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The improvement of accuracy in using the smoothing filter instead of the Kalman filter is discussed. Factors of improvement for velocity errors of up to four are shown for position measurements. Smoothing equations are presented, and it is shown that smoothing equations for the smoothing filter appear to be stable.
Algorithms have been developed for in-flight demonstration of spacecraft mass, center of mass, and inertia matrix which autonomously measure mass properties as they change in-flight due to consumable expenditures, payload deployment/retrieval, and docking. The testing of these algorithms can be conducted by means of a mass-properties estimator, which is a second-order nonlinear filter resembling an extended Kalman filter. The AeroAssist Flight Experiment, which will demonstrate the use of the earth's atmosphere to assist orbital changes, will carry the Rarefied-flow Aerodynamic Measurement Experiment (RAME); data taken by RAME will be used by the mass-properties estimator to ascertain spacecraft mass properties, and estimates from this filter will be compared to predicted values of the mass properties to validate the estimator.
A proposed method of processing the outputs of multiple gyroscopes to increase the accuracy of rate (that is, angular-velocity) readings has been developed theoretically and demonstrated by computer simulation. Although the method is applicable, in principle, to any gyroscopes, it is intended especially for application to gyroscopes that are parts of microelectromechanical systems (MEMS). The method is based on the concept that the collective performance of multiple, relatively inexpensive, nominally identical devices can be better than that of one of the devices considered by itself. The method would make it possible to synthesize the readings of a single, more accurate gyroscope (a virtual gyroscope) from the outputs of a large number of microscopic gyroscopes fabricated together on a single MEMS chip. The big advantage would be that the combination of the MEMS gyroscope array and the processing circuitry needed to implement the method would be smaller, lighter in weight, and less power-hungry, relative to a conventional gyroscope of equal accuracy. The method (see figure) is one of combining and filtering the digitized outputs of multiple gyroscopes to obtain minimum-variance estimates of rate. In the combining-and-filtering operations, measurement data from the gyroscopes would be weighted and smoothed with respect to each other according to the gain matrix of a minimum- variance filter. According to Kalman-filter theory, the gain matrix of the minimum-variance filter is uniquely specified by the filter covariance, which propagates according to a matrix Riccati equation. The present method incorporates an exact analytical solution of this equation.
Beginning with the mathematical prediction of planetary orbits in the early seventeenth century up through the most recent developments in sensor fusion methods, many techniques have emerged that can be employed on the problem of endo and exoatmospheric trajectory estimation. Although early methods were ad hoc, the twentieth century saw the emergence of many systematic approaches to estimation theory that produced a wealth of useful techniques. The broad genesis of estimation theory has resulted in an equally broad array of mathematical principles, methods and vocabulary. Among the fundamental ideas and methods that are briefly touched on are batch and sequential processing, smoothing, estimation, and prediction, sensor fusion, sensor fusion architectures, data association, Bayesian and non Bayesian filtering, the family of Kalman filters, models of the dynamics of the phases of a rocket's flight, and asynchronous, delayed, and asequent data. Along the way, a few trajectory estimation issues are addressed and much of the vocabulary is defined.
The Jet Propulsion Laboratory Kalman Earth Orientation Filter (KEOF) uses several of the Earth rotation data sets available to generate optimally interpolated UT1 and LOD series to support spacecraft navigation. This paper compares use of various data sets within KEOF.
The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here, we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed ensemble score filter (EnSF) is completely training free and can efficiently generate a set of analysis ensemble members. Here, in this study, we apply the EnSF to a surface quasigeostrophic model and compare its performance against the popular local ensemble transform Kalman filter (LETKF), which makes Gaussian assumptions in the analysis step. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that while LETKF maintains optimal performance in the case of linear observations of the entire state and a perfect model, EnSF shows improvements over LETKF when nonlinear observations are assimilated and the system is subject to unexpected model errors. A spectral decomposition of the analysis results in this nonlinear observation regime shows that the largest improvements over LETKF occur at large scales (small wavenumbers), where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity motivates further development of the algorithm for more realistic problems.
The interplanetary orbit problem has been traditionally solved using least-squares techniques. Due to operational limitations of this method, a Kalman filter approach has been proposed for future missions which includes all spacecraft and measurement modeling states in the filter.
The development of an approximate nonlinear filter using the Martingale theory and appropriate smoothing properties is considered. Both the first order and the second order moments were estimated. The filter developed can be classified as a modified Gaussian second order filter. Its performance was evaluated in a simulated study of the problem of estimating the state of an interplanetary space vehicle during both a simulated Jupiter flyby and a simulated Jupiter orbiter mission. In addition to the modified Gaussian second order filter, the modified truncated second order filter was also evaluated in the simulated study. Results obtained with each of these filters were compared with numerical results obtained with the extended Kalman filter and the performance of each filter is determined by comparison with the actual estimation errors. The simulations were designed to determine the effects of the second order terms in the dynamic state relations, the observation state relations, and the Kalman gain compensation term. It is shown that the Kalman gain-compensated filter which includes only the Kalman gain compensation term is superior to all of the other filters.
This paper presents a novel filter design for the single-output stochastic non-linear systems subjected to non-Gaussian noises and the proposed assumptions. Based on a state transformation, the unmeasurable states of the systems can be estimated where non-linear terms in the systems have been eliminated. It has been shown that the estimation error is linearly dynamical regarding to the presented vector-valued filter gain which can be optimised by minimising the entropy-based performance criterion. In addition, the convergence of the presented algorithm is analysed in mean-square sense and a numerical example is given to verify the effectiveness of the presented filtering algorithm. Meanwhile, the extended Kalman filter, unscented particle filter and minimum entropy filter are given for the comparisons of the filtering performance. Following the presented framework, some extensions of the presented filtering algorithm are discussed to indicate the flexibility of the filter design. The contribution of this paper can be summarised as establishing a novel minimum entropy filtering framework which consists of model transformation, entropy optimisation and convergence analysis.
A method is developed for extracting six degree-of-freedom stability and control derivatives from helicopter flight data. Different combinations of filtering and derivative estimate are investigated and used with a Bayesian approach for derivative identification. The combination of filtering and estimate found to yield the most accurate time response match to flight test data is determined and applied to CH-53A and CH-54B flight data. The method found to be most accurate consists of (1) filtering flight test data with a digital filter, followed by an extended Kalman filter (2) identifying a derivative estimate with a least square estimator, and (3) obtaining derivatives with the Bayesian derivative extraction method.
The computer program for the real-time acquisition and tracking program uses a variety of filtering algorithms including an extended Kalman filter to derive real-time orbit determination (position-velocity state vectors) from shipboard tracking and navigation data. Results from Apollo missions are given to show that orbital parameters can be estimated quickly and accurately using these methods.
The rank histogram filter (RHF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation using perfect model (identical twin) synthetic data assimilation experiments. The primary motivation is to gauge the impact on analysis quality attributable to the consideration of non-Gaussian forecast error distributions. Using the NASA Catchment land surface model, the two filters are compared at 18 globally-distributed single-catchment locations for a 10-year experiment period. It is shown that both filters yield adequate estimates of soil moisture, with the RHF having a small but significant performance advantage. Most notably, the RHF systematically increases the normalized information contribution (NIC) score of the mean absolute bias by 0.05 over that of the EnKF for surface, root-zone and profile soil moisture. The RHF also increases the NIC score for the anomaly correlation of surface soil moisture by 0.02 over that of the EnKF (at a 5% significance level). Results also demonstrate that the performance of both filters is somewhat improved when the ensemble priors are adaptively inflated to offset the negative effects of systematic errors.
Solar Cruiser is a small satellite Technology Demonstration Mission (TDM) to mature solar sail propulsion technology using a solar sail larger than 1600 square meters, demonstrating performance as a propulsion system and a stable pointing platform for science observations in an artificial halo orbit sunward of the Sun-Earth Lagrange Point 1 (sub-L1). For the “sailcraft” to meet mission ob- jectives, there are several unique attitude control challenges that the Attitude De- termination and Control System (ADCS) must overcome. Large disturbance tor- ques, primarily due to sail deformations coupled with off-sun pointing angles, make it more difficult to maintain adequate controls performance and manage accumulated momentum on the control actuators. The large-amplitude, low- frequency flexible body modes of the sail, in concert with noisy sensors and ac- tuators, make it challenging to mitigate control-structure interactions and main- tain fine pointing capabilities. Stability and control performance during sail de- ployment is complicated by rapidly and widely varying inertias. The Solar Cruiser ADCS effectively addresses these challenges using a simple, traditional control system – including momentum management actuators that use bang- bang control to constrain internal accumulated momentum, a low-pass controls filter and an attitude determination Kalman Filter (KF) that blends multiple star tracker solutions, and a reaction wheel assembly (RWA) with controller gains tuned to specific configurations or inertias. Solar Cruiser’s attitude control ap- proach, and lessons learned from its development, establishes a state of the art of high value to future solar sail missions and other small spacecraft with large de- ployable structures operating in deep space.
Solar Cruiser is a small satellite Technology Demonstration Mission (TDM) to mature solar sail propulsion technology using a solar sail larger than 1600 square meters, demonstrating performance as a propulsion system and a stable pointing platform for science observations in an artificial halo orbit sunward of the Sun-Earth Lagrange Point 1 (sub-L1). For the “sailcraft” to meet mission objectives, there are several unique attitude control challenges that the Attitude Determination and Control System (ADCS) must overcome. Large disturbance torques, primarily due to sail deformations coupled with off-sun pointing angles, make it more difficult to maintain adequate controls performance and manage accumulated momentum on the control actuators. The large-amplitude, low-frequency flexible body modes of the sail, in concert with noisy sensors and actuators, make it challenging to mitigate control-structure interactions and maintain fine pointing capabilities. Stability and control performance during sail deployment is complicated by rapidly and widely varying inertias. The Solar Cruiser ADCS effectively addresses these challenges using a simple, traditional control system – including momentum management actuators that use bang-bang control to constrain internal accumulated momentum, a low-pass controls filter and an attitude determination Kalman Filter (KF) that blends multiple star tracker solutions, and a reaction wheel assembly (RWA) with controller gains tuned to specific configurations or inertias. Solar Cruiser’s attitude control approach, and lessons learned from its development, establishes a state of the art of high value to future solar sail missions and other small spacecraft with large deployable structures operating in deep space.
The rank histogram filter (RHF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation using perfect model (identical twin) synthetic data assimilation experiments. The primary motivation is to gauge the impact on analysis quality attributable to the consideration of non-Gaussian forecast error distributions. Using the NASA Catchment land surface model, the two filters are compared at 18 globally distributed single-catchment locations for a 10-yr experiment period. It is shown that both filters yield adequate estimates of soil moisture, with the RHF having a small but significant performance advantage. Most notably, the RHF consistently increases the normalized information contribution (NIC) score of the mean absolute bias by 0.05 over that of the EnKF for surface, root-zone, and profile soil moisture. The RHF also increases the NIC score for the anomaly correlation of surface soil moisture by 0.02 over that of the EnKF (at a 5% significance level). Results additionally demonstrate that the performance of both filters is somewhat improved when the ensemble priors are adaptively inflated to offset the negative effects of systematic errors.
Kalman filter theory and sextant measurements for lunar midcourse guidance and navigation simulation
The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.