A single-step positioning error correction method for underwater dead reckoning navigation

Abstract

The application provides a single-step positioning error correction method for underwater dead reckoning navigation, which comprises the following steps: firstly, a position measured by GNSS is used to assist in calculating a single-step positioning error of dead reckoning navigation; secondly, a single-step input of dead reckoning navigation and the single-step positioning error are combined to form a sample, and the sample is filtered to obtain effective samples to form a training sample set; then, a RBF neural network is designed as a single-step positioning error predictor of dead reckoning navigation, and the training sample set is used to train the RBF neural network, so that the RBF neural network approximates a nonlinear error function between the single-step input of dead reckoning navigation and the single-step positioning error; finally, in the dead reckoning navigation, the trained RBF neural network is used as the single-step positioning error predictor; the single-step positioning error predictor works in parallel with the dead reckoning navigation, and the single-step positioning error predictor is used to correct a dead reckoning position. The application can significantly improve the positioning accuracy of underwater dead reckoning navigation.

Description

Technical Field

[0001] This invention relates to the field of underwater navigation technology, and in particular to a single-step positioning error correction method for underwater dead reckoning navigation, applicable to positioning error correction in underwater dead reckoning navigation systems. Background Technology

[0002] Currently, underwater robots are experiencing rapid development and widespread application, making the demand for high-precision underwater navigation technology increasingly urgent. Navigation systems provide underwater robots with real-time parameters such as position, velocity, and attitude, serving as a prerequisite and guarantee for their successful mission completion. Currently, underwater robots generally employ inertial-based integrated navigation technology. Among various inertial-based integrated navigation systems, the Inertial Navigation System (INS) / Doppler Velocity Log (DVL) integrated navigation requires no prior map or external navigation base station, possessing stealth and complete autonomy, and is widely used in underwater robots. Due to size and cost limitations, small and medium-sized underwater robots cannot be equipped with navigation-grade INS; instead, they utilize low-cost Inertial Measurement Units (IMUs) for DVL autonomous navigation. However, both INS / DVL integrated navigation and DVL autonomous navigation update position parameters through dead reckoning, leading to an accumulation of positioning errors with increasing distance, resulting in significant positioning errors after long-distance voyages. Therefore, it is of great significance to study error correction methods for dead reckoning navigation.

[0003] In dead reckoning, IMU / INS attitude errors and DVL velocity errors are cross-coupled and integrated, generating positioning errors. Existing error correction methods establish IMU / INS and DVL error models, and perform pre-calibration or online correction based on these models to improve positioning accuracy by reducing sensor error coupling terms in dead reckoning. However, in complex underwater environments, IMU / INS and DVL errors exhibit diversity, uncertainty, and time-varying characteristics, making them difficult to model accurately and impossible to completely correct through pre-calibration and online correction. Currently, there is a lack of end-point correction methods directly addressing dead reckoning navigation and positioning errors in the absence of external reference position information. The reasons are as follows: Dead reckoning navigation and positioning errors are affected by various sensor errors, and the way and extent of these errors affect positioning errors change continuously under different navigation trajectories. This results in positioning errors that are nonlinear, feature-rich, and difficult to model, posing challenges to error correction. Summary of the Invention

[0004] To address the shortcomings of the aforementioned background technologies, this invention proposes a single-step positioning error correction method for underwater dead reckoning navigation. It utilizes a radial basis function (RBF) neural network to approximate the nonlinear function between the single-step input and the single-step positioning error of the dead reckoning navigation, constructing a single-step positioning error predictor that works in parallel with dead reckoning navigation. This predictor then performs end-point correction of the dead reckoning position during real-time navigation by predicting the single-step positioning error. This invention can significantly improve the positioning accuracy of underwater dead reckoning navigation.

[0005] The technical solution of this invention is implemented as follows:

[0006] A single-step positioning error correction method for underwater dead reckoning navigation, comprising the following steps:

[0007] S1: Utilize GNSS measurements to assist in calculating dead reckoning navigation single-step positioning error;

[0008] S2: Combine the single-step input and single-step positioning error of dead reckoning navigation into a sample, and filter the sample to obtain valid samples to form a training sample set;

[0009] S3: Design an RBF neural network as a single-step positioning error predictor for dead reckoning navigation. Train the RBF neural network using a training sample set to make it approximate the nonlinear error function between the single-step input and the single-step positioning error of dead reckoning navigation.

[0010] S4: In dead reckoning navigation, a trained RBF neural network is used as a single-step positioning error predictor; the single-step positioning error predictor works in parallel with dead reckoning navigation, predicting the single-step positioning error to correct the dead reckoning position.

[0011] Preferably, the method for calculating the single-step positioning error of dead reckoning navigation is as follows:

[0012] The underwater robot simultaneously samples the velocity measured by DVL, the attitude measured by IMU / INS, and the position measured by GNSS on the water surface;

[0013] DVL measured speed V d for:

[0014] V d =f(V b );

[0015] In the formula, V b Let f(V) be the velocity within the coordinate system of the underwater robot carrier. b ) is V b The nonlinear error function;

[0016] Attitude measured by IMU / INS I for:

[0017] att I =g(att);

[0018] In the formula, att represents the attitude of the underwater robot, and g(att) is the nonlinear error function of att;

[0019] Using V d and att I Dead reckoning is performed to obtain the displacement of the underwater robot within a single reckoning period. for:

[0020]

[0021] In the formula, t k For the estimated time of the k-th dead reckoning, t k+1 The estimated time is for the (k+1)th position. The velocity measured by DVL at time k; for The obtained transformation matrix, The attitude measured by the IMU / INS at time k;

[0022] At the same time, t is calculated using the position measured by GNSS. k to t k+1 Displacement ds of an underwater robot k GNSS for

[0023]

[0024] In the formula, Let k be the position measured by GNSS at time k. The position measured by GNSS at time k+1;

[0025] calculate and The difference is used to obtain the dead reckoning navigation single-step positioning error δs. k for:

[0026]

[0027] In the formula, δs E For δs k The eastward error component, δs N For δs k The northward error component; for The eastern component, for The northward component; for The eastern component, for The northward component.

[0028] Preferably, the training sample set is obtained in the following way:

[0029] The single-step input for dead reckoning navigation at time k. With single-step positioning error δs k The sample consists of:

[0030]

[0031] In the formula, [·] T Represents the transpose of a matrix;

[0032] use Filtering for valid samples, where D TH The filtering threshold;

[0033] The selected samples form the training sample set:

[0034]

[0035] In the formula, p is the number of samples.

[0036] Preferably, the structure of the RBF neural network is as follows: the input is the same as the input of dead reckoning navigation, and the output is the single-step positioning error of dead reckoning navigation, that is:

[0037]

[0038] The RBF neural network is trained using a training sample set to approximate... and δs k The nonlinear error function between them; after training, the RBF neural network can be used as a single-step localization error predictor.

[0039] Preferably, the single-step positioning error predictor works in parallel with dead reckoning navigation, and the method for predicting the single-step positioning error to correct the dead reckoning position is as follows:

[0040] In real-time dead reckoning navigation, Inputting the data into the RBF neural network yields the predicted single-step localization error value:

[0041]

[0042] In the formula, Let k be the single-step localization error predicted by the RBF neural network at time k. for The eastward error component, for The northward error component;

[0043] Using the predicted value of single-step positioning error to correct the dead reckoning single-step displacement, we have:

[0044]

[0045] In the formula, To calculate the single-step displacement for the corrected dead reckoning; further, using replace Perform dead reckoning navigation.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] 1) This invention constructs a single-step positioning error predictor based on RBF neural network and works in parallel with dead reckoning navigation to realize the end-point correction of positioning error in dead reckoning navigation, providing a system-level end-point error correction method for dead reckoning navigation.

[0048] 2) This invention does not require modeling of dead reckoning navigation and positioning errors. It designs an RBF neural network to approximate the nonlinear function between the single-step input and single-step positioning error of dead reckoning navigation, thereby achieving model-free correction of dead reckoning navigation and positioning errors.

[0049] 3) This invention utilizes the superior nonlinear approximation capability of RBF neural networks to solve problems in the field of navigation technology, overcomes the problems of nonlinearity, numerous features, and difficulty in modeling of dead reckoning navigation positioning errors, and realizes an effective application of artificial intelligence algorithms in the field of navigation technology. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of the present invention.

[0052] Figure 2 This is a schematic diagram of the technical solution of the present invention.

[0053] Figure 3 This is a schematic diagram of the RBF neural network structure of the present invention.

[0054] Figure 4 This is a comparison chart of the single-step positioning error prediction results for dead reckoning navigation in a specific example of the present invention.

[0055] Figure 5 This is a comparison chart of trajectories before and after dead reckoning navigation and positioning error correction in a specific example of the present invention. Detailed Implementation

[0056] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0057] like Figure 1 As shown, this embodiment of the invention provides a single-step positioning error correction method for underwater dead reckoning navigation, the specific steps of which are as follows:

[0058] S1: Use the position measured by the Global Navigation Satellite System (GNSS) to assist in calculating the dead reckoning navigation single-step positioning error.

[0059] The underwater robot simultaneously samples the velocity measured by DVL, the attitude measured by IMU / INS, and the position measured by GNSS on the water surface;

[0060] Theoretically, the displacement ds of the underwater robot within a single dead reckoning cycle is... k for:

[0061]

[0062] In the formula, t k For the estimated time of the k-th dead reckoning, t k+1 For the time of calculation of the (k+1)th dead center, V n Let V be the velocity of the underwater robot in the navigation coordinate system (n-frame, XYZ-North-East-Sky). b Let be the velocity of the underwater robot in the carrier coordinate system (b-frame, XYZ-right-front-up). Let be the transformation matrix from the b-system to the n-system.

[0063] In SINS / DVL integrated navigation and DVL autonomous navigation, the velocity measured by DVL and the attitude measured by IMU / INS contain errors, which in turn cause positioning errors during dead reckoning.

[0064] DVL measured speed V d for:

[0065] V d =f(V b (2)

[0066] In the formula, f(V)b ) is V b The nonlinear error function.

[0067] Attitude measured by IMU / INS I for:

[0068] att I =g(att) (3)

[0069] In the formula, att represents the posture of the underwater robot, and g(att) is the nonlinear error function of att.

[0070] Using V d and att I Dead reckoning is performed to obtain the displacement of the underwater robot within a single reckoning period. for:

[0071]

[0072] In the formula, The velocity measured by DVL at time k; The attitude measured by the IMU / INS at time k. for The transformation matrix is ​​obtained.

[0073] At the same time, t is calculated using the position measured by GNSS. k to t k+1 Displacement of the underwater robot within a time period for:

[0074]

[0075] In the formula, Let k be the position measured by GNSS at time k. The position measured by GNSS at time k+1.

[0076] Furthermore, calculation and The difference is used to obtain the dead reckoning navigation single-step positioning error δs. k for:

[0077]

[0078] In the formula, δs E For δs k The eastward error component, δs N For δs k The northward error component; for The eastern component, for The northward component; for The eastern component, for The northward component.

[0079] S2: Combine the single-step input and single-step positioning error of dead reckoning navigation into a sample. To avoid the influence of outlier sensor measurements on sample quality, the sample is filtered to obtain valid samples that form a training sample set.

[0080] The single-step input for dead reckoning navigation consists of the velocity measured by DVL and the attitude measured by IMU / INS within a single cycle. The single-step input for dead reckoning navigation at time k... With single-step positioning error δs k The sample consists of:

[0081]

[0082] In the formula, [·] T This represents the transpose of a matrix.

[0083] To avoid the impact of outliers in DVL, IMU / INS, and GNSS measurements on the quality of training samples, the validity of a sample is determined using the following formula:

[0084]

[0085] Among them, D TH This is the filtering threshold.

[0086] If a sample satisfies equation (8), then the sample is valid; otherwise, the sample is invalid. The selected samples form the training sample set.

[0087]

[0088] In the formula, p is the number of samples.

[0089] S3: Design an RBF neural network as a predictor of single-step positioning error in dead reckoning navigation. Train the RBF neural network using a training sample set to make it approximate the nonlinear error function between the single-step input and the single-step positioning error in dead reckoning navigation.

[0090] Design as Figure 3 The RBF neural network shown is and For V d The components; θ, γ and Ψ are att I The components are the pitch angle, roll angle, and heading angle of the underwater robot. The input of the designed RBF neural network is the same as the input of dead reckoning navigation, and the output is the single-step positioning error of dead reckoning navigation, that is:

[0091]

[0092] The RBF neural network is trained using a training sample set to approximate... and δs k The nonlinear error function between them. After training, the RBF neural network can be used as a single-step localization error predictor.

[0093] S4: In dead reckoning navigation, a trained RBF neural network is used as a single-step positioning error predictor; the single-step positioning error predictor works in parallel with dead reckoning navigation, predicting the single-step positioning error to correct the dead reckoning position.

[0094] The velocity measured by DVL and the attitude measured by IMU / INS are simultaneously input into the dead reckoning navigation and the RBF neural network. The output of the RBF neural network is used to correct the output of the dead reckoning navigation.

[0095] In real-time dead reckoning navigation, Inputting the data into the RBF neural network yields the predicted single-step localization error value:

[0096]

[0097] In the formula, Let k be the single-step localization error predicted by the RBF neural network at time k. for The eastward error component, for The northward error component.

[0098] Using the predicted value of single-step positioning error to correct the dead reckoning single-step displacement, we have:

[0099]

[0100] In the formula, This is the corrected single-step displacement; further, using replace Perform dead reckoning navigation.

[0101] Calculate the change in position (latitude, longitude, and altitude) of the underwater robot within a single calculation period (dp). k for:

[0102]

[0103] In the formula, dL, dλ, and dh are dp k The components are the changes in latitude, longitude, and altitude within a single calculation period; for The eastern component, for The northward component, for The celestial component; R M R is the radius of the Earth's meridian. N L is the radius of the Earth's geocentric circle. k Let k be the latitude at time k.

[0104] Furthermore, the position vector p of the underwater robot at time k is calculated. k for:

[0105]

[0106] In the formula, p0 is the position of the underwater robot at the initial moment.

[0107] Figure 2 The technical solution of the present invention is shown. Furthermore, in order to obtain superior error correction results, the construction of the training sample set must meet the following criteria:

[0108] Define the process of collecting samples and training the RBF neural network in S1-S3 as the training experiment, and the real-time navigation process in S4 as the testing experiment, then:

[0109] ① The training experiment and the test experiment are independent of each other, and there are no duplicate samples between them.

[0110] ②The configuration and installation location of DVL, IMU / INS and GNSS remain unchanged in the training and testing experiments.

[0111] ③ The heading angle and velocity range of the underwater robot in the training experiment include its heading angle and velocity range in the test experiment.

[0112] The following examples demonstrate the effectiveness of the dead reckoning navigation and positioning error correction method of the present invention.

[0113] The underwater robot conducted independent training and testing experiments near the water surface, during which the configuration and installation positions of the DVL, IMU / INS, and GNSS remained unchanged.

[0114] S1: In the training experiment, the underwater robot traveled for 6840s with a speed range of 0.001m / s-0.989m / s and a heading angle range of 0.02°-359.96°. During this period, DVL, IMU / INS and GNSS measurements were sampled at a frequency of 1Hz. The dead reckoning single-step positioning error was calculated using formula (6), resulting in 6840 samples.

[0115] S2: Take D in formula (8) TH =0.1m, and 5348 valid samples were selected to form the training sample set.

[0116] S3: Using the training sample set constructed above... Figure 3 The RBF neural network shown is trained with the radial basis function expansion rate SP ranging from 0.5 to 2, and the error tolerance GOAL ranging from 1 × 10⁻⁶. -3 -5×10 -2 .

[0117] S4: In the test experiment, the underwater robot navigated for 579 seconds, with a speed ranging from 0.002 m / s to 0.742 m / s and a heading angle ranging from 0.13° to 359.19°. During this period, DVL, IMU / INS, and GNSS measurements were sampled at a frequency of 1 Hz. The DVL and IMU / INS measurements were used for dead reckoning navigation, while the GNSS measurements served as a reference position. Comparatively, two dead reckoning navigation channels were established: one channel without error correction and the other with error correction. Figure 4 The image shows a comparison of the prediction results of single-step positioning errors in dead reckoning navigation. It can be seen that the positioning error in the east is scattered around zero and has no obvious trend. Therefore, the RBF neural network does not output a trend-based prediction value. In contrast, the positioning error in the north has a significant bias, which is accurately predicted by the RBF neural network.

[0118] Figure 5 The image shows a comparison of the trajectories before and after dead reckoning navigation and positioning error correction. It can be seen that the positioning accuracy of the corrected trajectory is significantly improved. Quantitatively, the root mean square error (RMS) of the uncorrected trajectory was 15.41 m, while the RMS of the corrected trajectory was reduced by 72.1% to 4.30 m. These results verify the effectiveness of the present invention.

[0119] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for correcting single-step positioning errors in underwater dead reckoning navigation, characterized in that, The steps are as follows: S1: Utilize GNSS measurements to assist in calculating dead reckoning navigation single-step positioning error; The underwater robot simultaneously samples the velocity measured by DVL, the attitude measured by IMU / INS, and the position measured by GNSS on the water surface; DVL measured speed for: ； In the formula, The velocity within the coordinate system of the underwater robot carrier. for The nonlinear error function; Attitude measured by IMU / INS for: ； In the formula, The posture of the underwater robot. for The nonlinear error function; use and Dead reckoning is performed to obtain the displacement of the underwater robot within a single reckoning period. for: ； In the formula, Calculate the time for the k-th dead center. The estimated time is for the (k+1)th position. The velocity measured by DVL at time k; for The obtained transformation matrix, The attitude measured by the IMU / INS at time k; Simultaneously, position calculation using GNSS measurements arrive Displacement of the underwater robot for ； In the formula, Let k be the position measured by GNSS at time k. The position measured by GNSS at time k+1; calculate and The difference is used to obtain the dead reckoning navigation single-step positioning error. for: ； In the formula, for The eastward error component, for The northward error component; for The eastern component, for The northward component; for The eastern component, for The northward component; S2: Combine the single-step input and single-step positioning error of dead reckoning navigation into a sample, and filter the sample to obtain valid samples to form a training sample set; S3: Design an RBF neural network as a single-step positioning error predictor for dead reckoning navigation. Train the RBF neural network using a training sample set to make it approximate the nonlinear error function between the single-step input and the single-step positioning error of dead reckoning navigation. S4: In dead reckoning navigation, a trained RBF neural network is used as a single-step positioning error predictor. The single-step positioning error predictor works in parallel with dead reckoning navigation, predicting the single-step positioning error to correct the dead reckoning position.

2. The single-step positioning error correction method for underwater dead reckoning navigation according to claim 1, characterized in that, The training sample set is obtained as follows: The single-step input for dead reckoning navigation at time k. Compared with single-step positioning error The sample consists of: ； In the formula, Represents the transpose of a matrix; use Valid samples were selected, among which, The filtering threshold; The selected samples form the training sample set: ； In the formula, p is the sample size.

3. The single-step positioning error correction method for underwater dead reckoning navigation according to claim 2, characterized in that, The structure of the RBF neural network is as follows: the input is the same as the input of dead reckoning navigation, and the output is the single-step positioning error of dead reckoning navigation, that is: ； The RBF neural network is trained using a training sample set to approximate... and The nonlinear error function between them; After training, the RBF neural network is used as a single-step localization error predictor.

4. The single-step positioning error correction method for underwater dead reckoning navigation according to claim 3, characterized in that, The single-step positioning error predictor works in parallel with dead reckoning navigation. The method for predicting the single-step positioning error and correcting the dead reckoning position is as follows: In real-time dead reckoning navigation, Inputting the data into the RBF neural network yields the predicted single-step localization error value: ； In the formula, Let k be the single-step localization error predicted by the RBF neural network at time k. for The eastward error component, for The northward error component; Using the predicted value of single-step positioning error to correct the dead reckoning single-step displacement, we have: ； In the formula, To calculate the single-step displacement for the corrected dead reckoning; further, using replace Perform dead reckoning navigation.

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