A Carrier Estimation Method Based on MLE and KF for Weak GNSS Signals
<p>Block diagram of the conventional carrier tracking loop. NCO: numerically-controlled oscillator; IF: intermediate frequency.</p> "> Figure 2
<p>Normalized maximum likelihood estimation (MLE) cost function as a function of the frequency and phase errors.</p> "> Figure 3
<p>Block diagram of the LM algorithm. LM: Levenberg–Marquardt.</p> "> Figure 4
<p>Cramér–Rao bound (CRB) of <span class="html-italic">f</span> and <span class="html-italic">φ</span> with respect to carrier-to-noise spectral density ratio (<span class="html-italic">C</span>/<span class="html-italic">N</span><sub>0</sub>) of the IF signal. (<b>a</b>) CRB of <span class="html-italic">f</span>. (<b>b</b>) CRB of <span class="html-italic">φ</span>.</p> "> Figure 5
<p>Cost function with respect to the frequency error and various phase errors.</p> "> Figure 6
<p>Block diagram of the ML-KF loop. ML-KF: maximum likelihood and Kalman filter.</p> "> Figure 7
<p>Convergence performance of the LM algorithm. (<b>a</b>) Frequency and phase convergence curves of a single example; (<b>b</b>) Root-mean-square error (RMSE) of frequency and phase with respect to the iteration number.</p> "> Figure 8
<p>Tracking results of the ML (maximum likelihood) and ML-KF loops in different dynamic circumstances. (<b>a</b>) Frequency tracking results of pedestrian-level velocity; (<b>b</b>) Frequency tracking results of vehicle-level velocity.</p> "> Figure 9
<p>Performance comparison in pedestrian-level dynamic circumstances. (<b>a</b>) Tracking probability; (<b>b</b>) Frequency error; (<b>c</b>) Bit error rate. FPLL: two-order FLL-assisted three-order PLL.</p> "> Figure 10
<p>Performance comparison in vehicle-level dynamic circumstances. (<b>a</b>) Tracking probability; (<b>b</b>) Frequency error; (<b>c</b>) Bit error rate.</p> "> Figure 11
<p>Performance comparison between the optimal loop and FPLL.</p> ">
Abstract
:1. Introduction
2. Signal Model
3. MLE Discriminator
3.1. Cost Function of MLE
3.2. Parameters Estimation by LM Algorithm
3.3. Cramér–Rao Bound (CRB)
3.4. Dynamic Characteristics
3.5. Computation Cost
4. Adaptive Kalman Filter
4.1. Basic Equations of KF
4.2. ML-KF Loop
5. Simulation Results
5.1. Simulation Results of MLE Discriminator
5.2. Simulation Results of ML-KF Loop
5.3. Monte Carlo Simulations for Sensitivity and Accuracy
5.4. Optimal Loop Design
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Discriminator Update Time (ms) | 20 | 40 | 60 | 80 | 100 | 200 |
Dynamic Tolerance (m/s2) | 357 | 44.6 | 19.8 | 11.1 | 7.1 | 1.8 |
SNR Gain (dB) | 76.1 | 72.9 | 74.7 | 75.9 | 76.9 | 79.9 |
Parameter | Value |
---|---|
Carrier-to-noise ratio C/N0 | 28 dB-Hz |
Sampling rate fs | 5.714 MHz |
Integration time T | 1 ms |
Observation point number N | 20 |
Iteration number threshold M | 20 |
Gradient threshold | 0.01 |
Discriminator Algorithm | |
---|---|
Two-order FLL | where denotes four-quadrant arctangent, , |
Three-order PLL | where denotes the two-quadrant arctangent. |
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Zhang, H.; Xu, L.; Yan, B.; Zhang, H.; Luo, L. A Carrier Estimation Method Based on MLE and KF for Weak GNSS Signals. Sensors 2017, 17, 1468. https://doi.org/10.3390/s17071468
Zhang H, Xu L, Yan B, Zhang H, Luo L. A Carrier Estimation Method Based on MLE and KF for Weak GNSS Signals. Sensors. 2017; 17(7):1468. https://doi.org/10.3390/s17071468
Chicago/Turabian StyleZhang, Hongyang, Luping Xu, Bo Yan, Hua Zhang, and Liyan Luo. 2017. "A Carrier Estimation Method Based on MLE and KF for Weak GNSS Signals" Sensors 17, no. 7: 1468. https://doi.org/10.3390/s17071468