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Improve documentation

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Carles Fernandez
2019-09-28 00:26:50 +02:00
parent 879bf2aa25
commit 43eafdd484
2 changed files with 20 additions and 17 deletions
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36
src/algorithms/tracking/libs/lock_detectors.h
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@@ -54,19 +54,20 @@
/*! \brief cn0_svn_estimator is a Carrier-to-Noise (CN0) estimator
* based on the Signal-to-Noise Variance (SNV) estimator
*
* Signal-to-Noise (SNR) (\f$\rho\f$) estimator using the Signal-to-Noise Variance (SNV) estimator:
* Signal-to-Noise (SNR) (\f$ \rho \f$) estimator using the Signal-to-Noise Variance (SNV) estimator:
* \f{equation}
* \hat{\rho}=\frac{\hat{P}_s}{\hat{P}_n}=\frac{\hat{P}_s}{\hat{P}_{tot}-\hat{P}_s},
* \f}
* where \f$\hat{P}_s=\left(\frac{1}{N}\sum^{N-1}_{i=0}|Re(Pc(i))|\right)^2\f$ is the estimation of the signal power,
* \f$\hat{P}_{tot}=\frac{1}{N}\sum^{N-1}_{i=0}|Pc(i)|^2\f$ is the estimator of the total power, \f$|\cdot|\f$ is the absolute value,
* \f$Re(\cdot)\f$ stands for the real part of the value, and \f$Pc(i)\f$ is the prompt correlator output for the sample index i.
* where \f$ \hat{P}_s=\left(\frac{1}{N}\sum^{N-1}_{i=0}|Re(Pc(i))|\right)^2 \f$ is the estimation of the signal power,
* \f$ \hat{P}_{tot}=\frac{1}{N}\sum^{N-1}_{i=0}|Pc(i)|^2 \f$ is the estimator of the total power, \f$ |\cdot| \f$ is the absolute value,
* \f$ Re(\cdot) \f$ stands for the real part of the value, and \f$ Pc(i) \f$ is the prompt correlator output for the sample index i.
*
* The SNR value is converted to CN0 [dB-Hz], taking to account the coherent integration time, using the following formula:
* The SNR value is converted to CN0 [dB-Hz], taking into account the coherent integration time, using the following formula:
* \f{equation}
* CN0_{dB}=10*log(\hat{\rho})-10*log(T_{int}),
* \f}
* where \f$T_{int}\f$ is the coherent integration time, in seconds.
* where \f$ T_{int} \f$ is the coherent integration time, in seconds.
*
* Ref: Marco Pini, Emanuela Falletti and Maurizio Fantino, "Performance
* Evaluation of C/N0 Estimators using a Real Time GNSS Software Receiver,"
* IEEE 10th International Symposium on Spread Spectrum Techniques and
@@ -76,21 +77,22 @@ float cn0_svn_estimator(const gr_complex* Prompt_buffer, int length, float coh_i
/*! \brief cn0_mm_estimator is a Carrier-to-Noise (CN0) estimator
* based on the Moments Method (MM)
* based on the Second- and Fourth-Order Moments Method (M2M4)
*
* Signal-to-Noise (SNR) (\f$\rho\f$) estimator using the Moments Method:
* Signal-to-Noise (SNR) (\f$ \rho \f$) estimator using the Moments Method:
* \f{equation}
* \hat{\rho}=\frac{\hat{P}_s}{\hat{P}_n}=\frac{\sqrt{2*\hat{M}_2^2 - \hat{M}_4 }}{\hat{M}_2-\sqrt{2*\hat{M}_2^2 - \hat{M}_4 }},
* \hat{\rho}=\frac{\sqrt{2 \hat{M}_2^2 - \hat{M}_4 }}{\hat{M}_2-\sqrt{2 \hat{M}_2^2 - \hat{M}_4 }},
* \f}
* where \f$\hat{P}_s=\left(\frac{1}{N}\sum^{N-1}_{i=0}|Re(Pc(i))|\right)^2\f$ is the estimation of the signal power,
* \f$ \hat{M}_2=\frac{1}{N}sum^{N-1}_{i=0}|Pc(i)|^2 \f$, \f$\hat{M}_4 = \frac{1}{N}sum^{N-1}_{i=0}|Pc(i)|^4 \f$, \f$|\cdot|\f$ is the absolute value,
* \f$Re(\cdot)\f$ stands for the real part of the value, and \f$Pc(i)\f$ is the prompt correlator output for the sample index i.
* where
* \f$ \hat{M}_2=\frac{1}{N}\sum^{K-1}_{k=0}|P[k]|^2 \f$, \f$ \hat{M}_4 = \frac{1}{K}\sum^{K-1}_{k=0}|P[k]|^4 \f$, \f$ |\cdot| \f$ is the absolute value,
* and \f$ P[k] \f$ is the prompt correlator output for the sample index k.
*
* The SNR value is converted to CN0 [dB-Hz], taking to account the coherent integration time, using the following formula:
* The SNR value is converted to CN0 [dB-Hz] taking into account the coherent integration time, using the following formula:
* \f{equation}
* CN0_{dB}=10*log(\hat{\rho})-10*log(T_{int}),
* \f}
* where \f$T_{int}\f$ is the coherent integration time, in seconds.
* where \f$ T_{int} \f$ is the coherent integration time, in seconds.
*
* Ref: D. R. Pauluzzi, N. C. Beaulieu, "A comparison of SNR estimation
* techniques for the AWGN channel," IEEE Trans. on Comm., vol. 48,
* no. 10, pp. 1681–1691, Oct. 2000.
@@ -104,9 +106,9 @@ float cn0_mm_estimator(const gr_complex* Prompt_buffer, int length, float coh_in
* \f{equation}
* C2\phi=\frac{NBD}{NBP},
* \f}
* where \f$NBD=(\sum^{N-1}_{i=0}|Im(Pc(i))|)^2+(\sum^{N-1}_{i=0}|Re(Pc(i))|)^2\f$,
* \f$NBP=\sum^{N-1}_{i=0}Im(Pc(i))^2-\sum^{N-1}_{i=0}Re(Pc(i))^2\f$, and
* \f$Pc(i)\f$ is the prompt correlator output for the sample index i.
* where \f$ NBD=(\sum^{N-1}_{i=0}|Im(Pc(i))|)^2+(\sum^{N-1}_{i=0}|Re(Pc(i))|)^2 \f$,
* \f$ NBP=\sum^{N-1}_{i=0}Im(Pc(i))^2-\sum^{N-1}_{i=0}Re(Pc(i))^2 \f$, and
* \f$ Pc(i) \f$ is the prompt correlator output for the sample index i.
* Ref: Van Dierendonck, A.J. (1996), Global Positioning System: Theory and
* Applications,
* Volume I, Chapter 8: GPS Receivers, AJ Systems, Los Altos, CA 94024.