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Estimator-Based GPS Attitude and Angular Velocity Determination

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Computers, Materials & Continua 2022年第6期71卷 6107-6124页

作者： dah-jing jwo Department of Communications Navigation and Control EngineeringTaiwan Ocean UniversityKeelung202301Taiwan

In this paper,the estimator-based Global Positioning System(GPS)attitude and angular velocity determination is presented.Outputs of the attitude estimator include the attitude angles and attitude rates or body angular velocities,depending on the design of estimator.Traditionally as a position,velocity and time sensor,the GPS also offers a free attitude-determination interferometer.GPS research and applications to the field of attitude determination using carrier phase or Doppler measurement has been extensively conducted.The rawattitude solution using the interferometry technique based on the least-squares approach is inherently noisy.The estimator such as the Kalman filter(KF)or extended Kalman filter(EKF)can be incorporated into the GPS interferometer,potentially providing several advantages,such as accuracy improvement,reliability enhancement,and real-time characteristics.Three estimator-based approaches are investigated for performance comparison,including(1)KF with measurement involving attitude angles only;(2)EKF with measurements based on attitude angles only;(3)EKF with measurements involving both attitude angles and body angular rates.The assistance from body mounted gyroscopes,if available,can be utilized as the measurements for further performance improvement,especially useful for the case of signal-challenged environment,such as the GPS outages.Modeling of the dynamic process involving the body angular rates and derivation of the related algorithm will be presented.Simulation results for various estimator-based approaches are conducted;performance comparison is presented for the case of GPS outages.

关键词： Global positioning system(GPS) extended Kalman filter attitude determination angular velocity

Data Wipe-Off Technique for Tracking Weak GPS Signals

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Computers, Materials & Continua 2022年第3期70卷 6159-6176页

作者： dah-jing jwo Sheng-Feng Chiu Department of Communications Navigation and Control EngineeringTaiwan Ocean UniversityKeelung202301Taiwan

In this paper,the data wipe-off(DWO)algorithm is incorporated into the vector tracking loop of the Global Positioning System(GPS)receiver for improving signal tracking performance.The navigation data,which contains information that is necessary to perform navigation computations,are binary phase-shift keying(BPSK)modulated onto the GPS carrier phase with the bit duration of 20 ms(i.e.,50 bits per second).To continuously track the satellite’s signal in weak signal environment,the DWO algorithm on the basis of pre-detection method is adopted to detect data bit sign reversal every 20 ms.Tracking accuracy of a weak GPS signal is decreased by possible data bit sign reversal every 20 ms to the predetection integration time(PIT)or integration interval.To achieve better tracking performance in weak signal environment,the coherent integration interval can be extended.However,increase of the integration interval lead to decrease of the tracking accuracy by possible data bit sign reversal every 20 ms to the integration interval.When the integration interval of the correlator is extended over 20 ms in low C/No levels,the navigation DWO algorithm can be employed to avoid energy loss due to bit transitions.The method presented in this paper has an advantage to continuously estimate the navigation data bit and achieve improved tracking performance.Evaluation of the tracking performance based on the various integration intervals for the vector tracking loop of a GPS receiver will be presented.

关键词： Global positioning system(GPS) integration interval data wipeoff weak signal

Variational Bayesian Based IMM Robust GPS Navigation Filter

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Computers, Materials & Continua 2022年第7期72卷 755-773页

作者： dah-jing jwo Wei-Yeh Chang Department of Communications Navigation and Control EngineeringTaiwan Ocean University Keelung202301Taiwan TDK Taiwan Corp. YangmeiTaoyuan326021Taiwan

This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.The performance of the state estimation for GPS navigation processing using the family ofKalman filter(KF)may be degraded due to the fact that in practical situations the statistics of measurement noise might change.In the proposed algorithm,the adaptivity is achieved by estimating the timevarying noise covariance matrices based onVB learning using the probabilistic approach,where in each update step,both the system state and time-varying measurement noise were recognized as random variables to be estimated.The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning.One of the two major classical adaptive Kalman filter(AKF)approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate(MMAE).The IMM algorithm uses two or more filters to process in parallel,where each filter corresponds to a different dynamic or measurement model.The robust Huber’s M-estimation-based extended Kalman filter(HEKF)algorithm integrates both merits of the Huber M-estimation methodology and EKF.The robustness is enhanced by modifying the filter update based on Huber’s M-estimation method in the filtering framework.The proposed algorithm,referred to as the interactive multi-model based variational Bayesian HEKF(IMM-VBHEKF),provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors,such as the multipath effect.Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.

关键词： GPS variational bayesian Huber’sM-estimation interacting multiple model adaptive outlier multipath

Continuous Tracking of GPS Signals with Data Wipe-Off Method

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Computers, Materials & Continua 2022年第5期71卷 3803-3820页

作者： dah-jing jwo Kun-Chan Lee Department of Communications Navigation and Control EngineeringTaiwan Ocean UniversityKeelung202301Taiwan

The decentralized pre-filter based vector tracking loop(VTL)configuration with data wipe-off(DWO)method of the Global Positioning System(GPS)receiver is proposed for performance enhancement.It is a challenging task to continuously track the satellites’signals in weak signal environment for the GPS receiver.VTL is a very attractive technique as it can provide tracking capability in signal-challenged environments.In the VTL,each channel will not form a loop independently.On the contrary,the signals in the channels of VTL are shared with each other;the navigation processor in turn predicts the code phases.Thus,the receiver can successfully track signals even the signal strength from individual satellite is weak.The tracking loop based on the pre-filter provides more flexible adjustment to specific environments to reduce noise interference.Therefore,even if the signals from some satellites are very weak the receiver can track them from the navigation results based on the other satellites.The navigation data,which contains information necessary to perform navigation computations,are binary phase-shift keying(BPSK)modulated onto the GPS carrier phase with the bit duration of 20 ms(i.e.,50 bits per second)for the GPS L1 C/A signals.The coherent integration interval can be extended for improved tracking performance in signal-challenged environment.However,tracking accuracy is decreased by possible data bit sign reversal.The DWO algorithm can be employed to remove the data bit in I and Q correlation values so as to avoid energy loss due to bit transitions when the integration interval of the correlator is extended over 20 ms under the low carrier-to-noise ratio(C/No)environments.The proposed method has an advantage to provide continuous tracking of signals and obtain improved navigation performance.Performance evaluation of the tracking capability as well as positioning accuracy will be presented.

关键词： Global positioning system(GPS) vector tracking loop pre-filter data wipe-off weak signal

Estimation of Quaternion Motion for GPS-Based Attitude Determination Using the Extended Kalman Filter

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Computers, Materials & Continua 2021年第2期66卷 2105-2126页

作者： dah-jing jwo Department of Communications Navigation and Control EngineeringTaiwan Ocean UniversityKeelung202-24Taiwan

In this paper,the Global Positioning System(GPS)interferometer provides the preliminarily computed quaternions,which are then employed as the measurement of the extended Kalman filter(EKF)for the attitude determination system.The estimated quaternion elements from the EKF output with noticeably improved precision can be converted to the Euler angles for navigation applications.The aim of the study is twofold.Firstly,the GPS-based computed quaternion vector is utilized to avoid the singularity problem.Secondly,the quaternion estimator based on the EKF is adopted to improve the estimation accuracy.Determination of the unknown baseline vector between the antennas sits at the heart of GPS-based attitude determination.Although utilization of the carrier phase observables enables the relative positioning to achieve centimeter level accuracy,however,the quaternion elements derived from the GPS interferometer are inherently noisy.This is due to the fact that the baseline vectors estimated by the least-squares method are based on the raw double-differenced measurements.Construction of the transformation matrix is accessible according to the estimate of baseline vectors and thereafter the computed quaternion elements can be derived.Using the Euler angle method,the process becomes meaningless when the angles are at 90where the singularity problem occurs.A good alternative is the quaternion approach,which possesses advantages over the equivalent Euler angle based transformation since they apply to all attitudes.Simulation results on the attitude estimation performance based on the proposed method will be presented and compared to the conventional method.The results presented in this paper elucidate the superiority of proposed algorithm.

关键词： Global positioning system(GPS) quaternion extended Kalman filter attitude determination

Complementary Kalman Filter as a Baseline Vector Estimator for GPS-Based Attitude Determination

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Computers, Materials & Continua 2020年第11期65卷 993-1014页

作者： dah-jing jwo Department of Communications Navigation and Control EngineeringNational Taiwan Ocean UniversityKeelung202-24Taiwan

The Global Positioning System(GPS)offers the interferometer for attitude determination by processing the carrier phase observables.By using carrier phase observables,the relative positioning is obtained in centimeter level.GPS interferometry has been firstly used in precise static relative positioning,and thereafter in kinematic positioning.The carrier phase differential GPS based on interferometer principles can solve for the antenna baseline vector,defined as the vector between the antenna designated master and one of the slave antennas,connected to a rigid body.Determining the unknown baseline vectors between the antennas sits at the heart of GPS-based attitude determination.The conventional solution of the baseline vectors based on least-squares approach is inherently noisy,which results in the noisy attitude solutions.In this article,the complementary Kalman filter(CKF)is employed for solving the baseline vector in the attitude determination mechanism to improve the performance,where the receiver-satellite double differenced observable was utilized as the measurement.By using the carrier phase observables,the relative positioning is obtained in centimeter level.Employing the CKF provides several advantages,such as accuracy improvement,reliability enhancement,and real-time assurance.Simulation results based on the conventional method where the least-squares approach is involved,and the proposed method where the CKF is involved are compared and discussed.

关键词： Global positioning system(GPS) attitude determination complementary Kalman filter baseline vector

Minimum Error Entropy Based EKF for GPS Code Tracking Loop

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Computers, Materials & Continua 2021年第6期67卷 2883-2898页

作者： dah-jing jwo Jen-Hsien Lai Department of Communications Navigation and Control EngineeringTaiwan Ocean University202301TaiwanChina Chunghwa Precision Test Tech.Co. Ltd.Taoyuan City324TaiwanChina

This paper investigates the minimum error entropy based extended Kalman filter(MEEKF)for multipath parameter estimation of the Global Positioning System(GPS).The extended Kalman filter(EKF)is designed to give a preliminary estimation of the state.The scheme is designed by introducing an additional term,which is tuned according to the higher order moment of the estimation error.The minimum error entropy criterion is introduced for updating the entropy of the innovation at each time step.According to the stochastic information gradient method,an optimal filer gain matrix is obtained.The mean square error criterion is limited to the assumption of linearity and Gaussianity.However,non-Gaussian noise is often encountered in many practical environments and their performances degrade dramatically in non-Gaussian cases.Most of the existing multipath estimation algorithms are usually designed for Gaussian noise.The I(in-phase)and Q(quadrature)accumulator outputs from the GPS correlators are used as the observational measurements of the EKF to estimate the multipath parameters such as amplitude,code delay,phase,and carrier Doppler.One reasonable way to obtain an optimal estimation is based on the minimum error entropy criterion.The MEEKF algorithm provides better estimation accuracy since the error entropy involved can characterize all the randomness of the residual.Performance assessment is presented to evaluate the effectivity of the system designs for GPS code tracking loop with multipath parameter estimation using the minimum error entropy based extended Kalman filter.

关键词： Entropy extended Kalman filter multipath global positioning system tracking loop

GPS Vector Tracking Loop with Fault Detection and Exclusion

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Computers, Materials & Continua 2021年第8期68卷 1785-1805页

作者： dah-jing jwo Meng-Hsien Hsieh Department of Communications Navigation and Control EngineeringTaiwan Ocean UniversityKeelung202301Taiwan

In this paper,both the integrity monitoring and fault detection and exclusion(FDE)mechanisms are incorporated into the vector tracking loop(VTL)architecture of the Global Positioning System(GPS)receiver for reliability enhancement.For the VTL,the tasks of signal tracking and navigation state estimation no longer process separately and a single extended Kalman filter(EKF)is employed to simultaneously track the received signals and estimate the receiver’s position,velocity,etc.In contrast to the scalar tracking loop(STL)which utilizes the independent parallel tracking loop approach,the VTL technique is beneficial from the correlation of each satellite signal and user dynamics.The VTL approach provides several important advantages.One of the merits is that the tracking loop can be assisted for overcoming the problem of signal blockage.Although the VTL architectures provide several important advantages,they suffer some fundamental drawbacks.For example,the errors in the navigation solutions may degrade the tracking accuracy.The most significant drawback is that failure of tracking in one channel may affect the entire tracking loop and possibly lead to loss of lock.For reliability enhancement,the EKF based integrity monitoring and FDE algorithms are developed to prevent the error from spreading into the entire tracking loop.The integrity monitoring is utilized to check the possible fault in the pseudorange and the pseudorange rate,followed by the FDE mechanism employed to exclude the abnormal satellite signals.Performance assessment and evaluation for the proposed approach will be presented.

关键词： Global Positioning System vector tracking loop signal blockage integrity fault detection and exclusion

Kernel Entropy Based Extended Kalman Filter for GPS Navigation Processing

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Computers, Materials & Continua 2021年第7期68卷 857-876页

作者： dah-jing jwo Jui-Tao Lee Department of Communications Navigation and Control EngineeringTaiwan Ocean UniversityKeelung202301Taiwan

This paper investigates the kernel entropy based extended Kalman filter(EKF)as the navigation processor for the Global Navigation Satellite Systems(GNSS),such as the Global Positioning System(GPS).The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed(or impulsive)interference errors,such as the multipath.The kernel minimum error entropy(MEE)and maximum correntropy criterion(MCC)based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS.The standard EKF method is derived based on minimization of mean square error(MSE)and is optimal only under Gaussian assumption in case the system models are precisely established.The GPS navigation algorithm based on kernel entropy related principles,including the MEE criterion and the MCC will be performed,which is utilized not only for the time-varying adaptation but the outlier type of interference errors.The kernel entropy based design is a new approach using information from higher-order signal statistics.In information theoretic learning(ITL),the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE.To improve the performance under non-Gaussian environments,the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error(MMSE)is utilized for mitigation of the heavy-tailed type of multipath errors.Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

关键词： GPS satellite navigation extended Kalman filter entropy correntropy multipath non-Gaussian