location forum 2006, 7 november, 2006 school of surveying & spatial information systems the...

School of Surveying & Spatial Information SystemsThe University of New South Wales, Australia

Location Forum 2006, 7 November, 2006

Adaptive Kalman Filtering for Adaptive Kalman Filtering for GPS/INS IntegrationGPS/INS Integration

Weidong Ding

This research is supported by the Australian Cooperative Research Centre for Spatial Information (CRC-SI) under project 1.3

‘Integrated positioning and geo-referencing platform’.


School of Surveying and Spatial Information Systems Location Forum 2006, 7 November, 2006

2 presented by Weidong Ding

GPS/INS integrationGPS/INS integration Surveying, navigation, location based

services, etc. Solution of position & attitude Long term accuracy, high update rate,

robustness, INS calibration




Limitations of Kalman FilterLimitations of Kalman Filter Wrong parameters of system models and noise

properties may result in the filter being suboptimal or even cause it to diverge.

0 10 20 30 40 50 60-40

-20

0

20

40

60

80

100

Time (sec)

Pos

itio

n (

m)

Kalman Filter Performance

ReferenceMeasurementEstimated

0 10 20 30 40 50 60-40

-20

0

20

40

60

80

Time (sec)

Pos

itio

n (

m)



0 10 20 30 40 50 60-40

-20

0

20

40

60

80

100

Time (sec)

Pos

ition

(m

)






Adaptive Kalman FilterAdaptive Kalman Filter Covariance scaling method

• By applying a scale factor to the predicted state covariance matrix to deliberately decrease the weight of the state prediction, to improve KF stableness.

Multi-model adaptive estimation• A group of KF filters; each has slightly different configurations.• The output is the optimal combination of the outputs from

individual filters. Adaptive stochastic modelling (Innovation based,

Residual based)• Uncertain stochastic modelling parameters are estimated on-line

using the covariance information of the KF innovation and residual series.

A new process noise scaling method is proposed.




Results of on-line stochastic modelingResults of on-line stochastic modeling

0 200 400 600 800 10000

0.05

0.1

0.15

0.2

0.25

0.3

epoch

met

er

=128=256=384=512=640

0 200 400 600 800 10000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

epoch

met

er

=128=256=384=512=640

0 200 400 600 800 10000

0.05

0.1

0.15

0.2

0.25

0.3

epoch

met

er

=0.01=0.03=0.1

128 256 384 512 6400.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

ST

D

Window size for R estimation

NorthEastDown




Results using process noise scalingResults using process noise scaling

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

1.2

1.4

Epoch

RM

S o

f po

sitio

n er

ror

in m

XYZ

0 200 400 600 800 10000

1

2

3

4

5

6

7

8

9

10

11

12

EpochS

cale

fa

ctor

0 200 400 600 800 1000-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Epoch

KF

Re

sidu

als

in m

XYZ

-1000 -500 0 500 1000-1

-0.5

0

0.5

1

1.5

2

2.5

3x 10-3

Lags

Au

toco

rrel

atio

n fu

nctio

n

0 200 400 600 800 1000-0.05

0

0.05

0.1

0.15

Epoch

Acc

bia

s in

m/s

/s

XYZ

0 200 400 600 800 1000-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

Epoch

Gyr

o b

ias

in d

eg/s

XYZ




SummarySummary• The online stochastic modelling method can estimate the

individual elements of noise covariance matrix. However, it is vulnerable to the innovation and residual covariance estimation biases, and is not scalable to a large number of parameters.

• The covariance scaling method is more robust and suitable for practical implementations. The proposed covariance based adaptive process noise scaling method has demonstrated significant improvements on the filtering performance in the test.

• Optimal allocation of noise to each individual source is not possible using scaling factor methods, which is a topic for further investigation.

location forum 2006, 7 november, 2006 school of surveying & spatial information systems the...

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