Patent No. US 8433544 B2 for our Nonlinear Variable Lag Smoother was granted by the director of the United States Patent and Trademark Office on April 30, 2013. The Nonlinear Variable Lag Smoother, developed by myself and Dr. Jim Woodburn in 2008 for AGI, enables the solution of a new class of problems in estimation and control, with particular applications to spacecraft orbit determination.
When measurements are collected sequentially in real-time, the epoch for each optimal sequential real-time state estimate may be conveniently defined as the latest measurement time-tag. We call this estimator an optimal filter. Filter measurement information always sits in the present and past; that is, at filter epoch and prior to filter epoch.
Sequential smoothers are characterized by calculation of optimal state estimates derived from measurement data with time-tags after smoother epoch and measurement data with time-tags prior to smoother epoch. Any time prior to the last measurement time-tag may conveniently be defined as a smoother epoch.
Measurement information fades with time, looking forward or looking backward from any fixed epoch. Thus the most significant measurements referred to any fixed epoch are those with time-tags closest to the fixed epoch. As measurement time-tags become distant (either forward or backward) from the fixed epoch, the influence of those measurements on the state estimate fades to zero. Thus the length of the measurement span for a filtered estimate may be insignificant when compared to the existence of measurements both backward and forward of the state estimate for smoothing. Smoothed state estimates are superior in accuracy to filtered state estimates. On the other hand, filtered state estimates are available in real-time, but you must wait for smoothed state estimates. The wait is called the smoothing lag.
The Nonlinear Variable Lag Smoother (VLS) is equipped with a forward running filter and multiple simultaneous fixed-epoch smoothers. Each fixed-epoch smoother is initialized by the filter when the forward moving filter epoch reaches each smoother fixed-epoch. Measurement information, derived by filtering of measurements, is mapped linearly backwards to each fixed-epoch smoother as the filter moves forward through measurement time-tags. Thus the smoothing lag for each fixed-epoch smoother varies with time as the filter epoch moves forward. Sequential filter and smoother operations are performed simultaneously. Backward transition of the complete state estimate and covariance is not required. The VLS may initialize and run one or many fixed-epoch smoothers simultaneously with forward execution of the filter. The VLS may be run without state sized matrix inverse.
We have successfully implemented and validated the autonomous estimation of ΔV following any spacecraft thrusting maneuver using VLS in AGI's Orbit Determination Tool Kit
(ODTK) software. There are unimplemented applications of the VLS for solution of real unsolved problems in estimation and control, particularly associated with orbit determination.
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