1. Introduction
Global Navigation Satellite Systems (GNSSs) are one of the core technologies for civil navigation and positioning. As the application environment becomes more complex and profound, navigation and positioning are being continuously optimized for accuracy, stability, and reliability. Specifically, when GNSS signals are affected by occlusion or electromagnetic interference, this can easily cause delays or the short-term loss of positioning signals during transmission and reception. Being in the rejection environment for a short period rapidly increases errors in the system parameters over time, making it difficult to guarantee positioning accuracy and output stability. At this point, the limitations of using a single navigation and positioning method become apparent. To avoid this problem, scholars have introduced an additional navigation and positioning method, “GNSS+”, to build a combined navigation and positioning system (the connected navigation and positioning method). The more mature ones are GNSS and IMU, INS, DR, UWB, and vision [
1,
2,
3,
4] combined, which can provide complementary advantages and guarantee accuracy and stability. For example, one study [
5] combined RTK-GPS, IMU, and a laser scanner to design a navigation and positioning system based on an automatically tracked tractor with data processing using a Kalman filter, and the experiments showed that the lateral error was less than 0.05 m in a straight line. The authors of [
6] propose a combined navigation system based on SINS/GPS/TAN to address the problem of GPS/TAN signal failure in a denial environment, and a federal Kalman filter fuses the navigation information. The results show that the operating trajectory is close to the ideal course, and the positioning accuracy meets the requirements. In [
7], a combined SINS/GPS/ADS/DVL navigation system based on a navigation switching strategy is proposed; it uses a federal filtering method to improve navigation accuracy while avoiding navigation serial data processing errors, and the reliability of the system is verified. In [
8], a combined vision-assisted INS/odometer navigation and positioning method is proposed to calibrate the INS/odometer via image matching in a rejection environment, and a dual-rate Kalman filter is used to achieve the data fusion of vision, the inertial navigation system, and odometer. Its performance is verified by simulation and field tests. The authors of [
9] proposed a navigation system for agricultural robots based on GPS + monocular vision + a LiDAR sensor. The analysis shows that such schemes apply more mathematical models and model them differently. According to their systems, they usually design different navigation and positioning algorithms, such as Kalman filtering methods (KF, EKF, and UKF), which are essential for undertaking combined navigation and positioning.
Meanwhile, with the extension of artificial intelligence and intelligent optimization algorithms to navigation and positioning and information fusion technologies, navigation and positioning systems’ intelligence, flexibility, and adaptability have been improved. Commonly used methods include neural network algorithms [
10,
11], genetic algorithms [
12,
13], particle swarm optimization algorithms [
14,
15], and artificial bee colony algorithms [
16,
17], as well as the mutual fusion of each algorithm. For example, in [
18], for INS/GNSS systems, a combination of a trace-free Kalman filter (UKF) and external input (NARX) are proposed for navigation and positioning. In [
19], an EKF fusion algorithm based on a MEMS multi-sensor IMU system is designed to realize the fusion processing of multi-sensor measurement data. Meanwhile, ref. [
20] proposes an optimization method based on an adaptive Kalman filter, which maintains good navigation accuracy when GPS is interrupted. Moreover, ref. [
21] proposed a greedy sample gossip distributed filter fusion algorithm, introducing information-weighted fusion and sample insatiable gossip averaging protocol. The authors of [
22] presented an improved weighted particle-swarm-optimized Kalman filtering algorithm for agricultural machinery navigation. The study verified the feasibility and superiority of the modified weighted particle-swarm-optimized particle filtering through simulation experiments, which improved the positioning accuracy of the combined agricultural machinery navigation system. In [
23], an improved AUV combined navigation method with a genetic neural network is proposed for the problem of EKF filtering divergence, and its performance is verified. In [
24], an improved combined navigation positioning algorithm based on a multilayer perceptron neural network (MLPNN) was proposed to train the neural network when the GPS signal is valid and use the neural network to correct the navigation error of INS when it is out of the lock, in order to achieve the continuity of combined navigation.
It is worth noting that, because BP neural networks have strong self-learning and self-adaptive capabilities, and their fault tolerance and generalization capabilities are also excellent, they can also be optimized with the introduction of other algorithms and have a certain degree of open-source capability. Therefore, scholars have used this method to predict and correct the output of navigation and positioning [
25,
26,
27]. Typically, a multi-sensor information fusion algorithm based on a GA (genetic algorithm)-BP network is proposed in the literature [
28] for a combined RTK-GPS and IMU system, enabling the system to improve its accuracy to some extent. The authors of [
29] proposed an ABCBP neural-network-assisted Kalman filtering fusion algorithm for BDS/INS navigation signal fusion and error accumulation after the loss of the lock. Meanwhile, ref. [
30] proposed an improved UKF navigation and positioning algorithm based on particle-swarm-optimized BP networks to avoid the problem of UKF performance divergence caused by unknown system noise or inaccurate statistical features. In [
31], a GA-BP neural-network-based UWB/IMU localization fusion method was proposed, and the average localization error of this method was around 9.6 cm. The above analysis shows that the application of such schemes in combined navigation and positioning usually involves the idea of optimization. However, the BP network has a slow convergence speed and quickly falls into local extremes, making it difficult to guarantee the accuracy and reliability of navigation and positioning in the denial environment, and there are relatively few practical applications.
At the same time, researchers have also conducted a series of optimizations and improvements based on the BP model to enhance its stability and accuracy, achieving better results than the original BP model. The authors of [
32] used artificial neural networks to simulate errors that occur in integrated navigation systems without satellite navigation system signals and proposed a new method to improve the coordinate and velocity accuracy of integrated navigation systems without receiving global navigation satellite system signals. Meanwhile, [
33] proposes an extreme learning machine as a mechanism for learning stored digital elevation information to assist drones in traversing terrain without the need for GPS. This algorithm meets the needs of online implementation by supporting multi-resolution terrain access, thereby generating high-precision real-time paths within the allotted timeframe. The authors of [
34] proposed a uniform sensor fusion optimization method, which can not only estimate the calibration constant of sensors in real time but also automatically suppresses degraded sensors while maintaining the overall accuracy of the estimation. The weights of the sensors are adaptively adjusted based on RMSE, involving the weighted average of all sensors. Elsewhere, ref. [
35] utilized the Harris Hawks optimization algorithm (HHO) to optimize the random weights and thresholds of BPNN to obtain the optimal global solution that enhances UWB indoor positioning accuracy and NLOS resistance. This method has higher calibration accuracy and stability than BPNN, making it a feasible choice for scenarios that require high positioning accuracy.
Positioning information is diverse, scalable, and complex for combined systems. Therefore, navigation and positioning algorithms are designed with specific adaptability based on the basic requirements of robustness, parallel processing capabilities, and additional indicators of information samples such as operational speed and accuracy. Therefore, based on the above research analysis, this paper designs a Kalman system filter to improve the robustness of the information fusion of a BDS/INS navigation and positioning system for agricultural machinery, avoiding the problem of the gradual decrease in positioning accuracy and stability under a single INS system when the signal is out of the lock. On this basis, we propose a navigation and positioning algorithm based on an improved swarm-algorithm-optimized BP network (referred to as the IABC-BP algorithm). The main contributions of this paper are as follows:
An improved swarm algorithm is proposed to ensure the balance between convergence speed, swarm flexibility, and searchability. We introduce an adaptive judgment factor ξ and a convergence speed adjustment factor α to improve the search formula, which improves the convergence speed and prevents the algorithm from falling into a local optimum; meanwhile, the adaptive judgment factor ξ is used to optimize the selection probability to improve the global search ability and effectiveness of the colony.
This study proposes an adaptive implicit layer node selection formula by introducing a judgment coefficient σ to avoid the BP network’s overfitting problem and improve the network’s performance and generalization ability.
Using the weights and thresholds of the BP network as the optimization objectives and the mean square error of the sample correction value and the actual value as the objective function values of the improved ABC algorithm, the enhanced swarm algorithm is reasonably integrated with the BP network. The model can be trained when the BDS signal is valid, and the INS navigation deviation can be corrected when it is out of the lock, which prevents filtering divergence and improves the robustness, reliability, and continuity of the system time.
This study is organized as follows:
Section 2 introduces the experimental materials and methods, mainly introducing the BDS/INS model principle and related improvement work for experimental selection.
Section 3 mainly introduces the results of the experiment, and analyzes and demonstrates the experimental results.
Section 4 discusses the experimental results of this article and provides prospects for future research directions.
Section 5 summarizes and elaborates on the work and achievements of the entire article.
3. Results
3.1. Test Preparation and Protocol Design
The BDS/INS navigation and positioning system of the agricultural machine used in the experiment is shown in
Figure 5a, and the INS is embedded in the package box and connected to the industrial control computer. The test location is the engineering building and exhibition hall area of Qingdao Agricultural University (120.40° E, 36.32° N), and the movement route is shown in
Figure 5b, with the black curve indicating a straight path and the red angle indicating a turn. The test process shown in
Figure 6a shows the base station that was erected, and its operation conditions can be controlled according to the experimental needs.
Figure 6b shows the test process, and the agricultural system operates normally.
In this paper, the simulation software used is MATLAB R2020a, and the model of the experimental agricultural machinery is Weituo TY300 tractor, produced in Shandong Province, China, provided by Weifang Zhongte Agricultural Equipment Co., Ltd. In addition, the experimental device also includes: BDS receiver, INS (model: Y61 six axis attitude angle sensor), control execution device, and front wheel angle sensor.
For the purposes of illustration, the locations of this experiment are all latitude and longitude coordinates, with an initial position of (120.40° E, 36.32° N), an initial heading of 65.8° (north of east), an initial velocity of 0 m/s, a period of T = 310 s, and a sampling interval of 1 s. The experiments in this study are validated in three main aspects:
The feasibility, flexibility, and other performance metrics of the improved bee colony algorithm are assessed via test functions;
The performance, accuracy, and practical effect of the model before and after combining the Kalman filter are verified via the IABC-BP algorithm;
The performance of the combined BDS/INS navigation system after applying the IABC-BP fusion algorithm is verified and the comparison is illustrated.
The parameters of the swarm algorithm are described as follows: Maxcycle = 1000, the number of swarms N is related to the number of nodes in the BP network, = 1.1, and = 0.1. The parameters of the BP network are described as follows: the number of training step epochs = 1000, the learning rate = 0.01, the minimum error of the training target = 0.000001, and the input I and output node O are determined according to the actual number of samples are determined.
3.2. Improved Algorithm Performance Testing
The primary purpose of this experiment is to verify the feasibility and superiority of the improved bee colony algorithm proposed in this paper. Three test functions are selected for this experiment to verify this improved algorithm and compare it with the traditional ABC algorithm in order to demonstrate its superior performance.
The test functions are shown in
Table 1, where the swarm size
N is set to 100. Since the convergence speed of the improved algorithm is accelerated, dimension
D is set to 5, 50, and 100 as independent variables to avoid algorithm discontinuity for the purposes of comparison and illustration. The test results are shown in
Table 2,
Table 3 and
Table 4.
In this experiment, the effect of the randomness factor is taken into account. Therefore, under the same test conditions, the function optimization experiments of both traditional and modified swarm algorithms are conducted 20 times, and data such as the optimal value and mean squared error are recorded when downloading different dimensions. The optimal value reflects the quality of understanding, and the mean square deviation reflects the robustness and stability of the algorithm. Analyzing the data in
Table 2 and
Table 4, we can see that:
- (1)
The optimal values of both algorithms show a decreasing trend with a decrease in dimensionality. When the dimensionality is 100 (D = 100), the optimization index values of the algorithm proposed in this study are better than those of the ABC algorithm.
- (2)
When the dimension of the function is reduced to 5 dimensions, the advantage of this algorithm is more pronounced. The accuracy of the optimal value, the worst value, the average value, and the mean squared error in different dimensions (especially in high dimensions) is higher than that of the ABC algorithm, which indicates the high quality of the solution of the IABC algorithm and the improved robustness and stability of the algorithm.
- (3)
The comparison of the IABC algorithm in the two search intervals [−1, 1] and [0, 1] shows that the optimal solution and the variance are significantly smaller in the interval [−1, 1], which indicates that the IABC algorithm achieves better results in the overall search capability and in jumping out of the local optimum.
For the three functions listed in
Table 1, the ABC algorithm is compared with the IABC algorithm in 50 dimensions (interval [0, 1]); this method reflects the performance of the algorithm more intuitively, and the comparison results are shown in
Figure 7a–c. The comparison clearly shows that the improved algorithm has substantially improved convergence speed, accuracy, and global optimization capabilities. A comprehensive analysis shows that the IABC algorithm achieves better results and can be used for subsequent optimization work.
3.3. BP Neural Network Performance Analysis
This section focuses on the performance verification of the improved BP network and IABC-BP network algorithms, and the experimental data of the motion path trajectory in
Section 3.1 are selected. This experiment compares the BP network, Kalman filter–BP neural network (KF-BP), the IABC-BP network, and Kalman filter–IABC-BP network (KF-IABC-BP). The performance of the four methods was evaluated by filtering and correcting the velocity information values, and the comparison of the error curves of the velocity correction values of the four methods are shown in
Figure 8 and
Figure 9.
Considering the need for the convenient and intuitive analysis of the model’s performance in the experiment, the mean absolute error
MAE, mean square error
MSE, root mean square error
RMSE, and correlation coefficient
R are used as the judging indexes, and the related data statistics are shown in
Table 5.
Based on the analysis of the experimental results, it can be concluded that:
- (1)
All four models can filter the speed. However, there are certain differences in the indicators achieved by different models.
- (2)
The BP neural network model is relatively poor and has the largest error. The MAE, MSE, and RMSE values of the BP model are the largest, which indicates that the model is less accurate and does not reflect the actual situation of the error. In particular, the smallest R-value indicates that the traditional BP model has certain defects, which are mainly shown by the increase in the error with time. The performance of the BP model is improved by introducing the Kalman filter based on the BP model.
- (3)
Both the IABC-BP and KF-IABC-BP models exhibit better experimental results, and the error values are less than 0.037 regarding the differences between various evaluation indexes.
- (4)
Compared with other models, KF-IABCBP has the best performance, The value of the correlation coefficient R reached 0.9988, which is better than that of the other models; the relationship between the variables is closer, and the error will stabilize with time.
- (5)
With the RMSE value as the main evaluation index, the performance of the KF-IABC-BP model is improved by 90.65%, 84.11%, and 25.96% compared with the other models, which indicates that the Kalman-filter-based IABC-BP neural network algorithm model established in this paper has sufficient feasibility.
3.4. Performance Analysis under Different Modes
In this section, the performance of the BDS/INS system for agricultural machinery is verified after applying the IABC-BP navigation and positioning algorithm model. We ascertain the rationality, flexibility, and timeliness of information fusion, as well as demonstrating the working performance when the satellite signal is out of the lock or weak and the accuracy of the prediction correction of the data. The experimental protocols are:
- (1)
To verify the performance of the BDS/INS system when applying the IABC-BP model for information fusion and filter correction when the signal is not out of lock, and all sensor data are collected normally.
- (2)
To verify the performance of the IABC-BP model algorithm and the accuracy of the predicted output compensation system when setting the lock loss condition under the above conditions.
3.4.1. Performance Analysis of the System Information Fusion Model
When the signal is not out of the lock, the BDS receiver data are generally sent and received in the RTK positioning mode (sampling frequency 1 HZ), and the INS system data are collected normally (sampling frequency 10 HZ). At this time, model switch
S1 is connected,
S2 is not connected, and the information fusion mode is turned on. The comparison of longitude and latitude trajectories before and after filtering with the IABC-BP neural network fusion algorithm is shown in
Figure 10, and the comparison of velocity and course is shown in
Figure 11.
By comparing and analyzing the longitude and latitude trajectories, speed, and heading before and after comprehensive filtering, it can be seen that filtering speed and heading can eliminate coarse errors, improve accuracy, make speed changes smoother and more stable, and enable agricultural machinery to achieve a uniform acceleration movement.
The statistics of position, velocity, heading, and other related deviations are shown in
Table 6, which can be analyzed as follows:
- (1)
After the latitude and longitude data are processed by the model, the corresponding maximum deviation values are significantly smaller, but the data for altitude processing deviation are relatively large.
- (2)
MAE, MSE, and other indicators show that the model exhibits good performance in data signal fusion. The velocity deviation also falls within a small range, indicating that the agricultural machine can maintain a uniform acceleration movement.
- (3)
For heading processing, due to the small number of training samples, the maximum heading deviation is relatively large, with a value of 8°. In future research, the heading accuracy will continue to be improved.
Overall, the effectiveness and feasibility of the algorithm are relatively high and meet the requirements of high accuracy.
The processing results of the acceleration and attitude information collected using inertial sensors are shown in
Figure 12, which can be analyzed as follows:
Within a running time of 3500 ms, the model can effectively process acceleration and altitude information. The model handles the X, Y, and Z directions well.
Although the attitude changes quickly during the experiment, with the direction adjustment angle being especially large, the model still shows a good processing effect.
The model is relatively well trained, and the data-filtering process is maintained within a specific error range, with small errors that meet the requirements of the model.
The corresponding statistics are given in
Table 7, which shows that the error indicators are relatively small and the correlation coefficient
R > 0.90, meaning that the algorithm model accurately predicts the data and guarantees the subsequent correction of the compensated BDS information.
3.4.2. Performance Analysis of the System Compensation Correction Mode
In the agricultural navigation test, no signal loss lock occurred during the motion. However, to verify the performance of the IABC-BP model in the case of a satellite lockout, a satellite lockout duration of the 60 s was set manually, setting the following interference condition: turn off the base station during the test. The trajectory diagram and each part of the out-of-lock time are shown in
Figure 13.
Based on the above setup, corresponding experiments were conducted to compare three navigation and positioning methods before and after the satellite loss of lock: the INS system alone, Kalman filter correction after the loss of the lock, and the predictive correction of data using the IABC-BP algorithm proposed in this paper. The experimental results are shown in
Figure 14.
By analyzing the above experimental results, it can be concluded that:
- (1)
After the satellite loss of lock, the position, velocity, and attitude values all undergo unknown changes. At this point, the drift from the loss of lock is not changed because there are no observations of the satellite signal to update the measurement equations of the Kalman filter, resulting in the model’s inability to estimate the information values correctly (blue line).
- (2)
Since the IABC-BP model proposed in this paper is trained on the information data of BDS/INS when the signal is not out of the lock, the corresponding data are stored. Moreover, when the BDS signal is weak or out of the lock, the IABC-BP model proposed in this paper can be used instead of the BDS system to perform prediction corrections for the out-of-lock signal (green line).
- (3)
The IABC-BP model predicts the observed quantities. Therefore, the observed quantities can be filtered together with the state equation of the INS system data, which can better compensate for the information data in a loss of lock, avoiding the generation of large errors and the complete dependence on historical data.
A comprehensive analysis shows that the compensation correction model of the IABC-BP model proposed in this paper can be applied to a longer period of satellite loss of lock and has a better effect and performance.
In addition, the statistical data related to the position, velocity, and attitude errors of the three methods were further processed and analyzed, and the excellent performance of the proposed method was further demonstrated through the experimental indicator data. The comparison results are shown in
Table 8.
- (1)
When the BDS signal is out of the lock, both the navigation and positioning accuracy approaches are better than the single INS system, whether the Kalman filter is used for the correction output or the prediction compensation output using the Kalman-filter-based IABC-BP model in this paper.
- (2)
For the compensation correction of position and velocity, the MAE, RMSE, and MSE values of the Kalman-filter-based IABC-BP algorithm model are the smallest, which indicates that the model proposed in this paper has higher accuracy and better robustness and stability.
- (3)
At the same time, the compensation correction for the azimuth information is also minimal, and the pitch and roll angles are relatively small, which indicates that the farm machine can maintain a more stable motion when the model is corrected, and problems such as sideslip and cross-swing will not arise.
Overall, the model proposed in this paper exhibits relatively high accuracy and can effectively replace receiver information for the correction of outputs in case of lock loss.