CN102999696A - Capacity information filtering-based pure direction tracking method of noise-related system - Google Patents

Capacity information filtering-based pure direction tracking method of noise-related system Download PDF

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CN102999696A
CN102999696A CN2012104547494A CN201210454749A CN102999696A CN 102999696 A CN102999696 A CN 102999696A CN 2012104547494 A CN2012104547494 A CN 2012104547494A CN 201210454749 A CN201210454749 A CN 201210454749A CN 102999696 A CN102999696 A CN 102999696A
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CN102999696B (en
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文成林
许大星
葛泉波
骆光州
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Hangzhou Dianzi University
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Hangzhou Dianzi University
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Abstract

The invention relates to a capacity information filtering-based pure direction tracking method of a noise-related system, which belongs to the field of target tracking. The conventional capacity kalman non-linear system target tracking method is implemented on hypothetic premise that process noise is not related to measurement noise, so that the use range of the method is greatly limited. According to the method, on premise that expanded kalman information filtering related to the noise is deducted, capacity kalman information filtering is embedded into two processes of time updating and measurement updating. The problem of noise relevance is solved, and therefore the practicability of the method provided by the invention is greatly improved.

Description

Noise correlation system is based on the pure orientation tracking of volume information filtering
Technical field
The invention belongs to target tracking domain, relate generally to noise correlation system based on the pure orientation method for tracking target of volume information filtering.
Background technology
It is a multidisciplinary interleaving techniques that sensor target is followed the tracks of.In recent years, along with the development of sensor technology, computer technology, the communication technology and the information processing technology, particularly military active demand, the research contents of Multi-Sensor Target tracking technique is day by day deeply with extensive.Be mainly used in the Command, Control, Communication And Intelligence system in military affairs, in fields such as robot, civil aviaton's aviation managements, significant application value arranged also simultaneously.At present target following there have been a lot of reasonable algorithms, as Kalman filtering algorithm (KF), Unscented kalman filtering algorithm (UKF), ask volume Kalman filtering algorithm (CKF) etc., yet well-known, these algorithms have very high computation complexity when all the sensors measured value arrival fusion center focuses on.So information filter has been carried out and has been widely used due to performance and the easily initialization more superior than Kalman filtering algorithm being arranged aspect calculating.In fact, the information filter algorithm is the Kalman filtering algorithm with the reciprocal representation of covariance matrix in essence.
Target tracking algorism latest developments about nonlinear filtering are volume information filtering algorithm (SCIF) at present, but because the prerequisite of this algorithm is to be incoherent between any noise, so greatly limited its range of application.Often due to weather, follow the tracks of same target in the middle of reality, same environment may be relevant between the reasons such as the asynchronous-sampling of multisensor, process noise and observation noise, and this has just limited the use of SCIF greatly.
Summary of the invention
In order to solve the relevant situation of noise, the present invention proposes noise correlation system based on the pure orientation tracking of volume information filtering, thereby reach the purpose of tracking target.Content of the present invention, at first the present invention is directed to the single-sensor goal systems and set up model for convenience of description, and it comprises 2 equations, and state equation and observation equation are as follows respectively:
(1)
Figure 2012104547494100002DEST_PATH_IMAGE004
(2)
Here
Figure 2012104547494100002DEST_PATH_IMAGE006
It is time index;
Figure 2012104547494100002DEST_PATH_IMAGE008
It is the state vector of system;
Figure 2012104547494100002DEST_PATH_IMAGE010
For state vector
Figure 2012104547494100002DEST_PATH_IMAGE012
Observation vector; With
Figure 2012104547494100002DEST_PATH_IMAGE016
It is all known differentiable function; Process noise
Figure 2012104547494100002DEST_PATH_IMAGE018
With the measurement noise Be the white Gaussian noise of zero-mean, their variance is respectively With
Figure 2012104547494100002DEST_PATH_IMAGE024
, and satisfy:
Figure 2012104547494100002DEST_PATH_IMAGE026
(3)
Be the Cross-covariance of process noise and observation noise, can find out that process noise is relevant to measuring noise, Be impulse function, namely
Figure 2012104547494100002DEST_PATH_IMAGE032
The time,
Figure 2012104547494100002DEST_PATH_IMAGE034
,
Figure 2012104547494100002DEST_PATH_IMAGE036
The time, We make original state be
Figure 2012104547494100002DEST_PATH_IMAGE040
, and its expectation value is
Figure 2012104547494100002DEST_PATH_IMAGE042
, make the covariance matrix of original state error be
Figure 2012104547494100002DEST_PATH_IMAGE044
, and satisfy
(4)
For above-described system model and starting condition, the present invention provides following iterative algorithm, specifically comprises 2 modules: the time upgrades (elder generation) and state upgrades (afterwards), thereby reach the purpose of tracking target.
1. the time upgrades
Step 1.1 is calculated respectively k-1 i volume point constantly
Figure 2012104547494100002DEST_PATH_IMAGE048
, k-1 is i propagation volume point constantly
Figure 2012104547494100002DEST_PATH_IMAGE050
Constantly one go on foot status predication with k-1
Figure 2012104547494100002DEST_PATH_IMAGE052
At first, can suppose k-1 state estimation constantly
Figure 2012104547494100002DEST_PATH_IMAGE054
With its covariance matrix
Figure 2012104547494100002DEST_PATH_IMAGE056
Known, decompose
Figure 127822DEST_PATH_IMAGE056
Have:
Figure 2012104547494100002DEST_PATH_IMAGE058
(5)
Wherein Be called k-1 evolution value constantly.
Secondly, calculate k-1 i propagation volume point constantly from (6) formula
Figure 948011DEST_PATH_IMAGE050
,
Figure 2012104547494100002DEST_PATH_IMAGE062
Figure 2012104547494100002DEST_PATH_IMAGE064
(6)
Wherein,
(7)
And
Figure 2012104547494100002DEST_PATH_IMAGE068
Here, It is a set
Figure 2012104547494100002DEST_PATH_IMAGE072
I column vector, if for example
Figure 2012104547494100002DEST_PATH_IMAGE074
, the set below its expression so:
Figure 2012104547494100002DEST_PATH_IMAGE076
At last, calculate the k-1 one-step prediction of state constantly:
Figure 2012104547494100002DEST_PATH_IMAGE078
(8)
Step 1.2 is calculated a k-1 step evolution constantly according to following formula
Figure 2012104547494100002DEST_PATH_IMAGE080
(9)
Here
Figure 2012104547494100002DEST_PATH_IMAGE084
Expression QRDecompose, the transposition of the upper triangular matrix that decomposition is obtained is assigned to
Figure 48298DEST_PATH_IMAGE080
, Be
Figure 2012104547494100002DEST_PATH_IMAGE088
Root, that is:
Figure 2012104547494100002DEST_PATH_IMAGE090
, and
Figure 2012104547494100002DEST_PATH_IMAGE092
(10)
Formula below step 1.3 is used obtains a k-1 step information matrix constantly
Figure 2012104547494100002DEST_PATH_IMAGE094
Order
Figure 2012104547494100002DEST_PATH_IMAGE096
(11)
Then utilize
Figure 2012104547494100002DEST_PATH_IMAGE098
Can obtain a k-1 step information matrix constantly
Figure 217942DEST_PATH_IMAGE094
Step 1.4 use formula (12) formula is calculated k-1 one-step prediction information state vector constantly
Figure 2012104547494100002DEST_PATH_IMAGE100
Figure 2012104547494100002DEST_PATH_IMAGE102
(12)
2. measure and upgrade
Step 2.1 is calculated respectively k-1 i step volume point constantly
Figure 2012104547494100002DEST_PATH_IMAGE104
, an i step propagated the volume point to k-1 constantly
Figure 2012104547494100002DEST_PATH_IMAGE106
With k-1 step observation prediction constantly
Figure 2012104547494100002DEST_PATH_IMAGE108
At first, calculate a k-1 step volume point constantly
Figure 216729DEST_PATH_IMAGE104
, be shown below:
(13)
And then can utilize following formula to calculate k-1 i step propagation volume point constantly,
Figure 2012104547494100002DEST_PATH_IMAGE112
(14)
Then, utilize formula (15) to calculate k-1 step observation prediction constantly
Figure 778291DEST_PATH_IMAGE108
,
Figure 2012104547494100002DEST_PATH_IMAGE114
(15)
Step 2.2 utilizes following formula to calculate k-1 Cross-covariance constantly
Figure 2012104547494100002DEST_PATH_IMAGE116
At first, calculate k-1 moment evolution according to following formula and newly cease covariance matrix
Figure 2012104547494100002DEST_PATH_IMAGE118
,
Figure 2012104547494100002DEST_PATH_IMAGE120
(16)
Wherein, Expression
Figure 240409DEST_PATH_IMAGE024
Evolution, as
Figure 2012104547494100002DEST_PATH_IMAGE124
Order
Figure 2012104547494100002DEST_PATH_IMAGE126
Then, utilize following formula to calculate k-1 Cross-covariance constantly
Figure 790077DEST_PATH_IMAGE116
Figure 2012104547494100002DEST_PATH_IMAGE128
(17)
Step 2.3 utilizes formula to calculate respectively k time information matrix
Figure 2012104547494100002DEST_PATH_IMAGE130
With the information state vector
Figure 2012104547494100002DEST_PATH_IMAGE132
Figure 2012104547494100002DEST_PATH_IMAGE134
(18)
Figure 2012104547494100002DEST_PATH_IMAGE136
(19)
Step 2.4 utilizes following formula to obtain k state estimation constantly
Figure DEST_PATH_IMAGE138
With corresponding covariance matrix
Figure DEST_PATH_IMAGE140
.
(20)
Constantly repeat the content of top 2 modules, just can realize dbjective state
Figure 777624DEST_PATH_IMAGE138
Tracking estimate.
Beneficial effect of the present invention:
The method for tracking target that the present invention proposes, utilize volume information filtering to solve the correlativity of noise in upgrading and measure renewal in the time, thereby this method can also can well be followed the tracks of pure orientation target under the process noise condition relevant to measuring noise.
Description of drawings
Fig. 1 is the process flow diagram of tracking of the present invention;
Fig. 2 is the pure azimuth follow up system figure in the present invention;
Fig. 3 A is that emulation of the present invention is at the tracking effect figure of directions X (due east direction);
Fig. 3 B is that emulation of the present invention is at the tracking effect figure of Y-direction (direct north);
Fig. 3 C is that emulation of the present invention is at the tracking error figure of directions X (due east direction);
Fig. 3 D is that emulation of the present invention is at the tracking error figure of directions X (due east direction).
Embodiment
Implementing procedure figure of the present invention as shown in Figure 1, embodiment is as follows:
In order to solve the relevant situation of noise, the present invention proposes volume information wave filter (SCIF-CN) method for designing under the noise correlated condition, thereby reach the purpose of tracking target.Content of the present invention, at first the present invention is directed to the single-sensor goal systems and set up model for convenience of description, and it comprises 2 equations, and state equation and observation equation are as follows respectively:
Figure DEST_PATH_IMAGE143
(1)
(2)
Here
Figure DEST_PATH_IMAGE006A
It is time index;
Figure 438150DEST_PATH_IMAGE008
It is the state vector of system;
Figure 578276DEST_PATH_IMAGE010
For state vector Observation vector;
Figure 71891DEST_PATH_IMAGE014
With
Figure 429053DEST_PATH_IMAGE016
It is all known differentiable function; Process noise
Figure 610635DEST_PATH_IMAGE018
With the measurement noise Be the white Gaussian noise of zero-mean, their variance is respectively
Figure 841076DEST_PATH_IMAGE022
With
Figure 469504DEST_PATH_IMAGE024
, and satisfy:
Figure 505593DEST_PATH_IMAGE026
(3)
Be the Cross-covariance of process noise and observation noise, can find out that process noise is relevant to measuring noise,
Figure 627188DEST_PATH_IMAGE030
Be impulse function, namely
Figure 996989DEST_PATH_IMAGE032
The time, ,
Figure 825585DEST_PATH_IMAGE036
The time,
Figure 434421DEST_PATH_IMAGE038
We make original state be , and its expectation value is
Figure 664600DEST_PATH_IMAGE042
, make the covariance matrix of original state error be
Figure 694872DEST_PATH_IMAGE044
, and satisfy
Figure 604054DEST_PATH_IMAGE046
(4)
For above-described system model and starting condition, the present invention provides following iterative algorithm, specifically comprises 2 modules: the time upgrades (elder generation) and state upgrades (afterwards), thereby reach the purpose of tracking target.
1. the time upgrades
Step 1.1 is calculated respectively k-1 i volume point constantly , k-1 is i propagation volume point constantly
Figure 508742DEST_PATH_IMAGE050
Constantly one go on foot status predication with k-1
Figure 959184DEST_PATH_IMAGE052
At first, can suppose k-1 state estimation constantly
Figure 277032DEST_PATH_IMAGE054
With its covariance matrix
Figure 854644DEST_PATH_IMAGE056
Known, decompose
Figure 652967DEST_PATH_IMAGE056
Have:
Figure 962726DEST_PATH_IMAGE058
(5)
Wherein
Figure 830188DEST_PATH_IMAGE060
Be called k-1 evolution value constantly.
Secondly, calculate k-1 i propagation volume point constantly from (6) formula
Figure 883594DEST_PATH_IMAGE050
, (
Figure 40818DEST_PATH_IMAGE062
)
Figure 583795DEST_PATH_IMAGE064
(6)
Wherein,
Figure 141815DEST_PATH_IMAGE066
(7)
And
Figure 546383DEST_PATH_IMAGE068
Here
Figure 568566DEST_PATH_IMAGE070
It is a set
Figure 220127DEST_PATH_IMAGE072
I column vector, if for example
Figure 311448DEST_PATH_IMAGE074
, the set below its expression so:
Figure 768975DEST_PATH_IMAGE076
At last, calculate the k-1 one-step prediction of state constantly:
Figure 583347DEST_PATH_IMAGE078
(8)
Step 1.2 is calculated a k-1 step evolution constantly according to following formula
Figure 218859DEST_PATH_IMAGE080
(9)
Here
Figure 58693DEST_PATH_IMAGE084
Expression QRDecompose, the transposition of the upper triangle after decomposing is assigned to
Figure 727572DEST_PATH_IMAGE080
,
Figure 783253DEST_PATH_IMAGE086
Be
Figure 350632DEST_PATH_IMAGE088
Root, that is:
Figure 353223DEST_PATH_IMAGE090
, and
(10)
Formula below step 1.3 is used obtains a k-1 step information matrix constantly
Figure 103190DEST_PATH_IMAGE094
Order
Figure 656400DEST_PATH_IMAGE096
(11)
Then utilize
Figure 259419DEST_PATH_IMAGE098
Can obtain a k-1 step information matrix constantly
Figure 637311DEST_PATH_IMAGE094
Step 1.4 use formula (12) formula is calculated k-1 one-step prediction information state vector constantly
Figure 51106DEST_PATH_IMAGE100
(12)
2. measure and upgrade
Step 2.1 is calculated respectively k-1 i step volume point constantly
Figure 921159DEST_PATH_IMAGE104
, an i step propagated the volume point to k-1 constantly
Figure 459282DEST_PATH_IMAGE106
With k-1 step observation prediction constantly
At first, calculate a k-1 step volume point constantly , be shown below:
Figure 939439DEST_PATH_IMAGE110
(13)
And then can utilize following formula to calculate k-1 i step propagation volume point constantly,
Figure 291923DEST_PATH_IMAGE112
(14)
Then, utilize formula (15) to calculate k-1 step observation prediction constantly
Figure 608373DEST_PATH_IMAGE108
,
Figure 108624DEST_PATH_IMAGE114
(15)
Step 2.2 utilizes following formula to calculate k-1 Cross-covariance constantly
Figure 607870DEST_PATH_IMAGE116
At first, calculate k-1 moment evolution according to following formula and newly cease covariance matrix
Figure 814860DEST_PATH_IMAGE118
,
Figure 990627DEST_PATH_IMAGE120
(16)
Wherein,
Figure 915857DEST_PATH_IMAGE122
Expression
Figure 451750DEST_PATH_IMAGE024
Evolution, as
Figure 841143DEST_PATH_IMAGE124
Order
Figure 859914DEST_PATH_IMAGE126
Then, utilize following formula to calculate k-1 Cross-covariance constantly
Figure 85491DEST_PATH_IMAGE116
(17)
Step 2.3 utilizes formula to calculate respectively k time information matrix
Figure 357389DEST_PATH_IMAGE130
With the information state vector
Figure 124225DEST_PATH_IMAGE132
Figure 758469DEST_PATH_IMAGE134
(18)
Figure 386897DEST_PATH_IMAGE136
(19)
Step 2.4 utilizes following formula to obtain k state estimation constantly
Figure 501614DEST_PATH_IMAGE138
With corresponding covariance matrix
Figure 127768DEST_PATH_IMAGE140
.
Figure 311624DEST_PATH_IMAGE142
(20)
Constantly repeat the content of top 2 modules, just can realize dbjective state
Figure 681426DEST_PATH_IMAGE138
Tracking estimate.
Methods experiment
In this test, we adopt above-mentioned algorithm to carry out the target following estimation to pure azimuth system.For better this experiment of explaination, at first the parameters in Fig. 2 is explained:
Figure DEST_PATH_IMAGE146
With 2 sensors, Be the observation angle of these two sensors,
Figure DEST_PATH_IMAGE152
Be the coordinate position of sensor, It is the distance of two sensors.In this experiment, target has 4 states, namely
Figure DEST_PATH_IMAGE156
, With Be target at the position coordinates of due east direction and direct north,
Figure DEST_PATH_IMAGE162
With
Figure DEST_PATH_IMAGE164
That target is in the velocity magnitude of due east direction and direct north.If target is done linear uniform motion, state equation is:
Figure DEST_PATH_IMAGE166
, observation equation is:
Figure DEST_PATH_IMAGE168
, this experiment parameter arranges as follows:
Figure DEST_PATH_IMAGE170
,
Figure DEST_PATH_IMAGE172
Be the fusion cycle of Target Tracking System, arrange
Figure DEST_PATH_IMAGE174
,
The process noise covariance matrix
Figure DEST_PATH_IMAGE176
,
Original state and covariance matrix are respectively:
Figure DEST_PATH_IMAGE178
For the display noise correlativity, we use Produce observation noise, wherein
Figure DEST_PATH_IMAGE182
Be noise correlation coefficients, arrange here
Figure DEST_PATH_IMAGE184
Fig. 3 A is the state estimation tracking effect figure to directions X, in figure X-Displacement be target in the state position of directions X, the curve of tracking SCIF-CN of the present invention overlaps with the state of target at directions X substantially, tracking effect is fine.
Fig. 3 B is the state estimation tracking effect figure to Y-direction, in figure Y-Displacement be target in the state position of Y-direction, the curve of tracking SCIF-CN of the present invention overlaps with the state of target in Y-direction substantially, tracking effect is fine.
Fig. 3 C is the error that tracking SCIF-CN of the present invention follows the tracks of Target state estimator at directions X, and its error is shaken in 2.5 left and right, and error is in actual allowed band.
Fig. 3 D is the error that tracking SCIF-CN of the present invention follows the tracks of Target state estimator in Y-direction, and its error is shaken in 1.2 left and right, and error is in actual allowed band.

Claims (1)

1. noise correlation system based on the pure orientation tracking of volume information filtering, is characterized in that:
Set up model for the single-sensor goal systems, it comprises 2 equations, and state equation and observation equation are as follows respectively:
Figure 2012104547494100001DEST_PATH_IMAGE002
(1)
Figure 2012104547494100001DEST_PATH_IMAGE004
(2)
Here
Figure 2012104547494100001DEST_PATH_IMAGE006
It is time index;
Figure 2012104547494100001DEST_PATH_IMAGE008
It is the state vector of system;
Figure 2012104547494100001DEST_PATH_IMAGE010
For state vector
Figure 2012104547494100001DEST_PATH_IMAGE012
Observation vector; With It is all known differentiable function; Process noise
Figure 2012104547494100001DEST_PATH_IMAGE018
With the measurement noise
Figure 2012104547494100001DEST_PATH_IMAGE020
Be the white Gaussian noise of zero-mean, their variance is respectively
Figure 2012104547494100001DEST_PATH_IMAGE022
With , and satisfy:
Figure DEST_PATH_IMAGE026
(3)
Figure 2012104547494100001DEST_PATH_IMAGE028
Be the Cross-covariance of process noise and observation noise, can find out that process noise is relevant to measuring noise,
Figure 2012104547494100001DEST_PATH_IMAGE030
Be impulse function, namely
Figure 2012104547494100001DEST_PATH_IMAGE032
The time,
Figure DEST_PATH_IMAGE034
,
Figure DEST_PATH_IMAGE036
The time,
Figure DEST_PATH_IMAGE038
Make original state be
Figure 2012104547494100001DEST_PATH_IMAGE040
, and its expectation value is
Figure 2012104547494100001DEST_PATH_IMAGE042
, make the covariance matrix of original state error be
Figure 2012104547494100001DEST_PATH_IMAGE044
, and satisfy
Figure 2012104547494100001DEST_PATH_IMAGE046
(4)
For above-described system model and starting condition, provide following iterative algorithm, specifically comprise 2 modules: the time upgrades and state upgrades, thereby reaches the purpose of tracking target;
(1). the time upgrades
Step 1.1 is calculated respectively k-1 i volume point constantly
Figure 2012104547494100001DEST_PATH_IMAGE048
, k-1 is i propagation volume point constantly
Figure 2012104547494100001DEST_PATH_IMAGE050
Constantly one go on foot status predication with k-1
At first, can suppose k-1 state estimation constantly
Figure 2012104547494100001DEST_PATH_IMAGE054
With its covariance matrix
Figure 2012104547494100001DEST_PATH_IMAGE056
Known, decompose Have:
Figure 2012104547494100001DEST_PATH_IMAGE058
(5)
Wherein
Figure 2012104547494100001DEST_PATH_IMAGE060
Be called k-1 evolution value constantly;
Secondly, calculate k-1 i propagation volume point constantly from (6) formula
Figure 948864DEST_PATH_IMAGE050
,
Figure 2012104547494100001DEST_PATH_IMAGE062
Figure 2012104547494100001DEST_PATH_IMAGE064
(6)
Wherein,
(7)
And
Figure 2012104547494100001DEST_PATH_IMAGE068
Here
Figure 2012104547494100001DEST_PATH_IMAGE070
It is a set
Figure DEST_PATH_IMAGE072
I column vector;
At last, calculate the k-1 one-step prediction of state constantly:
Figure DEST_PATH_IMAGE074
(8)
Step 1.2 is calculated a k-1 step evolution constantly according to following formula
Figure DEST_PATH_IMAGE076
Figure DEST_PATH_IMAGE078
(9)
Here
Figure DEST_PATH_IMAGE080
Expression QRDecompose, the transposition of the upper triangular matrix that decomposition is obtained is assigned to
Figure 988059DEST_PATH_IMAGE076
, Be
Figure DEST_PATH_IMAGE084
Root, that is:
Figure DEST_PATH_IMAGE086
, and
Figure DEST_PATH_IMAGE088
(10)
Formula below step 1.3 is used obtains a k-1 step information matrix constantly
Figure DEST_PATH_IMAGE090
Order (11)
Then utilize
Figure DEST_PATH_IMAGE094
Can obtain a k-1 step information matrix constantly
Step 1.4 use formula (12) formula is calculated k-1 one-step prediction information state vector constantly
Figure DEST_PATH_IMAGE096
Figure DEST_PATH_IMAGE098
(12)
(2). measure and upgrade
Step 2.1 is calculated respectively k-1 i step volume point constantly , an i step propagated the volume point to k-1 constantly
Figure DEST_PATH_IMAGE102
With k-1 step observation prediction constantly
Figure DEST_PATH_IMAGE104
At first, calculate a k-1 step volume point constantly
Figure 779090DEST_PATH_IMAGE100
, be shown below:
(13)
And then can utilize following formula to calculate k-1 i step propagation volume point constantly,
(14)
Then, utilize formula (15) to calculate k-1 step observation prediction constantly
Figure 622412DEST_PATH_IMAGE104
,
Figure DEST_PATH_IMAGE110
(15)
Step 2.2 utilizes following formula to calculate k-1 Cross-covariance constantly
At first, calculate k-1 moment evolution according to following formula and newly cease covariance matrix ,
Figure DEST_PATH_IMAGE116
(16)
Wherein,
Figure DEST_PATH_IMAGE118
Expression
Figure 160622DEST_PATH_IMAGE024
Evolution;
Order
Figure DEST_PATH_IMAGE120
Then, utilize following formula to calculate k-1 Cross-covariance constantly
Figure 747592DEST_PATH_IMAGE112
Figure DEST_PATH_IMAGE122
(17)
Step 2.3 utilizes formula to calculate respectively k time information matrix
Figure DEST_PATH_IMAGE124
With the information state vector
Figure DEST_PATH_IMAGE126
Figure DEST_PATH_IMAGE128
(18)
Figure DEST_PATH_IMAGE130
(19)
Step 2.4 utilizes following formula to obtain k state estimation constantly
Figure DEST_PATH_IMAGE132
With corresponding covariance matrix
Figure DEST_PATH_IMAGE136
(20)
Constantly repeat the content of top 2 modules, just can realize dbjective state
Figure 862048DEST_PATH_IMAGE132
Tracking estimate.
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