30.5.2012

1

SIMA – Raw Data Simulation Software for the Development and Validation of Algorithms for GNSS and MEMS based Multi‐Sensor Navigation 

Platforms 

30.05.2012 Seite 1

Andreas Hoscislawski

HS‐Karlsruhe, Germany

FIG working week 2012 ‐ Rome

NAVIGATION STATE & FRAMES

30.05.2012 Seite 2

t B, L, h | v , v , v | r, p, yNavigation state vector:

xn

yn

zn

xb

yb

zb

y

zb

yb

xb

Body

position (B,L,h) + velocity ( , , ) + orientation (r,p,y)

30.5.2012

2

SENSORS FOR ROBUST AND GLOBAL APPLICATIONS

30.05.2012

References: Inertial Space and Gravity Field

1.) GNSS

2.) Accelerometers

3.) Gyroscopes

4.) Magnetic field sensors

5.) Inclinometers

References: Inertial Space 

References: Earth Magnetic Field

References: Gravity Field

References: Inertial Space or e‐frame 

Seite 3

SENSOR CONCEPT FOR STATE ESTIMATION

30.05.2012 Seite 4

General concept for robust algorithms & sensor simulation:

„Multiplatform‐“(several platforms (p) navigate one body (b))

and„Multisensor‐Leverarm‐“ – Concept

(several coordinated sensors on each platform)

30.5.2012

3

SIMA: SIMULATION OF MULTISENSOR ARRAYS

• Numerical comparison of optimized sensor platforms

• Numerical proof of functionality of new platforms

– with redundant sensors

– with sensors in motion

• Further system tests:

– Can additional parameters be estimated?

– Filter reaction on gross errors?

– Filter reactions on different trajectories?

• Simplified implementation because true numerical values are known

• Reference state known from trajectory model

30.05.2012 Seite 5

SIMA LEVER ARM CONCEPT & PARAMETRIZATION

30.05.2012 Seite 6

Xe

Ye

Ze

Yp

Xp

Zp

Ys

Xs

Zs

t(t) esensor

sensitive axisof sensor j

platform i

body

x(t)ebody

x(t)esensor

t eplat

t t t,

5 LA‐parameter sensor j

, α, δ,

6 LA‐parameter platform i

, , , ε , ε , ε

30.5.2012

4

SIMA LEVER ARM CONCEPT & M‐FRAME

Xe

Ye

Ze

Yp

Xp

Zp

Ys

Xs

Zs

t(t) ssensor

sensitive axisof sensor j

platform i

body

x(t)mbody

x(t)esensor

t pplat

t _ t t t,

Xm

Zmx

eorigin m‐frame

Seite 7

tt t

t

,

.

LEVER ARM CONCEPT – SENSOR VELOCITY & ACCELERATION

Seite 8

tt t

t

,

constant

constant

, , , , , , , , , , , , ,

Necessary parameters for observation modeling:

30.5.2012

5

TRAJECTORY GENERATION

• Trajectory parameters: 

• Standard models: straight line, circle, helix, in rest, rotating, 2D‐trajectory

• Example: Body orientation in a circle

30.05.2012 Seite 9

t t t t t t

y t atanv  

v

v =cos(v t / R)

v sin vt/R v

GNSS OBSERVATIONS

• GNSS position

• GNSS velocity

30.05.2012 Seite 10

t t t,

, ,

t t

t,

, ,

constant I

constant

30.5.2012

6

l , , , , , c Δt , Δt , λ N λ D,

ΔIon ΔTrop

GNSS OBSERVATIONS

• Raw data observation equations:

– pseudorange

– phase

– Doppler

30.05.2012 Seite 11

, , , , c Δt , Δt , ,ΔIon ΔTrop

l , f 1 ,

cf

,

sX

sY

sZ

ACCELEROMETER OBSERVATIONS

• Navigation equation in the inertial frame:

• Navigation equation in the earth frame:

• Rotation to the s‐frame:

• Adding sensor errors:

30.05.2012 Seite 12

t2 .

a , 1 0 0 ∙

l , a , ∙ κ b n .

t

30.5.2012

7

• Gyro observation model:

• for one sensor j on platform i:

• Adding sensor errors:

GYROSCOPE OBSERVATIONS

30.05.2012 Seite 13

.

.

ω , 1 0 0 ∙ .

l,

ω , ∙ κ b n .

ωsis, y

ωsis, z

ωsis, x

MEMS3D‐Gyroskop22 x 22 mm

MAGNETIC FIELD OBSERVATIONS

• Magnetic field observation:

• World Magnetic Model 2010 from NOAA (National Oceanic andAtmospheric Administration) & BGS (British Geological Survey):

• for one sensor j on platform i:

• Error model:

30.05.2012 Seite 14

, t

m,

1 0 0 ∙

l,

m,

n .

30.5.2012

8

• Observation equation inclinometer:

• Rotation of sensitive axis in s‐frame to LAV:

• Adding sensor errors:

INCLINOMETER OBSERVATIONS

30.05.2012 Seite 15

θ , cos

0 0 1

1 0 0

,

l θ c n , .

direction of gravity:

SIMA – GUI

30.05.2012 Seite 16

30.5.2012

9

EXAMPLE – ATTITUDE HEADING REFERENCE SYSTEM

• Navigation state vector

• Trajectory: Body rotates in rest

• Accelerometer biases:

30.05.2012 Seite 17

t , ,

1.0 2.0 3.0

0,0

10.0 20.0 30.0

EXAMPLE – ATTITUDE HEADING REFERENCE SYSTEM

30.05.2012 Seite 18

Kalmal filtered pitch angle: Kalmal filtered accelerometer biases

30.5.2012

10

CONCLUSION

• SIMAs features:

– arbitrary number of different types of sensors

– freely open platform design  

– consideration of the lever‐arm effects

– modeling of sensorerrors

– different trajectories

– known reference data for filter validation

• Perspective:

– enhanced error modeling

– adding additional trajectories

– …

30.05.2012 Seite 19

Thank you for your attention!

www.navka.de

30.05.2012 Seite 20

SIMA available at:

30.5.2012

11

ENHANCED NAVIGATION‐ALGORITHMS

• Platform optimization in a similar manner as in the conventionalclassification in the optimization of geodetical nets:

– design of 0th order: choise of the appropriate sensor type

– design of 1th order: choice of optimal sensor position and orientationon platform at given variance for the observationsand system state

– design of 2nd order: choice of optimal observation accuracy at givenplatform design and variance of the system state

– design of 3rd order: choice of additional sensors to optimize givenplatform design

30.05.2012 Seite 21

Sensor raw data simulation tool required

• Sensor design differs in

– sensor type

– sensor quantity

– sensor quality

– location

• Different sensor designs for different applications depends on:

– navigation parameters

– body tractory

– required accuracy

MULTI‐SENSOR‐ALGORITHMS DEVELOPMENT

30.05.2012 Seite 22

Sensor raw data simulation tool required