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An actual account of the angle random walk (ARW) coefficients of gyros in the constant rate biased rate ring laser gyro (RLG) inertial navigation system (INS) is very important in practical engineering applications. However, no reported experimental work has dealt with the issue of characterizing the ARW of the constant rate biased RLG in the INS. To avoid the need for high cost precise calibration tables and complex measuring set-ups, the objective of this study is to present a cost-effective experimental approach to characterize the ARW of the gyros in the constant rate biased RLG INS. In the system, turntable dynamics and other external noises would inevitably contaminate the measured RLG data, leading to the question of isolation of such disturbances. A practical observation model of the gyros in the constant rate biased RLG INS was discussed, and an experimental method based on the fast orthogonal search (FOS) for the practical observation model to separate ARW error from the RLG measured data was proposed. Validity of the FOS-based method was checked by estimating the ARW coefficients of the mechanically dithered RLG under stationary and turntable rotation conditions. By utilizing the FOS-based method, the average ARW coefficient of the constant rate biased RLG in the postulate system is estimated. The experimental results show that the FOS-based method can achieve high denoising ability. This method estimate the ARW coefficients of the constant rate biased RLG in the postulate system accurately. The FOS-based method does not need precise calibration table with high cost and complex measuring set-up, and Statistical results of the tests will provide us references in engineering application of the constant rate biased RLG INS.

A ring laser gyro (RLG) is an ideal angular measurement sensor for a high precision inertial navigation system (INS) [

The rate biased technique requires only a single drive

All types of inertial sensors exhibit errors such as bias, scale factor, and noise, among others. As a rotation modulation system for the constant rate biased RLG INS, eliminating fixed or slowly changing bias errors of equivalent horizontal sensors through turntable rotation guarantees significantly higher navigation accuracy [

With its potential for high measuring accuracy, it is valuable to study the operation performance of the constant rate biased RLG to best exploit the inherent quality of the RLG system. The most compelling evidence is the fact the way to improve operation performance of the inertial sensor is to know more details about the noise components in the sensor measured data [

An actual account of ARW coefficients of the gyros in the constant rate biased rate RLG INS is most important to determine the a prior probability for the Kalman filtering in initial alignment or integrated navigation and so on. However, there is still a dearth of effective experimental methods to characterize the constant rate biased RLG noise. To avoid the need for high cost precise calibration tables and complex measuring set-ups, estimating the ARW coefficients of the gyros in the constant rate biased RLG INS directly is attractive. Since ARW is a high frequency noise, high frequency data is acquired for proper determination of the ARW error using AVAR [

This paper aims to develop a practical method for characterizing ARW error present in the constant rate biased RLG measured data. Since turntable dynamics and other external noises would corrupt AVAR calculation, we present an experimental method for separating them from the constant rate biased RLG measured data and verify the effectiveness of this method on a postulate system.

The remaining of this paper is organized as follows: Section 2 presents a brief description of the postulate system used as the experiment platform and an overview of the AVAR technique. In Section 3, an ideal observation model of the RLG triad mounted on a turntable is firstly discussed, and a method based on sampling the RLG measured angle at full rotation interval is then introduced. Next, problems of characterizing ARW of the constant rate biased RLG are addressed. To tackle these problems, a practical observation model is discussed, and an experimental method based on the fast orthogonal search (FOS) is proposed. Section 4 presents the validity check of the FOS-based method and the estimation results of the ARW coefficients for both the mechanically dithered RLG and the constant rate biased RLG. Conclusions are drawn in Section 5.

To characterize the ARW of the RLG in the two operation modes and make comparisons between them, we set up a postulate system [

With angular divisions in the form of a line grid which is read out photoelectrically, divisions of up to 7,200,000 lines on the circle perimeter of the angle encoder are realized, corresponding to an angular resolution of 0.18”. Furthermore, when the system passes each full rotation, the photoelectric null indicator on the angle encoder permits one to determine the 360° angle with an accuracy of 2”.

Without loss of generality, the local-level frame _{n}_{n}_{n}

Ignoring the fact that errors due to precision limitations in manufacture and installation of the installation structure are extraordinarily small, we denote by

We denote by _{b}_{s}_{b}_{b}_{0} frame when axis _{b}

The transformation matrix from the _{x}_{y}_{z}_{x}_{y}_{z}_{x}_{y}_{z}

Many possible noise sources mentioned in [

Considering two data records, AVAR of each data record at any given _{1}(_{2}(

Theoretically, angular rate vector as measured by the RLG triad on the experimental platform is given by:

As the experiment platform is placed on a vibration insulating foundation in laboratory, which means that

From the above equations, measured angle of each RLG is determined as the integral of
_{xi}_{yi}_{zi}_{b}

According to [_{θ}_{(}_{t}_{)} at the time the turntable shaft passes each full rotation. Assuming that turntable rotation angle is 2π from _{1} to _{2}, from

Taking the difference between two components of the resultant difference data record

Considering that δ_{x}_{y}_{z}_{x}_{z}

To verify its precision for characterizing ARW of the constant rate biased RLG, we process

Using least mean squares fit, a value of

The first problem involves turntable dynamics and other external noises. In

The second problem relates to the correlation time of the ARW error of RLG. An appropriate sample rate/data record length should be chosen to overlap about the correlation time of the ARW error [

Using least mean squares fit, the estimated ARW coefficients of

To tackle the problems formulated above, a practical observation model is discussed first. Then an experimental method based on the FOS is proposed to separate periodic components due to turntable motion and other external disturbances from the RLG measured angle in a two-step procedure. At last, the resultant gyro noise difference data record can be sampled at 1 s time interval to improve the estimation resolution of the ARW coefficient of RLG using AVAR.

Taking _{x,rot}_{xi}

Other external periodic disturbances, denoted as Δ_{x,elec}_{j}

From _{x}_{x, t}_{x}_{α} caused by the turntable motion.

Due to the variation of turntable rotation rate, Δ_{x,rot}_{x,elec}

As can be seen in

To describe _{xi}_{i}

The RLG measured angle is sampled at a fixed time interval in the postulate system, however variation of turntable rotation rate causes

Frequencies of periodic components in

The FOS has been illustrated for efficiently constructing accurate and parsimonious models of nonlinear dynamic systems (

We may write _{i}

_{0} is a constant value which can be easily eliminated:

For convenience, this four-step method proposed above to characterize ARW of the RLG triad mounted on a turntable is called as the FOS-based method.

By characterizing ARW of the mechanically dithered RLG under stationary and turntable rotation conditions, validity of the FOS-based method is checked. Then, the average ARW coefficient of the constant rate biased RLG is estimated by utilizing the FOS-based method.

On the experimental platform, sample time of the RLG measured angle, denoted as _{s}, is 2 ms. In the AVAR calculation, the unit of _{0} = 1 s. Taking the long-term stability of the gyros into account, required tests are done three times on different days under respective turntable rotation conditions. Laboratory tests are done by fixing the experimental platform on a vibration insulating foundation, without any temperature control device or other such instruments. Only

Let the RLG triad on the experiment platform operate in the mechanically dithered mode. The RLG triad measured angle is collected for two hours on the experimental platform when the turntable is stationary and the turntable rotates continuously in a single direction at 10°/s, 20°/s, 30°/s and 40°/s respectively.

(1) For data collected when the turntable is stationary, the ARW coefficient of the mechanically dithered RLG can be estimated after simple post-processing of the measured data with sampling the data records at a time interval _{0} = 1 s. To provide a reference for the FOS-based method, the average ARW coefficient of

(2) For data collected under turntable rotation, the average ARW coefficient of

Estimation results of the ARW coefficient of the mechanically dithered RLG under different turntable rotation conditions are listed in

Comparing

Let the RLG triad on the experimental platform operate in the constant rate biased mode, and turntable rotates continuously in a single direction at different turntable rotation rate, such as 10°/s, 20°/s, 40°/s,

Comparing

Taken together, the FOS-based method has been experimentally verified to be effective in characterization of the ARW of the RLG triad mounted on a turntable in the postulate system. In addition, statistic of our experimental tests have been used in the first laboratory tests of initial alignment on the experiment platform and achieved high initial alignment precision presented in [

An actual account of ARW coefficients of the gyros in the constant rate biased rate RLG INS is most important to determine the

A practical observation model of the RLG triad for denoising and increasing sample rate in AVAR calculation, and an experimental method based on the FOS was proposed to extract gyro noises from the RLG measured data were discussed. Validity of the FOS-based method was experimentally checked among the mechanically dithered RLG data collected on the experiment platform under stationary and turntable rotation conditions.

The experimental results show that the FOS-based method can estimate the ARW coefficients of the mechanically dithered RLG and the constant rate biased RLG accurately. Statistical results of the tests will provide us references in many aspects as mentioned above. Therefore, the FOS-based method is algorithmically simple and possessed of low cost attribute, and it will be greatly helpful in engineering application of the constant rate biased RLG INS.

This work was supported by Research Fund for the Doctoral Program of Higher Education of China (

(

AVAR result of

AVAR results of one measured data of

AVAR results of the resultant gyro noise difference data of

AVAR result of the resultant gyro noise difference data of

AVAR result of the resultant gyro noise difference data of

Estimation results of the ARW coefficient of the mechanically dithered RLG under different turntable rotation conditions.

1 | 3.6427 | 3.3903 | 4.2517 | 3.4121 | 3.4328 |

2 | 3.3709 | 3.4392 | 3.1152 | 3.2906 | 6.5700 |

3 | 3.7997 | 3.0869 | 3.6555 | 4.1709 | 4.5071 |

(a) Unit of the results is

Estimation results of the average ARW coefficient of

1 | 8.3297 | 6.7278 | 7.4707 | 2.1993 | 3.4774 |

2 | 4.6176 | 2.6117 | 2.3985 | 2.9396 | 2.3414 |

3 | 6.8846 | 3.2470 | 2.3238 | 2.5313 | 2.6234 |

(a) Unit of the results is