883
ANALYSIS OF THE KALMAN FILTER WITH DIFFERENT INS ERROR MODELS
FOR GPS/INS INTEGRATION IN AERIAL REMOTE SENSING APPLICATIONS
Hongxing Sun a , Jianhong Fu a , Xiuxiao Yuan 3 , Weiming Tang b
a School of Remote Sensing & Info. Eng., Wuhan University, P. R. China 430079
b GNSS Eng. Technology Research Center, Wuhan University, P. R. China 430079
Commission V, ICWG V/I
KEY WORDS: Direct Georeferencing, Aerial Triangulation, GPS/INS Integration, Kalman Filter
ABSTRACT:
In the Kalman filter used for the integration of GPS/INS, the inertial sensor error model is usually considered as a random constant or
random walk for both gyroscopes and accelerometers. However, the Inertial Measurement Unit (IMU) used in aerial remote sensing
applications for sensor positioning and orientation is typically of tactical grade, i.e., the gyroscope drifts are on the order of 0.1 deg/h
and the accelerometer biases are 1 OOug respectively. In this case, there is the room to improve the system performance by developing
more complicated error models for the inertial sensors. In this paper, 6-state, 12-state and 15-state error models for the inertial
sensors are implemented, and their performance of each in the Kalman filter is compared and analyzed. Firstly, the commonly used
6-state error model that includes three random walks for gyroscopes and three random walks for accelerometers is implemented.
Then, a 12-state error model is formed by augmenting the 6-state model with three scale factors for the gyroscopes and three scale
factors for the accelerometers. Thirdly, three first-order Markov procedures are considered for the gyroscopes in addition to the
random walks and scale factors, thus resulting in a 15-state error model. Aerial GPS/INS data collected in the field with a tactical
grade IMU and dual frequency GPS receivers is processed with these three error models. In the data processing, the loosely-coupled
Kalman filter, which is the common coupling method for the aerial GPS/INS integration, is used. The 12-state and 15-state error
models show obvious advantages over the 6-state error model in the test results. The accuracies of the integrated position (5cm),
velocity (3cm/s) and attitude (0.002 degree for pitch and roll, 0.008 degree for heading) in the 12-state model are all better than that
of the 6-state error model. However, the improvement of the 15-state error model relative to the 12-state error model is limited and
insignificant.
1. INTRODUCTION
Direct georeferencing, also referred to as direct platform
orientation (DPO), is defined as direct measurement of the
imaging sensor external orientation parameters (EOP), using
positioning and orientation sensors, typically the Global
Positioning System (GPS) and Inertial Navigation System (INS)
or Inertial Measurement Unit (IMU). With the increasing use of
multi-sensor mapping, the DPO of the integrated GPS/IMU
systems has become a crucial component of spatial data
processing algorithms, and substantial research effort has been
devoted to extensive algorithmic developments, performance
analysis and practical implementations of GPS/IMU systems
(Skaloud et al, 1996; Abdullah, 1997; Grejner-Brzezinska,
1997; Toth and Grejner-Brzezinska, 1998; Grejner-Brzezinska,
1999; Grejner-Brzezinska, 2001; Mostafa et al., 2001; Cramer
et al., 2000; Cramer, 2001). However, investigation of the
GPS/INS integration itself, especially for the inertial sensor
error model, is not focused on as much. Grejner-Brzezinska et
al., (2005) attempted to improve the performance of GPS/IMU
integration by using a precise gravity model, signal de-noising
and parameter refinement of the inertial sensor stochastic model,
nevertheless the sensor stochastic model was still of 12 states.
The commonly used IMU sensor stochastic model in the
Kalman Filter (KF) supports 6 states (i.e., gyroscope drift and
accelerometer bias) to 12 states (for which the scale factors of
both of gyroscope and accelerometer are also included) (Cramer,
2001; Grejner-Brzezinska et al., 2005). In aerial
photogrammetric mapping or remote sensing, the IMU
hardware is typically classified as high-end tactical grade sensor,
i.e., the gyroscope drifts are on the order of 0.1 deg/h and the
accelerometer biases are lOOug respectively. In this case, there
is the room to improve the system performance by developing
more complicated error models for the inertial sensors. In this
paper, the 6-state, 12-state and 15-state inertial sensor error
models are implemented, and the KF performance of each is
compared and analyzed.
2. STOCHASTIC ERROR MODEL OF THE INERTIAL
SENEORS
The performance characteristic of a gyroscope (or
accelerometer) is determined by the dynamic model, which
involves a scale factor, bias and random, random environmental
sensitivity and misalignment (IEEE std. 952-1997). The
situation is similar for accelerometers (IEEE std. 1293-1998).
The environmental sensitivity and misalignment are generally
ignored in the stochastic error model, so the focus in this paper
is mainly on the first two items. The scale factor of the sensor is
calibrated by the manufacturers in the factory before the sale.
But post-factory calibration of the instrument can still influence
the navigation performance significantly, therefore it can also
be considered in the stochastic error model. The random
component of the gyroscope and accelerometer data mainly
include: (a) the gyro rate ramp (trend) defined as a gyro
behavior characterized by quadratic growth within a certain
range of time, (b) gyro rate (acceleration) random walk due to
white noise in the angular acceleration (jerk) which is defined as
the drift rate error (acceleration) build-up with time, (c) flicker
noise (bias instability), defined as a random variation in bias,
computed over a specific finite sample time and averaging time
interval; (d) angle (velocity) random walk due to the white noise
of gyroscope angular rate (acceleration) data, (e) quantization
noise, defined as a random variation in the digitized output