|
| The implementation of an Extended Particle Filter (EPF) was proposed as an estimation
technique for integrated GPS and low-cost inertial MEMS navigation systems |
|
| Pseudo Code for
Implementing EPF |
Generate independent and
identically distributed (i.i.d.) N samples  from the previous
posterior density function p(x0). |
|
| For k = 1,….. till end of trajectory
Importance Sampling Step |
2. For k = 1,….. till end of trajectory
Importance Sampling Step
• For i = 1..N, where N is the total
number of particles, update the
particles with EKF equations
which are given below:
i. Calculate Jacobians
 of the models. |
| Update the state vector
by following eq. |
 |
Sample particles from
obtained updated particles
i.e. proposal density |
 |
| 3. For i = 1………N, evaluate
the importance weights of each
particle according to eq. 6. |
 |
| where the proposal density
is obtained from EKF. |
4. Normalize the weights of the particles
5. Compute the effective weights and
threshold according to eq 3.
6. If Neff > Nth, particles remain as
such, else resample particles and
assign equal weights to them.
7. Once resampling is done, time epoch
is incremented, new articles are
predicted and steps from 2 are repeated. |
 |
| 8. This process is repeated till end
of the test trajectory is reached. |
The state vector for this Extended
Particle filter (EPF) is given in Table 1.
In EPF, the system process comprises
of the INS mechanization and the
sensor error models. Sensor errors are
being modelled as a random process
(Hou, 2004) to compensate the effect of
biases and scale factor errors on the INS
measurements. The INS mechanization
applied in this paper is described in
(Shin and El-Sheimy, 2004,2005). |
To compensate for large sensor errors,
these are modelled as component of
the state vector as given in Table 1.
Differential GPS (DGPS) is used as aiding
source for the EPF after compensating
for the lever arm effect between the
IMU unit and the GPS antenna. |
| Results |
| Field Test Data Description |
Field tests using MicroElectroMechanical
Systems (MEMS) based IMUs were
conducted. The MEMS units being tested
is the BEI Motion Pak II, which is (gyro
drift rate of 1200 deg/hr) a solid-state
MEMS six degree of freedom inertial
sensing system that uses micromachined
quartz rate sensors and silicon based
accelerometers. The field tests were
conducted in March 2005, where Motion
Pak II was mounted on the test vehicle and
the NovAtel OEM4 GPS receivers were
mounted on the vehicle as shown in Fig |
| 1. Using this setup, test trajectories was
generated for Motion Pak II as can be seen. |
| The test trajectory covered number
of vehicle dynamics and throughout |
 |
the test a minimum of seven satellites
was visible, except for several short
natural GPS signal outages caused by
bridges or trees. These natural outages
are avoided for testing purposes, while
simulated GPS outages have been
carefully picked to cover number of
vehicle dynamics as shown in Fig 2. |
The results
obtained from
implementing
EKF for Motion
Pak II are
shown in Fig 3
and for EPF are
shown in Fig 4
respectively. |
In these
simulations,five 60 sec GPS signal
outages are simulated for Motion Pak II. |
 |
The input data file is at 50 Hz while the
output file is at 10 Hz. Table 2, lists the
drift errors obtained at all the five outages
for both EKF and EPF for Motion Pak
II sensor. The table clearly indicates
that EPF gives slightly better results (2
% improvement) than that of the EKF
when GPS outages occur. The individual
maximum drift errors for each GPS
outage along with the mean of all these maximum drift errors are also provided.
Here the numbers of particles used are
35 as this value gives best results. |
| |
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| November 2007 |
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