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COMPASS is an indigenously developed Chinese global navigation satellite system and will share many features in common with GPS (Global Positioning System). Since the ultratight GPS/INS (Inertial Navigation System) integration shows its advantage over independent GPS receivers in many scenarios, the federated ultratight COMPASS/INS integration has been investigated in this paper, particularly, by proposing a simplified prefilter model. Compared with a traditional prefilter model, the state space of this simplified system contains only carrier phase, carrier frequency and carrier frequency rate tracking errors. A twoquadrant arctangent discriminator output is used as a measurement. Since the code tracking error related parameters were excluded from the state space of traditional prefilter models, the code/carrier divergence would destroy the carrier tracking process, and therefore an adaptive Kalman filter algorithm tuning process noise covariance matrix based on state correction sequence was incorporated to compensate for the divergence. The federated ultratight COMPASS/INS integration was implemented with a hardware COMPASS intermediate frequency (IF), and INS's accelerometers and gyroscopes signal sampling system. Field and simulation test results showed almost similar tracking and navigation performances for both the traditional prefilter model and the proposed system; however, the latter largely decreased the computational load.
The global COMPASS or Beidou II is a second generation Chinese satellite navigation system being developed from its first generation predecessor, Beidou I, which was a regionallybased system [
Like a GPS receiver, the COMPASS receiver also faces the paradoxical situation in optimising the carriertracking loop bandwidth to guarantee antijamming capability and dynamics adaptation simultaneously,
Generally, the ultratight GPS/INS integrated navigation systems can be classified as central architecture [
In federated architecture, the large integrated Kalman filter is decomposed into two filters operating at different rates [
A common characteristic of traditional prefilter models is that the signal amplitude is independent of other state variables and discriminator outputs, such that the observability of normalized signal amplitude would be a substantial problem in actual implementation [
This paper has proposed a simplified prefilter model and a corresponding adaptive Kalman filter algorithm to replace the traditional one. The state space of this simplified prefilter model consists of only carrier phase tracking error, carrier frequency tracking error and carrier frequency rate tracking error, and the twoquadrant arctangent discriminator output is used as a measurement. Since the code tracking error component has been excluded from the state space, if the code/carrier divergence was ignored it will destroy the carrier tracking process [
The remainder of this paper is organized as follows: Section 2 introduces a commonly used prefilter and integrated navigation filter models in federated GPS/INS architecture, Section 3 introduces the simplified prefilter model and corresponding adaptive Kalman filter algorithm, in addition, the COMPASS/INS integrated navigation filter model is also proposed. Section 4 evaluates the performance of SAKF and TKF through simulation and field experiments. The paper finishes with conclusions and an outline of future work in Section 5.
Before introducing the simplified adaptive prefilter model of ultratight COMPASS/INS integration, a brief introduction is given on traditional prefilter and integrated navigation model of federated GPS/INS integration. Expanding
Traditionally, the state vector of navigation filter is defined as [
The corresponding system model of navigation filter is:
For the integrated navigation filter, the error components of pseudo range, pseudo range rate and pseudo range acceleration are used as measurements which are proportional to corresponding estimated states of prefilter [
In federated ultratight GPS/INS integration, the prefilters are responsible for implementing code and carrier tracking, and also providing measurement information and corresponding measurement noise matrices for the integrated navigation filter [
The outputs of normalized earlyminuslate envelope code discriminator and twoquadrant arctangent carrier discriminator are used as measurements, and the measurement equation is written as follows [
As shown in
A simplified prefilter model for the federated ultratight COMPASS/INS integration is investigated for the reduction in the calculation load, and the corresponding integrated navigation filter model is also analyzed.
For the
The measurement is the output of twoquadrant arctangent carrier discriminator, and the corresponding measurement model is:
Since the navigation solution accuracy is insufficient for carrier phase tracking [
In
Since the code tracking related parameter has been excluded from the state space of this simplified prefilter model, the code tracking is controlled by the carrier tracking process. The code NCO control information is provided as:
Comparing
The state correction sequence is used to adapt the process noise covariance matrix
While a standard Kalman filter, shown in
Associated matrix multiplication operations in above Kalman filter algorithms are implemented to compare the computational complexities of both filter models.
In
The COMPASS B3 frequency signal considered in this paper is BPSK modulated as GPS L1 frequency signal [
The corresponding measurement equation of integrated navigation filter is as follows (only a single channel is list):
The variances of measurement noises can be obtained from estimation error covariance matrices of prefilters as follows [
With the simplified prefilter model and adaptive Kalman filter, the federated COMPASS/INS integration implementation process is shown in
COMPASS IF data was sampled through a hardware sampling system, which will be discussed in “Test description” in detail.
The acquisition process gets the initial code phase and carrier Doppler frequency for different visible satellites, which will be used to set the initial values for prefilters.
Adaptive Kalman filter algorithm is implemented in each prefilter to implement code and carrier tracking, and provide measurement information to the integrated navigation filter.
With measurement information from the prefilters and INS, a classical Kalman filter algorithm is implemented for integrated navigation filter, and the corresponding INS correction information is fed back to update INS errors.
Modified INS information and COMPASS ephemeris are used to generate carrier frequency for different satellites [
Repeat steps (3) to (5).
Federated COMPASS/INS integration with SAKF and TKF were implemented in software. Two sets of data were used to compare the performance of SAKF and TKF. First, data were collected using a hardware complex GNSS/INS signal simulator to assess the performance in high dynamic case. Second, field data were collected with a COMPASS B3 frequency antenna and an INS to assess the tracking performance of the above two methods.
The comparison of the performance of SAKF and TKF is made in both the tracking domain and navigation domain. In tracking domain, Phase Lock Indicator (PLI) and Doppler frequency tracking error are used to evaluate the carrier phase tracking ability. In navigation domain, the position and velocity errors in Earth Centered Earth Fixed (ECEF) frame were compared.
For the simulation tests, a complex GNSS/INS signal hardware simulator was used to generate the COMPASS radio frequency(RF) signal and INS's accelerometers and gyroscopes data (INS data for short). A hardware sampling system was constructed to sample and store the digitized COMPASS IF signal and INS data. Data collection process for the simulation case is shown in
The data collection system consists of complex GNSS/INS signal hardware simulator, COMPASS B3 RF module, FCFRPCIe9801 data sampling card [
GNSS/INS hardware simulator provides synchronized COMPASS B3 frequency RF signal and INS data; the vehicle scenario and signal strength can be configured by users for their corresponding applications.
COMPASS B3 RF module is responsible for downconverting B3 RF signal into IF signal and providing driving clock for FCFRPCIe9801 data sampling card. A reference sampling clock from Rubidium Oscillator is used for the data sampling card.
FCFRPCIe9801 data sampling card completes the data sampling process of IF signal and transfers the sampled data to electronic disk in real time.
RCKIET224MC electronic disk is responsible for storing sampled IF data from sampling card.
FS725 rubidium clock provides reference clock for radio frequency module.
The ultratight COMPASS/INS integration algorithm was implemented in MATLAB, and the parameters defined in baseband signal processing part are listed in
In
Phase lock indicator (PLI) and Doppler frequency tracking errors were used to evaluate the tracking performance. The PLI is calculated as described by [
Simplifying
As shown in
The variations of PLI and Doppler frequency tracking errors for SV04 and SV05 are shown in
For federated COMPASS/INS integrated navigation system with SAKF and TKF, the estimated velocity and position errors in ECEF frame were used to compare the navigation performance as shown in
The statistics of position and velocity estimation errors are summarized in
A field test was conducted to collect real COMPASS B3 frequency IF data and INS data. A COMPASS B3 frequency antenna and an INS were used to replace the complex GNSS/INS signal hardware simulator in simulation case. The corresponding data collection process in the field is shown in the
The antenna was located on the roof of an office building to guarantee a strong COMPASS signal (
The variations of PLI and Doppler frequency tracking errors for SV01 and SV03 are shown in
The RMS of the tracking Doppler frequency errors are summarized in
For the field test case, the estimated velocity and position errors with SAKF and TKF in ECEF frame are shown in
This paper investigated a simplified prefilter model for the ultratight COMPASS/INS integrated system. When compared to a traditional 5dimension state prefilter model, the normalized signal amplitude and code tracking error were excluded, and only carrier phase, carrier frequency and carrier frequency rate tracking errors were included in the state space. However, as the code is not considered and there is a possibility of code/carrier divergence resulting in degradation in the carrier tracking process, an adaptive Kalman filter has been used to compensate for the divergence. Based on the COMPASS B3 frequency signal a federated COMPASS/INS integration system was implemented in software. A hardware sampling system was constructed to collect COMPASS IF data and INS data. Simulation and field tests showed an almost similar tracking and navigation performances of federated COMPASS/INS integration with traditional prefilter model and the proposed models. However, scalar measurement prefilter model with a 3dimension state, even with an inclusion of an adaptive Kalman filter, has been observed to have significant reduction in the calculation load when compared to a traditional 5dimension state and 2dimension measurement prefilter model.
As with the GPS case, the ultratight COMPASS/INS integration shows an advantage over independent COMPASS receivers, particularly in low signaltonoise and high dynamics environment. Only a static field test and a high dynamic simulation test were conducted for this analysis, and the future work will focus on further quantifying the benefits of ultratight COMPASS/INS integrations. The same simulation or field test will be conducted as the COMPASS, which is still a ‘local navigation’ satellite system, evolves into a global navigation satellite system in the future. Finally, although the COMPASS IF data and INS data collection was implemented in hardware, and the ultratight integration part was implemented in software, the future work will focus on the hardware implementation for the entire system.
This work was supported by the National Natural Science Foundation of China (Grant No. 61104201) and Program for New Century Excellent Talents (Grant No. NCET070225).
Central design of ultratight GPS/INS integration.
Federated design of ultratight GPS/INS integration.
Federated ultratight GPS/INS integration with one channel in detail.
Flow diagram for federated COMPASS/INS integration complementation with the simplified prefilter model and adaptive Kalman filter.
COMPASS IF data and INS data collection process with GNSS/INS hardware simulator.
(
(
(
COMPASS IF data and IMU data collection process in field environment.
COMPASS satellite skyplot of field test.
(
(
Computational Complexities of Kalman filter implementation.
State dimension 
State dimension  

2( 
 
Φ 

Φ 
2 
2 
1+ 

( 


0  
Total number of multiplications  128 + 9 
503 
Parameters defined in softwaredefined COMPASS Receiver.
 

Coherent integration time  1 ms 
Prefilter update period  1 ms 
Correlator spacing  0.5 chip 
Adaptive window length ( 
5 
1.82 × 10^{−21} (  
1.51 × 10^{−20} (1/Hz) 
RMS Doppler frequency errors of tracked SVs with different prefilter models.
 

SV = 04  SV = 05  
 
Simplified prefilter model with adaptive Kalman filter  3.773  3.094 
Traditional prefilter model  3.687  2.974 
Statistics of position and velocity errors in ECEF frame with different prefilter models.
 

X  Y  Z  X  Y  Z  
 
Mean Position Error(m)  −13.436  −5.886  −30.279  −14.064  −6.036  −30.936 
Std Position Error(m)  4.372  3.612  4.973  4.153  3.687  5.378 
Mean Velocity Error(m/s)  −0.623  −0.267  −1.501  −0.639  −0.274  −1.406 
Std Velocity Error(m/s)  0.199  0.207  0.237  0.188  0.197  0.244 
RMS Doppler frequency errors of tracked SVs with different prefilter models.
 

SV = 01  SV = 03  
 
Simplified prefilter model with adaptive Kalman filter  0.663  0.744 
Traditional prefilter model  0.613  0.778 
Statistics of position and velocity errors in ECEF frame with different prefilter models.
 

X  Y  Z  X  Y  Z  
 
Mean Position Error(m)  −9.231  −4.952  −18.953  −9.543  −5.011  −19.256 
Std Position Error(m)  1.591  2.748  3.316  1.697  3.031  3.443 
Mean Velocity Error(m/s)  −0.151  −0.069  −0.299  −0.164  −0.074  −0.312 
Std Velocity Error(m/s)  0.030  0.047  0.052  0.028  0.049  0.055 