The well-known extended Kalman filter (EKF) has been widely applied to the Global Positioning System (GPS) navigation processing. The adaptive algorithm has been one of the approaches to prevent the divergence problem of the EKF when precise knowledge on the system models are not available. One of the adaptive methods is called the strong tracking Kalman filter (STKF), which is essentially a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. Traditional approach for selecting the softening factors heavily relies on personal experience or computer simulation. In order to resolve this shortcoming, a novel scheme called the adaptive fuzzy strong tracking Kalman filter (AFSTKF) is carried out. In the AFSTKF, the fuzzy logic reasoning system based on the Takagi-Sugeno (T-S) model is incorporated into the STKF. By monitoring the degree of divergence (DOD) parameters based on the innovation information, the fuzzy logic adaptive system (FLAS) is designed for dynamically adjusting the softening factor according to the change in vehicle dynamics. GPS navigation processing using the AFSTKF will be simulated to validate the effectiveness of the proposed strategy. The performance of the proposed scheme will be assessed and compared with those of conventional EKF and STKF

This paper revisits the characteristics of windowing techniques with various window functions involved, and successively investigates spectral leakage mitigation utilizing the Welch method. The discrete Fourier transform (DFT) is ubiquitous in digital signal processing (DSP) for the spectrum analysis and can be efficiently realized by the fast Fourier transform (FFT). The sampling signal will result in distortion and thus may cause unpredictable spectral leakage in discrete spectrum when the DFT is employed. Windowing is implemented by multiplying the input signal with a window function and windowing amplitude modulates the input signal so that the spectral leakage is evened out. Therefore, windowing processing reduces the amplitude of the samples at the beginning and end of the window. In addition to selecting appropriate window functions, a pretreatment method, such as the Welch method, is effective to mitigate the spectral leakage. Due to the noise caused by imperfect, finite data, the noise reduction from Welch’s method is a desired treatment. The nonparametric Welch method is an improvement on the periodogram spectrum estimation method where the signal-to-noise ratio (SNR) is high and mitigates noise in the estimated power spectra in exchange for frequency resolution reduction. The periodogram technique based on Welch method is capable of providing good resolution if data length samples are appropriately selected. The design of finite impulse response (FIR) digital filter using the window technique is firstly addressed. The influence of various window functions on the Fourier transform spectrum of the signals is discussed. Comparison on spectral resolution based on the traditional power spectrum estimation and various window-function-based Welch power spectrum estimations is presented.

Several machine learning (ML) methodologies are gaining popularity as artificial intelligence (AI) becomes increasingly prevalent. An artificial neural network (ANN) may be used as a “black-box” modeling strategy without the need for a detailed system physical model. It is more reasonable to solely use the input and output data to explain the system’s actions. ANNs have been extensively researched, as artificial intelligence has progressed to enhance navigation performance. In some circumstances, the Global Navigation Satellite System (GNSS) can offer consistent and dependable navigational options. A key advancement in contemporary navigation is the fusion of the GNSS and inertial navigation system (INS). Numerous strategies have been put out recently to increase the accuracy for jamming, GNSS-prohibited environments, the integration of GNSS/INS or other technologies by means of a Kalman filter as well as to solve the signal blockage issue in metropolitan areas. A neural-network-based fusion approach is suggested to address GNSS outages. The overview, inquiry, observation, and performance evaluation of the present integrated navigation systems are the primary objectives of the review. The important findings in ANN research for use in navigation systems are reviewed. Reviews of numerous studies that have been conducted to investigate, simulate, and integrate navigation systems in order to produce accurate and dependable navigation solutions are offered.

For a GPS receiver, decreasing the receiver tracking loop bandwidth reduces the probability of loss of lock if there are no vehicle dynamics. However, reduced bandwidth increases tracking errors due to dynamics. Beyond a certain limit it causes a serious degradation in the dynamic tracking performance. Therefore, there is involvement of a tradeoff between two opposing considerations: narrow tracking loop bandwidths are desired for filtering noise due to thermal effects, but wide tracking loop bandwidths are desired to permit tracking of vehicle dynamics. Optimal tracking loop bandwidths, which yield the minimum errors in a certain dynamics environment, are first investigated. The linear Kalman filter is employed as the optimal estimator. The covariance for the arbitrary gain model is solved and applied to the sensitivity analysis for investigating error growth due to incorrect noise level estimate. Theoretical results are verified by numerical simulation, and results from both approaches are in very good agreement.