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We consider N independent stochastic processes (Xi (t), t ∈ [0, T]), i = 1, . . . , N, defined by a one-dimensional stochastic differential equation, which are continuously observed throughout a time interval [0, T] where T is fixed. We study nonparametric estimation of the drift function on a given subset A of ℝ. Projection estimators are defined on finite dimensional subsets of 𝕃²(A, dₓ). We stress that the set A may be compact or not and the diffusion coefficient may be bounded or not. A data-driven procedure to select the dimension of the projection space is proposed where the dimension is chosen within a random collection of models. Upper bounds of risks are obtained, the assumptions are discussed and simulation experiments are reported.

The problem of drift estimation for the solution X of a stochastic differential equation with Lévy-type jumps is considered under discrete high-frequency observations with a growing observation window. An efficient and asymptotically normal estimator for the drift parameter is constructed under minimal conditions on the jump behavior and the sampling scheme. In the case of a bounded jump measure density, these conditions reduce to n Δ n 3 − ε → 0 , where n is the number of observations and Δn is the maximal sampling step. This result relaxes the condition n Δ n 2 → 0 usually required for joint estimation of drift and diffusion coefficient for SDEs with jumps. The main challenge in this estimation problem stems from the appearance of the unobserved continuous part Xc in the likelihood function. In order to construct the drift estimator, we recover this continuous part from discrete observations. More precisely, we estimate, in a nonparametric way, stochastic integrals with respect to Xc . Convergence results of independent interest are proved for these nonparametric estimators.

The problem of pointwise adaptive estimation of the drift coefficient of a multivariate diffusion process is investigated. We propose an estimator which is sharp adaptive on scales of Sobolev smoothness classes. The analysis of the exact risk asymptotics allows to identify the impact of the dimension and other influencing values—such as the geometry of the diffusion coefficient—of the prototypical drift estimation problem for a large class of multidimensional diffusion processes. We further sketch generalizations of our results to arbitrary diffusions satisfying suitable Bernstein-type inequalities.

We consider the problem of asymptotically efficient estimation of drift parameters of the ergodic fractional Ornstein-Uhlenbeck process under continuous observations when the Hurst parameter H < 1 / 2 and the mean of its stationary distribution is not equal to zero. In this paper, we derive asymptotically efficient rates and variances of estimators of drift parameters and prove an asymptotic efficiency of a maximum likelihood estimator of drift parameters.

Here we propose a real-time method for low-drift odometry and mapping using range measurements from a 3D laser scanner moving in 6-DOF. The problem is hard because the range measurements are received at different times, and errors in motion estimation (especially without an external reference such as GPS) cause mis-registration of the resulting point cloud. To date, coherent 3D maps have been built by off-line batch methods, often using loop closure to correct for drift over time. Our method achieves both low-drift in motion estimation and low-computational complexity. The key idea that makes this level of performance possible is the division of the complex problem of Simultaneous Localization and Mapping, which seeks to optimize a large number of variables simultaneously, into two algorithms. One algorithm performs odometry at a high-frequency but at low fidelity to estimate velocity of the laser scanner. Although not necessary, if an IMU is available, it can provide a motion prior and mitigate for gross, high-frequency motion. A second algorithm runs at an order of magnitude lower frequency for fine matching and registration of the point cloud. Combination of the two algorithms allows map creation in real-time. Our method has been evaluated by indoor and outdoor experiments as well as the KITTI odometry benchmark. The results indicate that the proposed method can achieve accuracy comparable to the state of the art offline, batch methods.

Atomic clocks, which lock the frequency of an oscillator to the extremely stable quantized energy levels of atoms, are essential for navigation applications such as deep space exploration 1 and global navigation satellite systems 2 , and are useful tools with which to address questions in fundamental physics 3 – 6 . Such satellite systems use precise measurement of signal propagation times determined by atomic clocks, together with propagation speed, to calculate position. Although space atomic clocks with low instability are an enabling technology for global navigation, they have not yet been applied to deep space navigation and have seen only limited application to space-based fundamental physics, owing to performance constraints imposed by the rigours of space operation 7 . Methods of electromagnetically trapping and cooling ions have revolutionized atomic clock performance 8 – 13 . Terrestrial trapped-ion clocks operating in the optical domain have achieved orders-of-magnitude improvements in performance over their predecessors and have become a key component in national metrology laboratory research programmes 13 , but transporting this new technology into space has remained challenging. Here we show the results from a trapped-ion atomic clock operating in space. On the ground, NASA’s Deep Space Atomic Clock demonstrated a short-term fractional frequency stability of 1.5 × 10 −13 / τ 1/2 (where τ is the averaging time) 14 . Launched in 2019, the clock has operated for more than 12 months in space and demonstrated there a long-term stability of 3 × 10 −15 at 23 days (no drift removal), and an estimated drift of 3.0(0.7) × 10 −16 per day. Each of these exceeds current space clock performance by up to an order of magnitude 15 – 17 . The Deep Space Atomic Clock is particularly amenable to the space environment because of its low sensitivity to variations in radiation, temperature and magnetic fields. This level of space clock performance will enable one-way navigation in which signal delay times are measured in situ, making near-real-time navigation of deep space probes possible 18 . Operating in space, NASA’s Deep Space Atomic Clock, a trapped-ion clock, is shown to have long-term stability and drift that are an order of magnitude better than current space clocks.

This work mainly delves into the parameter estimation problem concerning Ornstein-Uhlenbeck processes with time-periodic modulated drift based on continuous observations. A least squares estimator is constructed by minimizing a contrast function. It is demonstrated that as the number of observed periods approaches infinity, the least squares estimator exhibits asymptotic unbiasedness, strong consistency, and asymptotic normality. The important technique in the asymptotic study relies on the central limit theorem for multiple Wiener integrals. Finally, numerical simulations of the least squares estimator are presented.

Measuring gravity from an aircraft or a ship is essential in geodesy, geophysics, mineral and hydrocarbon exploration, and navigation. Today, only relative sensors are available for onboard gravimetry. This is a major drawback because of the calibration and drift estimation procedures which lead to important operational constraints. Atom interferometry is a promising technology to obtain onboard absolute gravimeter. But, despite high performances obtained in static condition, no precise measurements were reported in dynamic. Here, we present absolute gravity measurements from a ship with a sensor based on atom interferometry. Despite rough sea conditions, we obtained precision below 10 −5  m s −2 . The atom gravimeter was also compared with a commercial spring gravimeter and showed better performances. This demonstration opens the way to the next generation of inertial sensors (accelerometer, gyroscope) based on atom interferometry which should provide high-precision absolute measurements from a moving platform. Measuring gravitational and inertial acceleration in a moving platform is important for sensing and navigation but is also very challenging. Here the authors demonstrate the ship-borne absolute gravity acceleration measurements using an atom interferometer.

We introduce three new estimators of the drift parameter of a fractional Ornstein–Uhlenbeck process. These estimators are based on modifications of the least-squares procedure utilizing the explicit formula for the process and covariance structure of a fractional Brownian motion. We demonstrate their advantageous properties in the setting of discrete-time observations with fixed mesh size, where they outperform the existing estimators. Numerical experiments by Monte Carlo simulations are conducted to confirm and illustrate theoretical findings. New estimation techniques can improve calibration of models in the form of linear stochastic differential equations driven by a fractional Brownian motion, which are used in diverse fields such as biology, neuroscience, finance and many others.

This paper presents a novel system for autonomous, vision-based drone racing combining learned data abstraction, nonlinear filtering, and time-optimal trajectory planning. The system has successfully been deployed at the first autonomous drone racing world championship: the 2019 AlphaPilot Challenge. Contrary to traditional drone racing systems, which only detect the next gate, our approach makes use of any visible gate and takes advantage of multiple, simultaneous gate detections to compensate for drift in the state estimate and build a global map of the gates. The global map and drift-compensated state estimate allow the drone to navigate through the race course even when the gates are not immediately visible and further enable to plan a near time-optimal path through the race course in real time based on approximate drone dynamics. The proposed system has been demonstrated to successfully guide the drone through tight race courses reaching speeds up to 8m/s and ranked second at the 2019 AlphaPilot Challenge.