Information processing unit, information processing method,...

Details Information processing unit, information processing method,... Information processing unit, information processing method,...

1999-11-23

2003-12-30

Kelley, Chris (Department: 2613)

Pulse or digital communications

Bandwidth reduction or expansion

Television or motion video signal

Reexamination Certificate

active

06671317

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to information processing units, information processing methods, and recording media therewith. More particularly, the present invention relates to an information processing unit, an information processing method, and a recording medium therewith, for accurately predicting subsequent motion by storing motion information and torque information in advance and predicting the subsequent motion based on the stored motion information and torque information.
2. Description of the Related Art
Hitherto, conventional systems for measuring or estimating motion parameters of an object based on an input of an image or a sensor output fail to accurately estimate these parameters due to noise included in the input data and the inadequacy of data relative to the parameters to be estimated.
To this end, Kalman filters described in “A New Approach to Linear Filtering and Prediction Problems” by R. E. Kalman, Trans. ASME-J. Basic Eng., pp. 35-45 March 1960, or recursive estimation filters derived from the Kalman filters have been used.
In linear systems, Kalman filters are often used as the recursive estimation filters. In nonlinear systems, extended Kalman filters (hereinafter referred to as “EKF”) are the most popular. The EKF is described in “Applied Optimal Estimation” by A. Gelb, The Analytic Science Corp., 1974. Other applications of Kalman filters include unscented filters described in “A New Extension of the Kalman Filter to Nonlinear Systems” by S. J. Julier, Proc. of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Control, and pseudo-Kalman filters described in “Using Pseudo Kalman Filters in the Presence of Constraints, Application to Sensing Behaviours” by T. Vileville and P. Sander, Technical Report 1669, INRIA-Sophia, Valbonne, France, 1992.
FIG. 11
is a block diagram of a Kalman filter
120
. The Kalman filter
120
employs an efficient least-square method. The Kalman filter
120
estimates states in the past, present, and future. The Kalman filter
120
is capable of estimating state variables based on incomplete information. In addition to the state variables to be estimated, the Kalman filter
120
updates simultaneously error covariance indicating estimation accuracy. Use of the Kalman filter
120
is known as a robust estimation method.
The Kalman filter
120
is one of the recursive estimation filters. The Kalman filter
120
always exclusively uses the most recent data from observed values input in series. The Kalman filter
120
includes a predicting unit
131
for predicting motion and an updating unit
132
for updating the predicted data. Estimation is carried out by alternatively repeating prediction and updating of the data by, respectively, the predicting unit
131
and the updating unit
132
.
Referring to
FIG. 12
, operation of the Kalman filter
120
is described. A set of state variables to be estimated is defined as a state vector x. When the number of the state variables is n, the state vector x is n-dimensional. A k-th cycle (one cycle corresponds to one observation cycle) state vector x is expressed by a state vector X
k
. A prediction process for predicting a subsequent state is expressed by an expression (1). In expressions illustrated hereinafter, a vector is expressed with an arrow at the top thereof; a first order time differential of a vector is indicated by a dot ({dot over ( )}) at the top thereof; and a second order time differential is indicated by two dots at the top ({dot over ( )}) thereof:
{right arrow over (x
k+1
)}=
A
k
{right arrow over (x
k
)}+
{right arrow over (w
k
)}
  (1)
In the above expression, a matrix A
k
is the k-th cycle state transition matrix with n rows and n columns. w
k
represents prediction process noise generated in the prediction process. It is assumed that w
k
is normally distributed Gaussian noise.
An observation process is expressed by an expression (2):
{right arrow over (y
k
)}=
H
k
{right arrow over (x
k
)}+
{right arrow over (v
k
)}
  (2)
The covariance matrix of the process noise generated in the process shown by the expression (1) is expressed by Q
k
.
In the expression (2), y
k
indicates an observation vector representing a set of the k-th cycle observed values, and H
k
represents the k-th cycle observation matrix. The observation vector y
k
does not necessary have the same number of dimensions as the state vector. If the observation vector y
k
is assumed to be m-dimensional, the observation matrix H
k
has m rows and n columns. v
k
represents a vector of observation noise generated in the observation process, which is assumed to be Gaussian noise. The covariance matrix of the observation noise is expressed by R
k
.
The Kalman filter
120
performs estimation through repetitions of predicting and updating. The estimated state vector before the updating is expressed by an expression (3), and the estimated state vector after the updating is expressed by an expression (4):
{right arrow over (X
{overscore (k)})}
  (3)
{right arrow over (X
k
)}
  (4)
Let P
k
represent the estimated error covariance after the updating. The estimated error covariance before the updating is expressed by an expression (5):
P
−
k
  (5)
Assuming the above, processing of the predicting unit
131
is described. As shown in
FIG. 12
, the predicting unit
131
performs process e
1
to predict the next state based on an expression (6):
{right arrow over (X
{overscore (k)})}+
1=
A
k
{right arrow over (X
k
)}
  (6)
The predicting unit
131
performs process e
2
to predict the next estimated error covariance P
−
k+1
based on an expression (7):
 
P
−
k+1
=A
k
P
k
A
k
T
+Q
k
  (7)
In the above expression, A
k
T
represents a transposed matrix of the state transition matrix A
k
.
Next, processing of the updating unit
132
is described. The updating unit
132
performs process c
1
to compute a Kalman gain K
k
based on an expression (8):
K
k
=P
−
k
H
k
T
(
H
k
P
−
k
H
k
T
+R
k
)
−1
  (8)
In the above expression, H
k
T
represents a transposed matrix of the observation matrix H
k
, and ( )
−1
represents an inverse matrix of the matrix within the parentheses ( ).
The updating unit
132
performs process c
2
to update the estimated value of the state variable based on the input observed value using an expression (9):
{right arrow over (X
k
)}=
{right arrow over (X
{overscore (k)})}
+
K
k
(
{right arrow over (y
k
)}−
H
k
{right arrow over (X
{overscore (k)})}
)  (9)
The updating unit
132
performs process c
3
to update the estimated error covariance P
k
based on an expression (10):
P
k
=(
I−K
k
H
k
)
P
−
k
  (10)
In the above expression, I represents a unit matrix that has n×n dimensions.
The above-described Kalman filter
120
assumes that both the prediction process and the observation process are linear. In practice, however, the prediction process and the observation process are often nonlinear. To accommodate such nonlinear processes, various types of derived filters including the EKF have been proposed. The EKF, which is most commonly used, is described below.
The EKF expresses a prediction process as an expression (11) (corresponding to the expression (1) of the Kalman filter
120
), and an observation process as an expression (12) (corresponding to the expression (2) of the Kalman filter
120
):
{right arrow over (x
k+1
)}=
f{right arrow over ((x
k
))}+
{right arrow over (w
k
)}
  (11)
{right arrow over (y
k
)}=
h{right arrow over ((x
k
))}+
{right arrow over (v
k
)}
  (12)
In the expression (11), f represents a nonlinear state transition matrix. In the expression (12), h represents a nonlinear observation matrix.
In the EKF, the actual estimation framework is expressed by an expression (13) which

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