# A New MIMU/GNSS Ultra-Tightly Coupled Integration Architecture for Mitigating Abrupt Changes of Frequency Tracking Errors

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## Abstract

**:**

_{0}) estimate and an increase in the code discriminator estimation error. The disruptive effects of frequency errors on the estimation of C/N

_{0}and on the code discriminator are quantitatively evaluated via theoretical analyses and Monte Carlo simulations. The new MIMU/GNSS UTC architecture introduces a large frequency error detector and a refined frequency processor based on a retuned frequency in each tracking channel. In addition, an adaptive channel prefilter with multiple fading factors is introduced as an alternate to the conventional prefilter. Numerical simulations based on a highly dynamic trajectory are used to assess performance. The simulation results show that when there is an abrupt step change in the frequency tracking error, the new UTC architecture can effectively suppress the divergence of navigation solutions and the loss of tracking lock, and can significantly reduce the deviation of the C/N

_{0}estimation.

## 1. Introduction

_{0}) and an increase in the code tracking error. In highly dynamic environments, if the large frequency tracking error cannot be mitigated in time, it may even result in loss of the tracking lock.

_{0}will suddenly drop for all tracking channels [9]. For this reason, the estimated C/N

_{0}is used as an indicator to detect large frequency errors in [9]. The optimal frequency offset compensation is obtained through a search algorithm. This method is very effective for the large frequency error caused by the crystal oscillator. However, the frequency error caused by MIMU measurement errors depends on the line-of-sight direction of the satellite being tracked. The estimated C/N

_{0}of each tracking channel may not drop suddenly at the same time. For frequency errors induced by MIMU errors, the effect of this technique based on C/N

_{0}is limited.

## 2. Conventional MIMU/GNSS UTC Integration Architecture

#### 2.1. Channel Prefilter Model

#### 2.2. Integration Kalman Filter

## 3. Quantitative Analyses of Disruptive Effects of Large Frequency Errors

_{0}estimation errors and code tracking estimation errors to increase. In this section, we explore the disruptive effects of large frequency tracking errors via theoretical analyses and Monte Carlo simulations.

#### 3.1. Effects on the C/N_{0} Estimation

_{0}is usually estimated using the coherent integration values from prompt correlators [20]. When a code loop is in a stable tracking state, the code phase tracking error is nominal. The autocorrelation function corresponding to the prompt code phase error $R\left({\tau}_{p}\right)$ is equal to one. When the coherent integration time does not cross data bits, the data bit is constant, and the influence on the coherent integration can be omitted. For these reasons, the coherent integration values of the prompt correlators can be simplified as

_{0}to decrease significantly in the case of a large frequency error. It should be pointed out that the true C/N

_{0}is not related to ${f}_{e}$. The frequency error affects the estimated C/N

_{0}from coherent integration values.

_{0}by means of various C/N

_{0}estimation algorithms [27,28]. In the GNSS context, the narrow-to-wideband power ratio (NWPR) method is usually used as a standard estimator. Therefore, we used the NWPR method as an example to analyze the effects of large frequency tracking errors on the C/N

_{0}estimation results.

_{0}is modeled as

_{0}can be expressed as

_{0}attenuation due to large frequency tracking errors is obtained as

_{0}estimation. The theoretical C/N

_{0}attenuation was obtained from Equations (19)–(21). M was set to 20. T

_{coh}and τ were 1 ms and 20 ms, respectively. In the Monte Carlo simulation, the true C/N

_{0}was set to 40 dB-Hz. Again, N was set to 50, that is, the power ratio was averaged over a time interval of 1 s. The estimated C/N

_{0}and the true C/N

_{0}were substituted into Equation (21) to obtain the C/N

_{0}attenuation.

_{0}attenuation and the 1000 Monte Carlo simulation results. The two sets of results are relatively consistent. For the case of ${N}_{2}=1$, the attenuation of the estimated C/N

_{0}caused by large frequency errors is less than 1 dB, and the effect of frequency errors is negligible. However, when ${N}_{2}$ is greater than 5 and frequency errors are greater than 20 Hz, the effect of frequency errors on the estimated C/N

_{0}is very significant. When ${N}_{2}=50$ and ${f}_{e}>30$ Hz, the ${\mathrm{sinc}}^{2}(\cdot )$ term in the numerator of Equation (16) quickly decays to near zero. The estimated C/N

_{0}and C/N

_{0}attenuation also drop sharply. Therefore, there is a jump in the C/N

_{0}attenuation curve of ${N}_{2}=50$ at ${f}_{e}=40$ Hz. In addition, we limited the minimum value of C/N

_{0}to 0 dB-Hz, that is, the maximum attenuation of C/N

_{0}is –40 dB, as seen in Figure 2.

#### 3.2. Effects on the Code Tracking Error Estimation

_{0}was set to 40 dB-Hz.

## 4. Proposed MIMU/GNSS UTC Integration Architecture

_{0}to rapidly decrease. Furthermore, the code discriminator estimation error caused by the large frequency error is greater than the error without frequency error. If the large frequency tracking error cannot be eliminated in time, especially in highly dynamic environments, it will seriously impair the performance of the navigation system.

#### 4.1. Large Frequency Error Detector

_{0}estimator. Otherwise, it means that the current epoch is affected by a large frequency tracking error.

#### 4.2. Refined Frequency Processor

_{0}estimator to obtain a more accurate C/N

_{0}estimate. The carrier frequency tracking error of the current epoch can be expressed as

#### 4.3. Adaptive Prefilter with Multiple Fading Factors

## 5. Simulation Experiment Results

#### 5.1. Simulation Setup

- Starting position: longitude (108.9°), latitude (34.2°) and altitude (350 m);
- Trajectory duration: 110 s;
- Maximum velocity: 1500 m/s;
- Highly dynamic segment 1: linear acceleration = 100 g, time interval = (70, 71) s;
- Highly dynamic segment 2: centripetal acceleration > 100 g, time interval = (81, 90) s.

_{0}of all tracking channels was set to the same value (50 dB-Hz), so the tracking status of each tracking channel was similar. In the following, one of the tracking channels is chosen as an example to show the channel-dependent simulation results. Before the system was switched to the UTC mode, it was necessary to perform the scalar tracking and tight integration. The simulation results of the UTC integration were obtained starting from 40 s.

#### 5.2. Results and Analysis

_{0}of the two integrated architectures. We observe that the estimated C/N

_{0}of the CUTC system rapidly drops to zero in the presence of a large frequency error. The estimated C/N

_{0}of the EUTC system decreases only slightly in a short time. After 70 s, the estimated C/N

_{0}of the EUTC system recovers quickly. Hence, the EUTC integration can provide continuous and accurate C/N

_{0}estimates.

## 6. Conclusions

_{0}output by the enhanced UTC integration is hardly affected by large frequency errors. Again, with the aid of the adaptive prefilter, the maximum velocity error does not exceed 2 m/s. Position errors are also significantly smaller than the counterpart without the adaptive prefilter.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

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**Figure 2.**Estimated C/N

_{0}attenuation caused by frequency tracking errors. The solid lines represent the theoretical analysis results, and Monte Carlo simulation results are represented by discrete points.

**Figure 7.**Simulation reference trajectory: (

**a**) horizontal trajectory; (

**b**) velocity profiles; and (

**c**) acceleration profiles.

**Figure 8.**Tracking errors for the CUTC integration simulation: (

**a**) carrier frequency tracking errors; (

**b**) code phase tracking errors.

**Figure 9.**Navigation solution errors of the CUTC integration simulation: (

**a**) attitude errors; (

**b**) velocity errors; and (

**c**) position errors.

**Figure 10.**Tracking errors for the EUTC integration simulation: (

**a**) carrier frequency tracking errors; (

**b**) code phase tracking errors.

**Figure 11.**Navigation solution errors of the EUTC integration simulation: (

**a**) attitude errors; (

**b**) velocity errors; and (

**c**) position errors.

**Figure 15.**Navigation solution errors of the simplified EUTC integration simulation: (

**a**) attitude errors; (

**b**) velocity errors; and (

**c**) position errors.

Items | Gyroscope | Accelerometer |
---|---|---|

Bias | 30°/h | 500 μg |

Random walk | 0.3°/sqrt(h) ^{1} | 50 μg/sqrt(Hz) ^{1} |

Time-dependent bias | 1°/h | 50 μg |

Correlation time | 300 s | 300 s |

Scale factor error | 500 ppm | 200 ppm |

^{1}sqrt(·) denotes the square root operation.

Types | Parameters | Values |
---|---|---|

Initial errors | Initial attitude errors | (0.1; 0.1; 2)° |

Initial velocity errors | (0.1; 0.1; 0.1) m/s | |

Initial position errors | (3; 3; 5) m | |

Prefilter process noise variances | Code phase | 8 × 10^{−4} (code chip) ^{2} |

Carrier frequency | 0.1 (Hz) ^{2} | |

Carrier frequency rate | 5 (Hz/s) ^{2} | |

Update frequency | Integration filter | 10 Hz ^{1} |

Prefilter | 50 Hz ^{2} | |

Code NCO | 50 Hz | |

Carrier NCO | 1000 Hz |

^{1}Measurement update frequency.

^{2}Time update frequency is the same as the measurement update frequency.

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**MDPI and ACS Style**

Liu, S.; Li, S.; Fu, Q.; Tao, Y.; Wu, F.
A New MIMU/GNSS Ultra-Tightly Coupled Integration Architecture for Mitigating Abrupt Changes of Frequency Tracking Errors. *Micromachines* **2020**, *11*, 1117.
https://doi.org/10.3390/mi11121117

**AMA Style**

Liu S, Li S, Fu Q, Tao Y, Wu F.
A New MIMU/GNSS Ultra-Tightly Coupled Integration Architecture for Mitigating Abrupt Changes of Frequency Tracking Errors. *Micromachines*. 2020; 11(12):1117.
https://doi.org/10.3390/mi11121117

**Chicago/Turabian Style**

Liu, Shiming, Sihai Li, Qiangwen Fu, Yuanbo Tao, and Feng Wu.
2020. "A New MIMU/GNSS Ultra-Tightly Coupled Integration Architecture for Mitigating Abrupt Changes of Frequency Tracking Errors" *Micromachines* 11, no. 12: 1117.
https://doi.org/10.3390/mi11121117