Many psychological processes are characterized by recurrent shifts between distinct regimes or states. Examples that are considered in this paper are the switches between different states associated with premenstrual syndrome, hourly fluctuations in affect during a major depressive episode, and shifts between a “hot hand” and a “cold hand” in a top athlete. We model these processes with the regime switching state-space model proposed by Kim (J. Econom. 60:1–22, 1994), which results in both maximum likelihood estimates for the model parameters and estimates of the latent variables and the discrete states of the process. However, the current algorithm cannot handle missing data, which limits its applicability to psychological data. Moreover, the performance of standard errors for the purpose of making inferences about the parameter estimates is yet unknown. In this paper we modify Kim’s algorithm so it can handle missing data and we perform a simulation study to investigate its performance in (relatively) short time series in cases of different kinds of missing data and in case of complete data. Finally, we apply the regime switching state-space model to the three empirical data sets described above.

A dynamic factor model is proposed for the analysis of multivariate nonstationary time series in the time domain. The nonstationarity in the series is represented by a linear time dependent mean function. This mild form of nonstationarity is often relevant in analyzing socio-economic time series met in practice. Through the use of an extended version of Molenaar's stationary dynamic factor analysis method, the effect of nonstationarity on the latent factor series is incorporated in the dynamic nonstationary factor model (DNFM). It is shown that the estimation of the unknown parameters in this model can be easily carried out by reformulating the DNFM as a covariance structure model and adopting the ML algorithm proposed by Jöreskog. Furthermore, an empirical example is given to demonstrate the usefulness of the proposed DNFM and the analysis.

In this—partly—expository paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation will be considered from a system theoretic perspective. The general dynamic model covers (dynamic) factor analytic models, (dynamic) MIMIC models and Jöreskog's linear structural model as special cases. Its reduced form is—under a slightly different specification—known in system theory and econometrics as the stochastic, stationary version of the state-space model. By using concepts and methods from system theory, such as the observability and controllability concept, the (steady-state) Kalman filter and a general nonlinear ML-estimation procedure known as prediction-error estimation the general dynamic model will be identified. It will be shown that Jöreskog's LISREL-procedure is a special case of the prediction-error estimation procedure.

Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback–Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.

This paper proposes to solve the vortex gust mitigation problem on a 2D, thin flat plate using onboard measurements. The objective is to solve the discrete-time optimal control problem of finding the pitch rate sequence that minimizes the lift perturbation, that is, the criterion where is the lift coefficient obtained by the unsteady vortex lattice method. The controller is modeled as an artificial neural network, and it is trained to minimize using deep reinforcement learning (DRL). To be optimal, we show that the controller must take as inputs the locations and circulations of the gust vortices, but these quantities are not directly observable from the onboard sensors. We therefore propose to use a Kalman particle filter (KPF) to estimate the gust vortices online from the onboard measurements. The reconstructed input is then used by the controller to calculate the appropriate pitch rate. We evaluate the performance of this method for gusts composed of one to five vortices. Our results show that (i) controllers deployed with full knowledge of the vortices are able to mitigate efficiently the lift disturbance induced by the gusts, (ii) the KPF performs well in reconstructing gusts composed of less than three vortices, but shows more contrasted results in the reconstruction of gusts composed of more vortices, and (iii) adding a KPF to the controller recovers a significant part of the performance loss due to the unobservable gust vortices.

In practical applications, many robots equipped with embedded devices have limited computing capabilities. These limitations often hinder the performance of existing dynamic SLAM algorithms, especially when faced with occlusions or processor constraints. Such challenges lead to subpar positioning accuracy and efficiency. This paper introduces a novel lightweight dynamic SLAM algorithm designed primarily to mitigate the interference caused by moving object occlusions. Our proposed approach combines a deep learning object detection algorithm with a Kalman filter. This combination offers prior information about dynamic objects for each SLAM algorithm frame. Leveraging geometric techniques like RANSAC and the epipolar constraint, our method filters out dynamic feature points, focuses on static feature points for pose determination, and enhances the SLAM algorithm’s robustness in dynamic environments. We conducted experimental validations on the TUM public dataset, which demonstrated that our approach elevates positioning accuracy by approximately 54% and boosts the running speed by 75.47% in dynamic scenes.

This paper presents the AffineMortality R package which performs parameter estimation, goodness-of-fit analysis, simulation, and projection of future mortality rates for a set of affine mortality models for use in pricing and reserving. The computational routines build on the univariate Kalman Filtering approach of Koopman and Durbin ((2000). Journal of Time Series Analysis, 21(3), 281–296.) along other numerical methods to enhance the robustness of the results. This paper provides a discussion of how the package works in order to effectively estimate and project survival curves, and describes the available functions. Illustration of the package for mortality analysis of the US male data set is provided.

A closed-form solution for zero-coupon bonds is obtained for a version of the discrete-time arbitrage-free Nelson-Siegel model. An estimation procedure relying on a Kalman filter is provided. The model is shown to produce adequate fit when applied to historical Canadian spot rate data and to improve distributional predictive performance over benchmarks. An adaptation of the mixed fund return model from Augustyniak et al. ((2021). ASTIN Bulletin: The Journal of the IAA, 51(1), 131–159.) is also provided to include the discrete-time arbitrage-free Nelson-Siegel model as one of its building blocks.

An accurate dynamic model of a robot is fundamentally important for a control system, while uncertainties residing in the model are inevitable in a physical robot system. The uncertainties can be categorized as internal disturbances and external disturbances in general. The former may include dynamic model errors and joint frictions, while the latter may include external payloads or human-exerted force to the robot. Disturbance observer is an important technique to estimate and compensate for the uncertainties of the dynamic model. Different types of disturbance observers have been developed to estimate the lumped uncertainties so far. In this paper, we conducted a brief survey on five typical types of observers from a perspective of practical implementation in a robot control system, including generalized momentum observer (GMO), joint velocity observer (JVOB), nonlinear disturbance observer (NDOB), disturbance Kalman filter (DKF), and extended state observer (ESO). First, we introduced the basics of each observer including equations and derivations. Two common types of disturbances are considered as two scenarios, that is, constant external disturbance and time-varying external disturbance. Then, the observers are separately implemented in each of the two simulated scenarios, and the disturbance tracking performance of each observer is presented while their performance in the same scenario has also been compared in the same figure. Finally, the main features and possible behaviors of each type of observer are summarized and discussed. This survey is devoted to helping readers learn the basic expressions of five typical observers and implement them in a robot control system.

A relatively novel approach of autonomous navigation employing platform dynamics as the primary process model raises new implementational challenges. These are related to: (i) potential numerical instabilities during longer flights; (ii) the quality of model self-calibration and its applicability to different flights; (iii) the establishment of a global estimation methodology when handling different initialisation flight phases; and (iv) the possibility of reducing computational load through model simplification. We propose a unified strategy for handling different flight phases with a combination of factorisation and a partial Schmidt–Kalman approach. We then investigate the stability of the in-air initialisation and the suitability of reusing pre-calibrated model parameters with their correlations. Without GNSS updates, we suggest setting a subset of the state vector as ‘considered’ states within the filter to remove their estimation from the remaining observations. We support all propositions with new empirical evidence: first in model-parameter self-calibration via optimal smoothing and second through applying our methods on three test flights with dissimilar durations and geometries. Our experiments demonstrate a significant improvement in autonomous navigation quality for twelve different scenarios.

For a common micro-satellite, orbiting in a circular sun-synchronous orbit (SSO) at an altitude between 500 and 600km, the satellite attitude during off-nadir imaging and staring-imaging operations can be up to ±45 degree on roll and pitch angles. During these off-nadir pointing for both multi-trip operation and staring imaging operations, the spacecraft body is commonly subject to high-rate motion. This posts challenges for a spacecraft attitude determination subsystem called Gyro Stellar Inertial Attitude Estimate (GS IAE), which employs gyros and star sensors to maintain the required attitude knowledge, since star trackers will severely degrade attitude estimation accuracies when the spacecraft is subject to high-rate motion. This paper analyses the star motion-induced errors for a typical star tracker, models the star motion-induced errors to assess the performance impact on the attitude estimation accuracy, and investigates the adaptive extended Kalman filter design in the GS IAE while evaluating its effectiveness.

In traditional satellite navigation receivers, the parameters of tracking loop such as loop bandwidth and integration time are usually set in the design of the receivers according to different scenarios. The signal tracking performance is limited in traditional receivers. In addition, when the tracking ability of weak signals is improved by extending the integration time, negative effect of residual frequency error becomes more and more serious with extension of the integration time. To solve these problems, this paper presents out research on receiver tracking algorithms and proposes an optimised tracking algorithm with inertial information. The receiver loop filter is designed based on Kalman filter, reducing the phase jitter caused by thermal noise in the weak signal environment and improving the signal tracking sensitivity. To confirm the feasibility of the proposed algorithm, simulation tests are conducted.