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This paper presents a Multiplicative Extended Kalman Filter (MEKF) framework using a state-of-the-art velocimeter Light Detection and Ranging (LIDAR) sensor for Terrain Relative Navigation (TRN) applications. The newly developed velocimeter LIDAR is capable of providing simultaneous position, Doppler velocity, and reflectivity measurements for every point in the point cloud. This information, along with pseudo-measurements from point cloud registration techniques, a novel bulk velocity batch state estimation process and inertial measurement data, is fused within a traditional Kalman filter architecture. Results from extensive emulation robotics experiments performed at Texas A&M’s Land, Air, and Space Robotics (LASR) laboratory and Monte Carlo simulations are presented to evaluate the efficacy of the proposed algorithms. 

Particle pair statistics of inertial particles having average Stokes numbers of 2.1 and 14 are measured in isotropic turbulence at a Reynolds number of Reλ = 240. The radial distribution function (RDF) and mean relative approach velocity are obtained at small separation distances using 2-frame stereoscopic particle tracking velocimetry (stereo-PTV). At small separation distance, the RDF varies by an order of magnitude in the range of Stokes numbers investigated. However, the mean relative approach velocity is found to have a weak dependence on Stokes number. The results are shown to have high accuracy when compared to analogous mono-PTV datasets, and can be used to provide a more reliable estimate of the inter-particle collision rate. The main limitation of the measurement is observed at separation distances less than the laser sheet thickness, where the technique tended to underestimate the mean relative approach velocity. 

Observations of relative paleointensity reveal several forms of asymmetry in the time dependence of the virtual axial dipole moment (VADM). Slow decline of the VADM into a reversal is often followed by a more rapid rise back to a quasi‐steady state. Asymmetry is also observed in trends of VADM during times of stable polarity. Trends of increasing VADM over time intervals of a few 10s of kyr are more intense and less frequent than decreasing trends. We examine the origin of this behavior using stochastic models. The usual (Langevin) model can account for asymmetries during reversals, but it cannot reproduce the observed asymmetry in trends during stable polarity. Better agreement is achieved with a different class of stochastic models in which the dipole is generated by a series of impulsive events in time. The timing of each event occurs randomly as a Poisson process and the amplitude is also randomly distributed. Predicted trends replicate the observed asymmetry when the generation events are large and the recurrence time is long (typically longer than 3 kyr). Large and infrequent generation events argue against dipole generation by small‐scale turbulent flow. Instead, the observations favor a mechanism that relies on expulsion of poloidal magnetic field from the core.

 

The historical trend in the axial dipole is sufficient to reverse the field in less than 2 kyr. Assessing the prospect of an imminent polarity reversal depends on the probability of sustaining the historical trend for long enough to produce a reversal. We use a stochastic model to predict the variability of trends for arbitrary time windows. Our predictions agree well with the trends computed from paleomagnetic models. Applying these predictions to the historical record shows that the current trend is likely due to natural variability. Furthermore, an extrapolation of the current trend for the next 1 to 2 kyr is highly unlikely. Instead, we compute the trend and time window needed to reverse the field with a specified probability. We find that the dipole could reverse in the next 20 kyr with a probability of 2%.