Comparison of Several Nonlinear Filters for Mars Entry Navigation Using Radiometric Measurements

2017 ◽  
Vol 70 (5) ◽  
pp. 983-1001 ◽  
Author(s):  
Yuanqing Xia ◽  
Zirui Xing ◽  
Liansheng Wang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Computation Time ◽  
Measurement Model ◽  
Nonlinear Filters ◽  
Estimation Errors ◽  
Consistency Test ◽  
Radiometric Measurements ◽  
Error Standard Deviation ◽  
Difference Filter

This paper studies the application of several nonlinear filters for the problem of Mars entry navigation by using radiometric measurements from Mars orbiters and Mars Surface Beacons (MSBs). A suitable dynamic model of Mars entry is developed. The movement of MSBs due to Mars rotation is also considered in the measurement model. The performance of an Extended Kalman Filter (EKF), First-order Divided Difference Filter (DDF1), Unscented Kalman Filter (UKF), and Particle Filter (PF) is compared in terms of estimation capability and computation costs. The theoretical Cramer-Rao Lower Bound (CRLB) of estimation errors are derived for Mars entry to evaluate the performance of the filters. A consistency test is also carried out to verify the filters. In simulations, by the comparison of estimation errors, position and velocity Root Mean Square Error (RMSE), error standard deviation versus Square Root of CRLB (SR CRLB), credibility and computation time, it is concluded that DDF1 is preferred for Mars entry navigation.

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.

An improved measurement variable estimation model for positioning mobile robot

2019 ◽  
Vol 20 (1) ◽  
pp. 78-101 ◽  
Author(s):  
Junsuo Qu ◽  
Leichao Hou ◽  
Ruijun Zhang ◽  
Zhiwei Zhang ◽  
Qipeng Zhang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Mobile Robot ◽  
Manufacturing Industry ◽  
Unscented Kalman Filter ◽  
Measurement Model ◽  
Smart Manufacturing ◽  
Key Factors ◽  
Estimation Model ◽  
Robot Positioning ◽  
Time Update

Abstract The localization and navigation technology are the key factors in the research of mobile robots. With the demand of smart manufacturing industry and the development of robotics technology, the importance of mobile robot has become increasingly prominent. Mobile robot positioning research is mostly based on odometry, however, it has cumulative errors that would affect the accuracy of positioning results. This paper describes an improved measurement model that suitable from 0° to 180° and used this model in the Extended Kalman Filter (EKF) and Unscented Kalman Filter(UKF) time update step respectively, the method can address the interference of kinematics model predicted position and heading angle, both of them are easily disturbed by noises and other factors. Designing a tracked mobile robot as experimental platform to collect the raw data, conducting experimental research including the performance of hardware platform and autonomous obstacle avoidance, the real-time and stability of remote data interaction, and the accuracy of optimal pose estimation. The simulation results have been verified the accuracy of the improved measurement model applied to UKF.

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.

scholarly journals Optimization of an unscented Kalman filter for an embedded platform

2022 ◽  
Author(s):  
Philip P Graybill ◽  
Bruce J. Gluckman ◽  
Mehdi Kiani
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Forecast Error ◽  
Regulatory System ◽  
Computation Time ◽  
Optimization Method ◽  
Forecasting Accuracy ◽  
State Reconstruction ◽  
Embedded Platform ◽  
Three Stages

The unscented Kalman filter (UKF) is finding increased application in biological fields. While realizing a complex UKF system in a low-power embedded platform offers many potential benefits including wearability, it also poses significant design challenges. Here we present a method for optimizing a UKF system for realization in an embedded platform. The method seeks to minimize both computation time and error in UKF state reconstruction and forecasting. As a case study, we applied the method to a model for the rat sleep-wake regulatory system in which 432 variants of the UKF over six different variables are considered. The optimization method is divided into three stages that assess computation time, state forecast error, and state reconstruction error. We apply a cost function to variants that pass all three stages to identify a variant that computes 27 times faster than the reference variant and maintains required levels of state estimation and forecasting accuracy. We draw the following insights: 1) process noise provides leeway for simplifying the model and its integration in ways that speed computation time while maintaining state forecasting accuracy, 2) the assimilation of observed data during the UKF correction step provides leeway for simplifying the UKF structure in ways that speed computation time while maintaining state reconstruction accuracy, and 3) the optimization process can be accelerated by decoupling variables that directly impact the underlying model from variables that impact the UKF structure.

scholarly journals Vehicle Driving State Estimation Using an Improved Adaptive Unscented Kalman Filter

2021 ◽  
Author(s):  
Hui Pang ◽  
Peng Wang ◽  
Zijun Xu ◽  
Gang Wang
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Unscented Kalman Filter ◽  
Estimation Method ◽  
Estimation Errors ◽  
Adaptive Unscented Kalman Filter ◽  
Adjustment Strategy ◽  
Noise Covariance ◽  
Adaptive Noise ◽  
Three Degree Of Freedom

Abstract This paper proposes an improved adaptive unscented Kalman filter (iAUKF)-based vehicle driving state estimation method. A three-degree-of-freedom vehicle dynamics model is first established, then the varying principles of estimation errors for vehicle driving states using constant process and measurement noises in the standard unscented Kalman filter (UKF) are compared and analyzed. Next, a new type of normalized innovation square-based adaptive noise covariance adjustment strategy is designed and incorporated into the UKF to derive our expected vehicle driving state estimation method. Finally, a comparative simulation investigation using CarSim and MATLAB/Simulink is conducted to validate the effectiveness of the proposed method, and the results show that our proposed iAUKF-based estimation method has higher accuracy and stronger robustness against the standard UKF algorithm.

scholarly journals Nonlinear Estimation for Autonomous Optical Navigation

2021 ◽  
Author(s):  
Stefan Hallgrimson
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Nonlinear Estimation ◽  
Computation Time ◽  
Low Earth Orbit ◽  
Reference Scenario ◽  
Optical Navigation ◽  
State Estimator ◽  
Initial State ◽  
The Cost

Many interplanetary mission concepts can benefit from autonomous orbit estimation, particularly during critical mission phases. Previous studies have examined the feasibility of optical navigation using nanosatellite class instruments. While promising, these techniques are not without drawbacks. Convergence of the navigation estimates are often sensitive to errors in initial state estimates. This thesis compares various methods to perform nonlinear estimation for autonomous optical navigation. These methods include an extended Kalman filter (EKF), an unscented Kalman filter (UKF), a particle filter (PF), a fixed-lag smoother (FLS), and moving horizon estimation (MHE). The EKF, UKF, and PF can be implemented in real time, while the FLS and MHE implement a delay into the estimation process. To compare the performance of each state estimator three initial reference scenarios around Mars were considered: a hyperbolic flyby, an elliptic orbit and a orbital maneuver using observations of Mars and its moons. Parameter estimation was also explored, where the mass of Mars was to be estimated as a reference parameter in both the hyperbolic and elliptical trajectories. One last reference scenario included a low Earth orbit (LEO) using observations of satellites in a geosynchronous equatorial orbit. In each case, the FLS and MHE showed similar or better performance over each state estimator but at the cost of an increased computation time with respect to the reference EKF. Similarly the UKF was able to provide improved results withe respect to the EKF. While, the PF provided poor estimates in the Mars trajectories but improvements were seen from the UKF and EKF in the LEO scenario.

Unscented Kalman filter approach to tracking a moving interfacial boundary in sedimentation processes using three-dimensional electrical impedance tomography

2009 ◽  
Vol 367 (1900) ◽  
pp. 3095-3120 ◽  
Author(s):  
Anil Kumar Khambampati ◽  
Ahmar Rashid ◽  
Umer Zeeshan Ijaz ◽  
Sin Kim ◽  
Manuchehr Soleimani ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Unscented Kalman Filter ◽  
Phase Interface ◽  
Three Dimensional ◽  
Measurement Model ◽  
Impedance Tomography ◽  
Filter Approach ◽  
Sedimentation Processes

The monitoring of solid–fluid suspensions under the influence of gravity is widely used in industrial processes. By considering sedimentation layers with different electrical properties, non-invasive methods such as electrical impedance tomography (EIT) can be used to estimate the settling curves and velocities. In recent EIT studies, the problem of estimating the locations of phase interfaces and phase conductivities has been treated as a nonlinear state estimation problem and the extended Kalman filter (EKF) has been successfully applied. However, the EKF is based on a Gaussian assumption and requires a linearized measurement model. The linearization (or derivation of the Jacobian) is possible when there are no discontinuities in the system. Furthermore, having a complex phase interface representation makes derivation of the Jacobian a tedious task. Therefore, in this paper, we explore the unscented Kalman filter (UKF) as an alternative approach for estimating phase interfaces and conductivities in sedimentation processes. The UKF uses a nonlinear measurement model and is therefore more accurate. In order to justify the proposed approach, extensive numerical experiments have been performed and a comparative analysis with the EKF is provided.

A novel metaheuristic model-based approach for accurate online broken bar fault diagnosis in induction motor using unscented Kalman filter and ant lion optimizer

2019 ◽  
Vol 42 (8) ◽  
pp. 1537-1546 ◽  
Author(s):  
Marouane Rayyam ◽  
Malika Zazi
Keyword(s):  
Kalman Filter ◽  
Fault Diagnosis ◽  
Unscented Kalman Filter ◽  
Superior Performance ◽  
Simultaneous Estimation ◽  
Estimation Errors ◽  
Model Based ◽  
Ant Lion Optimizer ◽  
Detection And Identification ◽  
Ant Lion

This paper introduces a novel metaheuristic model-based scheme for fault monitoring in squirrel cage induction motors (SCIMs). This method relies on the combination of the ant lion optimizer (ALO) and the unscented Kalman filter (UKF) to detect and quantify the number of broken bars. Contrary to the UKF-based fault diagnosis, the improved ALO-UKF algorithm tunes optimally and automatically the noise covariance matrices Q and R, which reduces the estimation errors, and then obtains an effective and accurate fault diagnosis. Firstly, a mathematical model of the fault under study has been developed based on rotor parameter value as signature. Secondly, a sixth order ALO-UKF algorithm has been synthesized for simultaneous estimation of rotor resistance and speed. Several broken bar fault conditions have been simulated. Simulation results show the effectiveness and robustness of the proposed ALO-UKF scheme in broken bar detection and identification, and exhibit a more superior performance than the simple-UKF and EKF algorithms in term of stability, accuracy and response time.

scholarly journals Autonomous Positioning of Satellite Constellations via X-ray Pulsar Measurements

2013 ◽  
Vol 66 (5) ◽  
pp. 671-682 ◽  
Author(s):  
Li Liu ◽  
Wei Zheng ◽  
Guojian Tang
Keyword(s):  
Numerical Simulation ◽  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Measurement Model ◽  
Orbital Dynamics ◽  
Satellite Constellations ◽  
X Ray ◽  
Measurement Models ◽  
Measurement Scheme ◽  
Dynamics Models

A novel autonomous positioning approach based on X-ray pulsars is proposed in this paper. First, the principles of the pulsar–based measurement model and the inter-satellite range model in the autonomous positioning of satellite constellations are presented. The observability of the pulsar-based measurement model is then shown. Second, the autonomous positioning algorithms, including measurement models and orbital dynamics models, are formulated using an unscented Kalman filter to estimate the position vectors of satellites. Finally, the feasibility of the proposed measurement scheme compared with an inter-satellite range scheme is illustrated by numerical simulation. The results show that the proposed approach can keep the satellite state convergent, and achieve position accuracies of 2 m. The proposed scheme provides a promising approach for autonomous absolute positioning of constellation systems by using X-ray pulsars.

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