Filtering process for stable and accurate estimation

• US 6,757,569 B2
• Filed: 04/20/2001
• Issued: 06/29/2004
• Est. Priority Date: 04/19/2000
• Status: Expired due to Term

• Current Assignee: American GNC Corporation
• Original Assignee: American GNC Corporation
• Inventors: Lin, Ching-Fang
• Primary Examiner(s): PATEL, RAMESH B
• Application Number:
  US09/840,511
• Publication Number:
  US 20020032490A1
• Time in Patent Office: 1,166 Days
• Field of Search: 700/2, 700/55, 700/50, 700/52, 700/53, 700/44, 700/305, 706/900, 708/300, 708/303, 701/3, 701/13, 701/213, 701/214, 701/200, 701/207, 701/208, 701/226
• US Class Current: 700/29
• CPC Class Codes: G05B 13/0275 using fuzzy logic only
• CPC Class Codes: G05B 13/04 involving the use of models or simulators
• CPC Class Codes: G05B 17/02 electric
• CPC Class Codes: Y10S 706/90 Fuzzy logic

Abstract

A filtering process is adapted for eliminating the need of prediscretizing a continuous-time differential model into a discrete-time difference model. It provides a universal robust solution to the most general formulation, in the sense that the system dynamics are described by nonlinear continuous-time differential equations, and the nonlinear measurements are taken at intermittent discrete times randomly spaced. The filtering process includes the procedures of validating the measurement using fuzzy logic, and incorporating factorized forward filtering and backward smoothing to guarantee numerical stability. It provides users a reliable and convenient solution to extracting internal dynamic system state estimates from noisy measurements, with wider applications, better accuracy, better stability, easier design, and easier implementation.

Claims

1. A filtering process, comprising the steps of:

(a) computing a model relevant information for a time update and a measurement update in a model selection; and

(b) providing, from said model selection, an initial condition of a system estimate for a system model computation in said time update, an initial condition of a covariance error matrix for a derivative system model computation in said time update, a system model for said system model computation in said time update, a derivative system model for said derivative system model computation in said time update, a measurement model for a measurement model computation in said measurement update, and a derivative measurement model for a derivative measurement model computation in said measurement update.

2. The filtering process, as recited in claim 1, further comprising the steps of:

(c) propagating said state estimate during an interval of last two consecutive valid measurements in said time update which is based upon a system model; and

(d) correcting said state estimate by using a latest measurement data in said measurement update, said measurement update being based upon said measurement model and said measurement data.

3. The filtering process, as recited in claim 2, wherein said step (c) further comprises the steps of:

(c-1) computing an interval span between said last two consecutive valid measurements in order to determine how long said time update propagates without said measurement update;

(c-2) receiving said system model from a model selection and computing a time derivative of said system state at a latest estimate of said system state in said system model computation;

(c-3) receiving said derivative system model from said model selection and computing a time derivative of a covariance error matrix for said system state at said latest estimate of said system state in said derivative system model computation;

(c-4) propagating said state estimate by utilizing said time derivative of said system state computed in said system model computation in a prediction update, using a Runge-Kutta integration algorithm with adaptive stepsize control; and

(c-5) propagating said covariance error matrix of said state estimate by utilizing said time derivative of said covariance error matrix computed in said derivative system model computation in a prediction covariance update, using a factorized implementation.

4. The filtering process, as recited in claim 2, wherein said step (d) further comprises the steps of:

(d-1) receiving said measurement model from said model selection and computing a predicted measurement at a latest estimate of system state in said measurement model computation,

(d-2) receiving said derivative measurement model from said model selection and computing a measurement Jacobian matrix at said latest estimate of system state in said derivative measurement model computation,

(d-3) updating said covariance error matrix by using measurement update equations in said estimate covariance update, and

(d-4) updating an optimal estimate of system state by using said measurement update equations in said estimate update.

5. The filtering process, as recited in claim 3, wherein said step (d) further comprises the step of:

(d-1) receiving said measurement model from said model selection and computing a predicted measurement at a latest estimate of system state in said measurement model computation,

(d-2) receiving said derivative measurement model from said model selection and computing a measurement Jacobian matrix at said latest estimate of system state in said derivative measurement model computation,

(d-3) updating said covariance error matrix by using measurement update equations in said estimate covariance update, and

(d-4) updating an optimal estimate of system state by using said measurement update equations in said estimate update.

6. The filtering process, as recited in claim 4, after the step (d), further comprising the steps of:

(e) calculating an interval from which a backward smoothed estimate is extracted;

(f) obtaining said forward state estimate and a covariance error matrix thereof in a forward measurement update and a forward time update by performing the step (c) and the step (d);

(g) propagating a backward estimate during said interval of said last two consecutive reversed measurements in a backward time update based upon said backward system model so as to define said backward state estimate and said associated covariance error matrix thereof for said backward system model respectively, just after said last reversed measurement being processed by said backward measurement update;

(h) correcting said backward state estimate by using said reversed measurement data in a backward measurement update based upon said measurement model and said measurement data, wherein results obtained in said backward time update are utilized as initial conditions, wherein a state estimate and an associated covariance error matrix thereof obtained from said backward time update just before a new measurement is processed by said backward measurement update;

(i) computing a covariance error matrix for a smoothed state estimate using said covariance error matrix of said forward system estimate and said covariance error matrix of said backward system estimate in a smoothed estimate covariance update; and

(j) computing said smoothed state estimate using said forward system estimate and said backward system estimate in a smoothed estimate update.

7. The filtering process, as recited in claim 5, after the step (d), further comprising the steps of:

(e) calculating an interval from which a backward smoothed estimate is extracted;

(f) obtaining said forward state estimate and a covariance error matrix thereof in a forward measurement update and a forward time update by performing the step (c) and the step (d);

(g) propagating a backward estimate during said interval of said last two consecutive reversed measurements in a backward time update based upon said backward system model so as to define said backward state estimate and said associated covariance error matrix thereof for said backward system model respectively, just after said last reversed measurement being processed by said backward measurement update;

(h) correcting said backward state estimate by using said reversed measurement data in a backward measurement update based upon said measurement model and said measurement data, wherein results obtained in said backward time update are utilized as initial conditions, wherein a state estimate and an associated covariance error matrix thereof obtained from said backward time update just before a new measurement is processed by said backward measurement update;

(i) computing a covariance error matrix for a smoothed state estimate using said covariance error matrix of said forward system estimate and said covariance error matrix of said backward system estimate in a smoothed estimate covariance update; and

(j) computing said smoothed state estimate using said forward system estimate and said backward system estimate in a smoothed estimate update.

8. The filtering process, as recited in claim 6, wherein said step (g) further comprise said steps of:

(g-1) computing said interval span between said last two consecutive reserved valid measurements so as to determine how long said backward time update propagates without a measurement update;

(g-2) receiving said system model and said derivative system model from a model selection, computing a system function and a Jacobian matrix at said forward state estimate obtained in forward filtering, and calculating a time derivative of said backward system state in a system model computation;

(g-3) receiving said derivative system model from said model selection and computing a time derivative of said covariance error matrix for said backward system state at said forward state estimate in a derivative system model computation;

(g-4) propagating said backward state estimate by utilizing said time derivative of said backward system state computed in said system model computation in a backward prediction update, using a Runge-Kutta integration algorithm with adaptive stepsize control; and

(g-5) propagating said covariance error matrix of said backward state estimate by utilizing said time derivative of said covariance error matrix computed in said derivative system model computation in a backward prediction covariance update, using a factorized implementation.

9. The filtering process, as recited in claim 7, wherein said step (g) further comprise said steps of:

(g-1) computing said interval span between said last two consecutive reserved valid measurements so as to determine how long said backward time update propagates without a measurement update;

(g-2) receiving said system model and said derivative system model from a model selection, computing a system function and a Jacobian matrix at said forward state estimate obtained in forward filtering, and calculating a time derivative of said backward system state in a system model computation;

(g-3) receiving said derivative system model from said model selection and computing a time derivative of said covariance error matrix for said backward system state at said forward state estimate in a derivative system model computation;

(g-4) propagating said backward state estimate by utilizing said time derivative of said backward system state computed in said system model computation in a backward prediction update, using a Runge-Kutta integration algorithm with adaptive stepsize control; and

(g-5) propagating said covariance error matrix of said backward state estimate by utilizing said time derivative of said covariance error matrix computed in said derivative system model computation in a backward prediction covariance update, using a factorized implementation.

10. The filtering process, as recited in claim 6, wherein said step (h) further comprise said steps of:

(h-1) receiving said measurement model from said model selection and computing a predicted measurement at said forward state estimate in a measurement model computation;

(h-2) receiving said derivative measurement model from said model selection and computing a measurement Jacobian matrix at said forward state estimate in a derivative measurement model computation;

(h-3) updating said covariance error matrix of said backward system estimate using said backward measurement update equations in a backward estimate covariance update; and

(h-4) updating said backward state estimate by using said backward measurement update equations in a backward estimate update.

11. The filtering process, as recited in claim 7, wherein said step (h) further comprise said steps of:

(h-1) receiving said measurement model from said model selection and computing a predicted measurement at said forward state estimate in a measurement model computation;

(h-2) receiving said derivative measurement model from said model selection and computing a measurement Jacobian matrix at said forward state estimate in a derivative measurement model computation;

(h-3) updating said covariance error matrix of said backward system estimate using said backward measurement update equations in a backward estimate covariance update; and

(h-4) updating said backward state estimate by using said backward measurement update equations in a backward estimate update.

12. The filtering process, as recited in claim 8, wherein said step (h) further comprise said steps of:

(h-1) receiving said measurement model from said model selection and computing a predicted measurement at said forward state estimate in a measurement model computation;

(h-2) receiving said derivative measurement model from said model selection and computing a measurement Jacobian matrix at said forward state estimate in a derivative measurement model computation;

(h-3) updating said covariance error matrix of said backward system estimate using said backward measurement update equations in a backward estimate covariance update; and

(h-4) updating said backward state estimate by using said backward measurement update equations in a backward estimate update.

13. The filtering process, as recited in claim 9, wherein said step (h) further comprise said steps of:

(h-1) receiving said measurement model from said model selection and computing a predicted measurement at said forward state estimate in a measurement model computation;

(h-2) receiving said derivative measurement model from said model selection and computing a measurement Jacobian matrix at said forward state estimate in a derivative measurement model computation;

(h-3) updating said covariance error matrix of said backward system estimate using said backward measurement update equations in a backward estimate covariance update; and

(h-4) updating said backward state estimate by using said backward measurement update equations in a backward estimate update.