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In Compass/INS integrated navigation systems, feedback inertial navigation solutions to baseband tracking loops may eliminate receiver dynamic effects, and effectively improve the tracking accuracy and sensitivity. In the conventional inertially-aided tracking loop, the satellite-receiver line-of-sight velocity is used directly to adjust local carrier frequency. However, if the inertial solution drifts, the phase tracking error will be enlarged. By using Kalman filter based carrier phase tracking loop, this paper introduces a new inertial aid method, in which the line-of-sight jerk obtained from inertial acceleration by a nonlinear tracking differentiator is used to adjust relevant parameters of the Kalman filter's process noise matrix. Validation is achieved through high dynamic Compass B3 signal with line-of-sight jerk of 10 g/s collected by a GNSS simulator. Experimental results indicate that the new inertial aid method proposed in this paper is free of the impact of the receiver dynamic and inertial errors. Therefore, when the integrated navigation system is starting or re-tracking after losing lock, the inertial error is absent from the navigation solution correction that induces large drift, and the new aid method proposed in this paper can track highly dynamic signals.

The new Beidou (Compass) Navigation Satellite System network, consisting of five GEO satellites and 30 non-GEO satellites, is designed to provide positioning service with an accuracy of 10 m, speed measurement service with an accuracy of 0.2 m/s and time service with an accuracy of 10 ns within the whole global area. By the end of April 2012, 13 navigation satellites will have been launched. Some signal parameters of Compass were publicized in the 2010 Munich Satellite Navigation Summit [

The receiver's baseband tracking loop, normally, consists of a phase locked loop (PLL) for carrier tracking and a delay locked loop (DLL) for code tracking. Generally, the receiver adopts a third-order PLL, and loop parameters are determined with the controlled-root method [

In a highly dynamic situation, the inertial sensor's bias will be increased. For instance, the bias of an accelerometer with a ±100 g measuring range is approximately 0.1 g to 1 g [

If the integrated navigation system is starting or re-tracking, or the satellite signal is interfered or blocked, the inertial solution error fails to be corrected without the help of integration output. Under such conditions, will the inertial aid still be efficient?

These problems will both result in large offsets or drifts in the inertial aid information. Since the code tracking loop is less affected by receiver dynamics, and its dynamic influence can be overcame through carrier frequency aiding, our research emphasis shall be given to inertially-aided PLL.

Nowadays most GNSS/INS integrated navigation systems based on inertially aided baseband tracking are in the form of tightly integration or ultra-tightly integration [

Hence, it is necessary to consider the influence of Doppler shift rate variation. Doppler shift rate value is relative to line-of-sight acceleration, so line-of-sight jerk can be considered as the coefficient of Kalman states or noise. Considering that increasing Kalman states will accordingly increase the computation burden and large jerk normally has short duration (for jerk 30 g/s, only 2 s are needed to reach an acceleration of 60 g), this paper takes line-of-sight jerk as the process noise. Then it is feasible to consider a new inertial aid method, using the line-of sight jerk as aid information to adjust the noise coefficient of the Doppler shift rate state in real time.

Line-of-sight jerk can be acquired through time difference of line-of-sight acceleration calculated by inertial measurements and Compass ephemeris. The time difference method can eliminate the influence of acceleration offset or drift induced by INS bias, but the line-of-sight jerk acquired by the time differentiator will have a large noise. The nonlinear tracking differentiator presented by Han Jingqing [

The inertial aided Kalman-PLL is adopted in the Compass/INS integrated navigation system. With carrier phase, Doppler frequency shift, and Doppler shift rate as the system states, carrier phase as the observation, and phase discriminator output as the innovation, the carrier phase and Doppler frequency shift are estimated and used to compute the carrier NCO, as shown in

The system matrix of Kalman-PLL is demonstrated as:
_{k}

The measurement matrix of Kalman-PLL is demonstrated as:

Observation noises are also approximated as white noises:

The covariance matrix of observation noise _{k}

Adopt an arctan phase discriminator, and the output of phase discriminator is demonstrated as:
_{p}_{p}

Take the PLL discriminator output _{k}

The computation of Kalman-PLL is presented with two steps, prediction and update:

Prediction:

Update:
_{k} is the optimal gain matrix.

The carrier NCO is:
_{k}_{k}_{k}

The essential part of inertial aided tracking is to use the inertial aid information to predict the Doppler frequency shift, and then eliminate the loop's dynamic stress error. The traditional aid method is velocity aiding, and acceleration aiding is also practical [

The velocity aid method involves computing the Doppler frequency shift through the line-of-sight velocity, and correcting the estimated Doppler frequency shift before the update step (8), as shown in

Acceleration aiding involves computing the Doppler shift rate through the line-of-sight acceleration, and correcting the estimated Doppler shift rate before the update step (8), as shown in _{k} is the line-of-sight velocity vector, _{k} is the line-of-sight acceleration vector, and _{k} is line-of-sight unit vector. In a highly dynamic situation with satellite-receiver line-of-sight jerk, if there is large offset or drift in inertial aiding information, the aided Kalman-PLL will diverge.

The process noise covariance matrix _{k} of Kalman-PLL is demonstrated as [

The Doppler shift rate value is related to satellite-receiver line-of-sight acceleration. Parameters of process noise covariance matrix _{k} are related to the line-of-sight jerk. When the line-of-sight jerk is constant or it varies slowly,

The Doppler shift rate is related to satellite-receiver line-of-sight acceleration, is demonstrated as:
_{ca}_{k} is the satellite-receiver line-of-sight acceleration vector.

The jerk aided PLL involves performing time difference of line-of-sight acceleration, obtaining the line-of-sight jerk, and correcting the process noise matrix relevant coefficient

If the input signal with noise is

The above equation matches

If R is larger, the tracking is faster, but the noise will be accordingly increased. The nearer α approaches 1, the more the system approaches linearity. The setting of threshold value _{0} = 60, a_{1} = 60, a_{2} = 60, α = 6/9.

Firstly, let us take the Micro-Electromechanical System (MEMS) acceleration data collected under static conditions as an example (

Secondly, let us take the simulated line-of-sight acceleration with 50 g to 80 g variation within one second as an example (

As shown in

Because the inertial measurement unit with wide measuring range has large bias, the acceleration aiding information will have a constant offset;

When the integrated navigation system is starting, or the satellite signal is interfered or blocked, the integrated navigation output will be halted. The inertial error will fail to be corrected, and the inertial error will be enlarged gradually with time.

Under general conditions, the third-order PLL or traditional inertially-aided PLL can track the satellite signal with any line-of-sight acceleration. If the above situation occurs and the receiver-satellite line-of-sight jerk is large, it is feasible to track the high dynamic signal with the proposed jerk aided PLL,

Due to the limited hardware conditions and difficulties in collecting actual high dynamic satellite signals and synchronous inertial measurement data, it is optimal to use: (1) the high dynamic simulated intermediate frequency data generated by Matlab; (2) the high dynamic data collected based on GNSS signal simulator to verify the proposed aiding methods.

First of all, we use the simulated high dynamic GNSS intermediate frequency data generated by Matlab and synchronous line-of-sight aiding data to verify the PLL performance with the following three aid methods and make a comparison:

Aid method 1: PLL without assistance

Aid method 2: acceleration aided PLL

Aid method 3: jerk aided PLL based on a nonlinear tracking differentiator

The above three aid methods are all based on Kalman-PLL. The acceleration-aided PLL involves adjusting the value of Kalman states according to

The one second duration high dynamic intermediate frequency data produced by the Matlab satellite signal simulator is used here, and the SNR is −15 dB. As shown in

As shown in

It is concluded on the above experimental results of simulated high dynamic signal that if there is a large offset or drift in the inertial aid information, the jerk-aided PLL based on a nonlinear tracking differentiator can be efficiently used to track the Compass B3 signal with line-of-sight jerk of 30 g/s.

The next used the Compass B3 signal collected with the GNSS signal simulator to verify the proposed aid method. The experimental facility consists of a control computer, a GNSS signal simulator, a radio frequency front end and a high-speed data collection card, as illustrated in

The test adopts the scene of satellite-to-receiver relative motion, with the initial line-of-sight velocity of 8,000 m/s, initial acceleration of 100 g, constant jerk of 10 g/s, signal power of −110 dBm. We collect intermediate frequency data for a duration of 6 seconds. Taking the PRN 6 satellite signal as an example, it is difficult to obtain the correct line-of-sight acceleration, so the jerk-aided PLL based on the nonlinear tracking differentiator is verified according to the constant line-of-sight jerk of 10 g/s. The performance of jerk-aided Kalman-PLL is compared with the PLL without assistance. The results are shown in

From the test results based on the GNSS simulator, the jerk-aided Kalman-PLL can efficiently track the highly dynamic GNSS signal with constant line-of-sight jerk of 10 g/s. Meanwhile, it is concluded from

This paper introduces a jerk-aided Kalman-PLL in the Compass/INS integrated navigation system, where the jerk is estimated through inertial acceleration measurements based on the nonlinear tracking differentiator. This aid method can eliminate the impact of inertial error on the aided tracking loop. Based on the test of high dynamic Compass B3 signals collected by the GNSS simulator, it is concluded that the proposed new aid method can efficiently help track highly dynamic signals with 10 g/s line-of-sight jerk. In conclusion, if the Compass/INS integrated navigation system is starting or re-tracking after losing lock, the inertial error correction by integrated navigation solution hasn't been implemented, then the jerk-aided Kalman-PLL based on the nonlinear tracking differentiator as presented herein can work efficiently.

This work was supported in part by Program for New Century Excellent Talents in University (NCET) and National Natural Science Foundation of China (Grant No. 61104201). The work described in this paper was carried out at the Laboratory of Inertial Technology, College of Mechanical Engineering and Automation, National University of Defense Technology. The authors are grateful to Bing Luo for his help in the test system implementation, and also to Songlai Han for his valuable suggestions for the manuscript revisions.

Inertial aided PLL in Compass/INS integrated navigation system.

Jerk estimated from the MEMS acceleration with the two methods (

Jerk estimated from the simulated high dynamic acceleration with the two methods (

The high dynamic characteristics of simulated signal (line-of-sight direction).

(

Estimated Doppler frequency and Doppler shift rate with jerk aided PLL.

The test system composition based on GNSS simulator.

Phase tracking errors comparison of GNSS simulator collected signal.

(

Offset and noise standard deviation of estimated jerk in static condition with the two methods.

^{2}) |
^{2}) | |||||
---|---|---|---|---|---|---|

| ||||||

offset | 0.0001 | 0.0002 | 0.0001 | 0.00003 | 0.00004 | −0.00008 |

std | 0.1911 | 0.1870 | 0.2026 | 0.0565 | 0.0567 | 0.0619 |

Offset and noise standard deviation of estimated jerk in high dynamic condition with the two methods.

^{2}) |
^{2}) | |
---|---|---|

offset | 2.7396 | 0.0059 |

std | 1,359.8 | 13.7883 |