Performance Evaluation of Adaptive Tracking Techniques with Direct-State Kalman Filter

This paper evaluates the performance of robust adaptive tracking techniques with the direct-state Kalman filter (DSKF) used in modern digital global navigation satellite system (GNSS) receivers. Under the assumption of a well-known Gaussian distributed model of the states and the measurements, the DSKF adapts its coefficients optimally to achieve the minimum mean square error (MMSE). In time-varying scenarios, the measurements’ distribution changes over time due to noise, signal dynamics, multipath, and non-line-of-sight effects. These kinds of scenarios make difficult the search for a suitable measurement and process noise model, leading to a sub-optimal solution of the DSKF. The loop-bandwidth control algorithm (LBCA) can adapt the DSKF according to the time-varying scenario and improve its performance significantly. This study introduces two methods to adapt the DSKF using the LBCA: The LBCA-based DSKF and the LBCA-based lookup table (LUT)-DSKF. The former method adapts the steady-state process noise variance based on the LBCA’s loop bandwidth update. In contrast, the latter directly relates the loop bandwidth with the steady-state Kalman gains. The presented techniques are compared with the well-known state-of-the-art carrier-to-noise density ratio (C/N0)-based DSKF. These adaptive tracking techniques are implemented in an open software interface GNSS hardware receiver. For each implementation, the receiver’s tracking performance and the system performance are evaluated in simulated scenarios with different dynamics and noise cases. Results confirm that the LBCA can be successfully applied to adapt the DSKF. The LBCA-based LUT-DSKF exhibits superior static and dynamic system performance compared to other adaptive tracking techniques using the DSKF while achieving the lowest complexity.

LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications.

A Nonlinear Model Predictive Control Design for Autonomous Multivehicle Merging into Platoons

Integrated control for automated vehicles in platoons with nonlinear coupled dynamics is developed in this article. A nonlinear MPC approach is used to address the multi-input multi-output (MIMO) nature of the problem, the nonlinear vehicle dynamics, and the platoon constraints. The control actions are determined by using model-based prediction in conjunction with constrained optimization. Two distinct scenarios are then simulated. The first scenario consists of the multivehicle merging into an existing platoon in a controlled environment in the absence of noise, whereas the effects of external disturbances, modeling errors, and measurement noise are simulated in the second scenario. An extended Kalman filter (EKF) is utilized to estimate the system states under the sensor and process noise effectively. The simulation results show that the proposed approach is a suitable tool to handle the nonlinearities in the vehicle dynamics, the complication of the multivehicle merging scenario, and the presence of modeling uncertainties and measurement noise.

Denoising MAX6675 reading using Kalman filter and factorial design

This paper aims to tune the Kalman filter (KF) input variables, namely measurement error and process noise, based on two-level factorial design. Kalman filter then was applied in inexpensive temperature-acquisition utilizing MAX6675 and K-type thermocouple with Arduino as its microprocessor. Two levels for each input variable, respectively, 0.1 and 0.9, were selected and applied to four K-type thermocouples mounted on MAX6675. Each sensor with a different combination of input variables was used to measure the temperature of ambient-water, boiling water, and sudden temperature drops in the system. The measurement results which consisted of the original and KF readings were evaluated to determine the optimum combination of input variables. It was found that the optimum combination of input variables was highly dependent on the system's dynamics. For systems with relatively constant dynamics, a large value of measurement error and small value of process noise results in higher precision readings. Nevertheless, for fast dynamic systems, the previous input variables' combination is less optimal because it produced a time-gap, which made the KF reading differ from the original measurement. The selection of the optimum input combination using two-level factorial design eased the KF tuning process, resulting in a more precise yet low-cost sensor.

Online Dynamic Response Reconstruction in the Presence of Observation Outliers

Previous studies show that Kalman filter (KF)-based dynamic response reconstruction of a structure has distinct advantages in the aspects of combining the system model with limited measurement information and dealing with system model errors and measurement Gaussian noises. However, because the recursive KF aims to achieve a least-squares estimate of state vector by minimizing a quadratic criterion, observation outliers could dramatically deteriorate the estimator’s performance and considerably reduce the response reconstruction accuracy. This study addresses the KF-based online response reconstruction of a structure in the presence of observation outliers. The outlier-robust Kalman filter (OKF), in which the outlier is discerned and reweighted iteratively to achieve the generalized maximum likelihood (ML) estimate, is used instead of KF for online dynamic response reconstruction. The influences of process noise and outlier duration to response reconstruction are investigated in the numerical study of a simple 5-story frame structure. The experimental work on a simply-supported overhanging steel beam is conducted to testify the effectiveness of the proposed method. The results demonstrate that compared with the KF-based response reconstruction, the proposed OKF-based method is capable of dealing with the observation outliers and producing more accurate response construction in presence of observation outliers.

Novel Process Noise Model for GNSS Kalman Filter Based on Sensitivity Analysis of Covariance with Poor Satellite Geometry

One of the great unsolved GNSS problems is inaccuracy in urban canyons due to Non-Line-Of-Sight (NLOS) signal reception. Owing to several studies about the NLOS signal rejection method, almost all NLOS signals can be excluded from the calculation of the position. However, such precise NLOS rejection would make satellite geometry poor, especially in dense urban environments. This paper points out, through numerical simulations and theoretical analysis, that poor satellite geometry leads to unintentional performance degradation of the Kalman filter with a conventional technique to prevent filter divergence. The conventional technique is to bump up process noise covariance, and causes unnecessary inflation of estimation-error covariance when satellite geometry is poor. We propose a novel choice of process noise covariance based on satellite geometry that can reduce such unnecessary inflation. Numerical and experimental results demonstrate that performance improvement can be achieved by the choice of process noise covariance even for a poor satellite geometry.

State of Power Estimation of Echelon-Use Battery Based on Adaptive Dual Extended Kalman Filter

Owing to the degradation of the performance of a retired battery and the unclear initial value of the state of charge (SOC), the estimation of the state of power (SOP) of an echelon-use battery is not accurate. An SOP estimation method based on an adaptive dual extended Kalman filter (ADEKF) is proposed. First, the second-order Thevenin equivalent model of the echelon-use battery is established. Second, the battery parameters are estimated by the ADEKF: (a) the SOC is estimated based on an adaptive extended Kalman filtering algorithm, that uses the process noise covariance and observes the noise covariance , and (b) the ohmic internal resistance and actual capacity are estimated based on the aforementioned algorithm, that uses the process noise covariance and observes the noise covariance . Third, the working voltage and internal resistance are predicted using optimal estimation, and the SOP of the echelon-use battery is estimated. MATLAB simulation results show that, regardless of whether or not the initial value of the SOC is clear, the proposed algorithm can be adjusted to the adaptive algorithm, and if the estimation accuracy error of the echelon-use battery SOP is less than 4.8%, it has high accuracy. This paper provides a valuable reference for the prediction of the SOP of an echelon-use battery, and will be helpful for understanding the behavior of retired batteries for further discharge and use.