A novel feature extraction method of direction navigability analysis for geomagnetic navigation

Abstract

In geomagnetic navigation, the estimation of vehicle’s location is only reliable when the matching method is used in some magnetic areas and directions. In order to evaluate the applicable directions, effective direction matching features (DMFs) play an important role. Aiming at this problem, a novel feature extraction method based on the slice lines of the magnetic surface is proposed. Firstly, the demerits of current feature extraction methods are analyzed. Secondly, principle of the proposed method is illustrated and a description system of the DMFs is established based on the slice features. Then in the view of pattern recognition, a BP neural network is trained to evaluate the direction navigability of a magnetic area. Finally, geomagnetic matching experiments are conducted to prove the validity of the slice features. Compared with the features obtained from the Gray Level Co-occurrence Matrix (GLCM), the proposed method is able to extract the features in any direction of the magnetic area and has a higher stability in classification as well.

Keywords

Geomagnetic navigation direction navigability direction matching feature feature extraction GLCM

1. Introduction

Geomagnetic navigation is based on geographic information. It is passive and has no radiation. Most importantly, its location error doesn’t accumulate over time. As a result, geomagnetic navigation is considered an important supplement for inertial system (INS) [1, 2]. On the one hand, the INS provides a rough scale for geomagnetic navigation to confirm its search range of the matching algorithm. On the other hand, the matching results of the geomagnetic navigation can limit the drift of the INS which accumulates along with time. It has been proved that an accurate and real-time geomagnetic matching can be obtained in the magnetic fields with obvious features, rich magnetic information and good navigability [3]. Therefore, it is of great importance and significance to study the magnetic fields’ navigability.

In the view of pattern recognition, the problem of navigability analysis can be divided into two sub-problems: feature extraction and navigability evaluation. Scholars have discussed from different angles and some achievements have been made centered on the two problems. In 2006, Goldernberg [4] pointed out the availability of the magnetic field is different from one place to another and successfully estimated the navigability with several statistical parameters, such as the deviation and correlation radius of the magnetic field. Similarly, Lee and Kwon [5] noticed the importance of choosing an appropriate area for terrain aided navigation. Wang et al. [6] used variance and energy as the features to select a proper area for gravity aided navigation. As only one feature is not enough to evaluate the navigability of a magnetic field, Zhu et al. [7] proposed a comprehensive evaluation method with multiple features. These methods give the principles to find some suitable areas for geomagnetic navigation.

However, with the development of navigability analysis theory, the direction navigability problem is put forward [8]. As geomagnetic navigation is accomplished by matching the magnetic values measured by the magnetic sensor in a vehicle with the stored magnetic map, it is a one-dimensional matching. When the vehicle enters an area in different directions, the matching accuracy is different. It is closely related to the information of the magnetic area in that direction. Meanwhile, it is noted that the problem of direction navigability analysis also exists in other one-dimensional matching circumstances, such as terrain and gravity navigation. Currently, studies on this issue are scant and existed works still have some shortcomings to overcome.

The direction navigability is a property of the magnetic field itself, and it is determined by the magnetic features in that direction. Aiming at extracting effective DMFs for direction navigability analysis (DNA), a novel method is proposed in this paper. By generating a cluster of planes in a given direction and calculating the slice lines between these planes and the magnetic surface, the statistical features in the given direction can be obtained. The paper is organized as follows. The related work is reviewed in Section 2. After that, principle of the proposed method is detailed in Section 3. In Section 4, the DNA model is established. The results of confirmatory and comparative experiments are presented in Section 5. Finally, important conclusions are drawn in Section 6.

2. Related works

Strictly speaking, navigability of a magnetic area presents the “mean” matching suitability in all directions for geomagnetic navigation, while the direction navigability describes the matching suitability in different directions.

At present, methods to extract features to analyze the direction navigability are usually based on statistics or direction filter. For example, with the DMFs extracted from the GLCM of the magnetic field, Zhao et al. [9] preliminarily builds the rules to choose a suitable direction. Wang et al. [10, 11] established a layered decision-making model with the GLCM features and the DMFs extracted by the Gabor filters in four given directions.

GLCM is first proposed by Haralick and Shapiro in the 1970s [12], and it is a statistical method that describes the grayscale’s correlation from a scaled version of the image. GLCM calculats how often a pixel ( $x$ , $y$ ) with gray-level value $i$ occurs horizontally adjacent to a pixel ( $x+a,y+b$ ) with the value $j$ . Each element ( $i, j$ ) in GLCM specifies the number of times that the pixel with value $i$ occurred horizontally adjacent to a pixel with value $j$ . As is in Eq. (1):

$p(i,j,d,\theta)=\{{[{(x,y),(x+a,y+b)|f(x,y)=i;f(x+a,y+b)=j}]}\}$ (1)

where $d=\sqrt{a^{2}+b^{2}}$ , representing the distance between the two pixels. $\theta$ is the angle between the two pixels and $x$ -axis. Theoretically, $\theta$ ranges from 0 ${}^{\circ}$ to 360 ${}^{\circ}$ . When ( $a$ , $b$ ) varies, the GLCMs in different directions are obtained.

GLCM is not directly used to describe the original image. Usually, some statistical features extracted from the GLCM are taken as the DMFs. Table 1 concluded several common features based on GLCM [13, 14].

Here energy measures the texture’s uniformity and roughness of an image. If the gray levels are uniformly distributed, that is all elements of a GLCM are close to each other, then the energy is nearly 0. Contrast is the inertia moment of the GLCM near its leading diagonal, measuring the sharpness of an image; correlation measures the similarity in row or column of an image; and homogeneity describes the closeness between the elements of a GLCM and its diagonal elements. In the formulas, $H$ is the gray level of an image, $P^{\prime}$ ( $i$ , $j$ , $d$ , $\theta$ ) is the normalized matrix of $P(i$ , $j$ , $d$ , $\theta$ ), $M$ represents the row number of the GLCM. $\mu_{i}$ and $\sigma_{j}$ in Eq. (4) are calculated in Eqs (6) and (7), and the calculation of $\mu_{j}$ and $\sigma_{j}$ follow the same principle.

$\displaystyle\mu_{i}=\sum_{i=1}^{H}i\sum_{j=1}^{H}p^{\prime}(i,j,d,\theta)$ (6) $\displaystyle\sigma_{i}=\sum_{i=1}^{H}(i-\mu_{i})\sum_{j=1}^{H}p^{\prime}(i,j,% d,\theta)$ (7)

Table 1

Several DMFs extracted from GLCM

Features	Formulas		Ranges
Energy	$\displaystyle E=\sum\limits_{i=1}^{H}{\sum\limits_{j=1}^{H}{p^{\prime}(i,j,d,% \theta)^{2}}}$	(2)	[0, 1]
Contrast	$\displaystyle\textit{Con}=\sum\limits_{i=1}^{H}{\sum\limits_{j=1}^{H}{\left\|{i% -j}\right\|^{2}p^{\prime}(i,j,d,\theta)}}$	(3)	[0, $M^{2}$ ]
Correlation	$\displaystyle\textit{Cor}=\sum\limits_{i=1}^{H}{\sum\limits_{j=1}^{H}{\frac{(i% -\mu_{i})(j-\mu_{j})p^{\prime}(i,j,d,\theta)}{\sigma_{i}\sigma_{j}}}}$	(4)	[ $-$ 1, 1]
Homogeneity	$\displaystyle\textit{Hom}=\sum\limits_{i=1}^{H}{\sum\limits_{j=1}^{H}{\frac{p^% {\prime}(i,j,d,\theta)}{1+\left\|{i-j}\right\|}}}$	(5)	[0, 1]

For an image, the GLCM can measure its correlation in space, but when it is used in geomagnetic navigation, there are some shortcomings to overcome. First, the GLCM is based on statistic theory and some local features can’t be completely reflected. Second, the magnetic matching is within a small magnetic field, in which the available data is limited. The parameter $\theta$ is determined by the distance between ( $x$ , $y$ ) and ( $x+a$ , $y+b$ ), As a result, $\theta$ cannot reach arbitrary value within 0 ${}^{\circ}$ to 360 ${}^{\circ}$ [15]. Usually, directions 0 ${}^{\circ}$ , 45 ${}^{\circ}$ , 90 ${}^{\circ}$ and 135 ${}^{\circ}$ are chosen to extract the DMFs for geomagnetic navigation.

Gabor filter is capable of direction selection and has good resolution both in space and frequency domain [16, 17]. If proper parameters are chosen, the filter response in arbitrary direction is obtained. And on basis of it, the DMFs for geomagnetic navigation can be extracted. However, versatile parameters of the Gabor filter make it very complicated to design the filter [18]. Currently, there are no general ways to solve the problem and specific issues should be analyzed in practice.

In order to overcome the shortcomings mentioned above, a novel DMF extraction method based on the slice lines of a magnetic field’s surface is proposed, which can be used to extract the features in any direction of the magnetic field. Meanwhile, the method hasn’t so many parameters to adjust and is easy to realize.

Figure 1.

A local magnetic anomaly field.

3. Principle of the method

3.1 Establishment of local magnetic model with high accuracy

Local magnetic model with high accuracy is the foundation to analyze the direction navigability. NGDC-720 is a world’s magnetic anomaly field model released by the USA’s National Oceanic and Atmospheric Administration (NOAA) [19]. Resolution of the model is about several kilometers, which is not applicable for geomagnetic navigation. In this case, some interpolation methods are usually taken to establish an accurate local magnetic model. Among these interpolation methods, the Kriging method is a local spatial interpolation method and has been widely used to establish a magnetic model.

We choose an area from the Y component of the NGDC-720 model, which is within the longitude of [34 ${}^{\circ}$ E, 39 ${}^{\circ}$ E] and latitude of [47.812 ${}^{\circ}$ N, 53.812 ${}^{\circ}$ N], and establish its accurate model with the Kriging interpolation method. Figure 1 shows the established local magnetic model, Fig. 1a is 3-D map and Fig. 1b is its contour map. After interpolation, the resolution of the model is 62.5 m.

3.2 Basic principle to extract the DMFs

In order to overcome the shortcomings of GLCM and make it easier to realize, a novel method to extract the DMFs for DNA is proposed. The main idea is shown in Fig. 2.

Suppose the magnetic field of a small area is:

$z=I(x,y)$ (8)

where ( $x$ , $y$ ) is the latitude and longitude of a place in the area.

As is shown, note $M_{0}(x_{0}$ , $y_{0}$ , $z_{0}$ ) as the location where the vehicle enters, and the angle between the vehicle’s direction and the east is $\theta$ , whose vector form is $\bm{m}$ . Suppose the vehicle moves at uniform speed in a straight line in that area and its altitude doesn’t change during the magnetic matching, then there is one, and only one plane that passes point $M_{0}$ and parallels to vector $\bm{m}$ . Note this plane as $\Pi$ , and $\Pi$ can be expressed as:

$A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0$ (9)

where $A$ , $B$ and $C$ are the coordinates of a non-zero vector $\bm{n}$ . Vectors $\bm{m}$ and $\bm{n}$ satisfies the condition: $\bm{m}$ $\bot$ $\bm{n}$ .

Figure 2.

Schematic diagram of DMF extraction method.

Use plane $\Pi$ to slice the surface of the magnetic field and a slice line on the surface is obtained. If measurement errors of the magnetic sensor and the disturbances from external circumstances aren’t considered, the magnetic data on the slice line can be regarded as the measured value of the magnetic sensor. Its information represents the magnetic information in direction $\theta$ , and the more abundant it is, the fewer location error is obtained. Combine Eqs (8) and (9) and the slice line between plane $\Pi$ and the magnetic surface, noting as C, can be expressed in Eq. (10):

$C:\begin{cases}{I(x,y)=f(x,y)}\\ {A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0}\\ \end{cases}$ (10)

However, it should be noted that only one slice line is not enough to represent the whole information of the magnetic field in a direction, a number of slice lines are needed to give a complete expression of the direction information. So consider the vehicle enters the area from other positions, noting as $M_{i}$ ( $i=$ 1: $N, N$ is the index of different positions), and follow the method mentioned above, $N$ slice lines in direction $\theta$ are obtained, noted separately as $C_{1}$ , $C_{2}$ , …, $C_{N}$ . They are the basis to extract the features for DNA. This covers the main idea of the proposed method. For convenience, the features extracted based on the slice lines are noted slice features in the following.

3.3 Extraction of the slice features

In this section, a slice line in direction $\theta$ is taken as an example to explain how to calculate the slice features. A total of 7 statistics are listed below:

(1) (1)
Mean value $\bar{I}$ and variance $\sigma^{2}$ . $\bar{I}$ reflects mean level of the data and $\sigma^{2}$ measures the total fluctuation and distribution of the magnetic field. And the greater the standard deviation is, the more drastically a magnetic field changes.

$\begin{cases}{\sigma=\sqrt{{\displaystyle\frac{1}{XY-1}}\sum\limits_{i=1}^{X}{% \sum\limits_{j=1}^{Y}{(I(i,j)-\bar{{I}})^{2}}}}}\\ {\bar{{I}}={\displaystyle\frac{1}{XY}}\sum\limits_{i=1}^{X}{\sum\limits_{j=1}^% {Y}{I(i,j)}}}\\ \end{cases}$ (11)

where $X$ and $Y$ are the dimension of $I(x$ , $y$ ) in $X$ -axis and $Y$ -axis.
(2)
Ratio of variance and mean value $r$ . It measures the relative fluctuation of the magnetic field.

$r=\frac{\sigma^{2}}{\bar{{I}}}$ (12)
(3)
Kurtosis coefficient $\kappa$ . $\kappa$ measures the centralization grade of the magnetic data around the mean value. Greater $\kappa$ represents higher centralization grade.

$\kappa=\frac{1}{XY}\sum\limits_{i=1}^{X}{\sum\limits_{j=1}^{Y}{\frac{(I(i,j)-% \bar{{I}})^{4}}{\sigma^{4}}-3}}$ (13)
(4)
Skewness coefficient $s$ . It measures the symmetry of the magnetic field. A bigger $s$ means the field is less symmetrical.

$s=\frac{1}{XY}\sum\limits_{i=1}^{X}{\sum\limits_{j=1}^{Y}{\frac{(I(i,j)-\bar{{% I}})^{3}}{\sigma^{3}}}}$ (14)
(5)
Information entropy $H$ . It reflects the mean information of the magnetic field. The smaller it is, the more unique the field changes.

$H=-\sum\limits_{i=1}^{X}{\sum\limits_{j=1}^{Y}{p(i,j)\cdot\log(p(i,j))}}$ (15)

where

$p(i,j)=\frac{I(i,j)}{\sum\limits_{i=1}^{X}{\sum\limits_{j=1}^{Y}{I(i,j)}}}$

.
(6)
Variation entropy of magnetic field $H_{d}$ . It reflects the distinctness of the magnetic field. The reason why adding this parameter is it shows better performance in describing the magnetic field’s information when it changes obviously.

$H_{d}=-\sum\limits_{i=1}^{X}{\sum\limits_{j=1}^{Y}{q(i,j)\cdot\log(q(i,j))}}$ (16)

where

$q(i,j)=\frac{C_{ij}}{\sum\limits_{i=1}^{X}{\sum\limits_{j=1}^{Y}{C_{ij}}}},% \quad C_{ij}=\frac{\left|{I(i,j)-\bar{{I}}}\right|}{\bar{{I}}}.$

Features of other slice lines can be obtained following the same steps. And they together make up the slice features in direction $\theta$ . Based on them, the DNA model is established in Section 4.
4. Establishment of DNA model

4.1 Evaluation criteria of the direction navigability

Generally, the matching probability is taken as the index to evaluate the navigability of an area [20]. It reflects the matching result’s reliability when the vehicle is located in that area. The matching probability can be calculated by simulation experiments. In this paper, we use the idea that computes the matching probability of an area to calculate the matching probability in different directions: fix a direction $d$ and simulate the matching process for $N$ times, let vehicle’s enter positions of $N$ times pass every possible grid point of the magnetic area, whose index is $i$ , then the matching probability $P_{r}(d,i)$ is the ratio of the correct matching times and the total matching times $N$ , as is in Eq. (17):

$\begin{cases}{\textit{Pr}(d,i)={\displaystyle\frac{\sum\limits_{i=1}^{N}{% \textit{CM}(d,i)}}{N}}}\\ {\textit{CM}(d,i)=\begin{cases}0&(E_{p}(d,i)>\textit{threshold})\\ 1&(E_{p}(d,i)\leqslant\textit{threshold})\\ \end{cases}}\\ \end{cases}$ (17)

where $\sum\nolimits_{i=1}^{N}{\textit{CM}(i,d)}$ counts the correct matching times of direction $d$ in magnetic area $i$ , $E_{p}(d,i)$ is the location error of the matching algorithm, threshold is a parameter to judge whether a matching is successful. In the paper, the threshold is set to 2 grids of the magnetic area, namely 125 m.

In practice, evaluating whether a given direction is suitable to match, i.e. whether the given direction can provide reliable location for the vehicle, is more meaningful than giving the precise correct matching probability. In this sense, the DNA for geomagnetic navigation can be regarded as a classification problem. In the paper, the directions are divided into two categories according to their matching probabilities: if $P_{r}(d,i)>$ 0.9, meaning the probability to have a reliable location by magnetic matching is larger than 0.9, then the corresponding direction is “suitable for matching”, noting as category “1”; if $P_{r}(d,i)\leqslant$ 0.9, then it is “unsuitable for matching”, noting as category “0”.

4.2 Direction navigability evaluation model

In this section, a BP network with good generalization ability is used to build the direction navigability evaluation model. First, we divide the local magnetic anomaly field in Section 3 into numbers of rectangular areas with the size of 20 $\times$ 20 and note them as candidate matching areas. Then the evaluation model is established following the next steps:

(1) (1)
Extract the DMFs. Randomly select a number of candidates and choose $N$ directions for navigability analysis, denoting by $\theta_{1},\theta_{2},\ldots,\theta_{N}$ . Generate 19 planes in a given direction, they are parallel to each other and the distances between them are equal. Slice a candidate and let the middle plane passes through the center point of the candidate, then 19 slice lines are obtained. Calculate their slice features with proposed method and 7 $\times$ 19 $=$ 133 statistical features are extracted to describe the information in a given direction. Calculate the slice features in other directions of the remained candidates with the same process.
(2)
Appoint category labels for each direction of all candidates according to their direction matching probabilities.
(3)
Select proper structure for the BP neural network (BPNN). According to the dimension of the slice features and the category labels, the input and output nodes of BPNN are set to 133 and 1. A two-hidden-layer of 50 $\times$ 10 is chosen by experience.
(4)
Select samples to train and test the BPNN. By times of supervised learning, a DNA model for geomagnetic navigation is established.

Once the DNA model is built and the extracted DMFs are input, the model will predict whether a direction of a magnetic area is suitable to provide a reliable matching result for the vehicle. In Section 5.1, geomagnetic matching experiments will prove the validity of the proposed method.

As the initial weights of the BPNN are randomly set, we train and test the BPNN for 50 times and select the network with the best performance as the final model for DNA. Meanwhile, the classification accuracy of each time is recorded to evaluate the stability of the slice features. In the paper, three kinds of classification accuracies, namely one category accuracy (CA), the average accuracy (AA) and the overall accuracy (OA) are introduced, as is in Eqs (18)–(20):

$\displaystyle\textit{CA}_{i}=\frac{N(\textit{PredictionC}=\omega_{i}\cap% \textit{RealC}=\omega_{i})}{N(\textit{RealC}=\omega_{i})}$ (18) $\displaystyle\textit{AA}=\frac{1}{2}\sum\limits_{i=1}^{2}{\frac{N(\textit{% PredictionC}=\omega_{i}\cap\textit{RealC}=\omega_{i})}{N(\textit{RealC}=\omega% _{i})}}$ (19) $\displaystyle\textit{OA}=\frac{\sum\limits_{i=1}^{2}{N(\textit{PredictionC}=% \omega_{i}\cap\textit{RealC}=\omega_{i})}}{\sum\limits_{i=1}^{2}{N(\textit{% PredictionC}=\omega_{i})}}$ (20)

where $\omega_{i}$ is category label, corresponding to 0 and 1. $N(\textit{PredictionC}=\omega_{i})$ is the number of samples in category $\omega_{i}$ , $N(\textit{PredictionC}=\omega_{i}\cap\textit{RealC}=\omega_{i})$ is the number of samples in category $\omega_{i}$ , meanwhile they are classified as category $\omega_{i}$ .
5. Experiment results

5.1 Geomagnetic matching experiments

In order to prove the validity of the slice features, we randomly select 400 candidates from the local magnetic anomaly model in 3.1 and choose six representative directions, namely 0 ${}^{\circ}$ , 30 ${}^{\circ}$ , 60 ${}^{\circ}$ , 90 ${}^{\circ}$ , 120 ${}^{\circ}$ and 150 ${}^{\circ}$ , to analyze. First, following the steps in Section 4.2, a direction navigability evaluation model for the given directions are built. After that, select several candidates from remained areas and extract their features in six directions above. Then the trained BPNN model is used to evaluate their direction navigability. Figure 3 shows four candidates’ 3-D view and Table 2 lists out their navigability in six directions.

In Table 2, output “1” means the corresponding direction is suitable for geomagnetic navigation and “0” is unsuitable. In order to test the predicted results, simulated matching experiments are conducted in six directions of the four candidates. The matching algorithm is the Terrain Contour Matching (TERCOM). Figure 4 and Table 3 show the matching results and location errors. Due to space limitations, the matching results of Candidate 1 in 30 ${}^{\circ}$ and 90 ${}^{\circ}$ , Candidate 2 in 0 ${}^{\circ}$ and 30 ${}^{\circ}$ , Candidate 3 in 30 ${}^{\circ}$ and 120 ${}^{\circ}$ , Candidate 4 in 60 ${}^{\circ}$ and 150 ${}^{\circ}$ are listed.

Table 2
Predicted direction navigability of four candidates

Directions	0 ${}^{\circ}$	30 ${}^{\circ}$	60 ${}^{\circ}$	90 ${}^{\circ}$	120 ${}^{\circ}$	150 ${}^{\circ}$
Candidate 1	0	0	0	1	0	0
Candidate 2	1	0	1	1	1	1
Candidate 3	1	0	1	1	1	1
Candidate 4	1	1	1	1	1	1

Table 3

Location errors of the four candidates (Unit: m)

Candidates	Candidate 1		Candidate 2		Candidate 3		Candidate 4
	30 ${}^{\circ}$	90 ${}^{\circ}$	0 ${}^{\circ}$	30 ${}^{\circ}$	30 ${}^{\circ}$	120 ${}^{\circ}$	60 ${}^{\circ}$	150 ${}^{\circ}$
Latitude error	21.07	0	5.00	21.08	21.07	$-$ 2.50	2.50	41.39
Longitude error	207.86	5.00	62.50	193.35	190.25	21.20	16.79	2.51

Figure 3.

3-D views of four candidates.

Figure 4.

Matching results of four candidates in six directions.

In Table 3, the location errors of Candidate 1 in 90 ${}^{\circ}$ , Candidate 2 in 30 ${}^{\circ}$ , Candidate 3 in 30 ${}^{\circ}$ and Candidate 4 in 60 ${}^{\circ}$ and 150 ${}^{\circ}$ are within 2 grids, so the matching results can be used to locate the vehicle and eliminate the accumulated errors of INS. In other words, these directions of the four candidates are suitable for matching. On the other hand, location errors of Candidate 1, 2 and 3 in 30 ${}^{\circ}$ are beyond the set threshold, they are considered unsuitable to locate the vehicle. Compare the matching results with the predicted direction navigability in Table 2 we can see the results of the direction navigability evaluation model and the matching experiments are consistent. It proves the validity of the slice features.

5.2 Comparison between GLCM features and slice features

As is mentioned, the GLCM features cannot extract the features in arbitrary angle, and 0 ${}^{\circ}$ , 45 ${}^{\circ}$ , 90 ${}^{\circ}$ and 135 ${}^{\circ}$ are usually selected to extract their DMFs. In order to compare the performance of slice features and GLCM features, we randomly choose 400 candidates from the local magnetic area and calculate the two kinds of features in four directions. As a result, 1,600 features in different directions are obtained, among which 2/3 are used to build the direction navigability evaluation model, the other 1/3 are to test the model.

It should be noted, as the dimensions of the slice features and GLCM features differ, the input nodes of BPNN are different. According to Table 1, the GLCM features in a direction contain 4 statistic parameters, so the input nodes of GLCM model are 4. Structure of the slice model and other parameters of the GLCM model are the same as it is in Section 4.2. Figures 5 and 6 show test samples’ prediction navigability categories and their real navigability categories.

Table 4
Classification accuracies of two features

	CA ${}_{1}$	CA ${}_{0}$	AA	OA
GLCM features	87.39	83.68	85.53	85.77
Slice features	86.41	83.86	85.14	85.30

Figure 5.

Classification results of GCLM features.

Figure 6.

Classification results of slice features.

Obviously, though a few exceptions exist, most test samples are correctly classified, their prediction results are consistent with their matching experiments’ results. In Table 4, the classification accuracies of the slice features and the GLCM features are calculated according to their definitions in Section 4.2.

As is shown, the overall classification accuracies (OA) of the slice features and GLCM features respectively are 85.77% and 85.30%, proving they are both effective to predict the direction navigability. On the other hand, the classification accuracy within category “1” (CA ${}_{1}$ ) of the GLCM features is 87.39%, which is a bit higher than the slice features’ 86.41%. But for category “0” (CA ${}_{0}$ ), GLCM features’ classification accuracy is lower than the slice features. The average classification accuracies (AA) of the two features show little difference. If we slice the magnetic area with more planes, more DMFs can be extracted and the classification accuracy can be enhanced. This will be discussed in our later research.

Divide the OA of 50 times of BPNN’s training into three scales: [0, 70%), [70%, 80%) and [80%, 90%], and record the times they appear in each scale. Results show there are 23 times that the GLCM features’ OAs are below 80% and 12 times below 70%. While there are only 2 times that the slice features’ OAs are below 80%, other OAs are all above 80%. It means the slice features have better stability than the GLCM features when they are used to analyze the direction navigability for geomagnetic navigation.

6. Summary

To sum up, the following conclusions can be drawn: (1) The feature extraction method based on the slice lines is feasible and effective. (2) The slice features have better stability than the GLCM features for direction navigability analysis. (3) The GLCM method cannot extract features in any direction of the magnetic area, while the proposed method can. (4) The proposed method has less parameters to be adjusted than the Gabor filter, which simplifies the procedures to extract DMFs. In further study, the proposed DMF extraction method can be combined with the Gabor filter to improve the model’s prediction accuracy and lay the foundation for geomagnetic navigation.

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A novel feature extraction method of direction navigability analysis for geomagnetic navigation

Abstract

Keywords

1. Introduction

2. Related works

3.1 Establishment of local magnetic model with high accuracy

3.2 Basic principle to extract the DMFs

4.1 Evaluation criteria of the direction navigability

5.1 Geomagnetic matching experiments

Table 2 Predicted direction navigability of four candidates

Table 4 Classification accuracies of two features

References

Table 2
Predicted direction navigability of four candidates

Table 4
Classification accuracies of two features