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Ultra-tight integration was first proposed by Abbott in 2003 with the purpose of integrating a global navigation satellite system (GNSS) and an inertial navigation system (INS). This technology can improve the tracking performances of a receiver by reconfiguring the tracking loops in GNSS-challenged environments. In this paper, the models of all error sources known to date in the phase lock loops (PLLs) of a standard receiver and an ultra-tightly integrated GNSS/INS receiver are built, respectively. Based on these models, the tracking performances of the two receivers are compared to verify the improvement due to the ultra-tight integration. Meanwhile, the PLL error distributions of the two receivers are also depicted to analyze the error changes of the tracking loops. These results show that the tracking error is significantly reduced in the ultra-tightly integrated GNSS/INS receiver since the receiver's dynamics are estimated and compensated by an INS. Moreover, the mathematical relationship between the tracking performances of the ultra-tightly integrated GNSS/INS receiver and the quality of the selected inertial measurement unit (IMU) is derived from the error models and proved by the error comparisons of four ultra-tightly integrated GNSS/INS receivers aided by different grade IMUs.

The global navigation satellite system (GNSS) can only work in those environments where the number of GNSS satellites in view is no less than four. This leads to inconveniences and difficulties for GNSS applications in high-dynamic or weak signal scenarios where it is not easy to acquire navigation satellites. Hence, integrated GNSS/INS navigation systems have been developed for these GNSS-challenged environments. Inertial navigation systems (INSs) are capable of high update rates, while GNSS has high navigation accuracy. By fusing them together, the strengths and weaknesses of GNSS receivers and INS uniquely complement each other. Generally, the three architectures of integrated navigation systems, listed in order of complexity, are loose integration, tight integration, and ultra-tight integration [

In the loose integration and tight integration, the GNSS needs stable and strong signals for navigation applications. However, these signals are difficult to receive in the environments where line of sight (LOS) to satellites is not readily available, e.g., urban areas, indoors and dense forest areas. Such environments either completely block the GNSS signals or attenuate them to a power level which is 10–30 dB lower than nominal signal power [

Gustafson at the Charles Stark Draper Laboratory proposed in 2000 an ultra-tightly integrated navigator with extended range code tracking [

In the ultra-tightly integrated GNSS/INS receiver, the level of the performance improvement is impacted by the quality of the inertial measurement unit (IMU) used. Some researchers have compared the tracking and navigation performances of ultra-tight integrations with different grade IMUs by simulation experiments [

There are two loops in receivers: delay lock loop (DLL) and phase lock loop (PLL). Compared to the DLL, the PLL is more sensitive to dynamic stress and it loses lock much easier since the carrier wavelength is much shorter than the code chip length. Therefore, the tracking performances of the PLL get more attention than that of the DLL. In this paper, PLL loop noises are analyzed to evaluate the improvement of the tracking performances.

In the standard receiver, the received signals are tracked by scalar tracking loops. The receiver's dynamics cannot be compensated in tracking processes and tracking loops easily lose lock in weak signal environments. Hence, the ultra-tightly integrated GNSS/INS receiver which can withstand signal interferences and achieve robust signal acquisitions and trackings is proposed.

The primary advantage of the ultra-tight integration method is the inherent robustness in the presence of intentional jamming or unintentional interference. A second advantage is that this method offers improved tracking and more accurate navigation solutions. Consequently, the ultra-tightly integrated GNSS/INS receiver does not easily lose lock on the satellite signals because the ultra-tight method continuously correlates received and replica signals over the entire integration Kalman cycle for all satellites in view [

There are two types of the ultra-tightly integrated GNSS/INS receiver. One is the vector tracking based ultra-tightly integrated GNSS/INS receiver, the other is the scalar tracking based ultra-tightly integrated GNSS/INS receiver.

In the vector tracking-based ultra-tightly integrated receiver, all tracking loops are coupled by a navigation filter. Each tracking loop includes six correlators, a pre-filter, a navigation filter, an aided parameter estimator and a local replica signal generator. The replica signals from all loops firstly correlate with received signals processed by a radio frequency (RF) front end. The in-phase (I) and quadra-phase (Q) outputs obtained from the correlators are used as the measurements of the pre-filters to estimate pseudorange residuals and pseudorange rate residuals. Then, these pseudorange and pseudorange rate residuals of all visible satellites are provided to the central navigation filter as the measurements needed to correct the position and velocity computed from an INS. Finally, the pseudoranges and pseudorange rates predicted from the corrected position and velocity by the LOS geometry algorithm are fed back to the local signal generators to adjust local replica signals [

Compared to the vector tracking loops, the tracking loops in the scalar tracking-based ultra-tightly integrated GNSS/INS receiver are independent each other. In this receiver, the INS aiding is added into the traditional scalar loops to estimate and compensated the vehicle's dynamics with respect to the satellites. The pseudorange and pseudorange-rate outputs obtained from the loop filters are provided to the central navigation filter as the measurements to correct the position and velocity computed from an INS. Then, the corrected position and velocity are further used to predict the pseudoranges and pseudorange rates for adjusting local replica signals.

The position and velocity outputs in the ultra-tight integration are obtained from the central navigation filter instead of the traditional navigation solution used in the standard receiver. The central navigation filter can estimate the receiver antenna's position and velocity, even though the number of the satellite measurements is less than four. Hence, the ultra-tightly integrated GNSS/INS receiver can achieve navigation in the environments where the number of GNSS satellites in view is less than four.

On the other hand, the GNSS-challenged environment where the number of visible satellites is less than four is caused by the high dynamics between the vehicle and the satellites and the low carrier to noise ratio density (C/N0) of the GNSS signal. In the ultra-tight integration, the vehicle's dynamics with the respect to the satellites are compensated by the INS aiding, and the lowest C/N0 accepted by the GNSS signal acquisition and tracking is reduced. Hence, some satellites which are considered not visible in the standard receiver can be acquired and tracked in the ultra-tightly integrated GNSS/INS receiver. The number of the GNSS satellites in view can increase in the ultra-tightly integrated GNSS/INS receiver due to the INS aid. In the following sections, the advantages of the ultra-tight integration in GNSS-challenged environments are analyzed in detail.

The precision of the receiver observations is affected by a set of factors. The most important one that limits the accuracy of a GNSS receiver is the tracking loop noise, including dynamic stress noise, thermal noise, Allan deviation phase noise and vibration-induced phase noise. As stated in [

The thermal noise in the PLL is related with the induced noise of electronic parts that compose a receiver. It is determined by the PLL bandwidth, carrier to noise ratio density, predetection integration time and carrier wavelength. The 1-sigma thermal noise error can be expressed as follows [_{c}_{PLL}_{PLL}_{0} is the carrier to noise power expressed as a ratio 10^{(}^{C}^{/}^{N}^{0)/10} (C/N0 expressed in [dB-Hz]).

The dynamic stress error is associated to the motions that the receiver antenna suffers. It is inevitable in the PLL tracking and plays a major role in the tracking performance. The purpose of the ultra-tight integration is just to reduce the dynamic stress error by estimating and compensating the receiver antenna's LOS dynamics from the INS. The dynamic stress error (1-sigma) depends on loop order and described as follows [^{k}R^{k}^{k}). _{PLL}_{c}_{k}_{2}=0.2809 for a second-order PLL, _{3}=0.4828 for a third-order PLL.

The Allan deviation phase noise is caused by the drift of the receiver oscillator, which is determined by the oscillator's material and craft. The phase noise induced by the frequency drift can be expressed as follows [_{φ}_{L}_{L}_{1} = 4_{PLL}_{L}_{2} = 1.885_{PLL}_{L}_{3} =1.2_{PLL}

In _{φ}_{c}_{y}

Combining

In this equation, the clock parameters _{−2}, _{−1}, and _{0} listed in

The vibration-induced phase noise is associated to the jitter in the receiver clock because of environmental vibrations. The model of the phase noise induced by environmental vibrations is similar to the Allan deviation phase noise. The model is written as follows:

In _{φ}_{g}_{g}^{2}/Hz).

Substituting _{φ}

The tracking threshold of the PLL is the maximum error accepted by the receiver to keep the PLL locked. It is usually obtained from multiple tracking experiments. However, these experiments are complicated and need to be repeated constantly in order to calculate the optimal tracking threshold. Hence, an empirical value (1-sigma) is gained from [

In this equation, 15° is the 1-sigma empirical threshold.

In the ultra-tightly integrated GNSS/INS receiver, the dynamic stress noise is reduced by using an additional IMU to measure and compensate the dynamics experienced by the receiver antenna. After the dynamics are compensated, the dynamic stress noise for second-order PLL is mainly affected by the acceleration measurement error caused by the IMU errors, not by the acceleration of the motions that the receiver antenna experiences in LOS. Therefore, the dynamic stress noise (1-sigma) for second-order PLL in the ultra-tightly integrated GNSS/INS receiver is expressed according to [

In the equation,

Meanwhile, the acceleration error vector caused by the IMU can be modeled by:
_{d}

Since the acceleration of the pseudorange is measured by the IMU in LOS, the _{IMU}

Similar to

In the ultra-tightly integrated GNSS/INS receiver, the tracking performances can be improved as the dynamic stress noise is reduced. According to the models analyzed in this paper, the PLL performances in the standard receiver and the ultra-tightly integrated GNSS/INS receiver are compared to verify the improvement induced by the ultra-tight integration. In the comparisons, an IMU is selected to estimate the acceleration of the pseudorange.

The gyro bias and accelerometer bias of the IMU are respectively 50°/h and 1 mg. The integration time length of the correlators is 1 ms. Moreover, a temperature compensated crystal oscillator (TCXO) is selected and the oscillator's g-sensitivity is 5 parts/g.

To reduce the loop error and improve the tracking performances, the ultra-tight integration is designed to reduce the dynamic stress noise. Since the tracking loop is aided by an INS, the dynamic stress error in the ultra-tightly integrated GNSS/INS receiver is associated to the IMU errors and not related with the dynamics of the receiver antenna in LOS. Therefore, in the ultra-tightly integrated GNSS/INS receiver, the dynamic stress noise is evidently reduced and does not change in different dynamics. As is seen in

In

The loop bandwidth of the PLL in the ultra-tightly integrated GNSS/INS receiver is assumed to be 20 Hz, which is the same as in the standard receiver. The error distributions in

Comparing

Based on

The biggest advantage of the ultra-tightly integrated GNSS/INS receiver is that it can perform in a highly dynamic scenario. Assumed that the C/N0 is 30 dB-Hz,

Based on the ultra-tight integration, the tracking performances of the receiver are enhanced by compensating the receiver antenna's dynamics and reducing the dynamic stress noise. The estimation accuracy of the dynamics is affected by the quality of the IMU. Therefore, the IMU quality becomes an impact factor in the tracking of the ultra-tightly integrated GNSS/INS receiver. The relation between the dynamic stress noise and the quality of the IMU, derived from

The dynamic stress noises in four ultra-tightly integrated GNSS/INS receivers aided by different grade IMUs are compared to verify the effect of the IMU quality.

Since the correction frequency of the INS in the ultra-tight integration is usually 1 Hz, the drift time _{d}

Based on the principle and definition of ultra-tight integration, this paper analyzes the performance improvements of the receiver tracking loops with Doppler aid from an INS. The models of every error source in the standard receiver and the ultra-tightly integrated GNSS/INS receiver are established and compared, respectively. By comparison of the tracking performances and the error distributions, we can conclude that the ultra-tight integration can improve the tracking performance of the receiver by compensating the receiver antenna's dynamics and reducing the dynamic stress noise. Moreover, the performance comparisons of the PLLs aided by different grade IMUs demonstrate that the quality of the IMU has an effect on the tracking performances in the ultra-tightly integrated GNSS/INS receiver.

This work was supported by a grant from National 863 Program “GNSS vulnerability analysis and signal transmission environment (2011AA120503)” in China.

The authors declare no conflict of interest.

The architecture of the vector tracking-based ultra-tightly integrated GNSS/INS receiver.

The architecture of the scalar tracking based ultra-tightly integrated GNSS/INS receiver.

2nd loop phase error _{PLL} with different C/N_{0} in the standard receiver (0.5 g LOS acceleration).

2nd loop error distributions with different C/N_{0} in the standard receiver (0.5 g LOS acceleration, 20 Hz PLL bandwidth).

2nd loop phase error _{PLL} with different dynamics in the standard receiver (30 dB-Hz C/N0).

2nd loop error distributions with different dynamics in the standard receiver (30 dB-Hz C/N0, 20 Hz PLL bandwidth).

Dynamic stress noise comparisons between the standard receiver and the ultra-tightly integrated GNSS/INS receiver (0.5 g LOS acceleration).

Loop phase error _{PLL} with different C/N_{0} in the ultra-tightly integrated GNSS/INS receiver.

Loop error distributions with different C/N_{0} in the ultra-tightly integrated GNSS/INS receiver (20 Hz bandwidth).

Loop error distributions with different C/N_{0} in the ultra-tightly integrated GNSS/INS receiver (5 Hz bandwidth).

Dynamic stress noises in the ultra-tightly integrated GNSS/INS receivers aided by different grade IMUs.

Clock parameters of different oscillators.

_{0}[ |
_{−1}[−] |
_{−2}[1/ | |
---|---|---|---|

TCXO | 1.00 × 10^{−21} |
1.00 × 10^{−20} |
2.00 × 10^{−20} |

OCXO | 2.51 × 10^{−26} |
2.51 × 10^{−23} |
2.51 × 10^{−22} |

Rubidium | 1.00 × 10^{−23} |
1.00 × 10^{−22} |
1.30 × 10^{−26} |

Cesium | 2.00 × 10^{−20} |
7.00 × 10^{−23} |
4.00 × 10^{−29} |

Tracking performance comparisons of two kinds of receiver with different C/N0 (0.5 g LOS acceleration).

_{0} |
|||||
---|---|---|---|---|---|

Standard Receiver | Optimal Bandwidth | 15 Hz | 22 Hz | 28 Hz | 35 Hz |

Tracking Error of the PLL in Optimal Bandwidth | 28 deg. | 15 deg. | 9 deg. | 7 deg. | |

Dynamic Stress Noise Proportion (B_{PLL} = 20 Hz) |
8% | 14% | 21% | 28% | |

| |||||

Ultra-tightly Integrated GNSS/INS Receiver | Optimal Bandwidth | 7 Hz | 9 Hz | 13 Hz | 25 Hz |

Tracking Error of the PLL in Optimal Bandwidth | 20 deg. | 12 deg. | 8 deg. | 6 deg. | |

Dynamic Stress Noise Proportion (B_{PLL} = 20 Hz) |
<1% | <1% | <1% | <1% |

Tracking performance comparisons of two kinds of receiver with different dynamics (30 dB-Hz C/N0).

Standard Receiver | Optimal Bandwidth | 14 Hz | 22 Hz | 28 Hz | 32 Hz |

Tracking Error of the PLL in Optimal Bandwidth | 13 deg. | 15 deg. | 17 deg. | 18 deg. | |

Dynamic Stress Noise Proportion (B_{PLL} = 20 Hz) |
3% | 14% | 25% | 33% | |

| |||||

Ultra-tightly Integrated GNSS/INS Receiver | Optimal Bandwidth | 9 Hz | 9 Hz | 9 Hz | 9 Hz |

Tracking Error of the PLL in Optimal Bandwidth | 12 deg. | 12 deg. | 12 deg. | 12 deg. | |

Dynamic Stress Noise Proportion (B_{PLL} = 20 Hz) |
<1% | <1% | <1% | <1% |

IMUs selected in the comparisons.

Gyro bias | 300°/h | 50°/h | 1°/h | 0.01°/h |

Accelerometer bias | 10 mg | 1 mg | 0.1 mg | 0.01 mg |