In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity ...Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.展开更多
Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matri...Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.展开更多
Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmissio...Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.展开更多
Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the...Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the rotor vibration in AMBs is to adopt a notch filter or adaptive filter in the AMB controller. However, these methods cannot obtain the precise amplitude and phase of the compensation current. Thus, they are not so effective in terms of suppressing the vibrations of the fundamental and other harmonic orders over the whole speed range. To improve the vibration suppression performance of AMBs,an adaptive filter based on Least Mean Square(LMS) is applied to extract the vibration signals from the rotor displacement signal. An Iterative Search Algorithm(ISA) is proposed in this paper to obtain the corresponding relationship between the compensation current and vibration signals. The ISA is responsible for searching the compensating amplitude and shifting phase online for the LMS filter, enabling the AMB controller to generate the corresponding compensation force for vibration suppression. The results of ISA are recorded to suppress vibration using the Look-Up Table(LUT) in variable speed range. Comprehensive simulations and experimental validations are carried out in fixed and variable speed range, and the results demonstrate that by employing the ISA, vibrations of the fundamental and other harmonic orders are suppressed effectively.展开更多
It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this...It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.展开更多
A functional model named EIO(Errors-In-Observations) is proposed for general TLS(total least-squares)adjustment. The EIO model only considers the correction of the observation vector, but doesn't consider to corre...A functional model named EIO(Errors-In-Observations) is proposed for general TLS(total least-squares)adjustment. The EIO model only considers the correction of the observation vector, but doesn't consider to correct all elements in the design matrix as the EIV(Errors-In-Variables) model does, furthermore, the dimension of cofactor matrix is much smaller. Iterative algorithms for the parameter estimation and their precise covariance matrix are derived rigorously, and the computation steps are also presented. The proposed approach considers the correction of the observations in the coefficient matrix, and ensures their agreements in every matrix elements. Parameters and corrections can be solved at the same time.An approximate solution and a precise solution of the covariance matrix can be achieved by corresponding algorithms. Applications of EIO model and the proposed algorithms are demonstrated with several examples. The results and comparative studies show that the proposed EIO model and algorithms are feasible and reliable for general adjustment problems.展开更多
Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE) criterion and has found ever-increasing applications in communications. This paper presents an alternative ad...Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE) criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate (MSER) criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.展开更多
In this paper a square wavelet thresholding method is proposed and evaluated as compared to the other classical wavelet thresholding methods (like soft and hard). The main advantage of this work is to design and imple...In this paper a square wavelet thresholding method is proposed and evaluated as compared to the other classical wavelet thresholding methods (like soft and hard). The main advantage of this work is to design and implement a new wavelet thresholding method and evaluate it against other classical wavelet thresholding methods and hence search for the optimal wavelet mother function among the wide families with a suitable level of decomposition and followed by a novel thresholding method among the existing methods. This optimized method will be used to shrink the wavelet coefficients and yield an adequate compressed pressure signal prior to transmit it. While a comparison evaluation analysis is established, A new proposed procedure is used to compress a synthetic signal and obtain the optimal results through minimization the signal memory size and its transmission bandwidth. There are different performance indices to establish the comparison and evaluation process for signal compression;but the most well-known measuring scores are: NMSE, ESNR, and PDR. The obtained results showed the dominant of the square wavelet thresholding method against other methods using different measuring scores and hence the conclusion by the way for adopting this proposed novel wavelet thresholding method for 1D signal compression in future researches.展开更多
In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original...In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error (MM) and the asymptotic bias (MB), respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.展开更多
工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小...工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小迭代修复和改进WGAN混合模型的时序数据修复方法.首先,在预处理阶段,保留异常数据,进行信息标注等处理,从而充分挖掘异常值与真实值之间的特征约束.其次,在噪声模块提出了近邻参数裁剪规则,用于修正最小迭代修复公式生成的噪声向量.将其传递至模拟分布模块的生成器中,同时设计了一个动态时间注意力网络层,用于提取时序特征权重并与门控循环单元串联组合捕捉不同步长的特征依赖,并引入递归多步预测原理共同提升模型的表达能力;在判别器中设计了Abnormal and Truth奖励机制和Weighted Mean Square Error损失函数共同反向优化生成器修复数据的细节和质量.最后,在公开数据集和真实数据集上的实验结果表明,该方法的修复准确度与模型稳定性显著优于现有方法.展开更多
Gravity/inertial combination navigation is a leading issue in realizing passive navigation onboard a submarine. A new rotation-fitting gravity matching algorithm, based on the Terrain Contour Matching (TERCOM) algorit...Gravity/inertial combination navigation is a leading issue in realizing passive navigation onboard a submarine. A new rotation-fitting gravity matching algorithm, based on the Terrain Contour Matching (TERCOM) algorithm, is proposed in this paper. The algorithm is based on the principle of least mean-square-error criterion, and searches for a certain matched trajectory that runs parallel to a trace indicated by an inertial navigation system on a gravity base map. A rotation is then made clockwise or counterclockwise through a certain angle around the matched trajectory to look for an optimal matched trajectory within a certain angle span range, and through weighted fitting with another eight suboptimal matched trajectories, the endpoint of the fitted trajectory is considered the optimal matched position. In analysis of the algorithm reliability and matching error, the results from simulation indicate that the optimal position can be obtained effectively in real time, and the positioning accuracy improves by 35% and up to 1.05 nautical miles using the proposed algorithm compared with using the widely employed TERCOM and SITAN methods. Current gravity-aided navigation can benefit from implementation of this new algorithm in terms of better reliability and positioning accuracy.展开更多
We propose a cavity length demodulation method that combines virtual reference interferometry(VRI) and minimum mean square error(MMSE) algorithm for fiber-optic Fabry–Perot(F-P) sensors. In contrast to the conv...We propose a cavity length demodulation method that combines virtual reference interferometry(VRI) and minimum mean square error(MMSE) algorithm for fiber-optic Fabry–Perot(F-P) sensors. In contrast to the conventional demodulating method that uses fast Fourier transform(FFT) for cavity length estimation,our method employs the VRI technique to obtain a raw cavity length, which is further refined by the MMSE algorithm. As an experimental demonstration, a fiber-optic F-P sensor based on a sapphire wafer is fabricated for temperature sensing. The VRI-MMSE method is employed to interrogate cavity lengths of the sensor under different temperatures ranging from 28°C to 1000°C. It eliminates the "mode jumping" problem in the FFT-MMSE method and obtains a precision of 4.8 nm, corresponding to a temperature resolution of 2.0°C over a range of 1000°C. The experimental results reveal that the proposed method provides a promising, high precision alternative for demodulating fiber-optic F-P sensors.展开更多
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.
基金The authors gratefully acknowledge the support of the National Natural Science Foundation of China(No.11574250).
文摘Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.
基金This work is supported by Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX18_0467)Jiangsu Province,China.During the revision of this paper,the author is supported by China Scholarship Council(No.201906840021)China to continue some research related to data processing.
文摘Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.
基金supported by the 2011 China Aerospace Science and Technology Foundationthe Certain Ministry Foundation under Grant No.20212HK03010
文摘Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.
基金supported by the Natural Science Foundation of China (U22A20214)。
文摘Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the rotor vibration in AMBs is to adopt a notch filter or adaptive filter in the AMB controller. However, these methods cannot obtain the precise amplitude and phase of the compensation current. Thus, they are not so effective in terms of suppressing the vibrations of the fundamental and other harmonic orders over the whole speed range. To improve the vibration suppression performance of AMBs,an adaptive filter based on Least Mean Square(LMS) is applied to extract the vibration signals from the rotor displacement signal. An Iterative Search Algorithm(ISA) is proposed in this paper to obtain the corresponding relationship between the compensation current and vibration signals. The ISA is responsible for searching the compensating amplitude and shifting phase online for the LMS filter, enabling the AMB controller to generate the corresponding compensation force for vibration suppression. The results of ISA are recorded to suppress vibration using the Look-Up Table(LUT) in variable speed range. Comprehensive simulations and experimental validations are carried out in fixed and variable speed range, and the results demonstrate that by employing the ISA, vibrations of the fundamental and other harmonic orders are suppressed effectively.
文摘It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.
基金supported by the Open Fund of Engineering laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science & Technology, Grant No:KFJ150602)Hunan Province Science and Technology Program Funded Projects, China (Grant No:2015NK3035)
文摘A functional model named EIO(Errors-In-Observations) is proposed for general TLS(total least-squares)adjustment. The EIO model only considers the correction of the observation vector, but doesn't consider to correct all elements in the design matrix as the EIV(Errors-In-Variables) model does, furthermore, the dimension of cofactor matrix is much smaller. Iterative algorithms for the parameter estimation and their precise covariance matrix are derived rigorously, and the computation steps are also presented. The proposed approach considers the correction of the observations in the coefficient matrix, and ensures their agreements in every matrix elements. Parameters and corrections can be solved at the same time.An approximate solution and a precise solution of the covariance matrix can be achieved by corresponding algorithms. Applications of EIO model and the proposed algorithms are demonstrated with several examples. The results and comparative studies show that the proposed EIO model and algorithms are feasible and reliable for general adjustment problems.
文摘Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE) criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate (MSER) criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.
文摘In this paper a square wavelet thresholding method is proposed and evaluated as compared to the other classical wavelet thresholding methods (like soft and hard). The main advantage of this work is to design and implement a new wavelet thresholding method and evaluate it against other classical wavelet thresholding methods and hence search for the optimal wavelet mother function among the wide families with a suitable level of decomposition and followed by a novel thresholding method among the existing methods. This optimized method will be used to shrink the wavelet coefficients and yield an adequate compressed pressure signal prior to transmit it. While a comparison evaluation analysis is established, A new proposed procedure is used to compress a synthetic signal and obtain the optimal results through minimization the signal memory size and its transmission bandwidth. There are different performance indices to establish the comparison and evaluation process for signal compression;but the most well-known measuring scores are: NMSE, ESNR, and PDR. The obtained results showed the dominant of the square wavelet thresholding method against other methods using different measuring scores and hence the conclusion by the way for adopting this proposed novel wavelet thresholding method for 1D signal compression in future researches.
基金The NSF(11271155) of ChinaResearch Fund(20070183023) for the Doctoral Program of Higher Education
文摘In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error (MM) and the asymptotic bias (MB), respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.
文摘工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小迭代修复和改进WGAN混合模型的时序数据修复方法.首先,在预处理阶段,保留异常数据,进行信息标注等处理,从而充分挖掘异常值与真实值之间的特征约束.其次,在噪声模块提出了近邻参数裁剪规则,用于修正最小迭代修复公式生成的噪声向量.将其传递至模拟分布模块的生成器中,同时设计了一个动态时间注意力网络层,用于提取时序特征权重并与门控循环单元串联组合捕捉不同步长的特征依赖,并引入递归多步预测原理共同提升模型的表达能力;在判别器中设计了Abnormal and Truth奖励机制和Weighted Mean Square Error损失函数共同反向优化生成器修复数据的细节和质量.最后,在公开数据集和真实数据集上的实验结果表明,该方法的修复准确度与模型稳定性显著优于现有方法.
基金supported by National Natural Science Foundation of China (Grant Nos. 41074051, 41021003 and 40874037)
文摘Gravity/inertial combination navigation is a leading issue in realizing passive navigation onboard a submarine. A new rotation-fitting gravity matching algorithm, based on the Terrain Contour Matching (TERCOM) algorithm, is proposed in this paper. The algorithm is based on the principle of least mean-square-error criterion, and searches for a certain matched trajectory that runs parallel to a trace indicated by an inertial navigation system on a gravity base map. A rotation is then made clockwise or counterclockwise through a certain angle around the matched trajectory to look for an optimal matched trajectory within a certain angle span range, and through weighted fitting with another eight suboptimal matched trajectories, the endpoint of the fitted trajectory is considered the optimal matched position. In analysis of the algorithm reliability and matching error, the results from simulation indicate that the optimal position can be obtained effectively in real time, and the positioning accuracy improves by 35% and up to 1.05 nautical miles using the proposed algorithm compared with using the widely employed TERCOM and SITAN methods. Current gravity-aided navigation can benefit from implementation of this new algorithm in terms of better reliability and positioning accuracy.
基金supported by the National Natural Science Foundation of China(NSFC)(Nos.61377091 and61505152)the Pre-research Field Foundation of China(No.6140243010116QT69001)the Applied Basic Research Program of Wuhan,China(No.2017010201010102)
文摘We propose a cavity length demodulation method that combines virtual reference interferometry(VRI) and minimum mean square error(MMSE) algorithm for fiber-optic Fabry–Perot(F-P) sensors. In contrast to the conventional demodulating method that uses fast Fourier transform(FFT) for cavity length estimation,our method employs the VRI technique to obtain a raw cavity length, which is further refined by the MMSE algorithm. As an experimental demonstration, a fiber-optic F-P sensor based on a sapphire wafer is fabricated for temperature sensing. The VRI-MMSE method is employed to interrogate cavity lengths of the sensor under different temperatures ranging from 28°C to 1000°C. It eliminates the "mode jumping" problem in the FFT-MMSE method and obtains a precision of 4.8 nm, corresponding to a temperature resolution of 2.0°C over a range of 1000°C. The experimental results reveal that the proposed method provides a promising, high precision alternative for demodulating fiber-optic F-P sensors.