# Deep Learning of GNSS Acquisition

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## Abstract

**:**

## 1. Introduction

## 2. GNSS Signal Model and Acquisition

#### 2.1. CAF Evaluation

- Maximum: This strategy evaluates the CAF all over the search space ${\mathbb{R}}^{{n}_{\tau}}\times {\mathbb{R}}^{{n}_{f}}$, such that each cell corresponds to a CAF value at the corresponding delay/Doppler pair. The overall maximum value of the ambiguity function is then selected and compared with the threshold $\beta $, if the maximum’s value is greater than $\beta $, the satellite is considered acquired, with the estimated code delay and Doppler frequency corresponding to those of the maximum’s cell.
- Serial: In this strategy, the ambiguity function is evaluated serially cell by cell. In each cell, when the ambiguity function (9) is computed, it is immediately compared with the threshold. If the value exceeds the threshold, the acquisition process stops, and the value of the estimated code delay and Doppler frequency are matched to those from the cell under the test. This strategy has the benefit of reducing the number of CAF evaluations, at the expense of some performance degradation.
- Hybrid: This strategy evaluates the ambiguity function row by row (or column by column), and at the end of each row (column), the values of the computed ambiguity functions are compared with the threshold. As soon as the maximum value in the current row (column) exceeds the threshold, the acquisition process stops, and the estimated code delay and Doppler frequency are set to the corresponding cell. This strategy brings in a balance between the two approaches above.

#### 2.2. Benchmark Performance Using the Receiver Operating Characteristic Function

## 3. Deep Learning Method for GNSS Acquisition

#### 3.1. Data-Driven, Physics-Based Signal Acquisition

#### 3.2. Model Structure

#### 3.3. Noncoherent Integration through Fusion of Classifiers

## 4. Model Training

## 5. Results

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**CAF evaluation at the delay/Doppler grid in the (

**a**) absence and (

**b**) presence of a signal with $C/{N}_{0}=39$ dB-Hz.

**Figure 2.**Classification of signal (${\mathcal{H}}_{1}$) or noise (${\mathcal{H}}_{0}$) in CAFs as part of the proposed GNSS signal acquisition scheme. Particularly, a set of convolutional layers followed by fully connected layers provide the capabilities of deep learning from large datasets.

**Figure 3.**Proposed acquisition method, where the CAF map ${\mathbf{Z}}_{i}$ is split into smaller subimages ${\mathbf{Z}}_{i}^{(m,n)}$ which are fed to a bank of parallel DNN binary classifiers to produce probability ratio maps. To increase accuracy, several ($K>1$) probability ratio maps can be noncoherently fused, as shown in the rightmost plot.

**Figure 4.**Portions of the CAF fed for processing to the NN with ${\Delta}_{m}=18$ and ${\Delta}_{n}=5$ defining the size of the $\{m,n\}$-th subimage The resulting subimage ${\mathbf{Z}}_{i}^{(m,n)}$ is shown on the reduced delay/Doppler grid in the case of the (

**a**) absence and (

**b**) presence of a GNSS signal with $C/{N}_{0}=39$ dB-Hz. In the absence of signal, samples are i.i.d., while a time–frequency correlation can be observed in the presence of signal.

**Figure 5.**Comparison of the delay/Doppler grid for (

**a**) standard CAF map with coherent integration only, (

**b**) probability map produced by the data-driven classifier with coherent integration only, and (

**c**) probability map after fusing $K=6$ noncoherent classifier outputs. The GNSS signal had a $C/{N}_{0}$ of 42 dB-Hz and the red circled highlights the location of the peak generated by the GNSS signal.

**Figure 6.**ROC curves (detection versus false-alarm probability) for a recording with 1 ms coherent integration and $K=6$ noncoherently processed blocks. Several relevant $C/{N}_{0}$ values are shown. The detection performance of the proposed scheme (dashed lines) is compared with the theoretical performance of standard methods (solid lines).

**Figure 7.**Probabilities for a 1 ms coherently integrated snapshot, $K=6$ noncoherent processing, and a variety of $C/{N}_{0}$ values.

**Figure 8.**Test statistic histograms under ${\mathcal{H}}_{0}$ and ${\mathcal{H}}_{1}$ hypotheses for a 1 ms coherent integration time for a range of relevant $C/{N}_{0}$ values. The two histograms have overlapping areas, which suggests poor detection performance in these conditions.

**Figure 9.**Test statistic histograms under ${\mathcal{H}}_{0}$ and ${\mathcal{H}}_{1}$ hypotheses for a 1 ms coherent integration time and $K=6$ noncoherent integrations for a range of relevant $C/{N}_{0}$ values. In this case, the two histograms are clearly separated, which supports the performance results in Figure 6.

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**MDPI and ACS Style**

Borhani-Darian, P.; Li, H.; Wu, P.; Closas, P.
Deep Learning of GNSS Acquisition. *Sensors* **2023**, *23*, 1566.
https://doi.org/10.3390/s23031566

**AMA Style**

Borhani-Darian P, Li H, Wu P, Closas P.
Deep Learning of GNSS Acquisition. *Sensors*. 2023; 23(3):1566.
https://doi.org/10.3390/s23031566

**Chicago/Turabian Style**

Borhani-Darian, Parisa, Haoqing Li, Peng Wu, and Pau Closas.
2023. "Deep Learning of GNSS Acquisition" *Sensors* 23, no. 3: 1566.
https://doi.org/10.3390/s23031566