x   =    ( x,   y,   z,   b ,   v ,   v ,   v ,   f )

T

u

x

y

z

u

The state transition matrix for the dynamic model can take various forms.  Often,

unaided receivers will model the vehicle motion as a constant velocity with process

noise to account for accelerations.  In that case the propagation equations are as

follows:

d( x,   y,  z) / dt   =   ( v

x

,   v

y

,   v

z

)

d(b

u

) / dt   =    f

u

d( v

x

,   v

y

,   v

z

) / dt   =   (0, 0,  0)

d( f ) / dt   =   0

u

For a small propagation time interval of Dt the F matrix would be:

I

I t

  =

O

I

where I is the 4 x 4 identity matrix.  The measurement vector for each (i

th

) satellite

measurement contains the pseudorange PR

i

 and pseudorange rate dPR

i

 (=

dPR

i

/dt):

T

z    =    (

y

i

PR ,  

i

dPR )

Define

range vector R

i

= (S

xi

 U

x

, S

yi

 U

y

, S

zi

 U

z

)

range R

i

= |R

i

|

PR

i

 measurement = (S

xi

 U

x

, S

yi

 U

y

, S

zi

 U

z

).R

i

/R

i

 + b

u

dPR

i

 measurement = (V

xi

 V

x

, V

yi

 V

y

, V

zi

 V

z

).R

i

/R

i

 + f

u

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