Derivative-free Nonlinear Version of Extended Recursive Three-step Filter for State and Parameter Estimation during Mars Entry

2018 ◽  
Vol 71 (3) ◽  
pp. 679-696
Author(s):  
Mengli Xiao ◽  
Yongbo Zhang ◽  
Huimin Fu ◽  
Zhihua Wang
Keyword(s):  
Unscented Kalman Filter ◽  
Velocity Estimation ◽  
Arbitrary Parameter ◽  
Parameter Uncertainties ◽  
Estimation Errors ◽  
Derivative Free ◽  
Nonlinear Version ◽  
Atmosphere Density ◽  
Navigation Accuracy ◽  
Drag Ratio

Parameter uncertainties which may lead to divergence of traditional Kalman filters during Mars entry are investigated in this paper. To achieve high precision navigation, a Derivative-free Nonlinear version of an Extended Recursive Three-Step Filter (DNERTSF) is introduced, which suits nonlinear systems with arbitrary parameter uncertainties. A DNERTSF can estimate the state and the parameters simultaneously, and Jacobian and Hessian calculations are not necessary for this filter. Considering the uncertainties in atmosphere density, ballistic coefficient and lift-to-drag ratio, a numerical simulation of Mars entry navigation is carried out. Compared with the standard Unscented Kalman Filter (UKF), DNERTSF can effectively reduce the adverse effects of parameter uncertainties and achieve a high navigation accuracy performance, keeping position and velocity estimation errors at a very low level. In all, the DNERTSF in this paper shows good advantages for Mars entry navigation, providing a possible application for a future Mars pinpoint landing.

scholarly journals INS/GPS for High-Dynamic UAV-Based Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Junchuan Zhou ◽  
Stefan Knedlik ◽  
Otmar Loffeld
Keyword(s):  
Carrier Phase ◽  
Velocity Estimation ◽  
Estimation Accuracy ◽  
Processing Load ◽  
Estimation Errors ◽  
Integration Interval ◽  
Sequential Processing ◽  
Large Velocity ◽  
Different Types ◽  
High Dynamic

The carrier-phase-derived delta pseudorange measurements are often used for velocity determination. However, it is a type of integrated measurements with errors strongly related to pseudorange errors at the start and end of the integration interval. Conventional methods circumvent these errors with approximations, which may lead to large velocity estimation errors in high-dynamic applications. In this paper, we employ the extra states to “remember” the pseudorange errors at the start point of the integration interval. Sequential processing is employed for reducing the processing load. Simulations are performed based on a field-collected UAV trajectory. Numerical results show that the correct handling of errors involved in the delta pseudorange measurements is critical for high-dynamic applications. Besides, sequential processing can update different types of measurements without degrading the system estimation accuracy, if certain conditions are met.

Stereovision-based relative states and inertia parameter estimation of noncooperative spacecraft

2018 ◽  
Vol 233 (7) ◽  
pp. 2489-2502 ◽  
Author(s):  
Xun Wang ◽  
Zhaokui Wang ◽  
Yulin Zhang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Target Surface ◽  
State Equation ◽  
Moment Of Inertia ◽  
Transition Rule ◽  
Estimation Errors ◽  
Fixed Frame ◽  
Adaptive Unscented Kalman Filter ◽  
Relative States

Autonomous proximity operations have recently become appealing as space missions. In particular, the estimation of the relative states and inertia properties of a noncooperative spacecraft is an important but challenging problem, because there might be poor priori information about the target. Using only stereovision measurements, this study developed an adaptive unscented Kalman filter to estimate the relative states and moment-of-inertia ratios of a noncooperative spacecraft. Because the accuracy of the initial relative states has an effect on the estimation convergence performance, attention was also given to their determination. The target’s body-fixed frame was defined in parallel to the chaser’s initial body-fixed frame, and then the initial relative attitude was known. After formulating kinematic constraint equations between the relative states and multiple points on the target surface, particle swarm optimization was utilized to determine the initial relative angular velocity. The initial relative position was also determined under the assumption that the initial relative translational velocity was known. To estimate the relative states and moment-of-inertia ratios using the adaptive unscented Kalman filter, the relative attitude dynamic model was reformulated by designing a novel transition rule with five moment-of-inertia ratios, described in the defined target’s body-fixed frame. The moment-of-inertia ratios were added to the state space, and a new state equation with variant process noise covariance matrix Q was formulated. The measurement updating errors of the relative states were utilized to adaptively modify Q so that the filter could estimate the relative states and moment-of-inertia ratios in two stages. Numerical simulations of the adaptive unscented Kalman filter with unknown moment-of-inertia ratios and the standard unscented Kalman filter with known moment-of-inertia ratios were conducted to illustrate the performance of the adaptive unscented Kalman filter. The obtained results showed the satisfactory convergence of the estimation errors of both the relative states and moment-of-inertia ratios with high accuracy.

scholarly journals Ground Reaction Force Estimation in Prosthetic Legs With Nonlinear Kalman Filtering Methods

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Seyed Fakoorian ◽  
Vahid Azimi ◽  
Mahmoud Moosavi ◽  
Hanz Richter ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Reaction Force ◽  
Force Estimation ◽  
Joint Angles ◽  
Estimation Errors ◽  
Reaction Forces

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-mean-square (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF.

scholarly journals Mars Cruise Orbit Determination from Combined Optical Celestial Techniques and X-ray Pulsars

2017 ◽  
Vol 70 (4) ◽  
pp. 719-734 ◽  
Author(s):  
Jiandong Liu ◽  
Erhu Wei ◽  
Shuanggen Jin
Keyword(s):  
Kalman Filter ◽  
Autonomous Navigation ◽  
Unscented Kalman Filter ◽  
Integrated System ◽  
Observation Data ◽  
X Ray ◽  
Celestial Navigation ◽  
Federated Kalman Filter ◽  
Mars Pathfinder ◽  
Navigation Accuracy

The precise autonomous navigation for deep space exploration by combination of multi-source observation data is a key issue for probe control and scientific applications. In this paper, the performance of an integrated Optical Celestial Navigation (OCN) and X-ray Pulsars Autonomous Navigation (XNAV) system is investigated for the orbit of Mars Pathfinder. Firstly, OCN and XNAV single systems are realised by an Unscented Kalman Filter (UKF). Secondly, the integrated system is simulated with a Federated Kalman Filter (FKF), which can do the information fusion of the two subsystems of UKF and inherits the advantages of each subsystem. Thirdly, the performance of our system is evaluated by analysing the relationship between observation errors and navigation accuracy. The results of the simulation experiments show that the biases between the nominal and our calculated orbit are within 5 km in all three axes under complex error conditions. This accuracy is also better than current ground-based techniques.

Autonomous Navigation of Mars Probes by Combining Optical Data of Viewing Martian Moons and SST Data

2015 ◽  
Vol 68 (6) ◽  
pp. 1019-1040 ◽  
Author(s):  
Pengbin Ma ◽  
Fanghua Jiang ◽  
Hexi Baoyin
Keyword(s):  
Kalman Filter ◽  
Autonomous Navigation ◽  
Unscented Kalman Filter ◽  
Optical Measurement ◽  
Optical Data ◽  
Deep Space Exploration ◽  
Rank Defect ◽  
The Difference ◽  
Navigation Accuracy ◽  
Navigation Information

Autonomous navigation has become a key technology for deep space exploration missions. Phobos and Deimos, the two natural moons of Mars, are important optical navigation information sources available for Mars missions. However, during the phase of the probe orbiting close to Mars, the ephemeris bias and the difference between the barycentre and the centre of brightness of a Martian moon will result in low navigation accuracy. On the other hand, Satellite-to-Satellite Tracking (SST) can achieve convenient and high accuracy observation for autonomous navigation. However, this cannot apply for a Mars mission during the Mars orbit phase only by SST data because of a rank defect problem of the Jacobian matrix. To improve the autonomous navigation accuracy of Mars probes, this paper presents a new autonomous navigation method that combines SST radio data provided by two probes and optical measurement by viewing the natural Martian moons. Two sequential orbit determination algorithms, an Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are compared. Simulation results show this method can obtain high autonomous navigation accuracy during the probe's Mars Orbit phase.

scholarly journals An improved estimation method for vehicle velocity of distributed drive electric vehicle

2021 ◽  
Author(s):  
Qingqing Xiang ◽  
Zhiqiang Liu ◽  
Guang Liu
Keyword(s):  
Electric Vehicles ◽  
Unscented Kalman Filter ◽  
Estimation Method ◽  
Estimation Algorithm ◽  
Velocity Estimation ◽  
Estimation Model ◽  
Time Performance ◽  
Vehicle Velocity ◽  
Distributed Drive Electric Vehicle ◽  
Tracking Filter

Abstract In this paper, Simulink and Carsim are combined to study the velocity estimation of distributed drive electric vehicles. Firstly, the minimum co-simulation system is established to complete the design and debugging of the algorithm. Then, a new algorithm combining unscented Kalman filter and strong tracking filter is proposed based on the vehicle estimation model. The accuracy and real-time performance of the velocity estimation algorithm are validated by simulation under snake-shaped driving conditions with different road adhesion coefficients. Finally, an experimental test is carried out to verify the effectiveness of the proposed algorithm in estimating vehicle velocity.

scholarly journals EKF- and UKF-Based Estimators for Radar System

2021 ◽  
Vol 1 ◽  
Author(s):  
U. K. Singh ◽  
A. K. Singh ◽  
V. Bhatia ◽  
A. K. Mishra
Keyword(s):  
Kalman Filter ◽  
Time Delay ◽  
Doppler Shift ◽  
Unscented Kalman Filter ◽  
Low Complexity ◽  
Least Mean Square ◽  
Estimation Errors ◽  
Incorrect Choice ◽  
Nonlinear Estimators ◽  
Kernel Least Mean Square

In radar, the measurements (like the range and radial velocity) are determined from the time delay and Doppler shift. Since the time delay and Doppler shift are estimated from the phase of the received echo, the concerned estimation problem is nonlinear. Consequently, the conventional estimator based on the fast Fourier transform (FFT) is prone to yield high estimation errors. Recently, nonlinear estimators based on kernel least mean square (KLMS) are introduced and found to outperform the conventional estimator. However, estimators based on KLMS are susceptible to incorrect choice of various system parameters. Thus, to mitigate the limitation of existing estimators, in this paper, two efficient low-complexity nonlinear estimators, namely, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are proposed. The EKF is advantageous due to its implementation simplicity; however, it suffers from the poor representation of the nonlinear functions by the first-order linearization, whereas UKF outperforms the EKF and offers better stability due to exact consideration of the system nonlinearity. Simulation results reveal improved accuracy achieved by the proposed EKF- and UKF-based estimators.

Ultra-tight GPS/IMU Integration based Long-Range Rocket Projectile Navigation

2016 ◽  
Vol 66 (1) ◽  
pp. 64 ◽  
Author(s):  
Handong Zhao ◽  
Zhipeng Li
Keyword(s):  
Kalman Filter ◽  
Long Range ◽  
High Performance ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Position Information ◽  
Cubature Kalman Filter ◽  
Carrier Phase Tracking ◽  
Output Information ◽  
Navigation Accuracy

<p>Accurate navigation is important for long-range rocket projectile’s precise striking. For getting a stable and high-performance navigation result, a ultra-tight global position system (GPS), inertial measuring unit integration (IMU)-based navigation approach is proposed. In this study, high-accuracy position information output from IMU in a short time to assist the carrier phase tracking in the GPS receiver, and then fused the output information of IMU and GPS based on federated filter. Meanwhile, introduced the cubature kalman filter as the local filter to replace the unscented kalman filter, and improved it with strong tracking principle, then, improved the federated filter with vector sharing theory. Lastly simulation was carried out based on the real ballistic data, from the estimation error statistic figure. The navigation accuracy of the proposed method is higher than traditional method.</p><p><strong>Defence Science Journal, Vol. 66, No. 1, January 2016, pp. 64-70, DOI: http://dx.doi.org/10.14429/dsj.66.8326</strong></p>

On the effect of random timing errors on velocity estimates derived from normal moveout estimates

Geophysics ◽  
1984 ◽  
Vol 49 (8) ◽  
pp. 1361-1364
Author(s):  
J. A. Powell
Keyword(s):  
Measurement Errors ◽  
Velocity Estimation ◽  
Statistical Techniques ◽  
Primary Concern ◽  
Random Errors ◽  
Estimation Errors ◽  
Timing Errors ◽  
Number Of Authors

A number of authors (e.g., Brown, 1969; Hubral and Krey, 1980) have discussed systematic velocity estimation errors caused by nonhyperbolic normal moveout. The primary concern of these authors is often the departure of (presumably perfectly accurate measurements of) normal moveout from that predicted by Dix’s (1955) equation. In this note the effect of measurement errors on velocity estimates is examined with the aid of standard statistical techniques. The concern is not deterministic errors, but those caused by random errors.

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