Constant-gain Kalman Filter Research Articles

Constant-gain EKF algorithm for satellite attitude determination systems

PurposeThis paper aims to propose a constant-gain Kalman Filter algorithm based on the projection method and constant dimension projection, which ensures that the dimension of the observation matrix obtained is maintained when there is a satellite with multiple sensors.Design/methodology/approachFirst, a time-invariant observation matrix is determined with the projection method, which does not require the Jacobi matrix to be calculated. Second, the constant-gain matrix replaces the EKF (extended Kalman filter) gain matrix, which requires online computation, considerably improving the stability and real-time properties of the algorithm.FindingsThe simulation results indicate that compared to the EKF algorithm, the constant-gain Kalman filter algorithm has a considerably lower computational burden and improved real-time properties and stability without a significant loss of accuracy. The algorithm based on the constant dimension projection has better real-time properties, simpler computations and greater fault tolerance than the conventional EKF algorithm when handling an attitude determination system with three or more star trackers.Originality/valueIn satellite attitude determination systems, the constant-gain Kalman Filter algorithm based on the projection method reduces the large computational burden and improve the real-time properties of the EKF algorithm.

A novel constant gain Kalman filter design for nonlinear systems

The constant gain Kalman filter (CGKF) is always a good choice for applications with limited computational power. The traditional CGKF for nonlinear systems is usually designed using the local linearization at the operation point of the system, which cannot guarantee the stability and performance globally and is even unsuitable for the system without operation points. To globally ensure the performance, this paper presents a novel CGKF design framework for general nonlinear systems, the key of which includes the single-domain nonlinear filtering and segmentation over domain of interest (DOI). The estimation error system is firstly transformed into a polytopic system through a global linearization procedure, such that the CGKF is formulated by linear matrix inequalities (LMIs). The prior polytopic linearization of the given nonlinear system is obtained by tensor product (TP) techniques, which is capable of manipulating the polytopic linearization for the conservativeness reduction. Because it is too conservative to share a common filter gain over the whole DOI, the clustering technique is applied to segment the DOI so that the filter can be finalized with multiple gains, each of which corresponds to one specific sub-domain. Finally, the effectiveness of the CGKF is verified by the detailed design example.

Vehicle Tracking in Video using Fractional Feedback Kalman Filter

Object tracking is a challenging and important area of research. The object tracking system must be capable of tracking abrupt variations in object state. Kalman filter is fundamental and widely used as an optimal state estimator in object tracking. With known noise and system parameters, Kalman filter tends to stabilize the gain. However, during sudden transitions of the object tracked, constant gain Kalman filter may diverge. This paper proposes a modified steady-state gain of the Kalman filter, which is achieved by introducing a fractional feedback loop across the Kalman gain. The modified Kalman gain is estimated by minimizing the cost function of the proposed Kalman filter. Results show that the accuracy and robustness of the Kalman filter are significantly improved. The performance of the proposed method is compared with that of the standard Kalman filter, fractional-order Kalman filter, and unscented Kalman filter. In this work, the root mean square error is used as the performance metric. The proposed method has been tested for different datasets, including traffic videos. Experiments show that RMSE is improved upto $17\%$ by using the proposed modified Kalman filter.

An Alternative Look at the Constant-Gain Kalman Filter for State Estimation Over Erasure Channels

This technical note studies state estimation problems subject to data loss. We consider a class of switched estimators, where missing data is replaced by optimal estimates. The considered class of estimators encompasses a number of estimation schemes proposed in the literature. We show that the estimator that minimizes the steady-state estimation error covariance within that class, is given by a constant-gain Kalman filter which was previously proposed as an alternative to the Kalman filter with intermittent observations. As a by-product of our results, we derive expressions that allow one to compare, analytically, popular suboptimal data-dropout compensation mechanisms.

Active suppression of imbalance vibration in the magnetically suspended control moment gyro

The magnetically suspended control moment gyro (MSCMG) system is an actuator for attitude control of spacecrafts. It consists of a gimbal and a high-speed rotor suspended by magnetic bearings (MBs). The imbalance vibration due to the high-speed rotor can cause a velocity ripple to the gimbal and be transmitted to the spacecraft to decrease its attitude control precision. To suppress the imbalance vibration, this paper introduces an active control method in both the MBs and gimbal systems. Firstly, the structure and dynamics of the MSCMG system with the MBs and gimbal are described, and the transmission of the imbalance vibration is discussed. Then a notch filter with a phase shift and a feedforward controller are designed to prevent the MB system from generating the imbalance vibration by making the rotor rotate around its inertial axis. To correct the feedforward control errors resulting from power amplifiers, phase and gain compensations are made. Finally, another notch filter with a phase shift is employed to suppress the velocity ripple caused by the residual vibration from the MB system, and a constant-gain Kalman filter is adopted to obtain the best real-time estimate value of the gimbal velocity. Stabilities of the vibration control method and the Kalman filter are analyzed. Simulations and experiments have been performed to validate the proposed control method, which has a short computation time and can be used in many practical applications.

Assimilation of satellite data into agrohydrological models to improve crop yield forecasts

This paper addresses the question of whether data assimilation of remotely sensed leaf area index and/or relative evapotranspiration estimates can be used to forecast total wheat production as an indicator of agricultural drought. A series of low to moderate resolution MODIS satellite data of the Borkhar district, Isfahan (Iran) was converted into both leaf area index and relative evapotranspiration using a land surface energy algorithm for the year 2005. An agrohydrological model was then implemented in a distributed manner using spatial information of soil types, land use, groundwater and irrigation on a raster basis with a grid size of 250 m, i.e. moderate resolution. A constant gain Kalman filter data assimilation algorithm was used for each data series to correct the internal variables of the distributed model whenever remotely sensed data were available. Predictions for 1 month in advance using simulations with assimilation at a regional scale were very promising with respect to the statistical data (bias = ±10%). However, longer‐term predictions, i.e. 2 months in advance, resulted in a higher bias between the simulated and statistical data. The introduced methodology can be used as a reliable tool for assessing the impacts of droughts in semi‐arid regions.

A constant gain Kalman filter approach for the prediction of re-entry of risk objects

The accurate estimation of the predicted re-entry time of decaying space debris objects is very important for proper planning of mitigation strategies and hazard assessment. This paper highlights the implementation strategies adopted for the online reentry prediction using Kalman filter approach with constant gains with the states being the semi-major axis, eccentricity and ballistic coefficient and using the measurements of the apogee height and perigee height derived from the Two Line Elements provided by agencies like USSPACECOM. Only a very simple model is utilised for the orbit propagation and a basic feature of the present approach is that any unmodellable state and measurement errors can be accounted for by adjusting the Kalman gains which are chosen based on a suitable cost function. In this paper we provide the details of validating this approach by utilising three re-entries of debris objects, namely, US Sat. No. 25947, SROSS-C2 Satellite and COSMOS 1043 rocket body. These three objects re-entered the Earth's atmosphere on 4th March 2000, 12th July 2001 and 19th January 2002, respectively.

Multitarget bayes filtering via first-order multitarget moments

The theoretically optimal approach to multisensor-multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. Even in single-target problems, this optimal filter is so computationally challenging that it must usually be approximated. Consequently, multitarget Bayes filtering will never be of practical interest without the development of drastic but principled approximation strategies. In single-target problems, the computationally fastest approximate filtering approach is the constant-gain Kalman filter. This filter propagates a first-order statistical moment - the posterior expectation - in the place of the posterior distribution. The purpose of this paper is to propose an analogous strategy for multitarget systems: propagation of a first-order statistical moment of the multitarget posterior. This moment, the probability hypothesis density (PHD), is the function whose integral in any region of state space is the expected number of targets in that region. We derive recursive Bayes filter equations for the PHD that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets. We also show that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense.

Assimilation of remotely sensed latent heat flux in a distributed hydrological model

This paper addresses the question of whether remotely sensed latent heat flux estimates over a catchment can be used to improve distributed hydrological model water balance computations by the process of data assimilation. The data used is a series of noaa-avhrr satellite images for the Drentse Aa catchment in the Netherlands for the year 1995. These 1×1 km resolution images are converted into latent heat flux estimates using sebal ( surface energy balance algorithm for land [J Hydrol 2000;229:87]). The physically-based distributed model simgro ( simulation of groundwater flow and surface water levels [J Hydrol 1997;192:158]) is used to compute the water balance of the Drentse Aa catchment for that same year. Comparison between model-derived and remotely sensed area-averaged evapotranspiration estimates show good agreement, but spatial analysis of the model latent heat flux estimates indicate systematic underestimation in areas with higher elevation. A constant gain Kalman filter data assimilation algorithm is used to correct the internal state variables of the distributed model whenever remotely sensed latent heat flux estimates are available. It was found that the spatial distribution of model latent heat flux estimates in areas with higher elevation were improved through data assimilation.