		After computing the quality parameters, the receiver checks their values against pre-defined thresholds, which may depend on the application. As an example, if the receiver is targeting high accuracy, these thresholds might be more restrictive, whereas if the priority is solution availability, then these thresholds are more likely to be relaxed.

			Once '''loss of lock''' is declared, the receiver may react in different ways. If only one of the loops loses lock (e.g. the PLL), then the receiver may decide to keep the other loops closed, and to restart only this loop. Conversely, the receiver may decide that this loss of lock is unrecoverable, and switches the channel back to acquisition (see also how [[Receiver Operations\|receiver operations]] are done). These decisions are closely related to the receiver design, as they are often the result of all the performance trade-offs tailored to the target application.

	==Code Lock Detectors==		==Code Lock Detectors==
	The concept behind the code lock detector is that, if the DLL is working correctly, then the received signal power is high. Since the received signal is noisy, code lock is often assessed by comparing the estimated Carrier to Noise ratio, <math>\hat{C}/N_0</math>, with a pre-defined threshold.		The concept behind the code lock detector is that if the DLL is working correctly, then the received signal power is high. Since the received signal is noisy, code lock is often assessed by comparing the estimated Carrier-to-Noise ratio, <math>\hat{C}/N_0\,</math>, with a pre-defined threshold.

			At the receiver, the <math>\hat{C}/N_0\,</math> can be computed using the ratio between signal plus noise power measured with different bandwidths<ref name="dierendonck">A. J. Van Dierendonck, “GPS Receivers”, from “Global Positioning System: Theory and Applications”, Volume I, Edited by B. W. Parkinson, J. J. Spilker Jr.</ref>. As such, the narrowband power computed over <math>M\,</math> and <math>k\,</math> integration periods can be written as:


	~~At the receiver, the~~ <math>\~~hat{C}/N_0~~</math> can be computed using the ratio between signal plus noise power measured with different bandwidths<ref name="dierendonck">A. J. Van Dierendonck, “GPS Receivers”, from “Global Positioning System: Theory and Applications”, Volume I, Edited by B. W. Parkinson, J. J. Spilker Jr</ref>.		<math>NBP_k=[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2\,</math>

	~~As such, the narrowband power computed over M and k integration periods can be written as:~~

	<math>~~NBP_k=[~~\~~sum_M I_P]_k^2 + [~~\~~sum_M Q_P]_k^2~~</math>		and the wide band power computed over <math>M\,</math> and <math>k\,</math> integration periods can be written as:

	~~and the wide band power computed over M and k integration periods can be written as:~~

	<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k</math>		<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k\,</math>

	where
	*<math>I_P</math> and <math>Q_P</math> are the In-phase and Quadrature outputs of the prompt correlator respectively, see [[Correlators\|~~Correlators~~]] for further information		where:
	*M is the number of coherent integrations for the lock detector
			*<math>I_P\,</math> and <math>Q_P\,</math> are the In-phase and Quadrature outputs of the prompt correlator, respectively (see [[Correlators\|correlators]] for further information).
			*<math>M\,</math> is the number of coherent integrations for the lock detector.


	The estimated mean of the narrow power is given by:		The estimated mean of the narrow power is given by:

	~~<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}</math>~~

	where K is the number of non-coherent integrations for the lock detector.		<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}\,</math>


			where <math>K\,</math> is the number of non-coherent integrations for the lock detector.


			Finally, the estimated Carrier-to-Noise ratio <math>\hat{C}/N_0\,</math> computed at the correlators is given by:


	~~Finally~~, ~~the estimated carrier to noise ratio computed at the correlators is given by:~~		<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})\,</math>

	~~<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})</math>~~

	where T is the integration time.		where <math>T\,</math> is the integration time.


	==Phase Lock Detectors==		==Phase Lock Detectors==
			The phase lock detector is based on the concept that, if the incoming signal is being correctly tracked, then the In-phase component ''I'' of the Prompt correlator is maximum, and its Quadrature component ''Q'' is minimum, as shown [[Phase Lock Loop (PLL)\|here]].

	~~The phase lock detector~~ is ~~based on~~ the ~~concept that, if~~ the ~~incoming signal is being correctly tracked, then the in-~~phase ~~component~~ of the prompt correlator ~~is maximum and its quadrature component is minimum~~, ~~as shown [[Phase Lock Loop (PLL)\|here]].~~		A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:

	~~A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:~~

	<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}</math>		<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}\,</math>

	~~Please note that, when in good lock conditions, this quality parameter is nearly 1.~~

			Note that, when in good lock conditions, this quality parameter is nearly 1.

	==Frequency Lock Detectors==		==Frequency Lock Detectors==
			Frequency lock detectors are not so common in receiver implementations, since the receiver mainly relies on phase lock detectors and code lock detectors<ref name="dierendonck"></ref>. In any case, one possible implementation of a frequency lock detector is to cross check that the carrier Doppler (velocity state) is consistent with the code Doppler (velocity state) measured at the DLL.
	Frequency lock detectors are not so common in receiver implementations, since the receiver mainly relies on phase lock detectors and code lock detectors<ref name="dierendonck"></ref>.
	In any case, one possible implementation of a frequency lock detector is to cross check that the carrier Doppler (velocity state) is consistent with the code Doppler (velocity state) measured at the DLL.


	==Related articles==		==Related articles==
Line 78:		Line 82:
	*[[Frequency Lock Loop (FLL)]]		*[[Frequency Lock Loop (FLL)]]
	*[[Delay Lock Loop (DLL)]]		*[[Delay Lock Loop (DLL)]]


	==References==		==References==

Teresa.Ferreira at 07:43, 6 May 2011

2011-05-06T07:43:49Z

← Older revision		Revision as of 07:43, 6 May 2011
Line 7:		Line 7:
	\|Logo=GMV		\|Logo=GMV
	}}		}}
	In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the tracking loops. The receiver must therefore ensure that the tracking loops are following correctly the incoming signal and that they have not diverged away from the solution. This is the purpose of the lock detectors that produce quality factors to assess how ~~good~~ the signal is being tracked.		In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the tracking loops. The receiver must therefore ensure that the tracking loops are following correctly the incoming signal and that they have not diverged away from the solution. This is the purpose of the lock detectors that produce quality factors to assess how well the signal is being tracked.

	==Concept==		==Concept==
	The objective of the lock detectors is to assess whether the incoming signal is being correctly tracked at channel level or not. For that purpose, the GNSS receiver evaluates ~~quality~~ pre-defined quality parameters in order to assess:		The objective of the lock detectors is to assess whether the incoming signal is being correctly tracked at channel level or not. For that purpose, the GNSS receiver evaluates pre-defined quality parameters in order to assess:
	*Code lock of the [[Delay Lock Loop (DLL)\|DLL]]		*Code lock of the [[Delay Lock Loop (DLL)\|DLL]]
	*Phase lock of the [[Phase Lock Loop (PLL)\|PLL]]		*Phase lock of the [[Phase Lock Loop (PLL)\|PLL]]
Line 17:		Line 17:
	These quality parameters may be obtained from the correlators’ outputs or cross-checking of internal information, as detailed hereafter.		These quality parameters may be obtained from the correlators’ outputs or cross-checking of internal information, as detailed hereafter.

	After computing these quality parameters, the receiver checks their values against pre-defined thresholds, which may depend on the application. As an example, if the receiver is targeting high accuracy, these thresholds might be ~~tighter~~, whereas if the priority is on availability, then these thresholds are more likely relaxed.		After computing these quality parameters, the receiver checks their values against pre-defined thresholds, which may depend on the application. As an example, if the receiver is targeting high accuracy, these thresholds might be more restrictive, whereas if the priority is solution availability, then these thresholds are more likely to be relaxed.
	Once loss of lock is declared, the receiver may react in different ways. If only one of the loops loses lock (e.g. the PLL), then the receiver may decide to keep the other loops closed and to restart only this loop. Conversely, the receiver may decide that this loss of lock is unrecoverable and switch back to acquisition, see also [[Receiver Operations\|Receiver Operations]].		Once loss of lock is declared, the receiver may react in different ways. If only one of the loops loses lock (e.g. the PLL), then the receiver may decide to keep the other loops closed and to restart only this loop. Conversely, the receiver may decide that this loss of lock is unrecoverable and switch back to acquisition, see also [[Receiver Operations\|Receiver Operations]].

	These decisions are closely related to the receiver design and they are often the result of all the performance trade-offs ~~related~~ to the target application.		These decisions are closely related to the receiver design and they are often the result of all the performance trade-offs tailored to the target application.

	==Code Lock Detectors==		==Code Lock Detectors==
Line 35:		Line 35:
	<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k</math>		<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k</math>

	~~Where~~		where
	*I_P and Q_P are the In-phase and Quadrature outputs of the prompt correlator respectively, see [[Correlators\|Correlators]] for further information		*<math>I_P</math> and <math>Q_P</math> are the In-phase and Quadrature outputs of the prompt correlator respectively, see [[Correlators\|Correlators]] for further information
	*M is the number of coherent integrations for the lock detector		*M is the number of coherent integrations for the lock detector


	The estimated mean of the narrow power is given by:		The estimated mean of the narrow power is given by:
Line 43:		Line 44:
	<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}</math>		<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}</math>

	~~Where~~ K is the number of non-coherent integrations for the lock detector		where K is the number of non-coherent integrations for the lock detector.


	Finally, the estimated carrier to noise ratio computed at the correlators is given by:		Finally, the estimated carrier to noise ratio computed at the correlators is given by:
Line 49:		Line 51:
	<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})</math>		<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})</math>

	~~Where~~ T is the integration time.		where T is the integration time.


	==Phase Lock Detectors==		==Phase Lock Detectors==
	The phase lock detector is based on the concept that, if the incoming signal is being correctly tracked, then the in-phase component of the prompt correlator is maximum and its quadrature component is minimum.
			The phase lock detector is based on the concept that, if the incoming signal is being correctly tracked, then the in-phase component of the prompt correlator is maximum and its quadrature component is minimum, as shown [[Phase Lock Loop (PLL)\|here]].

	A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:		A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:
Line 58:		Line 62:
	<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}</math>		<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}</math>

	Please note that, when in good lock conditions, this quality parameter ~~will be~~ nearly 1.		Please note that, when in good lock conditions, this quality parameter is nearly 1.


	==Frequency Lock Detectors==		==Frequency Lock Detectors==

	Frequency lock detectors are not so common in receiver implementations, since the receiver mainly relies on phase lock detectors and code lock detectors<ref name="dierendonck"></ref>.		Frequency lock detectors are not so common in receiver implementations, since the receiver mainly relies on phase lock detectors and code lock detectors<ref name="dierendonck"></ref>.
	In any case, one possible implementation ~~might be~~ to cross check that the carrier Doppler (velocity state) is consistent with the code Doppler (velocity state) measured at the DLL.		In any case, one possible implementation of a frequency lock detector is to cross check that the carrier Doppler (velocity state) is consistent with the code Doppler (velocity state) measured at the DLL.


	==Related articles==		==Related articles==
Line 68:		Line 75:
	*[[Multicorrelator]]		*[[Multicorrelator]]
	*[[Tracking Loops]]		*[[Tracking Loops]]
	*[[~~Baseband Processing~~]]		*[[Phase Lock Loop (PLL)]]
			*[[Frequency Lock Loop (FLL)]]
			*[[Delay Lock Loop (DLL)]]


	==References==		==References==

Timo.Kouwenhoven: /* Phase Lock Detectors */

2011-05-03T15:40:45Z

Phase Lock Detectors

← Older revision		Revision as of 15:40, 3 May 2011
Line 54:		Line 54:
	The phase lock detector is based on the concept that, if the incoming signal is being correctly tracked, then the in-phase component of the prompt correlator is maximum and its quadrature component is minimum.		The phase lock detector is based on the concept that, if the incoming signal is being correctly tracked, then the in-phase component of the prompt correlator is maximum and its quadrature component is minimum.

	A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:		A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:

	<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}</math>		<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}</math>

Timo.Kouwenhoven: /* Code Lock Detectors */

2011-05-03T15:40:31Z

Code Lock Detectors

← Older revision		Revision as of 15:40, 3 May 2011
Line 28:		Line 28:

	As such, the narrowband power computed over M and k integration periods can be written as:		As such, the narrowband power computed over M and k integration periods can be written as:

	<math>NBP_k=[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2</math>		<math>NBP_k=[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2</math>

	and the wide band power computed over M and k integration periods can be written as:		and the wide band power computed over M and k integration periods can be written as:

	<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k</math>		<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k</math>

Line 38:		Line 40:

	The estimated mean of the narrow power is given by:		The estimated mean of the narrow power is given by:

	<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}</math>		<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}</math>

Line 43:		Line 46:

	Finally, the estimated carrier to noise ratio computed at the correlators is given by:		Finally, the estimated carrier to noise ratio computed at the correlators is given by:

	<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})</math>		<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})</math>

Timo.Kouwenhoven at 15:39, 3 May 2011

2011-05-03T15:39:58Z

← Older revision		Revision as of 15:39, 3 May 2011
Line 7:		Line 7:
	\|Logo=GMV		\|Logo=GMV
	}}		}}

	In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the tracking loops. The receiver must therefore ensure that the tracking loops are following correctly the incoming signal and that they have not diverged away from the solution. This is the purpose of the lock detectors that produce quality factors to assess how good the signal is being tracked.		In nominal situations, GNSS receivers continuously output a navigation solution using the measurements generated by the tracking loops. The receiver must therefore ensure that the tracking loops are following correctly the incoming signal and that they have not diverged away from the solution. This is the purpose of the lock detectors that produce quality factors to assess how good the signal is being tracked.



	==Concept==		==Concept==

	The objective of the lock detectors is to assess whether the incoming signal is being correctly tracked at channel level or not. For that purpose, the GNSS receiver evaluates quality pre-defined quality parameters in order to assess:		The objective of the lock detectors is to assess whether the incoming signal is being correctly tracked at channel level or not. For that purpose, the GNSS receiver evaluates quality pre-defined quality parameters in order to assess:
	*Code lock of the [[Delay Lock Loop (DLL)\|DLL]]		*Code lock of the [[Delay Lock Loop (DLL)\|DLL]]
Line 27:		Line 23:

	==Code Lock Detectors==		==Code Lock Detectors==

	The concept behind the code lock detector is that, if the DLL is working correctly, then the received signal power is high. Since the received signal is noisy, code lock is often assessed by comparing the estimated Carrier to Noise ratio, <math>\hat{C}/N_0</math>, with a pre-defined threshold.		The concept behind the code lock detector is that, if the DLL is working correctly, then the received signal power is high. Since the received signal is noisy, code lock is often assessed by comparing the estimated Carrier to Noise ratio, <math>\hat{C}/N_0</math>, with a pre-defined threshold.

Line 33:		Line 28:

	As such, the narrowband power computed over M and k integration periods can be written as:		As such, the narrowband power computed over M and k integration periods can be written as:

	<math>NBP_k=[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2</math>		<math>NBP_k=[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2</math>

	and the wide band power computed over M and k integration periods can be written as:		and the wide band power computed over M and k integration periods can be written as:

	<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k</math>		<math>WBP_k=[\sum_M (I_P^2 + Q_P^2)]_k</math>


	Where		Where
Line 46:		Line 38:

	The estimated mean of the narrow power is given by:		The estimated mean of the narrow power is given by:

	<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}</math>		<math>\hat{\mu}_{NP}=\frac{1}{K}\sum_{k=1}^K \frac{NBP_k}{WBP_k}</math>

Line 52:		Line 43:

	Finally, the estimated carrier to noise ratio computed at the correlators is given by:		Finally, the estimated carrier to noise ratio computed at the correlators is given by:

	<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})</math>		<math>\frac{\hat{C}}{N_0}=10 log_{10} (\frac{1}{T} \frac{\hat{\mu}_{NP} - 1}{M - \hat{\mu}_{NP}})</math>



	Where T is the integration time.		Where T is the integration time.


	==Phase Lock Detectors==		==Phase Lock Detectors==

	The phase lock detector is based on the concept that, if the incoming signal is being correctly tracked, then the in-phase component of the prompt correlator is maximum and its quadrature component is minimum.		The phase lock detector is based on the concept that, if the incoming signal is being correctly tracked, then the in-phase component of the prompt correlator is maximum and its quadrature component is minimum.

	A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:		A quality parameter often used at the receiver is the cosine of twice the phase of the prompt correlator, given by<ref name="dierendonck"></ref>:

	<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}</math>		<math>cos(2\phi)=\frac{[\sum_M I_P]_k^2 - [\sum_M Q_P]_k^2}{[\sum_M I_P]_k^2 + [\sum_M Q_P]_k^2}</math>


	Please note that, when in good lock conditions, this quality parameter will be nearly 1.		Please note that, when in good lock conditions, this quality parameter will be nearly 1.


	==Frequency Lock Detectors==		==Frequency Lock Detectors==

	Frequency lock detectors are not so common in receiver implementations, since the receiver mainly relies on phase lock detectors and code lock detectors<ref name="dierendonck"></ref>.		Frequency lock detectors are not so common in receiver implementations, since the receiver mainly relies on phase lock detectors and code lock detectors<ref name="dierendonck"></ref>.
	In any case, one possible implementation might be to cross check that the carrier Doppler (velocity state) is consistent with the code Doppler (velocity state) measured at the DLL.		In any case, one possible implementation might be to cross check that the carrier Doppler (velocity state) is consistent with the code Doppler (velocity state) measured at the DLL.


	==Related articles==		==Related articles==
Line 86:		Line 67:
	==References==		==References==
	<references/>		<references/>


	[[Category:Receivers]]		[[Category:Receivers]]