First-order Gauss-Markov Research Articles

Thermospheric Density Estimation Method Using a First-Order Gauss–Markov Process

Low-Earth-orbit (LEO) spacecraft are significantly influenced by atmospheric drag. Accurately estimating thermospheric density is pivotal for the precise calculation of drag acceleration. However, thermospheric density along a specific orbit, computed using existing thermospheric models, has certain inaccuracies. In this work, a first-order Gauss–Markov process is used to model the deviation of atmospheric drag acceleration. With the Markov parameter of the initial state iteratively computed through sequential estimation and the smoothing method, the thermospheric density is derived from high-precision GPS measurements. In simulation scenarios, the root-mean-square error and relative error of the estimated thermospheric density reduce by about 45 and 50% relative to the prior density, respectively. Using the estimated density for orbit propagation, satellite trajectories’ one-day position and velocity error are, respectively, within 100 m and 0.1 m/s, and an average improvement in orbit precision is over 80%. The proposed method has been applied to the real Tsinghua Science Satellite (Q-SAT) GPS measurements for effectiveness verification. It shows strong adaptability under extreme space weather and during the occurrence of geomagnetic storms. Due to the estimated Markov parameter of the initial state obeying the Langevin dynamics properties, the proposed method also offers short-term thermospheric density forecasting potential.

UAV-Aided Vehicular Short-Packet Communication and Edge Computing System Under Time-Varying Channel

In this paper, a novel UAV-aided vehicular edge computing (VEC) network is proposed, where the vehicle and on-board UAV provide multi-access edge computing (MEC) service for the roadside Internet of Things (IoT) devices. In this system, considering the time-varying channel, we derive the lower bound of signal-to-noise ratio (SNR) based on the first-order Gauss-Markov process. Then, with the short-packet transmission, we maximize the total amount of computation by jointly optimizing the communication scheduling, the trajectories of the vehicle and on-board UAV, and the computing resource, subject to the mobility, connection and computation constraints. The formulated optimization problem is a mix-integer non-convex problem. To efficiently solve it, we propose an alternative algorithm based on the Lagrangian dual decomposition and successive convex approximation technique. Extensive simulation results are provided to show the performance gain of the proposed algorithm.

A POMDP-Based Approach to Joint Antenna Selection and User Scheduling for Multi-User Massive MIMO Communication

We devise a partially observable Markov decision process (POMDP) based joint antenna selection and user scheduling (JASUS) policy for a massive MIMO base station, equipped with only a small number of RF chains, that serves a large number of users. The users are served at different time slots within a frame. Relying on partial CSI obtained from training between the selected antennas and the users, at the beginning of each frame, the BS assigns each user to a time slot in the frame and selects a subset of antennas to serve the users scheduled in each time slot. Assuming that the channels evolve according to a Markov process and relying on zero-forcing beamforming, we formulate our JASUS problem using a POMDP framework to devise a real-time decision-making policy that maximizes the expected long-term sum-rate. We rigorously prove that for positively correlated two-state channel models, the myopic policy provides the optimal solution to our POMDP-based JASUS problem for any number of RF chains and for any number of users. Based on this, we model the Rayleigh fading channels as first-order Gauss-Markov processes and devise a low-complexity myopic policy-based JASUS algorithm for massive MU-MIMO systems that only relies on partial CSI.

Decoupled Planes’ Non-Singular Adaptive Integral Terminal Sliding Mode Trajectory Tracking Control for X-Rudder AUVs under Time-Varying Unknown Disturbances

This paper analyzes the trajectory tracking problem in decoupled planes for X-rudder AUVs under time-varying, unknown environmental interferences. The proposed scheme consists of the kinematic control law based on the compound line-of-sight guidance law and the dynamic control law based on a non-singular adaptive integral terminal sliding mode control (NAITSMC) to avoid the chattering problems, parameter perturbation, and time-varying disturbances. Meanwhile, we introduce a reduced-order extended state observer (RESO) to compensate for unknown ocean currents by the first-order Gauss–Markov process. We verify the whole system of the proposed scheme through global asymptotic stability, then present a set of numerical simulations revealing robustness and adaptability performances in decoupled planes.

HMM Based Adaptive Kalman Filter for Orientation Estimation

An adaptive orientation estimation method based on hidden Markov model (HMM) using multiple Magnetic Angular Rate Gravity (MARG) sensor is proposed to address the problem of linear acceleration and ferromagnetic disturbance. Two parallel Kalman filters containing first-order Gauss-Markov disturbance models are implemented to estimate the disturbances before estimating the orientation. It is important that the noise covariance of the disturbance model should match the magnitude of the disturbance to ensure the estimation performance; otherwise, the disturbance estimation accuracy will reduce significantly. Therefore, an adaptive Kalman filter based on HMM is designed to adjust the disturbance noise covariance. After the disturbances are separated, the estimated gravity acceleration and geomagnetic field as well as the gyroscope measurement are taken as the inputs, and the orientation estimation procedure is established by using the multiplicative extended Kalman filter (MEKF). Experiments show that the proposed method achieves a higher level of accuracy in comparison with other orientation estimation methods under various conditions.

Distributed robust power control in two-tier vehicle networks under uncertain channel environments

This paper proposes a novel optimization scheme to support stable and reliable vehicle-to-everything connections in two-tier networks, where the uplink channel of the cellular user is reused by underlay vehicle-to-vehicle communications. However, considering complex channel fading and high-speed vehicle movement, the certainty assumption is impractical and fails to maintain power control strategy in reality in the traditional statical vehicular networks. Rather than the perfect channel state information assumption, the first-order Gauss-Markov process which is a probabilistic model affected by vehicle speed and fading is introduced to describe imperfect channel gains. Moreover, interference management is a major challenge in reusing communications, especially in uncertain channel environments. Power control is an effective way to realize interference management, and optimal power allocation can ensure that interference of the user meets the communication requirements. In this study, the sum-rate-oriented power control scheme and minimum-rate-oriented power control scheme were implemented to manage interference and satisfy different design objectives. Since both of these schemes are non-convex and intractable, the Bernstein approximation and successive convex approximation methods were adopted to transform the original problems into convex ones. Furthermore, a novel distributed robust power control algorithm was developed to determine the optimal solutions. The performance of the algorithm was evaluated through numerical simulations, and the results indicate that the proposed algorithm is effective in vehicular communication networks with uncertain channel environments.

Globally Optimal Centralized and Sequential Fusion Filters for Uncertain Systems With Time-Correlated Measurement Noises

This paper is concerned with the fusion filtering problem for stochastic uncertain multi-sensor systems with time-correlated measurement noises, where the stochastic uncertainties are described by white multiplicative noises, and the additive measurement noises are first-order Gauss-Markov Processes. By introducing the recursive measurement noise estimators, the centralized fusion filter (CFF) based on the idea of batch process and sequential fusion filter (SFF) based on the idea of sequential process are designed in the linear minimum variance (LMV) sense by an innovation analysis approach, respectively. The proposed SFF can achieve the same estimation accuracy as the CFF. It is also globally optimal. The equivalence on estimation accuracy of the SFF and CFF is strictly proved by mathematical induction method. The stability and steady-state properties of the proposed fusion filters are analyzed. Two examples show the effectiveness of the proposed fusion algorithms.

Integrity Risk Under Temporal Correlation for Horizontal ARAIM

Integrity requirements for safety-critical global navigation satellite system applications, such as in civil aviation for the nonprecision approach through precision approach, are defined in a per hour or per approach (i.e., 150s) basis by the International Civil Aviation Organization. This article presents a novel methodology for mapping such operational requirements to the specific risk at an algorithmic level for advanced receiver autonomous integrity monitoring (ARAIM), in particular horizontal ARAIM (H-ARAIM). We thoroughly evaluated the actual risk over time by performing extensive first-order Gauss Markov Process Monte Carlo runs for the propagation of time-correlated position errors and test statistics over one hour exposure time and accounting for multiple events of loss of integrity over the time interval. A comparison of the risk over time and the risk for a single epoch leads to the number of effectively independent samples. The current integrity equation was modified using the number such that a specific risk requirement is allocated to a single sample for the determination of the protection level. This study also examined the impact of the modified risk allocation on the existing fault detection and exclusion algorithm by conducting H-ARAIM availability simulations and by comparing the results based on the newly proposed method with that obtained using the existing single sample-based risk allocation. In our preliminary assessment, little impact on the global availability (availability loss of approximately up to 1%) of the inflated terms of the integrity equation due to the number of valid samples was found.

Algorithm for Real-Time Cycle Slip Detection and Repair for Low Elevation GPS Undifferenced Data in Different Environments

Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, cycle slip detection and repair in low elevation GPS observation data are more complicated than those in normal environments. For low elevation GPS undifferenced carrier phase data in different environments, a combined cycle slip detection algorithm is proposed. This method uses the first-order Gauss–Markov stochastic process to model the pseudorange multipath in the wide-lane phase minus narrow-lane pseudorange observation equation, and establishes the state equation of the wide-lane ambiguity with the pseudorange multipath as a parameter, and it uses the Kalman filter for real-time estimation and detects cycle slips based on statistical hypothesis testing with a predicted residual sequence. Meanwhile, considering there are certain correlations among low elevation, observation epoch interval, and ionospheric delay error, a second-order difference geometry-free combination cycle slip test is constructed that takes into account the elevation. By combining the two methods, real-time cycle slip detection for GPS low elevation satellite undifferenced data is achieved. A cycle slip repair method based on spatial search and objective function minimization criterion is further proposed to determine the correct solution of the cycle slips after they are detected. The whole algorithm is experimentally verified using the static and kinematic measured data of low elevation satellites under four different environments: normal condition, high-voltage transmission lines, dynamic condition in the sea, and ionospheric disturbances. The experimental results show that the algorithm can detect and repair cycle slips accurately for low elevation GPS undifferenced data, the difference between the float solution and the true value for the cycle slip does not exceed 0.5 cycle, and the differences obey the normal distribution overall. At the same time, the wide-lane ambiguity and second-order difference GF combination sequence calculated by the algorithm is smoother, which give further evidence that the algorithm for cycle slip detection and repair is feasible and effective, and has the advantage of being immune to the special observation environments.

A linear Kalman filter-based integrity monitoring considering colored measurement noise

Apart from positioning accuracy, the reliability of a navigation system is also significant, especially for safety–critical applications, such as intelligent vehicle navigation. Generally, the Global Navigation Satellite System (GNSS) positioning algorithm assumed that measurement noise is uncorrelated white noise. However, the appearance of colored noise, which comes from various noise sources, does not follow the Gaussian white noise assumption in the Kalman filter and would degrade both the accuracy and reliability of positioning. To deal with this problem, we propose a linear Kalman filter-based integrity monitoring method, which is based on a linear colored Kalman filter (CKF) considering measurement time correlation colored noise by a first-order Gauss–Markov model. Both simulated and real dynamic experiments were conducted to test the proposed algorithm. The results proved that CKF is capable of modeling time correlation with a realistic filter covariance in both simulated static and in-field dynamic tests. Furthermore, the performance of an integrity monitoring system with a protection level based on the CKF has proved to be more feasible and effective to bound position errors. Besides, the simulated results demonstrate that it can typically reduce false alarm by 24.81% in the horizontal direction and 39.47% in the vertical direction in a simulated experiment. The dynamic test shows that the proposed method can reduce the false alarm rate by 22.11% and 15.62% in the horizontal and vertical directions, respectively.

Optimal linear recursive estimators for stochastic uncertain systems with time-correlated additive noises and packet dropout compensations

This paper is concerned with the state estimation problem over a packet-dropping network for stochastic uncertain systems with time-correlated additive noises. Additive process and measurement noises are both depicted by first-order Gauss-Markov processes. Stochastic parameter uncertainties are described by correlated white multiplicative noises. When a sensor measurement transmitted over networks is lost, its predictor is used for compensation. The optimal linear recursive full-order state filter, predictor and smoother are proposed under the linear minimum variance (LMV) criterion by an innovation analysis approach. They are calculated in terms of the filter of the product of the multiplicative noise and state, estimators of the process and measurement noises, and cross-covariance matrices for the state and/or noises. The steady-state estimators are also studied. A sufficient condition for convergence of optimal linear estimators is given. The simulation results verify the effectiveness of the proposed algorithms.

A Robust Indirect Kalman Filter Based on the Gradient Descent Algorithm for Attitude Estimation During Dynamic Conditions

The real-time response and accuracy of the attitude (i.e., roll and pitch) estimation from low-cost inertial measurement unit (IMU) have become the key issues restricting related applications. This paper proposes a robust attitude estimation scheme which can perform well under dynamic conditions. When only accelerometers are used to calculate and correct the attitude, the external acceleration becomes the main source of attitude estimation errors. Moreover, the truncation error in the linearization process of the nonlinear system also affects the attitude estimation. As our first contribution, the external acceleration is modeled as a first-order Gauss Markov model, and its value is calculated under the indirect Kalman filter (IKF) framework. The measurement noise covariance matrix of the IKF is adaptively adjusted to enhance its robustness and reduce the negative impact caused by inaccurate modeling. In the second part of our work, the two-step cascade filter method is used for attitude estimation. The attitude obtained from the gravity field based on the gradient descent (GD) algorithm shows fast response capabilities, and hence, it is embedded as a measurement in the IKF by using the chain-derivation rule. The truncation error introduced into the linearization process of the nonlinear system is effectively avoided. Both simulation and experiments are carried out to verify the feasibility and accuracy of the proposed algorithm. The results show that the approach proposed in this paper can meet the accuracy requirements of consumer products.

A Novel Adaptive Kalman Filtering Approach to Human Motion Tracking With Magnetic-Inertial Sensors

This article presents an adaptive Kalman filtering approach to estimate the orientation of human body segments by using magnetic-inertial measurement units (MIMUs) with three-axis gyroscope, accelerometer, and magnetometer. In order to mitigate the negative impact of the external accelerations and ferromagnetic disturbances, the disturbances are modeled by first-order Gauss–Markov processes, and two parallel adaptive Kalman filters containing disturbance models are implemented to eliminate the disturbances. An adaptive factor is introduced to adjust the process noise covariance matrix to compensate for modeling errors induced by unmodeled gyroscope biases and the erroneous process noise covariance matrices. Furthermore, the outliers are checked and discarded by hypothesis tests on the innovation, and the measurement is rejected when the innovation exceeds a given confidence interval. Then, the estimated gravity acceleration and geomagnetic field are used to calculate the orientation quaternion using triaxial attitude determination algorithm. Finally, experiments under different motion scenarios are carried out to evaluate the effectiveness of the proposed method, and the performance of the proposed method is discussed in comparison with existing ones. A forward kinematics three-dimensional (3-D) human motion reconstruction method is proposed to drive the human skeleton model to reproduce human motion with a visual interface based on ROS platform.

A channel state information updating method based on the first-order Gauss Markov model under time-varying underwater acoustic channel

Because of the time-varying characteristic and the large propagation delay in underwater acoustic (UWA) channel, adaptive resource allocation in UWA orthogonal frequency-division multiplexing access (OFDMA) system cannot be performed with the assumption of perfect channel state information (CSI) at the transmitter. Therefore, this paper focuses on the imperfect CSI and proposes a CSI updating method to reduce the impact of imperfect CSI on the performance of resource allocation under time-varying UWA channel. First, we analyze the channel estimation error of OFDM system under time-varying UWA channel and define the per-subcarrier channel temporal correlation (PSCTC). Finally, a CSI updating method based on the first-order Gauss-Markov model (GM-CSI) is proposed for optimizing CSI feedback in the UWA channel with large propagation delay, where the channel estimation error and PSCTC factor are considered as two influencing factors in this model. Simulation results show that the GM-CSI can effectively mitigate the effect of time on CSI effectiveness, and the resource allocation by using GM-CSI has higher effective throughput and lower BER than that of imperfect CSI.

정확한 방위각 추정을 위한 차수 변환 방식 자기왜곡 보상 메커니즘

One of the most problematic factors in inertial/magnetic sensing-based tilt/azimuth estimation is magnetic distortion that can be added in magnetometer signals and may decrease the azimuth estimation accuracy. In this paper, we propose an orderswitching magnetic distortion compensation mechanism for accurate azimuth estimation. The proposed compensation mechanism switches between a first-order Gauss-Markov (GM) model and a second-order GM model of magnetic distortion. When the secondorder model is selected, the time-derivative of the magnetic distortion is additionally augmented in the states of the corresponding second-order azimuth Kalam filter. The proposed mechanism was experimentally validated in four different magnetically distorted conditions. The results show that the azimuth estimation error of the proposed method was less than 3° in all the tests and the proposed mechanism outperformed conventional approaches in the azimuth estimation.

Real-time precise orbit determination of LEO satellites using a single-frequency GPS receiver: Preliminary results of Chinese SJ-9A satellite

Spaceborne Global Positioning System (GPS) receivers are widely used for orbit determination of low-Earth-orbiting (LEO) satellites. With the improvement of measurement accuracy, single-frequency receivers are recently considered for low-cost small satellite missions. In this paper, a Schmidt-Kalman filter which processes single-frequency GPS measurements and broadcast ephemerides is proposed for real-time precise orbit determination of LEO satellites. The C/A code and L1 phase are linearly combined to eliminate the first-order ionospheric effects. Systematic errors due to ionospheric delay residual, group delay variation, phase center variation, and broadcast ephemeris errors, are lumped together into a noise term, which is modeled as a first-order Gauss-Markov process. In order to reduce computational complexity, the colored noise is considered rather than estimated in the orbit determination process. This ensures that the covariance matrix accurately represents the distribution of estimation errors without increasing the dimension of the state vector. The orbit determination algorithm is tested with actual flight data from the single-frequency GPS receiver onboard China’s small satellite Shi Jian-9A (SJ-9A). Preliminary results using a 7-h data arc on October 25, 2012 show that the Schmidt-Kalman filter performs better than the standard Kalman filter in terms of accuracy.

Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using Relative Orbital Elements

This paper addresses the design and validation of an accurate estimation architecture for autonomous angles-only navigation in orbits of arbitrary eccentricity. The proposed filtering strategy overcomes the major deficiencies of existing approaches in the literature, which mainly focus on applications in near-circular orbits and generally suffer from poor dynamical observability due to linearizing the filter dynamics and measurement models. Consequently, traditional angles-only navigation solutions require conducting known orbital maneuvers to reconcile the ambiguous range. In contrast, the algorithms developed in this work enable accurate maneuver-free reconstruction of the relative orbital motion. This is done through the full exploitation of nonlinearities in the measurement model using the unscented Kalman filter to improve dynamical observability and filter performance. The filter estimates mean relative orbit elements, adopting a state transition matrix subject to secular and long-period perturbation effects to decouple observable from unobservable parameters. The complete state is then reconciled with the angle measurements in the measurement model through a nonlinear transformation that includes the conversion from mean to osculating orbital elements. The resulting linear dynamics model is supplemented by either first-order Gauss–Markov processes (that is, differential empirical accelerations) or by a covariance-matching approach to online adaptive process noise tuning to increase performance at minimal computational complexity. Finally, the estimation architecture is completed by a novel deterministic algorithm for batch initial relative orbit determination to accurately initialize the sequential filter.

Distortion Outage Analysis for Joint Space-Time Coding and Kalman Filtering

In this paper, we consider the scenario of transmitting a first-order Gauss–Markov vector signal over a multi-input multi-output (MIMO) Rayleigh nonfrequency selective fading channel. The signal is reconstructed at the receiver side with the help of a Kalman filter in order to minimize the mean squared error. Orthogonal space time codes are utilized in order to increase the quality of estimation and mitigate the destructing effects of the fading channel. As a criterion for estimation quality assessment, we use the distortion outage probability. We first obtain upper and lower bounds for the outage probability as a function of system parameters. We then perform high-SNR analysis of the bounds, through which we prove the achievability of the maximum diversity order for a $N\times K$ MIMO fading channel. In addition, we obtain upper and lower bounds for the coding gain of the distortion outage probability in the high-SNR regime, and outline the relation between system parameters and the coding gain.

A New Technique for Integrating MEMS-Based Low-Cost IMU and GPS in Vehicular Navigation

In providing acceptable navigational solutions, Location-Based Services (LBS) in land navigation rely mostly on integration of Global Positioning System (GPS) and Inertial Navigation System (INS) measurements for accuracy and robustness. The GPS/INS integrated system can provide better land-navigation solutions than the ones any standalone system can provide. Low-cost Inertial Measurement Units (IMUs), based on Microelectromechanical Systems (MEMS) technology, revolutionized the land-navigation system by virtue of their low-cost miniaturization and widespread availability. However, their accuracy is strongly affected by their inherent systematic and stochastic errors, which depend mainly on environmental conditions. The environmental noise and nonlinearities prevent obtaining optimal localization estimates in Land Vehicular Navigation (LVN) while using traditional Kalman Filters (KF). The main goal of this paper is to effectively eliminate stochastic errors of MEMS-based IMUs. The proposed solution is divided into two main components: (1) improving noise cancellation, using advanced stochastic error models in MEMS-based IMUs based on combined Autoregressive Processes (ARP) and first-order Gauss-Markov Process (1GMP), and (2) modeling the low-cost GPS/INS integration, using a hybrid Fuzzy Inference System (FIS) and Second-Order Extended Kalman Filter (SOEKF). The results obtained show that the proposed methods perform better than the traditional techniques do in different stochastic and dynamic situations.

UAV Attitude Estimation Using Nonlinear Filtering and Low-Cost Mems Sensors

Abstract: Integration of low-cost Micro-Electro-Mechanical Systems (MEMS) in the design of Inertial Navigation Systems (INS) for real-time guidance, navigation, and control of flying vehicles often results in low precision, poor accuracy, and degraded performance. Most of existing filtering and data fusion methods that have been applied to the problem of attitude estimation with use of low-cost MEMS-based INS fail in cases that have highly nonlinear process dynamics, nonlinear measurement models, and long-range navigation. This paper presents two nonlinear filtering algorithms for low-cost Unmanned Aerial Vehicles (UAVs) attitude and measurement biases estimation. An Unscented Kalman Filter (UKF) and a Minimum Energy Kalman Filter (MEKF) are designed using two different attitude parameterizations i.e. Euler Angle (EA) and Unit Quaternion (UQ). The two filters AE-UKF and UQ-MEKF use highly nonlinear process and measurements estimators, zero-mean Gaussian noises, and first-order Gauss-Markov biases models. Field experiments, adding systems, and data fusion algorithms are used to achieve real-time tracking and estimation. The results show that both AE-UKF and UQ-MEKF demonstrate high accuracy estimation and robustness for UAVs attitude as well as MEMS biases filtering.