The cost of inertial navigation systems (INS) has decreased significantly during recent years using micro-electro-mechanical system technology in production of inertial measurement units (IMUs). However, these IMUs do not provide the accuracy and stability of their classical mechanical counterparts which limit their applications. Hence, the error control of such systems is of the great importance which is achievable using external information via an appropriate fusion algorithm. Traditionally, this external information can be derived from global positioning system (GPS). But it is well known that GPS data availability and accuracy are vulnerable to signal-degrading circumstances and satellite visibility. We introduce a standalone attitude and heading reference system (AHRS) algorithm which employs the IMU and magnetometers data in an averaging manner. The averaging method is different from a simple smoothing procedure, since it takes the rotations of the platform (during the averaging interval) into account. The proposed AHRS solution is further used to provide additional attitude updates with adaptive noise variances for the integrated INS/GPS system during GPS outages via a refined loosely coupled filtering procedure, making the error growth well restrained. Functionality of the algorithm has been assessed via a field test. The results indicate that the proposed procedure outperforms the traditional integration scheme in different situations, while the latter almost loses track of the movements of the vehicle after 60-second GPS outages.
In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation spectra are introduced and estimated for the series to detect the regular and modulated dominant frequencies of the periodic patterns. Two significant periodic patterns are the diurnal and annual signals with periods of 24/n hours and 365.25/n days (n = 1, 2, …), which are the Fourier series decomposition of the regular daily and yearly periodic variations of the ionosphere. The spectrum shows a cluster of periods near 27 days, thereby indicating irregularities at this solar cycle period. A series of peaks, with periods close to the diurnal signal and its harmonics, are evident in the spectrum. In fact, the daily signal harmonics of x i = 2pi are modulated with the annual signal harmonics of x j = 2pj/365.25 as x ijM = 2pi(1 ± j/365.25i). Among them, at low and midlatitudes, the largest variations belong to the diurnal signal modulated to the semiannual signal. Some preliminary results on the modulated part are presented. The maximum ranges of the modulated daily signal are ±15 TECU and ±6 TECU at high and low solar periods, respectively. A model consisting of purely harmonic functions plus modulated ones is capable of studying known regular anomalies of the ionosphere, which is currently in progress.
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