Analysis of the Strapdown Inertial Navigation System (SINS) Error Genesis

Abstract Analysis and simulation of the Strapdown Inertial Navigation System (SINS) error genesis revealed that the East Feedback Contour has the greatest influence on the development of an error in this model, and angular velocity sensor Δω𝒚 is the critical element. In order to prevent the development of an error, structural correction in the East Feedback Contour, and elements that are more critical, namely in angular velocity measurement sensors is the best option.


I. INTRODUCTION
The described Strapdown Inertial Navigation System (SINS) error model with laser gyroscopes was developed in RTU [1]. The system is based on a classic SINS, except the correction for velocity. The main technical characteristics of the experimental data of the system are provided.
Feasibility of new high-precision development SINS is produced by the need to improve the accuracy of object positioning in the context of the possible lack of information through the channels of satellite navigation systems, as well as by the need to autonomously determine the parameters of the angular orientation, angular and linear velocities of an object.
This article describes the SINS error model with velocity correction, and the results of the simulation analysis.

II. STRAPDOWN INERTIAL NAVIGATION SYSTEM (SINS) ERROR MODEL
Inertial navigation systems are designed to determine the parameters of the spatial position, geographical coordinates and the parameters of aircraft movement data, which is transferred to onboard systems and displays in electronic cabin indicators [2]- [4].

A. Accelerometer signals
Errors in calculating the projections of accelerometer signals -, , on the axis of terrestrial geographical CS -, , will give the same results as for the original (classical) version SINS (SINS with the coordinates of the output signals of the accelerometers) [9]- [11].
Errors in the components ∆ , ∆ , ∆ angular velocity of geographic terrestrial CS -, , : Where A -Lift forces of the aeroplane, B -Air resistance forces of the aeroplane, C0 -Weight/gravity forces of the aeroplane.

C. Angular Velocity Transformation
The algorithm for calculating the projections of composite angles and velocity CS -, , on axes , , -in linked CS (Coordinate System) are the same as in classical SINS with the velocity correction, and hence the expressions for ∆ , ∆ , ∆ will be the same as in the classical version. And in the future, all the options for calculating errors will be the same as in the classical SINS version, since the calculation of angles , , at the SINS with the correction for speed is the same as for the classical version of SINS [12]- [15].
For axis:

III. SIMULATION AND RESULTS
In SINS error model with correction on velocity, there are both positive and negative feedback loops, which include two series-connected integrators. The presence of positive feedback leads to the development of an error in the system, and negative feedback produces stabilization of the system (Fig. 2). The main objective is to analyse the SINS error model and to determine the most critical feedback loop with the largest contribution of an error to this system.

Fig. 2. Negative and Positive Feedbacks.
To determine the feedback loops, which are the most critical, the SINS error model with velocity correction was implemented in Simulink program (Fig. 3). . NFC consists of 6 feedback loops, EFC -16 feedback loops and NFC2 -5 feedback loops. During the simulation were launched error to accelerometers and angular velocity sensors, equal to 1 m/s 2 and 1°, respectively. 50 different simulation scenarios were considered and processed to determine the most critical feedback loop.
The obtained data were recorded, analysed, and compared with each other, and with the results obtained during the simulation of the entire system (Fig. 4). Thus, based on simulations it was possible to determine that the most critical feedback loop, which had the greatest impact on the error development in SINS error model with correction on velocity which is EFC10 (Fig. 5).   Table I presents Accuracy Characteristics of the modern SINS-T. SINS-T was developed in AS "MIEA" and is a part of onboard equipment of modern military and civil aircrafts. Based on the data and values obtained from simulation we can make conclusion related on the influence of error development of exact feedback loop on SINS. The influence of East Feedback Loop is 131.8 %, which is 4.9 km per flight hour. Due to the presence of negative feedback loops this value is reduced to approximately 60 % (2.9 km per flight hour) [1][2][3][4][5][6][7][8]. The influence of East Feedback Loop on SINS-T model is 54 % (2 km per flight hour) in offline mode and 16.2 m per flight hour in correction mode.

V. CONCLUSION
In the conclusion of the conducted research on the analysis of error genesis in the simulation and comparison of the feedback loops of the SINS error model with velocity correction by entering an error in the accelerometers and angular velocity sensors it was revealed that the eastern feedback loop exerts the greatest influence on the development of error in this model since it contains the greatest number of positive feedbacks. After analysing the results, was defined that the greatest influence on the development of error is EFC10 loop, and the critical element is angular velocity sensor Δωy. The analysis shows that in order to prevent the development of an error, structural correction is best served both in the chain and in the elements that are more critical.