Analysis on Strong Tracking Filtering for Linear Dynamic Systems

Strong tracking filtering (STF) is a popular adaptive estimation method to effectively deal with state estimation for linear and nonlinear dynamic systems with inaccurate models or sudden change of state. The key of the STF is to use a time-variant fading factor, which can be evaluated based on the current measurement innovation in real time, to forcefully correct one step state prediction error covariance. The strong tracking filtering technology has been extensively applied in many practical systems, but the theoretical analysis is highly lacking. In an effort to better understand STF, a novel analysis framework is developed for the strong tracking filtering and some new problems are discussed for the first time. For this, we propose a new perspective that correcting the state prediction error covariance by using the fading factor can be thought of directly modifying the state model by correcting the covariance of the process noise. Based on this proposed point of view, the conditions for the STF function to be effective are deeply analyzed in a certain linear dynamic system. Meanwhile, issues of false alarm and alarm failure are also briefly discussed for the strong tracking filtering function. Some numerical simulation examples are demonstrated to validate the results

The discrete-time compensated Kalman filter

A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated

Adaptive Estimation of Signals of Opportunity

To exploit unknown ambient radio frequency signals of opportunity (SOPs) for positioning and navigation, one must estimate their states along with a set of parameters that characterize the stability of their oscillators. SOPs can be modeled as stochastic dynamical systems driven by process noise. The statistics of such process noise is typically unknown to the receiver wanting to exploit the SOPs for positioning and navigation. Incorrect statistical models jeopardize the estimation optimality and may cause filter divergence. This necessitates the development of adaptive filters, which provide a significant improvementover fixed filters through the filter learning process. This paper develops two such adaptive filters: an innovationbased maximum likelihood filter and an interacting multiple model filter and compares their performance and complexity. Numerical and experimental results are presented demonstrating the superiority of these filters over fixed, mismatched filters.Aerospace Engineering and Engineering Mechanic

The discrete-time compensated Kalman filter

Bibliography: leaf 39.NASA Grant NSG-1312. A revision of ESL-P748.Wing-Hong Lee, Michael Athans

Multiple Model Methods for Cost Function Based Multiple Hypothesis Trackers

Multiple hypothesis trackers (MHTs) are widely accepted as the best means of tracking targets in clutter. This research seeks to incorporate multiple model Kalman filters into an Integral Square Error (ISE) cost-function-based MHT to increase the fidelity of target state estimation. Results indicate that the proposed multiple model methods can properly identify the maneuver mode of a target in dense clutter and ensure that an appropriately tuned filter is used. During benign portions of flight, this causes significant reductions in position and velocity RMS errors compared to a single-filter MHT. During portions of flight when the mixture mean deviates significantly from true target position, so-called deferred decision periods, the multiple model structures tend to accumulate greater RMS errors than a single-filter MHT, but this effect is inconsequential considering the inherently large magnitude of these errors (a non-MHT tracker would not be able to track during these periods at all). The multiple model MHT structures do not negatively impact track life when compared to a single-filter MHT