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Adaptive filtering algorithm for GNSS/acoustic combined localization
Kwong Yingcai
, Lui Zhiping
, Wang Fangchao, Li Linyang, Yang Kaichun
Information Engineering University, Zhengzhou 450001, Henan
Abstract:The layout of seabed control points is an important part of the construction of marine spatio-temporal benchmarks, and the reliable marine reference positioning model and method are the premise and basis for achieving high-precision seabed control point layout. The widely used ship survey method combines flexibility and controllability, but the impact of carrier abnormal disturbance is inevitable, which can easily lead to distortion in the solution of the joint positioning model of seabed control points. Aiming at this problem, this paper proposes a GNSS/acoustic joint solution method based on adaptive weight filtering. Firstly, the GNSS/acoustic joint localization mathematical model of the unified sea surface and underwater observation process is derived, and then the discriminant criteria for carrier anomaly perturbation in the adaptive filter solution of the joint model are studied, and the construction method of the adaptive factors of each state parameter is given, and finally the simulation and measured data are verified by experiments. The results show that after the introduction of adaptive filtering algorithm, the abnormal influence of state disturbance on GNSS/acoustic joint positioning can be effectively improved, and the positioning stability and positioning accuracy can be improved, and the filtering effect can be optimal when the adaptive factors of various state parameters are reasonably constructed.
Keywords: Submarine control point GNSS/acoustic joint localization Adaptive selective filter Parameter anomaly Dynamic disturbance
Citation format: KWG Ying-cai, LV Zhi-ping, WANG Fang-chao, et al. Adaptive filtering algorithm for GNSS/acoustic joint localization. Journal of Geomatics,2020,49(7):854-864.] DOI: 10.11947/j.AGCS.2020.20190393.
Fund Project: National Key R&D Program of China (2016YFB0501701); National Natural Science Foundation of China (41674019)
Read more: http://xb.sinomaps.com/article/2020/1001-1595/2020-7-854.htm
Full text overview
The marine geodetic control network is an important part of the marine spatio-temporal reference network, and its accuracy and reliability maintain the strategic goal of building a maritime power in China[1-2]. In order to obtain three-dimensional coordinate information of seabed control points, the most effective technical means at this stage is to use the global navigation satellite system (GNSS) positioning combined with underwater acoustic signal ranging [3-7]. The United States first applied this technique to practice in the 1990s, and observed the laid seafloor control points for many years, which can obtain centimeter-level coordinate repeatability accuracy.[8] In the early days, Japan used a survey ship in the drifting state to observe the seabed control points, and then improved the structural design of the ship to make its navigation trajectory controllable, which greatly improved the positioning accuracy of the seabed control points, and has built a number of submarine base station arrays in the water depth of 5000 m [9]. In the 1990s, scholars in China discussed the accuracy of the GPS joint measurement seabed control network [10], but the current construction of marine spatio-temporal benchmarks is still in the theoretical verification stage, and the seabed control point belonging to China has not yet been established, and there is a big gap compared with the world's advanced level.
The convergence of multiple technologies and the complexity of the marine environment have brought challenges to determining high-precision seabed control points[11], and many scholars have tried to improve data processing strategies and positioning model construction in order to improve the stability and accuracy of the coordinates of seabed control points. Literature[12] proposes to obtain the integral by turning the sound velocity profile to the depth, and using this integral value to linearly represent the underwater propagation delay residual, which can estimate the acoustic ranging error and improve the quality of underwater observation data; literature[13] improves the accuracy of the vertical solution result of the underwater control point by introducing a semi-parametric adjustment model; literature[14] on the basis of circular navigation, the equivalent sound velocity profile error is regarded as the parameter to be estimated and participates in the adjustment, simplifying the operation process and improving the underwater transmission effect of the sea surface reference coordinates; literature [ 15-16] The effect of sound line incidence angle on underwater measurement was studied, and the underwater positioning accuracy was improved by constructing a more reasonable stochastic model. In addition, in order to constrain the influence of the uncertainty error of sound velocity on the vertical solution of the control point, some scholars have proposed that the high-precision relative bathymetric result between the transducer and the transponder can be added as a constraint condition when adjusting the difference[17], or when designing the survey ship track, it should be navigated along the vertical line of the sea surface of the multi-transponder, and the constraint equation can be increased according to the plane and depth difference between the seabed points, thereby improving the vertical positioning accuracy [18]. It should be pointed out that when the above research calculates the coordinates of the seabed control point, the sea surface observation process and the underwater observation process are solved separately and independently. With the gradual improvement of the integrated PNT (positioning, navigation and timing) system [19-20], the data processing strategy emphasizing multi-source observation information fusion will be more conducive to the long-term development of China's ocean spatio-temporal benchmark. In recent years, the increasing convergence of underwater acoustic positioning accuracy and sea surface dynamic positioning accuracy has also made it possible to combine GNSS and acoustic data to solve seabed control points. Some scholars have made preliminary explorations on the functional model and stochastic model construction of GNSS/acoustic joint positioning of seafloor control points[21-22], but the dynamic model anomalies have not been considered in the data processing. In fact, model distortion caused by carrier perturbation is inevitable, and due to the poor immunity of standard Kalman filtering, it will no longer be an effective solution for processing multi-source information .[23] In this case, an adaptive filtering algorithm should be used to control the influence of abnormal disturbances in dynamics in real time.
The adaptive filtering algorithm uses discriminant statistics to identify anomalous state parameters, and adjusts the contribution of anomalous parameters to the results by constructing adaptive factors to improve filter stability and accuracy. However, few scholars have studied its application effect in the calculation of the coordinates of seabed control points. Based on the above analysis, this paper proposes a GNSS/acoustic combined adaptive filtering algorithm for solving the control points of the seabed, and discusses many details of the algorithm, and finally uses the simulation and measured data to compare and verify the experiments.
1 Mathematical model of GNSS/acoustic joint localization
1.1 Joint observation equations
Shipboard dynamic precision point positioning (PPP) is carried out on the sea surface in a non-differential form, which is the main mode of operation in the far-reaching sea. Underwater, systematic and random errors in the velocity of sound need to be taken into account, and the connection is established with the back-and-forth propagation of acoustic signals between seastop transponders, as shown in Figure 1.
Fig. 1 GNSS/Acoustic joint positioning principle Fig. 1 The principle of the GNSS/acoustic joint positioning
Diagram options
The observational equations of the joint model can be obtained by combining the sea surface and underwater observation processes [24-25], see equation (1).
(1)
Wherein, the superscript s represents the satellite; P, Φ indicates the pseudo-distance and carrier phase view measurement after the linear combination of the ionospheric; ρ represents the distance from the bottom transducer to the seabed transponder, which is measured by the acoustic signal; c represents the speed of light in the vacuum;
TZWD represents the wet component of tropospheric delay projected onto the propagation path, εP and εΦ represent pseudo-distance and carrier phase observation noise and other unmodeled errors after the combination of the anionosphere, respectively; λ and Ñ represent the combined wavelength of the extinction ionospheric combination and the equivalent fuzziness parameters including the pseudo-distance and carrier phase hardware delay deviation, respectively; (x,y,z) is the shipboard antenna coordinate; (xρ, yρ, zρ) is the transponder coordinate; (xt, yt, zt) is the transducer coordinate δρd represents the error caused by delay during signal propagation, δρv represents the systematic error caused by the spatiotemporal change of the sound velocity structure, and ε represents the unmodeled random error.
1.2 Error equation establishment
The datum coordinates used in the underwater part are the bottom transducer coordinates, while the sea surface positioning can only obtain the geographical coordinates of the center of the shipboard GNSS antenna, and there is a position offset between the two datum points. When the observation information is unified for the overall solution, the three main attitude angles can be estimated together as parameters to be estimated [21]. In actual processing, it is generally necessary to calibrate the relative position between the measuring center points of the shipboard sensor in advance, and use the calibration value, the attitude angle measurement value and the geographical coordinates of the shipborne antenna center to obtain the absolute coordinates of the ship's bottom transducer under the global coordinate framework, as shown in equation (2), where R includes a posture conversion matrix and a rotation matrix between the local coordinate system and the global coordinate system
(2)
Linearization of the joint observation equation (1) can obtain the corresponding error equation, see Equation (3)
(3)
where V=[VPVΦVρ]T and L=[LPLΦLρ]T are the residual terms and freedom terms of the error equation, respectively; the coefficient array A=[APAΦAρ]T contains the corresponding terms of the three attitude angle parameters; the specific form of the parameter to be estimated is δX
(4)
2 GNSS/Acoustic Joint Localization Adaptive Selective Filtering Algorithm
The navigation vessel survey mode of the joint GNSS satellite is used to determine the seabed point, which can easily ensure the symmetry of the measurement trajectory and the redundancy rate of the observation data. However, it should also be noted that due to the frequent changes in the motion state of the measuring vessel, if the preset dynamic model is used in the data processing process, it will be difficult to accurately describe the motion state of the carrier in real time. When there is a significant difference between the dynamic model and the actual state of motion, the conventional filtering algorithm cannot weaken the error effect because it does not have the ability to self-regulate, and the positioning accuracy will be greatly reduced or even filter divergence. At this time, a reasonable adaptive filtering algorithm can be introduced to identify abnormal interference and adjust the result in real time.
2.1 Adaptive Kalman filtering
Suppose that the k-time has an error equation as shown in equation (5).
(5)
wherein, LXk is the forecast value vector Xk, whose covariance matrix is ΣXk, and the corresponding array is PXk; VXk represents its residual vector at k time; the covariance matrix of the observation value vector is Σk, and the corresponding array is Pk; Vk represents its residual vector at k time. When performing The Kalman filter estimation, using both dynamic model information and observation information to solve the optimal estimate of the state, the objective function as shown in equation (6) can be written according to the principle of least squares
(6)
If the one-way adaptive filtering is used to reduce the influence of the state parameter vector by abnormal forecast information, that is, the single adaptive factor αk (αk∈ [0, 1]) is used to adjust the forecast vector weight array in real time, and the objective function should be rewritten as
(7)
Further analysis, due to the variety of state parameters of the GNSS/acoustic joint localization model, the problem that may be faced is that some abnormal parameters in some enamels affect the filtering effect, but other normal parameters of this epoch provide real dynamic information. If a single adaptive factor is still used to adjust the weights of all parameters, the weights of normal parameters are correspondingly reduced, and their contribution to the filter valuation is lost. At this time, the basic idea of the adaptive filtering algorithm should not change, and the adaptive weight selection filtering method should be used for data processing. It is conceived that according to some criteria, the parameters of the current epoch are divided into normal parameters and abnormal parameters, and a special adaptive factor ωik (ωik∈ [0, 1]) is constructed for each forecast parameter, and an adaptive factor array composed of all adaptive factors is used, Wk=diag(ωik), i=1, 2, ...,n, and the forecast vector historical array is adjusted. At this point, the solution form of the GNSS/acoustic combined adaptive selective filtering algorithm should be
(8)
As can be seen from equation (8), the advantage of adaptive weight filtering is that the most appropriate weight can be selected according to the instantaneous state of each forecast parameter, so that the more accurate forecast information can achieve the highest utilization rate, and the adaptive factor of the abnormal parameter is adjusted to weaken its adverse effect on the filtering result.
2.2 Abnormal judgment and adaptive factor construction
Whether it is a one-way adaptive filtering or an adaptive weight-selective filtering algorithm, two key problems need to be solved, namely, how to determine state parameter anomalies and how adaptive factors or adaptive factor arrays are constructed. A reasonable discriminant statistic can reflect the difference between the forecast information provided by the forecast parameters and the actual state of motion, so as to construct a better adaptive factor. Commonly used discriminant statistics are prediction residual statistics, variance component ratio statistics, state discrepancies statistics, and so on.
Taking the coordinate parameters of the seabed transponder as an example, when constructing the discriminant statistics, for specific parameters, this paper writes the k-time forecast residual statistics as such
(9)
where v(*)ρk represents any counterpart of the transponder coordinate parameters in the new interest vector; σvXρk, σvYρk, and σvZρk represent the corresponding terms of the transponder coordinate parameters on the diagonal of the prediction residual covariance matrix, respectively.
In this paper, the residual result obtained by the standard Kalman filter is used to calculate the variance component corresponding to the submarine transponder parameters, combined with the diagonal element (σ(*)ρk) 2 in the forecast vector covariance matrix ΣXk, and the k-time variance component ratio statistic form is shown in equation (10).
(10)
However, the analysis of the constructed form of the state discrepancy statistic shows that the statistic is not suitable as the criterion basis for adaptive weight filtering in the combined model of this paper. The reason is that on the one hand, the state discrepancy statistic depends on the least squares result of each parameter of the current epoch, and the least squares solution needs to be performed first when constructing, but because the redundancy of the observation information in the single epoch in the GNSS/acoustic joint model is not high, the minimum squares solution accuracy of each parameter of the current almanac cannot be guaranteed; on the other hand, due to the specific settings of the state transfer matrix and the process noise matrix in the joint model, the influence of dynamic disturbance is not reflected in the forecast update process of some parameters, resulting in the inability to determine whether the parameters are abnormal. Therefore, this paper does not use the state discrepancy statistic in the subsequent selection filtering algorithm.
After selecting the appropriate discriminant statistic to reflect the error size of the dynamic model, for the model parameters in different states, it is necessary to construct the adaptive factor according to the adaptive factor function and adjust the corresponding weights or weights. Common adaptive factor function models include three-segment, two-segment, and exponential functions.
Three-stage function model[23]
(11)
where Δ(*) represents a discriminant statistic constructed according to any of the above methods; c0 and c1 are threshold constants, which are reasonably valued according to experience and carrier motion characteristics.
Two-stage function model[26]
(12)
Exponential function model[27]
(13)
In equation (12) and equation (13), the constant c is generally valued empirically. Unlike the three-segment adaptive factor function, the two-segment adaptive factor function and the exponential adaptive factor function are both non-zero functions.
The constructors of the respective adaptation factors in this article are shown in Table 1.
Table 1 Adaptive Factor Constructor Tab. 1 Adaptive factor construction method
type
The value method
Measure ship coordinate adaptive factors ωXk, ωYk, ωZk
The adaptive factor is judged and constructed by the discriminant statistic and the adaptive factor function
Underwater transponder coordinates adaptive factors ωXρk, ωYρk, ωZρk
Attitude angle adaptive factors ωαk, ωβk, ωλk
Receiver clock difference adaptive factor ωclkk
Tropospheric delay wet component adaptive factor ωzpdwk
01
Fuzziness parameter adaptive factor ωNik
Table options
Among them, the receiver clock difference parameter is set to zero weight due to its own stability difference, and the tropospheric delay wet component and fuzziness parameters obtained after additional constraints are more reliable, so the adaptive factor is directly set to 1. For the two coordinates and attitude parameters, it is necessary to construct a reasonable adaptive factor according to the discriminant statistics and the appropriate adaptive factor function threshold constants, the specific steps are:
(1) If the forecast residuals are used as the basis for the discriminant statistics, first of all, the new interest vector of the current calendar element needs to be calculated according to Vk=AkXk-Lk, combined with the prediction residual covariance matrix, the discriminant statistics are constructed according to the form of formula (9), and then the adaptive factor is determined by the adaptive factor function, and the state parameters are solved after updating the forecast vector array.
(2) If the variance component ratio is used as the basis for the discriminant statistic, the standard Kalman filter should first be performed to obtain the residual vector VXk corresponding to the current almanacic forecast vector, and calculate the variance factor corresponding to the parameters, and then combine the corresponding elements in the prediction vector covariance matrix, construct the discriminant statistic in the form of the ratio of the variance factor according to formula (10), and then determine the threshold range in which it is located, determine the reasonable adaptive factor through the adaptive factor function, update the corresponding forecast vector array, and solve the state parameters again. Obtain the adaptive filtering solution of the joint model.
(3) If the state discrepancy value is used as the discriminant statistic basis for the one-way adaptive filter, the least squares solution of the present epoch needs to be solved first
At this point, the adaptive factor array composed of all adaptive factors can be expressed as
(14)
The substitution formula (14) into equation (8) is the GNSS/acoustic combined adaptive selective filtering solution formula.
3 Test verification and analysis
In order to verify and analyze the application effect of adaptive filtering algorithm in GNSS/acoustic joint positioning model, based on the self-programmed software GNSSer, multiple sets of simulation and measured data experiments are designed. The initial setting of the filter is as follows: the corresponding state transfer coefficient is set to 0 for parameters that change with the movement of the carrier or have strong randomness, such as measuring ship antenna coordinates and satellite blur parameters that occur around the jump, etc.; and the corresponding state transfer coefficient for other slowly changing parameters is set to 1. The initial state parameter vector is taken as a full zero vector, in the initial system noise matrix, the corresponding terms of the shipboard antenna coordinate parameters, attitude parameters, and transponder coordinate parameters are taken as 202, 12, 0.012, respectively, pseudo-distance or carrier phase similar observation measurement adopts the height angle weighting model, the acoustic view measurement adopts the equal weight model, and the variance constant ratio between acoustic ranging, pseudo-distance, and carrier phase view measurement is set to 1:10:105, and in the solution process, the carrier abnormal disturbance is randomly increased within some calendar elements. The accuracy of the solution of the position of the subsea transponder under different conditions is evaluated.
3.1 Simulation test
The trajectory of the sea surface survey vessel is shown in Figure 2, assuming that a simulated control point has been laid out on the seabed, and its plane schematic position is shown at the five-star symbol. The GPS data measured in the sea area for about 2.5 h was used, and the sampling rate was 1 s. The seabed measurement coordinate system is established with the reference location of the seabed simulation control point as the coordinate origin, and its x-axis is fixed. The water depth is set to 1500 m, the underwater acoustic measurement interval is 15 times per second, and the acoustic ranging error and random noise are taken into account. Where the acoustic ranging error is obtained by empirical formulas in the literature [25], the random noise follows a normal distribution with a mean of zero and a variance of 5 cm. Since the survey ship is in a course adjustment or irregular sailing, it is impossible to guarantee a stable state of motion, and the solution result will be affected by carrier disturbance. In order to more intuitively reflect the adjustment effect of the adaptive factor in the filtering, the abnormal acceleration disturbance of| εa |≤10 m/s2 is added randomly in the sampling interval between the first 4000 calendar elements, 7500~8000 calendar elements, and the last 500 calendar elements.
图 2 测量船航迹Fig. 2 The track of the surveying vessel
(1) Simulation test 1: This test is to investigate the ability of one-way adaptive filtering algorithm to control the abnormal dynamic information under the abnormal judgment of three discriminant statistics. The adaptive factor function selects a two-stage function as an example, in which, after multiple simulation trials, the threshold constant c value is taken to 1, and a total of four schemes are designed:
Scenario 1: The conventional Kalman filter algorithm solves the seafloor transponder coordinates.
Scheme 2: Abnormal judgment is made by using the state non-conformance statistics, and the one-way adaptive filtering algorithm solves the coordinates of the seabed transponder.
Scenario 3: Abnormal judgment is made by using the predicted residual statistics, and the one-way adaptive filtering algorithm solves the coordinates of the seabed transponder.
Scheme 4: Abnormal judgment is made by using the variance component ratio statistic, and the one-way adaptive filtering algorithm solves the seabed transponder coordinates.
The comparison of the four schemes in 3 directions is shown in Figure 3. It can be seen that during the period of increasing the abnormal perturbation of the carrier, the standard Kalman filter is greatly affected, and the results show abnormal fluctuations, and the deviation of some almanacs in the Y and Z directions exceeds 20 m, and the filter convergence lags or even cannot converge. After adding three discriminant statistics and using the one-way adaptive filtering algorithm, the influence of dynamic model error on the positioning solution is controlled to varying degrees, indicating that the one-way adaptive filtering algorithm is effective. The results of adaptive filtering after the judgment of three statistics can be found that the one-way adaptive filtering algorithm based on the variance component ratio statistics has the best inhibition effect on abnormal perturbations.
Figure 3 Simulation Test 1: Fig. 3 Simulation experiment 1: the comparative results on each direction of different schemes
(2) Simulation test 2: This test is to investigate the ability of the adaptive weight filtering algorithm to control the dynamic information abnormality under the abnormal judgment of two discriminant statistics. The adaptive factor function selects a two-stage function as an example, the threshold constant c is taken as 1.1, and the corresponding adaptive factor structure is carried out by measuring the ship coordinates and the simulated transponder coordinates, and a total of three schemes are designed:
Scheme 2: Abnormal judgment is made by using the predicted residual statistics, and the adaptive selection filtering algorithm solves the coordinates of the seabed transponder.
Scheme 3: Abnormal judgment is made by using the variance component ratio statistic, and the adaptive selection filtering algorithm solves the coordinates of the seabed transponder.
The results of the test in 3 directions are shown in Figure 4. When there is a disturbance in kinetic information, it is based on the predicted residuals statistic ΔVk or the variance component ratio statistic
Figure 4 Simulation Test 2: Comparing the results of different schemes with Fig. 4 Simulation experiment 2: the comparative results on each direction of different schemes
(3) Simulation test 3: This test is to investigate the control ability of adaptive selection filtering algorithm for dynamic information anomalies under different selection construction strategies. The parametric anomaly discriminant statistic selects the variance component ratio statistic that is more sensitive, and the adaptive factor function selects the two-stage function as an example, where c=1.1, a total of 4 schemes are designed:
Scheme 2: The adaptive factor structure of the measuring ship coordinates is carried out, the simulated transponder coordinate parameters are regarded as reliable parameters, the adaptive factor is set to 1, and the adaptive selection filtering algorithm is used to solve the seabed transponder coordinates.
Scheme 3: The adaptive factor structure of the simulated transponder coordinates is carried out, the measurement ship coordinate parameters are regarded as reliable parameters, the adaptive factor is set to 1, and the adaptive weight filtering algorithm is used to solve the seabed transponder coordinates.
Scheme 4: The adaptive factor structure of the measuring ship coordinates and the simulated transponder coordinate parameters are carried out separately, and the seabed transponder coordinates are solved by the adaptive selection filtering algorithm.
After calculating the 3D point error in each of the four schemes, the comparison results are shown in Figure 5. The STD (standard deviation) values and RMS (root mean square) values of the statistical deviation results are also shown in Table 2.
Table 2 Standard deviation of 3D point deviation results of different schemes, rms statistics Tab. 2 The standard deviation and root-mean-square statistics of 3D point deviation results from different schemes
scheme
STD/m
RMS/m
Scenario 1
4.051
4.742
Scenario 2
3.193
4.566
Scenario 3
0.859
0.992
Scenario 4
0.256
0.335
Figure 5 Simulation Test 3: Comparing the results of different schemes upwards Fig. 5 Simulation experiment 3: the comparative results on each direction of different schemes
Analyze Figure 5 and Table 2 to draw the following conclusions:
(1) Comparing scheme 2 and scheme 1, it can be seen that if the initial normality of the coordinate parameters of the analog transponder is maintained, compared with the standard Kalman filter, the STD value and RMS value of the three-dimensional coordinate deviation result are reduced, the filtering effect is improved but not obvious, and the result is not stable enough, indicating that for this joint positioning process, the dynamic information corresponding to the transponder coordinate parameter is inaccurate, which will have a non-negligible impact on the result.
(2) From the results of scheme 3, it can be found that when the predicted value of the transponder coordinate parameter deviates, it has a direct impact on the estimation result, and when the corresponding weight of the simulated transponder coordinate parameter is adjusted, the STD value and RMS value of the three-dimensional point result are not more than 1 m, and the positioning stability and accuracy are significantly improved.
(3) In the process of joint solving, the estimation results of the two types of coordinate state parameters may not coincide with the actual situation, scheme 4 on the basis of scheme 3, the two types of coordinate parameters are selected and the adaptive factor is constructed, the impact of abnormal dynamic information on the model is reasonably adjusted, it can be seen from Figure 5 that the positioning filter of this scheme has basically no obvious jump, and the result is very stable. From Table 2, it can be found that the STD value and RMS value of the three-dimensional point deviation result are within 0.5 m, which is 93.68% lower than that of the standard Kalman filtering algorithm, and the RMS value is reduced by 92.94%, and the filtering and positioning effect is significantly improved.
3.2 Empirical testing
The measured data comes from the post-processing results of the sea area test on Lingshan Island. The date of the test is December 1, 2017, the measuring vessel is equipped with Tuopukang HiPer series GPS antenna, Canada AML company's SV Plus V2 sound velocity profiler, Canada's Applanix company POS-MV positioning and posture system and other sensors in the sea area for about 75 minutes of maritime observation, of which the average standard deviation of the attitude angle measurement sequence can reach 0.02 °, the sound velocity profiler can work at a depth of up to 6000 m, and the sound velocity measurement accuracy is ±0.025 m/ s, resolution up to ±0.001 m/s. The actual trajectory of the measuring vessel and its plane relationship to the transponder position are shown in Figure 6.
Figure 6 Measuring ship track and transponder plane position Fig. 6 The track of the surveying vessel and the schematic diagram of the transponder plane position
The water depth in the measuring area is about 25 m. A transponder was laid underwater, and 8 delay observations were returned from the same acquisition. The relative position relationship between the base array and the attitude sensor, the attitude sensor and the GPS antenna, and the measurement ship center of gravity and the attitude sensor has been accurately determined in advance, and can be used to convert between the shipboard antenna position and the bottom transducer position. The sound velocity profiler measures the sound velocity profile of the water, including sound velocity, water temperature, and pressure information. Sound velocity profile information is used to build a sound velocity tracking model. The raw underwater acoustic observation data are pre-processed prior to the experiment. First of all, time registration is carried out, and the underwater acoustic data recorded by UTC time is registered with the sea surface satellite observation data recorded when GPS is used, including the unification of the time benchmark and the interpolation and extrapolation of some observation moments to eliminate the error impact of such delay problems; then a rough underwater least squares solution is carried out to eliminate the anomalous result calendar element to avoid the interference caused by obvious observation differences. In addition, it can be seen from the trajectory chart that there are more large turning operations in the track of the survey ship in this test, and the motion model is also disturbed by many anomalies, similar to the simulation test setting, randomly added |εa|≤3 m/s2 abnormal acceleration disturbance in part of the sampling interval of the entire observation period, and the improved hierarchical isograde sound velocity tracking model is used to calculate the beam footprint position, and the obtained high-precision transponder coordinate results are regarded as reference values.
(1) Empirical test 1: Similar to simulation test 1 and simulation test 2, this test mainly investigates the ability of two adaptive filtering algorithms to regulate abnormal dynamic information under the condition of measured data. It can be seen from the simulation test results that compared with the other two discriminant statistics, the variance component can detect the abnormal parameters more accurately than the statistics, so the following experiments all choose the variance component ratio statistics for abnormal judgment. Among them, the adaptive selection filter algorithm constructs the corresponding adaptive factors for the shipboard GNSS antenna center coordinate parameters, attitude angle parameters, and transponder coordinate parameters, respectively, and the constructor takes the three-segment function model as an example, of which the threshold constants c0 and c1 take 1.1 and 3.1, respectively, and a total of 3 schemes are designed:
Scheme 2: The one-way adaptive filtering algorithm calculates the coordinates of the seabed transponder.
Solution 3: Adaptive weight-selective filtering algorithm to calculate the coordinates of the seabed transponder.
Because the experiment added carrier acceleration perturbation within multiple random observation epochs, the abnormal influence of kinetic information was amplified. As can be seen from Figure 7, the standard Kalman filtering algorithm has no regulation ability, and there is always a fluctuation of 5 to 10 m in the entire filtering process, and the results do not reflect the obvious filter convergence phenomenon. Scheme 2 and scheme 3, which introduce two adaptive filtering algorithms, have good adjustment and adaptability, the fluctuations are significantly reduced, and the positioning results are more stable, which is consistent with the simulation test results. On the one hand, it is shown that the introduction of adaptive filtering algorithms in the GNSS/acoustic joint localization model can help to suppress the effect of state disturbances on the results; on the other hand, although the one-way adaptive filtering algorithm uses a single adaptive factor to adjust the entire forecast vector array, the consequence of this is that the contribution of the parameters that have not occurred to the model estimation results is weakened, and the filtering effect is limited. From the figure, it is easy to find that the results of scheme 3 are more stable than that of scheme 2, the filter does not have a large jump, and the accuracy is significantly improved, because the adaptive selection filtering algorithm constructs the corresponding adaptive factors according to different types of state parameters, and adjusts the forecast array in the form of adaptive factor arrays, which is more in line with the requirements of adaptation, so as to effectively control the influence of the perturbation state on the filtering results.
Figure 7 Empirical Test Test 1: Comparison of the results of different schemes with Fig. 7 Measured experiment 1: the comparative results on each direction of different schemes
(2) Empirical test test 2: This test focuses on the influence of different adaptive factor functions on the effect of adaptive selection filtering algorithm. A total of three schemes are designed, and the same adaptive factor function is selected for the transponder coordinate parameters in each scheme, taking the two-segment function as an example, where c=1.1 is used, and the adaptive factor function selected by changing the other two types of parameters is compared and illustrated.
Scheme 1: The shipborne GNSS antenna center coordinate parameter and the attitude angle parameter select a three-segment function, so that c0 = 1.1, c1 = 3.1, and the adaptive selection filter algorithm solves the seabed transponder coordinates.
Scheme 2: Shipboard GNSS antenna center coordinate parameter and attitude angle parameter selection index function, so that c = 1.1, the adaptive selection filter algorithm to solve the seabed transponder coordinates.
Scheme 3: The shipboard GNSS antenna center coordinate parameter and the attitude angle parameter select two-segment function, so that c = 1.1, the adaptive selection filter algorithm solves the seabed transponder coordinates.
The comparison results of each scheme in the X, Y, and Z directions are shown in Figure 8, and the RMS values of the statistical deviation series are shown in Table 3.
Fig. 8 Empirical test test 2: Comparison of deviation results of different schemes Fig. 8 Measured experiment 2: the comparative results on each direction of different schemes
Table 3 Root mean square statistics for deviation results of different schemes tab. 3 The root mean square statistics of deviation results from different schemes
RMS
DX
DY
DZ
0.096
0.051
0.142
0.093
0.049
0.135
0.050
0.141
As can be seen from Figure 8 and Table 3, the filtering results of each scheme selecting different adaptive factor functions are basically the same. There are only millimeter-level differences in the upward RMS values of the three schemes, which can be regarded as the accuracy is basically the same for the existing subsea transponder positioning accuracy, indicating that the selection of the adaptive factor function has little effect on the application of the adaptive selection filtering algorithm in the GNSS/acoustic joint positioning filter.
Comprehensive analysis of simulation experiments and empirical test results can be found that the adaptive weight filtering algorithm for constructing adaptive factors based on variance component ratio statistics has stD values and RMS values within 0.5 m of the three-dimensional deviation results of the simulation test, and the horizontal direction of the RMS values of the actual tests does not exceed 0.1 m, and when the shipboard GNSS antenna center coordinate parameters, attitude angle parameters, and transponder coordinate parameters are constructed respectively, the influence of dynamic disturbances on the results is basically eliminated, and the filtering effect is optimal.
4 Conclusion
When determining the coordinates of the seabed control point, the multi-source observation information such as GNSS and acoustics is combined for fusion processing, which is closer to the core concept of the integrated PNT system. However, when there is an anomalous state disturbance effect, the standard Kalman filter solution of the joint model will be greatly biased. Aiming at this problem, this paper introduces an adaptive filtering algorithm to weaken the influence of abnormal perturbation on the results, thereby improving the filtering effect. Through theoretical analysis and experimental verification, the following conclusions can be drawn:
(1) Since the standard Kalman filter does not have self-regulation ability, when there is a state disturbance during the GNSS/acoustic joint positioning process, the filtering result of the conventional algorithm will be greatly biased. After the introduction of the adaptive filtering algorithm, the influence of abnormal perturbation on the results is weakened, and the positioning stability and positioning accuracy are improved. Among the three parametric anomaly discriminant statistics, the adaptive factor is constructed based on the variance component ratio statistics, and the filtering effect is the best.
(2) Compared with the one-factor adaptive filtering algorithm, the adaptive selection filtering algorithm can adjust the contribution of forecast information more reasonably, the positioning results are more stable, and the filtering effect is significantly improved. The three-dimensional deviation result of the simulation test is that the STD value and the RMS value are within 0.5 m, the horizontal direction of the RMS value of the test is not more than 0.1 m, and the Z direction is not more than 0.15 m, and the positioning stability and positioning accuracy are improved by more than 90% compared with the conventional algorithm.
(3) The selection of the adaptive factor function has almost no effect on the result, but because the GNSS/acoustic joint solution model involves multiple types of state parameters, it is necessary to reasonably construct the corresponding adaptive factor according to the individual characteristics of the state parameters, and when the corresponding adaptive factors are constructed for the ship-mounted GNSS antenna center coordinate parameters, attitude angle parameters, and transponder coordinate parameters according to the abnormal discrimination results, the filtering effect is significantly improved.
About the Author
The first author profile: Kwong Yingcai (1994-), male, doctoral student, research direction is measurement data processing theory and methods. E-mail: [email protected]
Second author, corresponding author profile: Lu Zhiping (1960-), male, doctoral supervisor, professor, mainly engaged in geodesy and survey data processing and other fields of scientific research and teaching. E-mail: [email protected]
Third Author Profile: Wang Fangchao (1995—), male, master's student, research direction is GNSS coordinate time series. E-mail: [email protected]
About the fourth author: Li Linyang (1991-), male, Ph.D., lecturer, research direction is GNSS data processing theory and methods. E-mail: [email protected]
Fifth Author Profile: Yang Kaichun (1997-), male, master's student, research direction is GNSS data processing theory and methods. E-mail: [email protected]
Team Profile
Professor Lu Zhiping's team has long been engaged in research on satellite navigation and positioning, spatial geodesy, survey data processing, etc., and the project "2000 China Geodetic Coordinate System (CGCS2000)" won the second prize of the National Science and Technology Progress Award, and other projects won 4 first prizes, 5 second prizes and 9 third prizes of the Military Science and Technology Progress Award. The scientific research GNSS data processing software GNSSer (www.gnsser.com) independently developed by the team adopts distributed and parallelized data processing technology, which can realize the rapid processing of high-precision, automated and cloud-based GNSS data of various systems including GPS, BDS, GLONASS and other systems, and has been applied in the geodetic data processing center of the military surveying and mapping department and the State Administration of Surveying, Mapping and Geoinformation. The self-developed GNSS Data Preprocessor (GNSS Data Preprocessor) is a multi-GNSS data parallel preprocessing software based on the link2.x to 3.x standard, written and designed in an object-oriented programming language, which can realize automatic acquisition, format conversion, file selection, data visualization and analysis of GNSS observation files including multiple GNSS files or IGS products. He has published many books such as Geodesy (Zhiping Lu et al., Springer, Germany, 2014), and more than 200 papers have been published in GPS Solution, Advances in Space Research, Journal of Spatial Science, Journal of Surveying and Mapping, Journal of Astronomical Journal, Journal of Seismology, Journal of Wuhan University • Information Science Edition, Chinese Journal of Inertial Technology, Journal of Surveying and Mapping Science and Technology, Bulletin of Surveying and Mapping and other Chinese and English publications. His conference papers have won many awards and patents at home and abroad in high-level conferences such as the China Satellite Navigation Academic Annual Conference, the CPGPS Forum, the Annual Conference of Geodesy and Navigation, and the National Doctoral Academic Forum (Surveying and Mapping Science and Technology).
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