# New Algorithms for Autonomous Inertial Navigation Systems Correction with Precession Angle Sensors in Aircrafts

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Generation of Errors and Measurements for Autonomous INS

#### 2.1. Errors of Autonomous Navigation Systems

#### 2.2. Method of Measurements Generation Based on Signals from Precession Angle Sensors

## 3. Correction of Autonomous INS by Kalman Filter

_{1}, Φ

_{2}, Φ

_{3}. In this case, it is possible to determine the projections of accelerations on the axis of GSP system:

_{x}, δa

_{y}are equivalent accelerometer errors, and then these signals from accelerometers can be used as measurements for the estimation algorithm:

## 4. Correction of Autonomous INS Using the Reduced Measurements

_{E}and Φ

_{N}characterizing the errors of horizontal orientation remain small values throughout the work period of the INS and angle Φ

_{up}, which characterizes the errors of azimuth orientation, can increase indefinitely. Then, the non-linear error model of the INS is defined by the following system of equations:

_{E}is small and thus we have the relationship that sinΦ

_{E}≈ Φ

_{E}. Substituting them into Equation (12), then the system of equations can be rewritten in matrix form:

#### 4.1. Method of Correction Signals Formation Using Non-Linear Errors Equations of INS

**x**, and the vectors

_{k}**x**

**,**

_{2}**x**, … by

_{3}**x**

**are formulated as follows [27]:**

_{1}#### 4.2. Generation of Correction Signals for the Northern Channel

**F**have the form, respectively,

**H**can be defined as: $\mathrm{H}=\left[0\text{}1\text{}0\right].$In this case, the matrix

**S**is determined by the following formula:

**S**

^{−1}is defined by the formula:

_{k}, z

_{k}

_{+1}, z

_{k}

_{+2}represent functions of the precession angles. They are formed on the basis of information from the precession angle sensors of the corresponding gyroscope according to Equation (5). Furthermore, the signals from the precession angle sensors are averaged preliminarily and a vector of the reduced measurements is formed from the already smoothed signals.

## 5. Simulation Results of Autonomous INS Correction Algorithms Using Signals from Precession Angle Sensors

_{0}, My

_{0}, Mz

_{0}present the imitation of moments of external and inertial forces.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Scheme of autonomous INS correction by KF in the flight with constant velocity of aircraft. Where, θ—true information about the navigation parameters of a dynamic object; x—error vector of INS; $\tilde{x}$—estimation of error vector; $\hat{x}$—estimation of vector x; z—measurements with accelerometers; ACM—accelerometer; KF—Kalman filter.

**Figure 2.**Scheme of autonomous INS correction using signals from precession angle sensors. Where $\mathsf{\delta}$ denotes the signal from the precession angle sensor; UF represents unit of measurement generation; Φ indicates the formed measuring deviation angles of GSP.

**Figure 3.**The scheme of signal generation for orientation angles of GSP. Where δ, λ, ϑ are precession angles of gyros, Φ

_{1}, Φ

_{2}, Φ

_{3}are the orientation angles of GSP, and UF represents the unit of signal generation.

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**MDPI and ACS Style**

Chen, D.; Neusypin, K.; Selezneva, M.; Mu, Z.
New Algorithms for Autonomous Inertial Navigation Systems Correction with Precession Angle Sensors in Aircrafts. *Sensors* **2019**, *19*, 5016.
https://doi.org/10.3390/s19225016

**AMA Style**

Chen D, Neusypin K, Selezneva M, Mu Z.
New Algorithms for Autonomous Inertial Navigation Systems Correction with Precession Angle Sensors in Aircrafts. *Sensors*. 2019; 19(22):5016.
https://doi.org/10.3390/s19225016

**Chicago/Turabian Style**

Chen, Danhe, Konstantin Neusypin, Maria Selezneva, and Zhongcheng Mu.
2019. "New Algorithms for Autonomous Inertial Navigation Systems Correction with Precession Angle Sensors in Aircrafts" *Sensors* 19, no. 22: 5016.
https://doi.org/10.3390/s19225016