The integration of strapdown inertial navigation system and Doppler velocity log (SINS/DVL) is widely used for navigation in automatic underwater vehicles (AUVs). In the integration of SINS/DVL, the velocity measured by DVL in body frame should be projected into navigation frame with the help of attitude matrix calculated by SINS to participate in data fusion. In the process of data fusion based on standard Kalman filter, the errors in calculated attitude matrix are characterized by state variance and process noise while the errors in measurement vector from DVL are by measurement noise. But the above projection will bring process noise into measurement noise, and thus the assumption of the independence between process noise and measurement noise will not stand. In this paper, the forming mechanism of crossnoise in SINS/DVL is studied in detail and Kalman filter for crossnoise is introduced to deal with this problem. Simulation results indicate that navigation accuracy, especially the position accuracy, can be improved when the crossnoise is processed in Kalman filter.
Automatic underwater vehicles (AUVs) are widely used in missions of science, military, and commerce, such as survey of ocean resources and cable tracking. Navigation is an important requirement for AUVs, because accurate navigation information is essential for safe operation and recovery. Due to the special characteristics of ocean environment, such as attenuation effect on Global Navigation Satellite System (GNSS) signals, navigation has become one of the primary and key challenges in AUV research [
Regular or irregular resetting with the help of external reference position information is an effective method to deal with the accumulated location errors in SINS [
Recently, with the development of acoustic correlation velocity measurement technology, the performance of Doppler velocity log (DVL), such as accuracy and range, has been greatly improved. The accuracy of DVL is as high as 0.2% of speed and the range is up to 90 m with a frequency of 600 kHz, and the accuracy is 0.5% and the range is 425–500 m with a frequency of 150 kHz [
Without other aided navigation systems, the accuracy of SINS/DVL integration with certain sensor precision for long time and long distance mission is mainly determined by data fusion algorithm [
The problems addressed in this paper are concentrated on the investigation of crossnoise in SINS/DVL. In general, DVL is installed on the shell and measures the velocity relative to Earth (or current) in body frame [
Crossnoise (or color noise) problem is a classical issue in data fusion and a large amount of paper published since the 1960s to deal with this problem [
The rest of this paper is organized as follows. The integrated navigation system structure and error propagation models for each subsystem of integration system are given in Section
Figure
Integrated navigation system structure.
In Figure
Navigation solution and data fusion are two independent and parallel processes in Figure
As a selfdepended navigation system, SINS is composed of inertial measurement unit (IMU) and navigation solution. In IMU, three gyros and three accelerometers are orthogonally installed to measure the vehicle’s movement in six degrees, and the navigation solution can calculate vehicle’s attitude, velocity, and position through integration operation on angular rate and acceleration measured by IMU. The equations describing SINS solution are three differential equations as follows [
Errors in attitude, velocity, and position will be generated because of initial errors such as misalignment, sensor errors such as gyro and accelerometer biases, and navigation algorithm errors such as cone error. Here, the Euler angles, which describe the rotation between calculated navigation frame
Doppler effects are used in DVL to measure velocity. With four acoustic beams in fixed direction that is, Janus configuration, three velocities along body frame axes can be measured. The precision of DVL is affected by many sources, such as installing error, scale factor error, and frequency measurement error [
Magnetic sensors are used in MCP to measure the direction of Earth’s magnetic field and give the angle between the magnetic meridian direction and AUV’s
In the integration system of SINS/DVL/MCP/PS, depth is provided by PS, which measures the depth information based on the principle that liquid internal pressure increases with the depth. In PS, the measurement precision of depth is affected by salinity and temperature. In this paper, the constant error of PS is assumed to be accurately compensated, and white Gaussian noise is used to describe the random error when AUV sails in a determined depth. Thus, the PS propagation model can be constructed as [
In this section, the crossproblem caused by the projection from process noise to measurement noise in SINS/DVL will be analyzed in detail.
The discrete random linear model without controlling terms is described as follows:
In standard Kalman filter, the process noise and measurement noise are assumed to satisfy the following assumptions:
If the estimation of
As for the integration system described in Section
The transition matrix
Take the velocity from DVL, the yaw from MCP, and the depth from PS as reference navigation information, and the measurement vector can be constructed as
According to the relationship between measurement and state vectors,
In the integrated system, DVL, MCP, and PS are independent systems and the reference information from them is also independent, so the measurement noise variance
As shown in Figure
Calculation process for DVL velocity in navigation frame.
The relationship between DVL, body, and navigation frame
Objection processes of DVL velocity
When considering the measurement error in DVL,
When considering the calculating error as shown in Figure
Then, the error in
The above equation indicates that the errors in the DVL projection velocity include not only the DVL measured error described by measurement noise but also SINS misalignment angles described by process noise and state variance. In this way, measurement noise is coupled by process noise and the assumption of independence between measurement noise and process noise in (
Equation (
Define the prediction error of state vector as
Covariance of the prediction for state vector and measurement noise can be constructed as
Variance of the prediction for state vector can be constructed as
Covariance of the prediction for state vector and measurement vector can be constructed as
Variance of the prediction for measurement vector can be constructed as
Gain matrix can be constructed as
Variance of the state vector can be constructed as
Here, physical meanings of
The subequations in (
According to the definition of state vector and measurement vector described in Sections
The gyro constant biases are all set as 0.01°/h and random biases are white Gaussian noise with zero mean and standard variance of 0.01°/h; the accelerometer constant errors are 500
AUV is with a swinging motion. The swinging amplitudes of pitch, roll, and yaw are set as 1.2°, 1.2°, and 1.8°, respectively, and the corresponding swinging cycles are 8 s, 10 s, and 6 s. The initial positions of AUV are 118° in longitude, 32° in latitude, and −20 m in height. The velocities of AVU along body frame axes are 0, 5 m/s and 0.
Based on the above ideal motion, the ideal sensor output can be gotten by backstepping of navigation solution. When sensor errors are added into ideal sensor output, the real sensor data can be simulated. In this simulation, the update frequencies of sensor data and navigation solution are both 100 Hz.
The errors in DVL, MCP, and PS are all set as white Gaussian noise with zero mean and standard variance of 0.02 m/s, 10°, and 0.5 m, respectively. When the above noise is added into ideal motion, the real reference velocity, yaw, and depth from DVL, MCP, and PS can be simulated, respectively. In this simulation, the update frequencies of reference data are all 1 Hz.
Straight line trajectory is chosen in simulation for the consideration that error growth is correlated with mission pattern and straight line trajectory has no cancelling effect on error growth [
Four filtering schemes are compared: in Scheme 1, the ideal AUV attitude matrix is used to project DVL velocity from body frame to navigation frame, and standard Kalman filter is adopted; in Scheme 2, the attitude matrix from SINS is used for DVL velocity projection and standard Kalman filter is adopted; Scheme 3 is the same as Scheme 2, but in Scheme 3, the measurement noise value is added; in Scheme 4, the attitude matrix from SINS is used while the Kalman filter for crossnoise is adopted. To evaluate the different effects of different schemes, the ideal motion is used as a reference.
After setting the initial parameters, the integrated navigation including initial alignment is run. The initial velocity and position parameters of SINS have no initial errors, while the attitude has misalignment angles of 0.5°, 0.5°, and 1.2° in pitch, roll, and yaw.
The initial parameters of Kalman filter are set as
For Scheme 3, the measurement noise is set as
For Scheme 4, the crossnoise is set as
Here,
The simulation lasts for 3600 s. The errors of attitude, velocity, and position of different schemes are shown in Figures
Curves of attitude errors.
Pitch
Roll
Yaw
Curves of velocity errors.
East velocity
North velocity
Up velocity
Curves of position errors.
East location
North location
Up location
The curves in Figure
The curves in Figure
The curves in Figure
Statistic results of level position errors in 3501~3600 s.
East  North  Error  Proportion of error to 


Scheme 1  −1093.5  0.8  1093.5  6.1% 
Scheme 2  18794.1  41.1  18794.1  104.4% 
Scheme 3  11340.2  31.3  11340.2  63.0% 
Scheme 4  3731.7  19.5  3731.8  20.7% 
From the above analysis, it can be concluded that, in the integration of SINS/DVL, the error in calculated attitude matrix will cause error in the projected DVL velocity, which will further decrease the accuracy of SINS/DVL, and the crossnoise should be processed to increase navigation accuracy; when the crossnoise is processed either by adding measurement noise or adding crossnoise term to standard Kalman filter, the accuracy is increased, but the effect of latter one is better than the first one.
The crossnoise problem in the integration of SINS/DVL is studied in this paper. Analysis indicates that in the projection of DVL velocity from body frame to navigation one, attitude errors from SINS will be also projected into DVL projected velocity, which causes crossnoise from process noise to measurement noise and destroys the assumption about the independence of process noise and measurement noise in standard Kalman filter. When this crossnoise cannot be neglected, data fusion accuracy will decrease and navigation accuracy will also decrease.
To deal with the crossnoise in SINS/DVL, a Kalman filter for crossnoise is introduced. In this filter, the crossnoise term appears in the numerator and denominator of gain matrix simultaneously, so the calculation for gain matrix is more reasonable, and the utility degree between measurement vector and state prediction vector is more reasonable.
Simulation results based on straight line trajectory indicate that when the crossnoise is processed in Kalman filter, navigation accuracy, especially level position accuracy, can be significantly increased.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported in part by the National Natural Science Foundation (61273056) and Chinese University Research and Operation Expenses (104.205.2.5).