Data processing: vehicles – navigation – and relative location – Vehicle control – guidance – operation – or indication – Aeronautical vehicle
Reexamination Certificate
2000-07-24
2001-11-13
Cuchlinski, Jr., William A. (Department: 3661)
Data processing: vehicles, navigation, and relative location
Vehicle control, guidance, operation, or indication
Aeronautical vehicle
C701S031000, C702S180000, C702S196000, C706S054000, C706S061000
Reexamination Certificate
active
06317662
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to state estimation processes and, more particularly, to spacecraft subsystems which use such processes.
2. Description of the Related Art
Kalman filtering is an estimation technique that combines a knowledge of the statistical nature of a system's measurement errors with a knowledge of the system's dynamics (as represented, for example, in a state space model) to arrive at an estimate of the system's state. In particular, a Kalman filter combines a current measurement y(t
n
) of a system state parameter x(t
n
) with measurement and state predictions y*(t
n
−
) and x*(t
n
−
) of the parameter x(t
n
) that are based on past measurements to thereby provide a filtered estimate x*(t
n
+
) of the parameter x(t
n
). As indicated by the time term t
n
, the filter successively and recursively combines the measurements and predictions to obtain estimates with a reduced variance (wherein t
n
−
and t
n
+
refer respectively to times just before and after each time t
n
).
In an exemplary spacecraft application, a Kalman filter processes attitude and inertial rate measurements to provide an attitude estimate. Although the filter is known to be an especially effective state estimator for these systems, the process tends to have numerical instabilities when it is implemented with digital processors and continued over extensive time periods. The instability has a source in the finite accuracy of digital processing and it represents a danger to long-term spacecraft missions that repeat the same operational mode for years (e.g., as in communication processes of geosynchronous spacecraft). In response to this danger, computationally expensive filter formulations (e.g., Joseph formulation and UDU factorization) have been used to increase numerical stability. These approaches, however, increase the use of processing time which is a limited and tightly budgeted spacecraft resource.
In addition, these stability solutions have a further problem. Because of the high cost of spacecraft missions and the critical nature of spacecraft attitude control systems, it is especially desirable to verify the stability of all such processes over time periods that correspond to those in which the mission will be operational. When these operational time periods are measured in years, such testing is not feasible and, thus, these solutions are not verifiable.
SUMMARY OF THE INVENTION
The present invention is directed to computationally simple methods for enhancing and verifying the long-term stability of a recursive process that generates estimates of a system's state. The stability is enhanced by periodically resetting an error covariance P(t
n
) of the system to a reset value P
r
that exceeds the operational values P
o
of the process. The recursive process is thus repetitively forced to start from a selected covariance and continue for a time period that is short compared to the system's total operational time period. Because the time period over which the process must maintain its numerical stability is significantly reduced, the demand on its inherent stability is also significantly reduced.
The stability for an extended operational time period T
o
is verified by performing the resetting step at the end of at least one reset time period T
r
whose duration is less than the operational time period T
o
and then confirming stability of the process over the reset time period T
r
. Because the process starts from a selected covariance at the beginning of each reset time period T
r
, confirming stability of the process over at least one reset time period substantially confirms stability over the longer operational time period T
o
.
Spacecraft system embodiments of the invention are also provided.
The novel features of the invention are set forth with particularity in the appended claims. The invention will be best understood from the following description when read in conjunction with the accompanying drawings.
REFERENCES:
patent: 5465321 (1995-11-01), Smyth
patent: 5506794 (1996-04-01), Lange
patent: 5918200 (1999-06-01), Tsutsui et al.
patent: 5991525 (1999-11-01), Shah et al.
Kaplan, Elliot D.,Understandning GPS, Artech House, Norwood, Massachusetts, 1996, pp. 391-395.
Brookner, Eli,Tracking and Kalman Filtering Made Easy, John Wiley and Sons, New York, 1998, pp. 69-74.
Li Rongsheng
Wu Yeong-Wei Andy
Cuchlinski Jr. William A.
Donnelly Arthur D.
Guamestad T.
Hughes Electronics Corporation
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