L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

A high precision indoor positioning method based on UKF

Aiming at the nonlinear filter problem in Ultra Wide Band (UWB) navigation and position, a high-order Unscented Kalman Filter (UKF) position method is proposed. On the one hand, the position and velocity are used as state variables to establish a nonlinear filtering model based on UWB position system. On the other hand, based on the fifth order cubature transform (CT), the analytical solution of the high-order unscented Kalman filter is obtained by introducing a free parameter δ. To verify the effectiveness of the proposed method, the Time of Arrival (TOA) location method, the least square method and fifth order CKF method are introduced as comparison methods. The simulation and experimental results show that the proposed high-order UKF method has good positioning accuracy in both static and dynamic UWB positioning methods.

L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

Optimal nonlinear filtering of M-PSK signals against a background of harmonic interference with a random initial phase

Objectives. The widespread use of radio data transmission systems using signals with multiposition phase shift keying (MPSK) is due to their high noise immunity and the simplicity of constructing the transmitting and receiving parts of the equipment. The conducted studies have shown that the presence of non-fluctuation interference, in particular, harmonic interference, in the radio channel significantly reduces the noise immunity of receiving discrete information. The energy loss in this case, depending on the interference intensity, can range from fractions of dB to 10 db or more. Therefore, interference suppression is an important task for such radio systems. The aim of the work is to synthesize and analyze an algorithm for optimal nonlinear filtering of MPSK signals against a background of harmonic interference with a random initial phase.Methods. The provisions of the theory of optimal nonlinear signal filtering and methods of statistical radio engineering are used.Results. The synthesis and analysis of the algorithm of optimal nonlinear filtering of MPSK signals against the background of harmonic interference with a random initial phase are carried out. The synthesized receiver contains a discrete symbol evaluation unit, two phase-locked frequency circuits of reference generators that form evaluation copies of the signal and interference, and cross-links between them. Analytical expressions are obtained that allow calculating the dependences of the bit error probability on the signal-to-noise ratio and the interference intensity µ. It is established that uncompensated fluctuations of the initial phase of the useful signal have a greater effect on the receiver noise immunity than similar fluctuations of the phase of harmonic interference, especially with low positional signals.Conclusions. Comparison of the obtained results with the results obtained in the case when there are no harmonic interference compensation circuits shows that the use of the obtained phase filtering algorithms allows for almost complete suppression of harmonic interference. Thus, if µ = 0.5 and the probability of error is 10−2, the energy gain at M = 2 is about 2.5 dB, at M = 4 – about 6 dB, at M = 8 and M = 16 – at least 10 dB.

A New Linear Regression Kalman Filter with Symmetric Samples

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

A multi-AUV cooperative navigation method

Cooperative navigation is one of the key methods for multiple autonomous underwater vehicles (AUVs) to obtain accurate positions when performing tasks underwater. In the realistic state-space model of the multi-AUV cooperative navigation system, where the system noise does not satisfy the additivity, it is necessary to augment the dimension of the state variables before nonlinear filtering. Aiming at the problem that the error of traditional algorithms increases linearly with the dimension of state-space, a cooperative navigation method based on Augmented Embedded Cubature Kalman filter (AECKF) algorithm is proposed. The experiment results show that the AECKF cooperative navigation algorithm has better positioning accuracy and stability than the traditional algorithm.

AlphaPilot: autonomous drone racing

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 $${8}\,{\hbox {m}/\hbox {s}}$$ 8 m / s and ranked second at the 2019 AlphaPilot Challenge.

Application of Adaptive Robust CKF in SINS/GPS Initial Alignment with Large Azimuth Misalignment Angle

When the strapdown inertial navigation system does not perform coarse alignment, the misalignment angle is generally a large angle, and a nonlinear error model and a nonlinear filtering method are required. For large azimuth misalignment, the initial alignment technology with a large azimuth misalignment angle is researched in this paper. The initial alignment technology with a large azimuth misalignment angle is researched in this paper. First, the SINS/GPS nonlinear error model is established. Secondly, in the view of observation gross errors and inaccurate noise statistical characteristics, an adaptive robust CKF algorithm is proposed. Finally, according to the simulation analysis and experiment, the adaptive robust CKF algorithm can augment the stability and improve the filter estimation precision and convergence rate.