US 7,605,747 B1 · Method for compensating for the positional errors of a sensor

Abstract

A method for determining or compensating for the positional errors of a sensor tracking a target comprises the steps of operating the sensor to generate sensed information relating to the target and adding any sensor positional bias update information to produce updated sensed information. The target state is propagated to produce time updated state estimates. The Jacobian of the state dynamics and the state transition matrix for the extended Kalman filter algorithm are computed. The covariance of a state vector is time propagated using the state transition matrix.

Claims9

Dependent claims

A method for compensating for the positional errors of a sensor tracking a target with known acceleration, said method comprising the steps of:

operating said sensor to generate sensed information relating to the target;
adding to said sensed information any sensor positional bias update information to produce updated sensed information which ultimately provides improved target state information;
propagating the target state to produce time updated state estimates comprising the target position and velocity and the positional bias of the sensor;
computing the Jacobian of the state dynamics vector of the target;
computing, from said Jacobian, the state transition matrix for the extended Kalman filter algorithm;
and
using said state transition matrix, time propagating the covariance of a state vector comprising the position and velocity states of said target and the positional bias of the sensor.

4 more elements

A method for compensating for the positional errors of a sensor tracking a target with known acceleration, said method comprising the steps of:

defining the estimator state given by
s
_
=
{
X
_
X
_
.
δ
⁢
X
_
}
comprising the target position X and velocity X and the positional bias δX of the sensor;
operating said sensor to generate sensed information Z relating to the target according to Z=L+X where L is the location of the reporting sensor;
adding to said sensed information any sensor positional bias update information Δ{tilde over (X)}=Δ{circumflex over (X)}+δ{circumflex over (X)}, where Δ{circumflex over (X)} is the position bias estimate from the previous cycle, Δ{tilde over (X)} is the position bias estimate from the current cycle, and δ{circumflex over (X)} is the position bias error estimate, where the tilde ˜ represents the update and the caret ^ represents an estimate, to produce updated sensed information which ultimately provides improved target state estimates;
propagating from the previous time ti−1 to the current time ti where the subscript i refers to the filter cycle iteration to produce time updated state estimates according to
s
_
^
⁡
(
t
i
)
=
s
_
^
⁡
(
t
i
-
1
)
+
∫
t
i
-
1
t
i
-
1
+
Δ
⁢
⁢
t
⁢
s
_
.
^
⁡
(
τ
)
⁢
⁢
ⅆ
τ
;
computing the Jacobian of the state dynamics of the target according to
J
=
[
∂
s
_
.
∂
s
_
]
=
[
∂
s
_
.
∂
X
_
⁢
∂
s
_
.
∂
X
_
.
⁢
∂
s
_
.
∂
δ
⁢
X
_
]
=
[
0
3
×
3
I
3
×
3
0
3
×
3
∂
X
¨
_
∂
X
_
∂
X
_
¨
∂
X
_
.
∂
X
_
¨
∂
δ
⁢
X
_
0
3
×
3
0
3
×
3
0
3
×
3
]
where
∂
X
¨
_
∂
X
_
=
-
μ
(
Z
_
^
·
Z
_
^
)
3
2
⁡
[
I
3
×
3
-
3
(
Z
_
^
·
Z
_
^
)
⁡
[
Z
_
^
·
Z
_
^
T
]
]
-
〚
ω
_
^
〛
·
〚
ω
_
^
〛
∂
X
_
¨
∂
X
_
.
=
-
2
·
〚
ω
_
^
〛
∂
X
_
¨
∂
δ
⁢
X
_
=
0
3
×
3
and the [[·]] notation denoting a skew symmetric matrix of the vector argument;
computing, from said Jacobian, the state transition matrix for the extended Kalman filter algorithm
Φ≈I+JΔt+0.5J2Δt2;
and
using said state transition matrix, time propagating the covariance of a state vector comprising the position and velocity states of said target and the positional bias of the sensor given by
P(ti)=ΦP(ti−1)ΦT+Q,
where Q is the state noise matrix.

257 more elements

Dependencies are inferred from the claim text.

Abstract

Method for compensating for the positional errors of a sensor

Life of this patent

Abstract

Claims9

Method for compensating for the positional errors of a sensor

Life of this patent

Abstract

Claims9