Optimum Steady State Position, Velocity, and Acceleration Estimation Using Noisy Sampled Position Data

A one-dimensional tracking filter based on the Kalman filtering techniques for tracking of a dynamic target such as an aircraft is discussed. The target is assumed to be moving with constant acceleration and is acted upon by a plant noise which perturbs its constant acceleration motion. The plant noise accounts for maneuvers and/or other random factors. Analytical results for estimating optimum steady state position, velocity, and acceleration of the target are obtained.     

Steady State Results for the X, Y, Z Kalman Tracking Filter

An X, Y, Z Kalman tracking filter is described and its steady state characteristics are analytically determined when the radar sensor meaures range, bearing, and elevation (?, ?, ?) at uniform intervals of time, T seconds. The relationship between the quantities measured by the sensor (?, ?,?) and the Cartesian coordinate system (X, Y, Z) is explicitly considered.     

Assimilation of endmember variability in spectral mixture analysis for urban land cover extraction

Variable Endmember Constrained Least Square (VECLS) technique is proposed to account endmember variability in the linear mixture model by incorporating the variance for each class, the signals of which varies from pixel to pixel due to change in urban land cover (LC) structures. VECLS is first tested with a computer simulated three class endmember considering four bands having small, medium and large variability with three different spatial resolutions. The technique is next validated with real datasets of IKONOS, Landsat ETM+ and MODIS. The results show that correlation between actual and estimated proportion is higher by an average of 0.25 for the artificial datasets compared to a situation where variability is not considered. With IKONOS, Landsat ETM+ and MODIS data, the average correlation increased by 0.15 for 2 and 3 classes and by 0.19 for 4 classes, when compared to single endmember per class.     

Analytical Results for a Kalman Tracker Using Position and Rate Measurements

Analytical results are presented for determining the steady-state components of the gain and error covariance matrices of the two-state Kalman tracking filter with white noise maneuver capability.     

Steady-State Covariance Matrix Determination for a Three-Dimensional Kalman Tracking Filter

The steady-state components of the covariance matrix of estimation errors after processing an observation have been analytically determined ined for a tree-dimensional Kalman tracking filter.     

A three-state Kalman tracker using position and rate measurements

A three-state Kalman tracker is described for tracking a moving target, such as an aircraft, making use of the position and rate measurements obtained by a track-white-scan radar sensor which employs pulsed Doppler processing, such as the moving target detector providing unambiguous Doppler data. The steady-state filter parameters have been analytically obtained under the assumption of white noise maneuver capability. The numerical computations of these parameters are in excellent agreement with those obtained from the recursive Kalman filter matrix equations. The solution for the case when only the range measurements are available is obtained as a special case of this model. Graphs of normalized covariances and gains are presented to illustrate how the solution depends on different parameters     

Identical Steady-State Results for a Kalman Tracker

It is shown that the analytical results presented in [2, 3] for determining the steady state gain and error covariance matrices of the two state Kalman tracker [1] are identical although they appear to be different.     

Velocity Estimation from Position Outputs of a Three-Dimensional Radar

Kalman filtering equations to obtain estimates of velocity from radar position information are defined. In a track-while-scan operation, a three-dimensional radar sensor measures range, bearing, and elevation (r, ?, ?) of an airborne target at uniform sampling intervals of time T. The noisy position measurements are converted to x, y, z coordinates and put through a Kalman filter to obtain x, y, z velocity components. The filtering equations together with steady-state error estimates are given.