Modified Gain Extended Kalman Filter Research Articles

Implementation of ensemble Kalman filter algorithm for underwater target tracking

Surveillance of underwater for maritime warfare is traditionally being carried out by bearings-only tracking from many decades. The measurements used for state estimation here are nonlinear. Also the noise in the measurements and the process cannot be always Gaussian. The traditional nonlinear filtering algorithms like extended Kalman filter and modified gain extended Kalman filter use the linearisation of the system. The unscented Kalman filter (UKF) uses the sigma point approach based on Gaussian distribution to deal with nonlinearity. The particle filter (PF) uses the randomly generated particles based on the pdf of the state. PF is highly complex to implement and it also suffers from sample impoverishment. Hence, ensemble Kalman filter (EnKF) which is a simplified form of PF will be tried out for bearings-only tracking in this research work. The performance of EnKF is compared with PF and UKF and the results obtained using these filters in Matlab are presented.

Practical Time-to-Go Estimation Based on Constant Relative Acceleration

This paper addressed the problem of computing practical time-to-go estimation,when constant relative acceleration and measurement distribution were considered . firstly,a time-to-go arithmetic was obtained based on missile and target engagement geometry. The method is a combination of three time-to-go estimate formulations . Then time-to-go estimator was designed by applying the modified gain extended Kalman filter theory.Simulation results show that the proposed estimator can estimate the time-to-go very effectively . The proposed method is simple and straightforward to implement for missiles.

Modified gain extended Kalman filter with application to bearings-only passive manoeuvring target tracking

The feasibility of Song and Speyer's modified gain extended Kalman filter using bearings-only measurements is explored for underwater applications. A much simpler version of the modified function introduced by Galkowski and Islam is considered for the development of this algorithm. This algorithm estimates target motion parameters and detects target manoeuvre, using zero mean chi-square distributed random sequence residuals, in sliding window format. During the period of target manoeuvring, the covariance of the process noise is increased sufficiently in such a way that the disturbance in the solution is less. When a target manoeuvre is completed, the covariance of process noise is lowered. The performance of this algorithm is evaluated in Monte Carlo simulation and results are shown for various typical geometries.

Algorithm for detection of manoeuvring targets in bearings-only passive target tracking

The feasibility of a modified gain extended Kalman filter using bearings-only measurements is explored for underwater applications. A much simpler version of the modified function is considered for the development of this algorithm. This algorithm estimates target motion parameters and detects target manoeuvres, using zero mean chi-square distributed random sequence residuals, in a sliding window format. The detection of target manoeuvres, in particular in highly nonlinear (high bearing-rate) scenarios, is explored. The performance of this algorithm is evaluated in Monte Carlo simulations, and results are shown for various typical geometries.

Bayesian state estimation for tracking and guidance using the bootstrap filter

The bootstrap filter is an algorithm for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples that are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: It may be applied to any state transition or measurement model. A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter. A preliminary investigation of an application of the bootstrap filter to an exoatmospheric engagement with non-Gaussian measurement errors is also given.

A method for improving extended Kalman filter performance for angle-only passive ranging

A relatively simple method is presented which eliminates previously reported (Oct. 1985) erratic estimation performance associated with Cartesian formulations of the extended Kalman filter (EKF) for the 2D angle-only emitter location problem. The technique is based on an initialization procedure which combines a priori probability density function (pdf) information with single measurement a posteriori pdf information in a manner which is more efficient than the EKF. Simulation results are presented which demonstrate the utility of the technique as compared with a previously offered modified gain EKF.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An alternative derivation of the modified gain function of Song and Speyer

A simpler derivation of the modified gain function for the bearings-only measurement problem as defined by T.L. Song et al. (see ibid vol.AC-30, no.30 (1985)) is presented. The form which results show the relationship between the modified gain and the standard gain. The relationship between the modified gain and the standard gain of an extended Kalman filter is shown. It is confirmed that the modified gain extended Kalman filter performs better than the standard extended Kalman filter. >

Passive homing missile guidance law based on new target maneuver models

Abstract : By using more realistic a priori knowledge about the target motion, tracking of maneuvering targets for homing missiles is enhanced. Since certain targets are assumed to execute evasive maneuvers orthogonal to their velocity vector, a new stochastic dynamic target model is proposed where this orthogonality is embedded. Along with this new acceleration dynamic model, the orthogonality is also enforced by the addition of a fictitious auxiliary measurement. The target states are estimated by the modified gain extended Kalman filter (MGEKF), and the angular target maneuver rate is constructed on- line. A guidance law that minimizes a quadratic performance index subject to the assumed stochastic engagement dynamics that includes state dependent noise is derived. This guidance law is determined in closed form where the gains are an explicit function of the estimated target maneuver rate as well as time to go. The numerical simulation for the two-dimensional angle-only measurement case indicates that the proposed target model with the MGEKF leads to remarkable estimation of the target states. Furthermore, the effect on terminal miss distance using this new guidance scheme is given. Keywords: Kalman filter; Target estimation; Linear quadratic guidance law; Guidance law.

Computer-aided Characteristic Analysis and Model Design of Flight

In this paper, a practical program package of computer-aided characteristic analysis of airacraft and mathematical model design of flight simulator is introduced. This CAD package consists of five parts: flight test data error precorrection, data compatibility check, aerodynamic coefficient identification, characteristic analysis of aircraft and mathematical model design of flight simulator. In order to get high accuracy, the modified gain extended Kalman filter and smoother algorithm, separated bias identification and state estimation algorithm and shifted orthogonal series algorithm are respectively used for data compatibility check, U-D covariance factorization being used for improving numerical stability and computational efficiency. In the identification program of aerodynamic coefficient, linear maximum likelihood method is suitable to the flight regime of low angle of attack, and for the flight regime of high angle of attack, nonlinear maximum likelihood method or shifted orthogonal series method should be used. The results show that with this package the performance stability and control characteristics of aircraft and the mathematical model of flight simulator can be determined satisfactorily.

On-line aircraft state and stability derivative estimation using themodified-gain extended Kalman filter

A new on-line state and parameter identification algorithm called the modified-gain extended Kalman filter (MGEKF) is applied to the problem of on-line state estimation and identification of the stability derivatives of a F-111 type of vehicle. The conceptual basis for the MGEKF is the existence of a class of nonlinear functions that allow a universal linearization with respect to the measurement function. This class includes the problem of identification of linear systems. The previous single-output formulation is extended to a multioutput formulation where the only available measurements are acceleration and pitch rate, but not elevator deflection. The filter formulation includes a simplified Dryden wind gust model. The inclusion of the wind gust model results mainly in a slowed response in the estimation of the stability derivatives associated with the acceleration state; estimates of the stability derivatives associated with the pitch rate still respond very quickly. The accuracy of the acceleration stability derivatives depends upon the amplitude and frequency components of the persistently exciting dither signal.

The modified gain extended Kalman filter and parameter identification in linear systems

For a special class of systems, a general formulation and stochastic stability analysis of a new nonlinear filter, called the modified gain extended Kalman filter (MGEKF), is presented. Used as an observer, it is globally exponentially convergent. In the presence of uncertainties a nominal nonrealizable filter algorithm is developed for which global stochastic stability is proven. With respect to this nominal filter algorithm, conditions are obtained such that the effective deviations of the realizable filter are not destabilizing. In an appropriate coordinate frame, the parameter identification problem of a linear system is shown to be a member of this special class. For the example problems, the MGEKF shows superior convergence characteristics without evidence of instability.

A stochastic analysis of a modified gain extended Kalman filter with applications to estimation with bearings only measurements

A new globally convergent nonlinear observer, called the modified gain extended Kalman observer (MGEKO), is developed for a special class of systems. This observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended Kalman filter (MGEKF). A sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square is obtained. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearings-only measurement problem where the extended Kalman filter often shows erratic behavior.