Least-squares Filter Research Articles

Measurability of the Heliocentric Momentum Enhancement from a Kinetic Impact: The Double Asteroid Redirection Test (DART) Mission

The NASA Double Asteroid Redirection Test (DART) has demonstrated the capability of successfully conducting kinetic impact-based asteroid deflection missions. The changes in the Didymos–Dimorphos mutual orbit as a result of the DART impact have already been measured. To fully assess the heliocentric outcome of deflection missions, the heliocentric momentum enhancement parameter, β ⊙, needs to be determined and disentangled from other nongravitational phenomena such as the Yarkovsky effect. Here we explore the measurability of β ⊙ resulting from DART, which we estimate simultaneously with nongravitational accelerations using a least-squares filter. Results show that successful stellar occultation measurements of the Didymos system in the second half of 2024 in addition to the ones in the 2022–2023 campaigns can achieve a statistically significant estimate of β ⊙, with an uncertainty slightly above 20% for an assumed β ⊙ = 3. Adding additional occultation measurements and pseudorange measurements from the Hera spacecraft operations at Didymos starting in 2027 decreases this relative uncertainty to under 6%. We find that pre-impact occultation observations combined with post-impact occultations would have yielded substantially higher signal-to-noise ratios on the heliocentric deflection. Additionally, pre-impact occultations would also have enabled a statistically significant β ⊙ estimate using only one additional occultation in 2023 September. Therefore, we conclude that future asteroid deflection missions would greatly benefit from both pre- and post-deflection occultation measurements to help assess the resulting orbital changes.

Synchronized Human-Humanoid Motion Imitation

We present a tele-operation control framework that (i) enhances the upper motion synchrony between a user and a robot using the minimum-jerk model coupled with a recursive least-square filter, and (ii) synchronizes the walking pace by predicting user's stepping frequency using motion capture data and a deep learning model. By integrating (i) and (ii) in a task-space whole-body controller, we achieve full-body synchronization. We assess our humanoid-to-human whole-body synchronized motion model on the HRP-4 humanoid robot in forward, lateral and backward walks with concurrent upper limbs motions experiments.

Alignment scheme optimization when gyro accuracy inconsistency for inertial navigation system

Rotation modulation technology can average out constant errors in fiber optic gyro (FOG) rotational inertial navigation system (RINS). As a result, angle random walk (ARW) of FOGs plays a significant role in the precision of initial alignment. Using different gyros as horizontal gyros gradually transitioned from theory to practical application with the advancement of design philosophy. The theoretical formula between azimuth alignment accuracy and random walk coefficients (RWCs) of two horizontal gyros is deduced in this paper. A completely new multiple rotations and stationary alignment scheme is suggested. A recursive least-squares filter with azimuth variation in body reference frame and accelerometer outputs in navigation frame as measurements is constructed. The efficiency of this method is demonstrated through simulation and experimentation. The findings demonstrate that using this formula and alignment scheme, azimuth alignment accuracy could be greatly increased, which can be improved by 10.85% compared to common continuous rotation alignment scheme.

Generating surface-offset common-image gathers with backward wavefield synthesis

Surface-offset common-image gathers (CIGs) are an important data format for seismic velocity analysis. However, the reverse time migration (RTM) method, which is wavefield propagation based, does not directly produce surface-offset CIGs because it propagates waves from all the offsets together. Here, we implement the generation of surface-offset CIGs by synthesizing the backward wavefields using the forward wavefields at locations where source and receiver locations overlap. This method produces surface-offset CIGs with high accuracy and low cost when compared with those generated by backpropagating each trace separately. We adopt nonnegative least-squares filters for sparse linear deconvolution. The computational effectiveness of the proposed method increases for higher dimensions, higher-order stencils, and more complicated wave equations. The proposed method works stably on a realistic towed-streamer acquisition system with moderate geometric positioning errors between the locations of airguns and hydrophones.

Development, Verification, and Analysis of a Small Satellite Thrust Determination Filter

A current challenge for the Advanced Propulsion Experiment (APEX) CubeSat, under development by Missouri University of Science and Technology, is the accurate determination of thrust for its experimental multimodal propulsion system main payload. A consider batch least-squares filter is proposed that processes downlinked dual-frequency GPS pseudorange data to estimate the average thrust magnitude of a maneuver in conjunction with the initial dynamic states, static coefficients of drag and solar radiation pressure, and GPS receiver clock biases from each measurement epoch. Two Monte Carlo analyses were performed to test the statistical consistency of the filter and the robustness under the influence of unmodeled dynamics. The filter was found to perform nominally with matching truth and filter dynamics models and acceptably when the truth model used to synthesize measurements was a higher fidelity than the filter model. Filter performance was assessed using flight data from NASA’s Gravity Recovery and Climate Experiment Follow-On mission. A trade study was conducted to identify acceptable orbital regimes for the APEX mission. Thrust estimates using this method were shown to meet APEX mission requirements for a range of acceptable orbits.

Beam and Channel Tracking for 5G Communication Systems Using Adaptive Filtering Techniques: A Comparison Study

In this paper, we study the problem of beam tracking of a multipath channel in millimeter-wave massive MIMO communication system using adaptive filters. We focus on the performance of least-mean-square filter (LMS) and recursive least-squares filter (RLS) algorithms, compared to a reference extended Kalman filter (EKF), in scenarios where the wireless channel is dominated by a single line of sight (LOS) path or a small number of strong paths. The signal direction and channel coefficients are tracked and updated using these filters. Our results recommend that beamforming systems at millimeter-wave bands should consider variable number of paths rather than a single dominant LOS path. Furthermore, we show that the mean squared-error (MSE) of the innovation process gives a better overall view of the tracking performance than the MSE of the state parameters.

Estimation of state-of-power capability for lithium-ion battery considering limiting conditions recalibration

ABSTRACT As one of the most significant deciding factors for energy management systems (EMSs) and battery management systems (BMSs) in electrified vehicles, battery state-of-power (SOP) estimation is an area of interest in battery research. Battery model parameters change obviously under the limiting working condition of SOP, and the available maximum current and state-of-charge (SOC) have to be updated for accurate SOP estimation. This paper tries to contribute to the existing literature as follows: Based on Thevenin model, recursive least-square (RLS) and H-infinity filter algorithm are adopted for parameter identification and SOC estimation for a recalibration purpose to improve the prediction of battery SOP under variable degradation. Multi-constraints are firstly adopted to calculate the limiting current, and the response function of capacity loss-temperature-discharge rate is brought back to correct the actual capacity at this current for the revised limiting current with consideration of weight distribution ratio. Finally, the experiment verifies that the final maximum charging-discharging current modifies the initial calculation value by 5% and 4%, and realizes the more accurate online SOP estimation. This method provides a more accurate and reliable SOP estimation method for electric vehicles.

Artificial intelligence-based approach for atrial fibrillation detection using normalised and short-duration time-frequency ECG

Atrial fibrillation (Afib) is a heart arrhythmia that is linked to a number of other cardiac-related issues. The incidence of Afib increases with age, causing high risks of stroke. Accurate and reliable detection of Afib remains a challenge and is valuable for clinical diagnosis. This work presents a novel approach for the detection of Afib using both 1-D electrocardiogram signal and its time-frequency representation as an image (2D). The signal was pre-processed utilising a 2-stage median filter and least-square filter followed by normalisation before applying it to artificial intelligence–based models for classification. Bi-directional long short-term memory network was trained and tuned to attain high accuracy. Our proposed method shows favourable performances applying ECG segment as short as 4 s. And it has achieved an accuracy of 98.85% in the 2-D time-frequency representation. Better classification accuracy and use of short-duration ECG signal compared to existing state-of-art methods make this method suitable for an automated, reliable, and timely detection of Afib.

Comparison of multichannel signal deconvolution algorithms in airborne LiDAR bathymetry based on wavelet transform

Airborne LiDAR bathymetry offers low cost and high mobility, making it an ideal option for shallow-water measurements. However, due to differences in the measurement environment and the laser emission channel, the received waveform is difficult to extract using a single algorithm. The choice of a suitable waveform processing method is thus of extreme importance to guarantee the accuracy of the bathymetric retrieval. In this study, we use a wavelet-denoising method to denoise the received waveform and subsequently test four algorithms for denoised-waveform processing, namely, the Richardson–Lucy deconvolution (RLD), blind deconvolution (BD), Wiener filter deconvolution (WFD), and constrained least-squares filter deconvolution (RFD). The simulation and measured multichannel databases are used to evaluate the algorithms, with focus on improving their performance after data-denoising and their capability of extracting water depth. Results show that applying wavelet denoising before deconvolution improves the extraction accuracy. The four algorithms perform better for the shallow-water orthogonal polarization channel (PMT2) than for the shallow horizontal row polarization channel (PMT1). Of the four algorithms, RLD provides the best signal-detection rate, and RFD is the most robust; BD has low computational efficiency, and WFD performs poorly in deep water (< 25 m).

SUPREME: an open-source single-frequency uncombined precise point positioning software

With the rapid development of Global Navigation Satellite Systems (GNSS), precise point positioning (PPP) has been widely used for positioning, navigation, timing (PNT), and atmospheric sensing. Currently, the demand for low-cost single-frequency hardware is increasing. However, open-source single-frequency PPP (SFPPP) software, in particular those that employ uncombined GNSS observations, is scarce. In view of this fact, we developed an open-source software, called Single-frequency Uncombined PREcise point positioning for Multi-parameter Estimation (SUPREME), which can process multi-GNSS observations collected from a low-cost single-frequency receiver. It can simultaneously estimate receiver coordinates, receiver clock offsets, zenith tropospheric delays, and ionospheric delays utilizing a least-squares filter. SUPREME is developed in the C/C++ computer language; thus, it has good portability and cross-platform capability. The formatted output is also beneficial for the post-analysis of results. We evaluated SUPREME using several experiments based on real single-frequency data, and the results indicate that it provides high accuracy and robust performance.

Underwater acoustic positioning based on the robust zero-difference Kalman filter

The accuracy of underwater acoustic positioning is greatly influenced by both systematic error and gross error. Aiming at these problems, the paper proposes a robust zero-difference Kalman filter based on the random walk model and the equivalent gain matrix. The proposed algorithm takes systematic error as a random walk process, and estimates it together with the position parameters by using zero-difference Kalman filter. In addition, the equivalent gain matrix based on the robust estimation of Huber function is constructed to resist the influence of gross error. The proposed algorithm is verified by the simulation experiment and a real one for underwater acoustic positioning. The results demonstrate that the robust zero-difference Kalman filter can control both the effects of systematic error and gross error without amplifying the influence of the observation random noise, which is obviously superior to the zero-difference least squares (LS), the single-difference LS and zero-difference Kalman filter in underwater acoustic positioning.

Neural Network Based Fault Diagnostics in Multi Phase Induction Machine

This article proposes a new method for solving the diagnosis of faults in a multiphase induction motor using a least-squares filter (LMS) and a neural network. The proposed hybrid fault diagnosis method includes an efficient LMS-based feature extractor and an artificial neural network fault classifier. First, the LMS method is used to obtain efficient functions. The performance and efficiency of the presented neural network hybrid classifier is evaluated by testing a total of 600 samples, which are modeled on a failure model. The average correct classification is 96.17% for different fault signals, respectively. The result obtained from the simulation analysis shows the effectiveness of the proposed neural network for the diagnosis of faults in the multiphase induction motor.

Precise Orbit Determination Based on the Unscented Transform for Optical Observations

In this study, the precise orbit determination (POD) software is developed for optical observation. To improve the performance of the estimation algorithm, a nonlinear batch filter, based on the unscented transform (UT) that overcomes the disadvantages of the least-squares (LS) batch filter, is utilized. The LS and UT batch filter algorithms are verified through numerical simulation analysis using artificial optical measurements. We use the real optical observation data of a low Earth orbit (LEO) satellite, Cryosat-2, observed from optical wide-field patrol network (OWL-Net), to verify the performance of the POD software developed. The effects of light travel time, annual aberration, and diurnal aberration are considered as error models to correct OWL-Net data. As a result of POD, measurement residual and estimated state vector of the LS batch filter converge to the local minimum when the initial orbit error is large or the initial covariance matrix is smaller than the initial error level. However, UT batch filter converges to the global minimum, irrespective of the initial orbit error and the initial covariance matrix.

Single-frame-based column fixed-pattern noise correction in an uncooled infrared imaging system based on weighted least squares.

Uncooled infrared images typically suffer from column fixed-pattern noise (FPN), which is introduced by the non-uniformity of the column-parallel readout circuit. It is a challenging task to remove column FPN without introducing stripe artifacts near strong vertical edges. In this paper, we introduce a novel single-frame-based algorithm to accurately correct column FPN. The algorithm contains two 1D filters. First, a 1D weighted least-squares filter is applied to perform edge-preserving filtering in the horizontal direction to obtain a coarse estimation of the clear scene. Then, a local weighted ridge regression is performed between the horizontal smoothed image and the raw infrared image in vertical direction to refine this estimation. Through an analysis on the cause of stripe artifacts, the proposed non-uniformity correction (NUC) algorithm is proved to be effective in eliminating this problem. The performance of our proposed algorithm is thoroughly investigated and compared to four state-of-the-art single-frame-based destriping methods using both simulated and real experiments.

Adaptive Control of a Piezo-Actuated Steering Mirror to Restrain Laser-Beam Jitter

Tracking, pointing, and imaging performances of precision laser systems are restricted by laser-beam jitter, which is time varying or uncertain. This paper proposes an adaptive control that uses a piezo-actuated steering mirror to actively resist the jitter and achieve precise pointing. First, in order to realize the single-valued linear input–output relationship, which can simplify the adaptive-control design and improve the stability and convergence rate of the adaptive filter algorithm, the hysteresis non-linearity of the piezo-actuators is feedforward compensated. Then, an adaptive controller is built based on an adaptive lattice recursive least-square filter that identifies the disturbance statistics in real-time by utilizing sensor data from a position sensing detector. The developed controllers are verified on a jitter-control system. Experimental results demonstrate that the adaptive-control method significantly extends the disturbance-rejection bandwidth, and that the control performance surpasses the conventional proportion-integral-differential (PID) control method.

Centralized, distributed and sequential fusion estimation from uncertain outputs with correlation between sensor noises and signal

ABSTRACTThis paper focuses on the least-squares linear fusion filter design for discrete-time stochastic signals from multisensor measurements perturbed not only by additive noise, but also by different uncertainties that can be comprehensively modeled by random parameter matrices. The additive noises from the different sensors are assumed to be cross-correlated at the same time step and correlated with the signal at the same and subsequent time steps. A covariance-based approach is used to derive easily implementable recursive filtering algorithms under the centralized, distributed and sequential fusion architectures. Although centralized and sequential estimators both have the same accuracy, the evaluation of their computational complexity reveals that the sequential filter can provide a significant reduction of computational cost over the centralized one. The accuracy of the proposed fusion filters is explored by a simulation example, where observation matrices with random parameters are used to describe different kinds of sensor uncertainties.

Non-Stationary Stabilized Fast Transversal RLS Filter for Online Power System Modal Estimation

Online monitoring of inter-area oscillations is a vital need for secure operation of large-scale power systems. This paper aims at online estimation of inter-area modes by a novel stabilized fast transversal recursive least squares (SFTRLS) filter running on ambient power system data received from phasor measurement units. The SFTRLS filter is a fast finite-impulse response adaptive filter that is widely used in communication applications, such as noise and echo cancelation. It has the lowest computational complexity among least-squares filters and directly calculates coefficients of the parametric model selected for identifying a system under study. In the proposed method, the SFTRLS filter along with digital band-pass Butterworth filter and down-sampling blocks are implemented in online manner for identification of an autoregressive model that describes the measured power system ambient signal. Applicability and accuracy of the proposed method are evaluated using real measurement data of western systems coordinating council (WSCC) breakup on August 10, 1996, as well as simulated ambient data of the IEEE 16-machine, 5-area test system excited by white noise random load modulations. Its performance is investigated under different conditions of load modulations, measurement noises, sudden change in damping ratio, and occurrence of three-phase faults. The simulation results verify efficient and robust performance of the proposed method for modal estimation of real large-scale power systems.

Classification of Tectonic and Nontectonic Earthquakes by an Integrated Learning Algorithm

A machine learning model for accurate and quick classification of tectonic and nontectonic earthquakes is proposed. Firstly, an improved method is proposed for detection of first arrivals. An iterative approach is applied for the multiwindow algorithm to decrease its computational cost, then a new method for detection of first arrivals is proposed by combining the improved multiwindow algorithm with a recursive least-squares filter and the Akaike information criterion. Secondly, it is shown that the integrated learning algorithm is a suitable method for classification, then four suitable features are manually selected to train it. Thirdly, the three parameter values of the integrated learning model are determined to improve its accuracy. Finally, based on seismic data from the China Earthquake Networks Center, simulations are conducted to test the validity of the proposed method for detection of first arrivals, then the classification accuracy is tested. The results show an accuracy of the model of 88.88%, indicating effective classification performance.

Transmission Line Protective Relay Based on Recursive Least-Square Filters and Weights Analysis

The purpose of this study takes advantage of real-time hardware and software co-simulation to integrate a recursive least-square adaptive filter into a relay design for transmission line protection. The relay trip logic is controlled with a recursive least-square filter that analyzes the weights and cumulative error auto-correlation for magnitude and angles per phase. This analysis allows to detect and identify the fault type. The study focuses on the modelling of a consistent testing case study designed for transmission lines protections based on the EMTP reference model. The proposed solution could be scalable to protect other elements in power systems. It is consistent with current technological tools, and the RLS algorithm optimizes the computational performance of the relay.

Robust deterministic least-squares filtering for uncertain time-varying nonlinear systems with unknown inputs

The augmented state robust regularized least-squares filter (ASRRLSF) and two-stage robust regularized least-squares filter (TSRRLSF) are proposed for discrete time-varying nonlinear systems with unknown inputs and norm-bounded uncertainties. Unknown inputs affect both state-space model and measurements equation of the system. Combining system states and unknown inputs as an augmented state, the ASRRLSF is developed by converting a deterministic min–max optimization problem to a robust regularized least-squares problem. If dimension of the augmented state increases, the performance of the proposed ASRRLSF will reduce and the computational cost will increase rapidly. Therefore, in the following, the TSRRLSF is proposed by decoupling the ASRRLSF to lower order filters as system states filter and unknown inputs filter using T transformation. Finally, two numerical examples are given in order to illustrate the performance of the proposed filtering approaches.