Aerospace and Electronic Systems Magazine August 2017 - 24
Inertial Navigation and Simultaneous Localization and Mapping
Figure 2.
The integrated navigation system architecture. A compressed-unscented filter is used with 17 inertial and
receiver states and 3N map states with N being the number of features. The raw GPS pseudorange and the
pseudorange rate, along with the IMU measurement, are directly fused in the filter and thus a tightly coupled
architecture.
the fusion filter. The inertial navigation system utilizes a localtangent frame with north, east, and down (NED) coordinates, and
the GNSS system is based on the ellipsoidal coordinates with the
World Geodetic System 1984 (WGS-84) Earth model. The map
features are maintained within the fusion filter, as are the satellite
ephemeris data.
UNSCENTED GNSS AND INERTIAL SLAM
The stochastic nonlinear state transition and observation models
are
x k +1 = f ( x k , u k , w k )
(1)
z k +1 = h ( x k , v k ) ,
(2)
The state vector of unscented inertial SLAM consists of 17
inertial and GNSS receiver states (15 inertial navigation system
states and 2 receiver clock states) and variable-size map states with
the control input from IMU measurement,
x kv = pT , vT ,ψ T , bTa , bTg , ctb , ctdT
m k = m1T , mT2 , , mTN
T
(4)
T
(5)
T
u k = f T , ω T ,
(6)
where xk and uk are the state and the control vector at current discrete time k, respectively, with wk as the process noise, and zk is the
observation vector, with wk as the observation noise.
In this work, the state vector is partitioned into a local map
and a global map, as shown in Figure 3. This limits the quadratic
complexity within the local region and is called compressed filtering. This approach is discussed further in the following section.
The estimates and covariance of the vehicle and local map states
are defined as
xˆ v
Pxx , k
xˆ k = k Pk =
ˆ
m
Pmx , k
k
Pxm, k
,
Pmm , k
(3)
with xˆ kv being the estimate of the vehicle state.
The unscented filter in SLAM utilizes a partial sampling
scheme, because the nonlinearity appears only in the vehicle state
transition, whereas map states have linear dynamics. The equivalence of the partial sampling and full sampling schemes was provided in [22], showing that the performance of the partially sampled filter is not affected by the number of feature landmarks.
24
Figure 3.
The large covariance matrix is partitioned into a local matrix PLL and
a global matrix PGG. The local covariance consists of the inertial and
receiver matrix and the local map matrix. The cross-covariance PLG is
accumulated, or compressed, during the local update cycle and only
used during a global update cycle.
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2017
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