On Convergence of Tracking Differentiator with Multiple Stochastic Disturbances

In this paper, the convergence and noise-tolerant performance of a tracking differentiator in the presence of multiple stochastic disturbances are investigated for the first time. We consider a quite general case where the input signal is corrupted by additive colored noise, and the tracking differentiator itself is disturbed by additive colored noise and white noise. It is shown that the tracking differentiator tracks the input signal and its generalized derivatives in mean square and even in almost sure sense when the stochastic noise affecting the input signal is vanishing. Some numerical simulations are performed to validate the theoretical results

Performance of Track-to-Track Association Algorithms Based on Mahalanobis Distance

In multi-sensor tracking system, the track-to-track association problem is to determine whether a set of local tracks from different sensor systems are represent the same target. This problem is usually formulated as a binary hypothesis test, and the most common statistics is defined as the squared Mahalanobis distance (SMD) between the kinematic state estimates of two tracks. In this paper, three types of SMD algorithms are investigated, i.e., the SMD algorithm, the cumulative SMD algorithm, and the Discrete Wavelet Transform (DWT) algorithm which can be regarded as a generalized SMD ratio algorithm. The first one can be looked as singlescan algorithm, and the rest two are multiscan approaches. From another viewpoint, the first two are time domain algorithms, and the last one is a transform domain algorithm. The probability distribution functions of statistics defined by these algorithms have been discussed under the assumption that the estimates errors are independent across time. The Operating Characteristic Function is used to describe association performance. It shows that the multiscan algorithm performs better than the singlescan algorithm. As to multiscan algorithms, the DWT algorithm is superior to time domain algorithm. But better algorithm is more sensitive to the residual bias because the statistic based on SMD of target state estimates is directly contaminated by the bias

Exploring the boundary of quantum correlations with a time-domain optical processor

Contextuality is a hallmark feature of the quantum theory that captures its incompatibility with any noncontextual hidden-variable model. The Greenberger--Horne--Zeilinger (GHZ)-type paradoxes are proofs of contextuality that reveal this incompatibility with deterministic logical arguments. However, the simplest GHZ-type paradox with the fewest number of complete contexts and the largest amount of nonclassicality remains elusive. Here, we derive a GHZ-type paradox utilizing only three complete contexts and show this number saturates the lower bound posed by quantum theory. We demonstrate the paradox with a time-domain fiber optical platform and recover all essential ingredients in a 37-dimensional contextuality test based on high-speed modulation, convolution, and homodyne detection of time-multiplexed pulsed coherent light. By proposing and observing a strong form of contextuality in high Hilbert-space dimensions, our results pave the way for the exploration of exotic quantum correlations with time-multiplexed optical systems.Comment: 19 pages, 8 figures, improved presentation with additional discussion