In order to ensure the effectiveness of geomagnetic navigation, as the foundation, the precise measurement of geomagnetic field must be guaranteed; namely, aircraft aeromagnetic compensation is worthy of being further studied. In this paper, the classical aircraft aeromagnetic compensation algorithm based on Leliak Model is analyzed and an aircraft aeromagnetic compensation algorithm based on fuzzy adaptive Kalman filter is proposed, which is a new approach for aircraft to achieve aeromagnetic compensation. Simulation results show that it has better compensation performance without relying on the aircraft attitude.

Measurement of geomagnetic field refers to obtaining the field strength of carrier location accurately and in a real-time manner, and to improve the accuracy of measurement, there are mainly two ways: on one hand, improving the measurement precision of the sensor and, on the other hand, overcoming the interference caused by carrier’s own magnetic field [

Leliak had a further study on this problem and found a 16th-order linear model, called “Leliak Model”, to achieve the aeromagnetic compensation, which is used as the standard method in practical application [

Kalman filter has been widely used to forecast system state vectors and estimate system parameters since it was invented by Stanley Schmidt because of its high accuracy with strong ability of interference suppression [

Due to the fact that the existing works on aeromagnetic compensation were all found to rely on the aircraft attitude angle, the accuracy and singularity will be influenced. Therefore, it is necessary to make researches on aeromagnetic compensation algorithm using Kalman filter, which has better compensation performance without relying on the aircraft attitude.

At present, the research on aeromagnetic compensation algorithm using Kalman filter is seldom. In this paper, we proposed a new way to achieve aircraft aeromagnetic compensation, which can avoid the classical method limitation of accuracy and singularity. The rest of this paper consists of four sections. Leliak Model is analyzed in Section

The classical aircraft aeromagnetic compensation algorithm based on Leliak Model can be expressed as follows:

Constant magnetic interference is caused by permanent magnet and ferromagnetic materials magnetized permanently, which cannot change according to the carrier attitude and can be considered as a constant, and it can be divided as follows:

Excitation magnetic interference is caused by soft iron material magnetized by earth’s magnetic field temporarily, which is proportional with the earth’s magnetic field, and its expression is

Eddy current interference is caused by the changes of magnetic flux when the carrier’s attitude is changing, and there is eddy current among the conductor materials, which will bring interference to the magnetic field. This kind of interference is relative to the change rate of magnetic field, and its expression is

The schematic diagram of the Leliak Model is shown in Figure

The schematic diagram of the Leliak Model.

From (

Above all, classical aircraft aeromagnetic compensation algorithm based on Leliak Model is effective to achieve the aircraft aeromagnetic compensation; however, there is coupling among the aircraft three channel motions, which cannot be ignored, and it will influence the measure precision.

In order to take the coupling among the aircraft three channels into consideration, we can establish the mathematical model in the carrier coordinate system according to the interference magnetic field generation mechanism in the following form [

We can obtain formula (

From formula (

Let

Kalman filter can be expressed as formula (

It is obvious that

Since the elements of state vector are constants, the state matrix of the Kalman filter is unit matrix; namely, the state equation is

Take observe error into consideration, the observe equation is

Above all, Kalman filter for aeromagnetic compensation has been established which is expressed by state equation (

Aeromagnetic compensation algorithm proposed here uses Kalman filter method to solve the problem that classical aeromagnetic compensation algorithm cannot ensure the geomagnetic interference being measured accurately [

Aeromagnetic compensation algorithm based on Kalman filter.

Firstly, the state equation of Kalman filter is used to achieve the state predicting, and it is in the following form:

Secondly, we calculate the covariance as follows:

Thirdly, combined with the predicting results and measuring results, the optimal value of

Fourthly, in order to ensure that Kalman filter keeps working until system process is finished, the covariance of

By repeating iteration process above, we can get the estimated

Above all, the aeromagnetic compensation algorithm estimates the elements of

In order to ensure the effectiveness of kalman filter under the noise unmeasured, fuzzy adaptive method is considered to estimate the process noise and observe noise, which can avoid divergent phenomenon caused by noise uncertainty [

Using adaptive method to adjust process noise

(i) Consider

(ii) Consider

(iii) Consider

In order to establish the FIS of aeromagnetic compensation algorithm, performance indicators used to evaluate estimation precision are introduced here with its definition as

From formulas (

Then, using FIS to calculate

(i) For observe noise, the FIS rules are as follows.

If

If

If

where

(ii) For process noise, the FIS rules are as follows.

If

If

If

where

The output of FIS can be plugged in formula (

In this section, experimental simulations will be carried out to evaluate the effectiveness of the proposed aeromagnetic compensation algorithm based on adaptive fuzzy Kalman filter.

Detailed parameters of this algorithm are presented as follows. We put the actual magnetic field data into adaptive Kalman filter proposed in this paper, and the observe noise and process noise are both white noise with 20 nT standard deviation in each axis. Initial condition is

Magnetic field calculated by proposed aeromagnetic compensation algorithm.

Kalman filter output of system state vector elements.

Compensation results of three-axis magnetic field and

From Figure

The limitations of classical aircraft aeromagnetic compensation algorithm based on Leliak Model have been analyzed in this paper and an aircraft aeromagnetic compensation algorithm based on fuzzy adaptive Kalman filter was proposed, which provided a new approach for aircraft to achieve aeromagnetic compensation. Simulation results confirmed the compensation performance of proposed algorithm and proved that FIS is effective in estimating process noise and observe noise. Furthermore, this algorithm does not rely on the aircraft attitude, which has high application value.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China (no. 51379049) and the Fundamental Research Funds for the Central Universities of China (nos. HEUCF110419 and HEUCFX41302).