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MEMS accelerometers are significantly impacted by temperature and noise, leading to a considerable compromise in their accuracy. In response to this challenge, we propose a parallel denoising and temperature compensation fusion algorithm for MEMS accelerometers based on RLMD-SE-TFPF and GRU-attention. Firstly, we utilize robust local mean decomposition (RLMD) to decompose the output signal of the accelerometer into a series of product function (PF) signals and a residual signal. Secondly, we employ sample entropy (SE) to classify the decomposed signals, categorizing them into noise segments, mixed segments, and temperature drift segments. Next, we utilize the time-frequency peak filtering (TFPF) algorithm with varying window lengths to separately denoise the noise and mixed signal segments, enabling subsequent signal reconstruction and training. Considering the strong inertia of the temperature signal, we innovatively introduce the accelerometer's output time series as the model input when training the temperature compensation model. We incorporate gated recurrent unit (GRU) and attention modules, proposing a novel GRU-MLP-attention model (GMAN) architecture. Simulation experiments demonstrate the effectiveness of our proposed fusion algorithm. After processing the accelerometer output signal through the RLMD-SE-TFPF denoising algorithm and the GMAN temperature drift compensation model, the acceleration random walk is reduced by 96.11 % , with values of 0.23032 g/h / Hz for the original accelerometer output signal and 0.00895695 g/h / Hz for the processed signal. [ABSTRACT FROM AUTHOR]

This document is an editorial for a special issue of the journal Micromachines on Micro-Electromechanical System (MEMS) inertial devices. It explains that MEMS are miniature systems that combine micro-mechanical sensors, actuators, and microelectronic circuits. MEMS inertial devices, such as accelerometers and gyroscopes, capture physical motion and convert it into electrical signals. The editorial highlights various applications of MEMS inertial devices, including aerospace, underwater exploration, robotics, and healthcare. It also discusses the challenges faced by these devices and presents 11 papers in the special issue that cover different aspects of MEMS inertial devices, including design, manufacturing, optimization, and maintenance. [Extracted from the article]

The micro-electro-mechanical system (MEMS) gyroscope is a micro-mechanical gyroscope with low cost, small volume, and good reliability. The working principle of the MEMS gyroscope, which is achieved through Coriolis, is different from traditional gyroscopes. The MEMS gyroscope has been widely used in the fields of micro-inertia navigation systems, military, automotive, consumer electronics, mobile applications, robots, industrial, medical, and other fields in micro-inertia navigation systems because of its advantages of small volume, good performance, and low price. The material characteristics of the MEMS gyroscope is very significant for its data output, and the temperature determines its accuracy and limits its further application. In order to eliminate the effect of temperature, the MEMS gyroscope needs to be compensated to improve its accuracy. This study proposed an improved variational modal decomposition—extreme learning machine (VMD-ELM) algorithm based on convolutional neural networks—long short-term memory (CNN-LSTM) and particle swarm optimization—support vector machines (PSO-SVM). By establishing a temperature compensation model, the gyro temperature output signal is optimized and reconstructed, and the gyro output signal with better accuracy is obtained. The VMD algorithm separates the gyro output signal and divides the gyro output signal into low-frequency signals, mid-frequency signals, and high-frequency signals according to the different signal frequencies. Once again, the PSO-SVM model is constructed by the mid-frequency temperature signal to find the temperature error. Finally, the signal is reconstructed through the ELM neural network algorithm, and then, the gyro output signal after noise is obtained. Experimental results show that, by using the improved method, the output of the MEMS gyroscope ranging from −40 to 60 °C reduced, and the temperature drift dramatically declined. For example, the factor of quantization noise (Q) reduced from 1.2419 × 10−4 to 1.0533 × 10−6, the factor of bias instability (B) reduced from 0.0087 to 1.8772 × 10−4, and the factor of random walk of angular velocity (N) reduced from 2.0978 × 10−5 to 1.4985 × 10−6. Furthermore, the output of the MEMS gyroscope ranging from 60 to −40 °C reduced. The factor of Q reduced from 2.9808 × 10−4 to 2.4430 × 10−6, the factor of B reduced from 0.0145 to 7.2426 × 10−4, and the factor of N reduced from 4.5072 × 10−5 to 1.0523 × 10−5. The improved algorithm can be adopted to denoise the output signal of the MEMS gyroscope to improve its accuracy. [ABSTRACT FROM AUTHOR]

This article investigates a neurodynamic quantized control problem with improved transient performances for microelectromechanical system (MEMS) gyroscopes subject to lumped disturbances induced by parameter uncertainties, dynamic coupling, and external disturbances. First, a modified prescribed performance control mechanism based on a hyperbolic cosecant performance function is proposed to specify the transient behavior of tracking errors with an arbitrarily small overshoot. Then, to eliminate the lumped disturbances with a better identification property, a novel echo state network approximator that uses the estimation error to learn neural weights is designed with the aid of a minimal learning parameter technique, which not only can exclude the poor transient behaviors occurring extensively in the existing neural control with a large adaptive gain, but also dramatically reduce the number of parameters to be updated online. Furthermore, contrasting to the available tracking results assuming a continuous control updating, a hysteresis quantizer is introduced to provide discrete values of control signals, supporting the use of digital devices in MEMS gyroscope implementations to realize a closed-loop error stabilization. Finally, ultimately uniformly bounded stability of closed-loop system is proved with the aid of Lyapunov function and nonsmooth analysis technique, while not only simulations but also experimental results are performed to validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

To solve the problem of micro-electro-mechanical system (MEMS) gyroscope noise, this paper presents a variational mode decomposition (VMD) method based on crow search algorithm. First, the signal was decomposed by variational mode decomposition for optimization of crow search algorithm (CSA-VMD) method. The parameters required by the VMD method (penalty parameter α and decomposition number K) are given by the crow search algorithm, and then the signal is decomposed into the superposition of multiple subsignals, called intrinsic mode functions (IMFs). The sample entropy (SE) corresponding to each IMF is then obtained. By calculating the sample entropy, the noise signal can be divided into pure noise part, mixing part, and temperature drift part. Second, Savitzky–Golay smoothing denoising (SG) is used to filter the mixed noise signal to eliminate the influence of noise. Third, for the filtering of the drift part, the least square support vector machine optimized by the crow search algorithm (CSA-LSSVM) was used to filter, so as to reduce the effect of temperature drift. Finally, the processed signal is reconstructed to achieve the goal of denoising. Through the results, it can be found that the optimized VMD and LSSVM using CSA algorithm can achieve more effective denoising. After using the method proposed in this paper, the angular random walk value is 1.1175 ∗ 10−4°/h/√Hz, and the bias stability is 0.0017°/h. Compared with the original signal, the two signals are optimized by 98.1% and 98.2%, respectively. It can be seen from the experimental results that the proposed CSA-VMD method, SG method, and CSA-LSSVM method can effectively eliminate noise effects. [ABSTRACT FROM AUTHOR]

This article suggested two methods to compensate for the temperature drift of the micro-electro-mechanical system gyroscopes, which are support vector machine method and C-means support vector machine. The output of X axis which was ranged from −40°C to 60°C based on the micro-electro-mechanical system gyroscope is reduced and analyzed in this article. The results showed the correctness of the two methods. The final results indicate that when the temperature is ranged from −40°C to 60°C, the factor of B is reduced from 0.424 (° h) to 0.02194 (° h) , and when the temperature is ranged from 60°C to −40°C, the factor of B is reduced from 0.1056 (° h) to 0.0329 (° h) , and the temperature drift trend and noise characteristics are improved clearly. [ABSTRACT FROM AUTHOR]

Animals have certain cognitive competence about the environment so they can correct their navigation errors. Inspired by the excellent navigational behavior of animals, this paper proposes a brain-like navigation scheme to improve the accuracy and intelligence of Micro-Electro-Mechanical System based Inertial Navigation Systems (MEMS-INS). The proposed scheme employs vision to acquire external perception information as an absolute reference to correct the position errors of INS, which is established by analyzing the navigation and error correction mechanism of rat brains. In addition, to improve the place matching speed and precision of the system for visual scene recognition, this paper presents a novel place recognition algorithm that combines image scanline intensity (SI) and grid-based motion statistics (GMS) together which is named the SI-GMS algorithm. The proposed SI-GMS algorithm can effectively reduce the influence of uncertain environment factors on the recognition results, such as pedestrians and vehicles. It solves the problem that the matching result will occasionally go wrong when simply using the scanline intensity (SI) algorithm, or the slow matching speed when simply using grid-based motion statistics (GMS) algorithm. Finally, an outdoor Unmanned Aerial Vehicle (UAV) flight test is carried out. Based on the reference information from the high-precision GPS device, the results illustrate the effectiveness of the scheme in error correction of INS and the algorithm in place recognition. [ABSTRACT FROM AUTHOR]

This paper proposed three methods to compensate the temperature energy influence drift of the MEMS vibration gyroscope, including radial basis function neural network (RBF NN), RBF NN based on genetic algorithm (GA), and RBF NN based on GA with Kalman filter (KF). Three-axis MEMS vibration gyroscope (Gyro X, Gyro Y, and Gyro Z) output data are compensated and analyzed in this paper. The experimental results proved the correctness of these three methods, and MEMS vibration gyroscope temperature energy influence drift is compensated effectively. The results indicate that, after RBF NN-GA-KF method compensation, the bias instability of Gyros X, Y, and Z improves from 139°/h, 154°/h, and 178°/h to 2.9°/h, 3.9°/h, and 1.6°/h, respectively. And the angle random walk of Gyros X, Y, and Z was improved from 3.03°/h1/2, 4.55°/h1/2, and 5.89°/h1/2 to 1.58°/h1/2, 2.58°/h1/2, and 0.71°/h1/2, respectively, and the drift trend and noise characteristic are optimized obviously. [ABSTRACT FROM AUTHOR]

This paper analyzes different noise components in MEMS gyroscope silicon structure, including mechanical–thermal noise (MTN), electronic-thermal noise (ETN), flicker noise (FN) and Coriolis signal in-phase noise (IPN). The structure equivalent electronic model is established, and the improved differential interface is proposed based on weak signal detection technology, after that, the noise components in silicon structure are introduced and analyzed in sense open loop. The quadrature error (QE) signal automatically cancellation loop is proposed, and the results of the experiment indicate that the equivalent angular rates of QE and IPN are 46°/s and 4.55°/s respectively. The interfaces contrast experiments show that the DC noise and the useful signal amplitudes of differential and single-side detection interfaces are −49.8 dBmV, −16.8 dBmV and −39.8 dBmV (−42.1 dBmV), −22.1 dBmV (−22.2 dBmV), which confirms the differential interface has better SNR. The carrier experiments also illustrate that higher carrier frequency (from 500 kHz to 10 MHz) can restrain DC noise (from −19.8 dBmV to −54.2 dBmV) better, which demonstrate the FN is the dominant noise component of the silicon structure under normal temperature. The temperature experiments show the DC noise enhances from −48.5 dBmV to −14.6 dBmV over the range 20 °C to 60°C while the useful signal amplitude remains around -16.6dBmV, and this phenomenon indicates the MTN and ETN become the dominant structure noise components gradually with temperature rising. [ABSTRACT FROM AUTHOR]

The traditional processing model of the temperature error for a gyroscope is serial, meaning that de-noising and temperature drift compensation are implemented in a two-step procedure. Hence, the result of the latter depends on the performance of the former; in particular, negative de-noising produces a negative compensation result. To reduce this dependence, we propose a parallel processing algorithm of the temperature error based on variational mode decomposition (VMD) and an augmented nonlinear differentiator (AND). An application to a micro-electro-mechanical system gyroscope is described to demonstrate the effectiveness and applicability of the proposed algorithm. Its major advantages are (i) a combination of VMD, extreme learning machines, and AND is proposed, and an adaptive accelerometer factor determination method for AND is given based on the VMD, both of which improve the effectiveness of the de-noising process; (ii) temperature drift and noise in the temperature error can be extracted and processed synchronously, thereby reducing the dependency of drift compensation on the de-noising result and making the temperature error process more efficient. [ABSTRACT FROM AUTHOR]

A novel method is investigated in this paper to estimate the temperature's influence upon the resonant frequency (RESF) and quality factor (Q) of a vacuum packaged Micro-Electro-Mechanical-System (MEMS) gyroscope, which can give suggestions to improve the architecture's temperature robustness. The dual-mass decoupled gyroscope's architecture is introduced, and the drive and sense modes' mechanical character are analyzed. The models of RESF and damping are established, and the influence factors are investigated. Four samples are tested and the results indicate that the models can estimate and evaluate the tendency of the RESF and Q in different temperature. The investigation also considers the Young Modulus is the dominate element influencing RESF and increasing the thickness and width of the U-shaped spring can decrease this influence; Q is impacted mainly by the air viscosity coefficient and ambient pressure. The errors of the models are caused by manufacture error and the air getter's influence. [ABSTRACT FROM AUTHOR]

To eliminate the noise and temperature drift in an Micro-Electro-Mechanical Systems (MEMS) gyroscope's output signal for improving measurement accuracy, a parallel processing model based on Multi-objective particle swarm optimization based on variational modal decomposition-time-frequency peak filter (MOVMD–TFPF) and Beetle antennae search algorithm- Elman neural network (BAS–Elman NN) is established. Firstly, variational mode decomposition (VMD) is optimized by multi-objective particle swarm optimization (MOPSO); then, the best decomposition parameters [kbest,abest] can be obtained. Secondly, the gyroscope output signals are decomposed by VMD optimized by MOPSO (MOVMD); then, the intrinsic mode functions (IMFs) obtained after decomposition are classified into a noise segment, mixed segment, and drift segment by sample entropy (SE). According to the idea of a parallel model, the noise segment can be discarded directly, the mixed segment is denoised by time-frequency peak filtering (TFPF), and the drift segment is compensated at the same time. In the compensation part, the beetle antennae search algorithm (BAS) is adopted to optimize the network parameters of the Elman neural network (Elman NN). Subsequently, the double-input/single-output temperature compensation model based on the BAS-Elman NN is established to compensate the drift segment, and these processed segments are reconstructed to form the final gyroscope output signal. Experimental results demonstrate the superiority of this parallel processing model; the angle random walk of the compensated gyroscope output is decreased from 0.531076 to 5.22502 × 10−3°/h/√Hz, and its bias stability is decreased from 32.7364°/h to 0.140403°/h, respectively. [ABSTRACT FROM AUTHOR]

For the sake of decreasing the effects of noise and temperature error on the measurement accuracy of micro-electro-mechanical system (MEMS) gyroscopes, a denoising and temperature drift compensation parallel model method based on wavelet transform and forward linear prediction (WFLP) and support vector regression based on the cuckoo search algorithm (CS-SVR) is proposed in this paper. First, variational mode decomposition (VMD) is proposed in this paper, which is aimed at dividing the output signal of the gyroscope into intrinsic mode functions (IMFs); then, the IMFs are classified into three features—drift, mixed, and pure noise features—by the sample entropy (SE) value. Second, a wavelet transform and forward linear prediction (WFLP) are combined to remove the noise from the mixed features. Meanwhile, the drift feature is compensated by support vector regression based on the cuckoo search algorithm (CS-SVR). Finally, through reconstruction, the final signal is obtained. Experimental results demonstrate that the VMD-SE-WFLP-CS-SVR method proposed in this paper can decrease noise and compensate the temperature error effectively (angular random walking value is optimized from 1.667°/√h to 0.0667°/√h and the bias stability is reduced from 30°/h to 4°/h). In terms of denoising, the performance of the WFLP algorithm is superior to the wavelet threshold and FLP, as it combines their advantages; furthermore, in terms of temperature compensation, the proposed CS-SVR algorithm uses the cuckoo search algorithm to find the optimal parameters of SVR, improving the accuracy of the model. [ABSTRACT FROM AUTHOR]

To deal with the influence of temperature drift for a Micro-Electro-Mechanical System (MEMS) gyroscope, this paper proposes a new temperature error parallel processing method based on a novel fusion algorithm. Firstly, immune based particle swarm optimization (IPSO) is employed for optimal parameters search for Variational Modal Decomposition (VMD). Then, we can get the optimal decomposition parameters, wherein permutation entropy (PE) is employed as the fitness function of the particles. Then, the improved VMD is performed on the output signal of the gyro to obtain intrinsic mode functions (IMFs). After judging by sample entropy (SE), the IMFs are divided into three categories: noise term, mixed term and feature term, which are processed differently. Filter the mixed term and compensate the feature term at the same time. Finally, reconstruct them and get the result. Compared with other optimization algorithms, IPSO has a stronger global search ability and faster convergence speed. After Back propagation neural network (BP) is enhanced by Adaptive boosting (Adaboost), it becomes a strong learner and a better model, which can approach the real value with higher precision. The experimental result shows that the novel parallel method proposed in this paper can effectively solve the problem of temperature errors. [ABSTRACT FROM AUTHOR]

This study presents a new microelectromechanical system, a vibration ring gyroscope with a double U-beam (DUVRG), which was designed using a combination of mathematical analysis and the finite element method. First, a ring vibration resonator with eight double U-beam structures was developed, and 24 capacitive electrodes were designed for drive and sense according to the advantageous characteristics of a thin-shell vibrating gyroscope. Then, based on the elastic mechanics and thin-shell theory, a mathematical stiffness model of the double U-beam was established. The maximum mode resonant frequency error calculated by the DUVRG stiffness model, finite element analysis (FEA) and experiments was 0.04%. DUVRG structures were manufactured by an efficient fabrication process using silicon-on-glass (SOG) and deep reactive ion etching (DRIE), and the FEA value and theoretical calculation had differences of 5.33% and 5.36% with the measured resonant frequency value, respectively. Finally, the static and dynamic performance of the fabricated DUVRG was tested, and the bias instability and angular random walk were less than 8.86 (°)/h and 0.776 (°)/√h, respectively. [ABSTRACT FROM AUTHOR]

This paper proposes an effective method to calibrate the microelectromechanical systems (MEMS) vibratory gyroscope based on the virtual Coriolis force. This method utilizes a series of voltage signals to simulate the Coriolis force input, and the gyroscope output is monitored to obtain the scale factor characteristics of the gyroscopes. The scale factor and bias parameters of the gyroscope can be calibrated conveniently and efficiently in the sense-mode open loop. The calibration error of the scale factor based on the turntable and the virtual Coriolis force method is only 1.515%, which proves the correction of the method proposed in this paper. Meanwhile, the non-linearity and bias value of the turntable and the virtual Coriolis force method are 742 ppm and 42.04 mV and 3389 ppm and 0.66 mV, respectively. [ABSTRACT FROM AUTHOR]

An adaptive multi-scale method based on the combination generalized morphological filter (CGMF) is presented for de-noising of the output signal from a MEMS gyroscope. A variational mode decomposition is employed to decompose the original signal into multi-scale modes. After choosing a length selection for the structure element (SE), the adaptive multi-scale CGMF method reduces the noise corresponding to the different modes, after which a reconstruction of the de-noised signal is obtained. From an analysis of the effect of de-noising, the main advantages of the present method are that it: (i) effectively overcomes deficiencies arising from data deviation compared with conventional morphological filters (MFs); (ii) effectively targets the different components of noise and provides efficacy in de-noising, not only primarily eliminating noise but also smoothing the waveform; and (iii) solves the problem of SE-length selection for a MF and produces feasible formulae of indicators such as the power spectral entropy and root mean square error for mode evaluations. Compared with the other current signal processing methods, the method proposed owns a simpler construction with a reasonable complexity, and it can offer better noise suppression effect. Experiments demonstrate the applicability and feasibility of the de-noising algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a high-G MEMS accelerometer (HGMA). HGMA employs our-beams and central-island mass silicon structure, which features a robust stability in shock environment. Theoretical analysis is conducted to investigate the influence of structure parameters on the Von Mises stress distribution, mechanical sensitivity and natural frequency. With consideration of smaller stress, higher mechanical sensitivity and natural frequency, the structure parameters are optimized and the theoretical sensitivity of HGMA is calculated as 0.488μV/g. Then, the optimized structure is analyzed with finite element analysis software, which shows a maximum stress of 23.19 MPa and a frequency response of 408.19 kHz when a 100 000 g shock is loaded. Finally, a processing flow is designed and the structure is fabricated. Hopkinson bar is utilized to calibrate HGMA sample, and shows an experimental sensitivity of 0.5611μV/g. Long-term static bias and temperature experiments are arranged to evaluate HGMA. Test results verify the presented theoretical analysis, processing flow, and experiment method, which are of great value for guiding the design, fabrication and calibration of other HGMAs. [ABSTRACT FROM AUTHOR]

In this paper, we design a symmetric quad-beam accelerometer structure for z-axis sensing. Considering the extremely high chemical stability of SiC, traditional dry etching is not suitable for machining SiC MEMS sensor. Thus, we put forward a method using ultraviolet laser cutting to release cantilever beam of SiC accelerometer and using laser ablating to process mass. Pulse Repetition Frequency (PRF) and processing laps are optimized to obtain high-quality surface morphology and much less thermal effect. Finally, we use the optimal parameters with 35 kHz pulse frequency, 4 processing laps, 200 mm/s scanning speed to process through-hole. Combing with Raman spectrum and EDS spectrum, the feasibility of laser machining SiC sensor is studied. The result shows that in machining cantilever beam the carbonization and generation of silicon accelerates the trepanning depth of SiC. However, in machining the hole, the thermal effect of photon energy barely adds influence on region from boundary of hole to 30 μm. Thus, it is feasible to use laser cutting to release cantilever beam while it is difficult to use laser ablating processing back cavity of accelerometer. The time of laser micromachining 4 H-SiC cantilever beam is less than 2 s. Compared with the traditional ICP etching (0.2–1.3 μm/min), etching rate with laser ablating in releasing cantilever beam significantly increases nowadays. Finally, the sensitivity of SiC accelerometer is measured to 0.644 μV/g. [ABSTRACT FROM AUTHOR]

A temperature error processing method for a dual-mass micro-electromechanical system (MEMS) gyroscope based on multi-scale parallel model is proposed. At first, a sample entropy based bounded ensemble empirical mode decomposition (SE-BEEMD) is proposed to decompose the original signal into different scales, include noise-only scale, mixed scale and drift scale; then forward linear prediction (FLP) is employed to eliminate the noise at mixed scale and extreme learning machine (ELM) based model is employed to compensate the drift at drift scale, the two steps are carried out paralleled; at last the final results can be obtained after reconstruction. Experimental results show that: (1) compared to tradition serial model, the proposed parallel model can eliminate the temperature errors more effectively, and each parameter of Allan analysis is improved. Specially, the quantification noise reduced from 0.035 μrad to 9.93e4 μrad, angle random walk reduced from 2.13e-5/s 1/2 to 7.94e-6/s 1/2 , bias instability reduced from 5.28e-4/s to 4.79e-4/s, rate random walk from 0.012/s 3/2 to 0.092/s 3/2 and angular rate ramp reduced from 0.013/s 2 to 0.011/s 2 ; (2) compared to traditional time consuming neural networks, the ELM has the best modeling accurate and shortest training time, which would be valuable for online temperature drift modeling and compensation. [ABSTRACT FROM AUTHOR]

• A dual-model instead of traditional single model comprised of CKF-MLP and RBF-CKF algorithms is proposed for position and velocity error compensation during GPS outages. • CKF is added in MLP to reduce network errors and improve modelling accuracy by estimating the weights of MLP adaptively for training process which is termed as CKF-MLP algorithm. • RBF is added in CKF to predict the errors caused by filter itself and improve INS error compensation accuracy which is termed as RBF-CKF algorithm. To improve the performance of a microelectromechanical-system (MEMS)-based inertial navigation system (INS)/Global Positioning System (GPS) integrated navigation system, a dual optimization scheme comprising a cubature Kalman filter (CKF)-multiple layer perceptron (MLP) and radial basis function (RBF)-CKF is proposed for the compensation of position and velocity errors during GPS outages. The proposed method has advantages: (i) The generalization ability of the CKF-MLP is much better than that of other methods, such as the extended Kalman filter (EKF)-MLP and unscented Kalman filter (UKF)-MLP, and the proposed CKF-MLP provides highly accurate position information even during long GPS outages; (ii) The accuracy of the error estimation of the RBF-CKF is higher than that of other neural-network-assisted CKF methods, such as the Adaboost-CKF and random forest (RF)-CKF, and the proposed CKF-MLP can estimate the weights of the MLP adaptively and achieve an appropriate internal structure when the GPS signal is available; (iii) The RBF is added to the CKF to establish the relationship between filter parameters and estimation error in the proposed RBF-CKF; (iv) During a GPS outage, position errors and velocity errors are predicted and compensated for in the proposed dual optimization scheme. Field test data are collected to evaluate the proposed solution. Experimental results show that (i) the root-mean-square error of the velocity for an eastern position is reduced by 77% to 0.34 m/s using the proposed CKF-MLP strategy; (ii) the root-mean-square error of a northern position determined by the proposed RBF-CKF remains at 23.11 m even during long outages of 500 s, and the RBF-CKF effectively suppresses the divergence seen for other methods; and (iii) the dual optimization process using different estimators provides better error compensation results than a single optimization method, which demonstrates that the proposed solution leads to the better performance of a MEMS-based INS/GPS navigation system. [ABSTRACT FROM AUTHOR]