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 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.

scholarly journals A Bayesian optimized framework for successful application of unscented Kalman filter in parameter identification of MDOF structures

2021 ◽  
pp. 146134842110143
Author(s):  
Mohamadreza Sheibani ◽  
Ge Ou
Keyword(s):  
Kalman Filter ◽  
Parameter Identification ◽  
Unscented Kalman Filter ◽  
Initial Conditions ◽  
Coupling Effect ◽  
Experimental Tests ◽  
Optimization Method ◽  
Bayesian Optimization ◽  
Noise Parameters ◽  
Inclusive Approach

The success of the unscented Kalman filter can be jeopardized if the required initial parameters are not identified carefully. These parameters include the initial guesses and the levels of uncertainty in the target parameters and the process and measurement noise parameters. While a set of appropriate initial target parameters give the unscented Kalman filter a head start, the uncertainty levels and noise parameters set the rate of convergence in the process. Therefore, due to the coupling effect of these parameters, an inclusive approach is desired to maintain the chance of convergence for expensive experimental tests. In this paper, a framework is proposed that, via a virtual emulation prior to the experiment, determines a set of initial conditions to ensure a successful application of the online parameter identification. A Bayesian optimization method is proposed, which considers the level of confidence in the initial guesses for the target parameters to suggest the appropriate noise covariance matrices. The methodology is validated on a five-story shear frame tested on a shake table. The results indicate that, indeed, a trade-off can be made between the robustness of the online updating and the final parameter accuracy.

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.

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.

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