Trajectory Optimization to Enhance Observability for Bearing-Only Target Localization and Sensor Bias Calibration.

This study addresses the challenge of bearing-only target localization with sensor bias contamination. To enhance the system's observability, inspired by plant phototropism, we propose a control barrier function (CBF)-based method for UAV motion planning. The rank criterion provides only qualitative observability results. We employ the condition number for a quantitative analysis, identifying key influencing factors. After that, a multi-objective, nonlinear optimization problem for UAV trajectory planning is formulated and solved using the proposed Nonlinear Constrained Multi-Objective Gray Wolf Optimization Algorithm (NCMOGWOA). Simulations validate our approach, showing a threefold reduction in the condition number, significantly enhancing observability. The algorithm outperforms others in terms of localization accuracy and convergence, achieving the lowest Generational Distance (GD) (7.3442) and Inverted Generational Distance (IGD) (8.4577) metrics. Additionally, we explore the effects of the CBF attenuation rates and initial flight path angles.

A reinterpretation of Heisenberg's Umdeutung in prescriptive-dynamical terms.

There has been a lot of discussion about Heisenberg's Umdeutung paper of 1925, which is universally credited as the first formulation of modern quantum mechanics. Much of this discussion has been characterized by puzzlement over the manner in which Heisenberg arrived at his formulation, supposedly through Bohr's atomic theory in conjunction with two philosophical principles, namely the Correspondence Principle and the Observability Principle. I provide textual, contextual, and philosophical evidence that the "prescriptive-dynamical framework" - recently advocated in the literature on independent grounds - is the perfect perspective from which to understand Heisenberg's work and the significance of the two principles he utilized to arrive at it.

Optimal location of PMUs for full observability of power system using coronavirus herd immunity optimizer.

Phasor measurement units (PMU) are currently considered as an essential step toward the future smart grid due to their capability in increasing the power system's situation awareness. Due to their high costs and limited resources, optimal placement of PMUs (OPP) is an important challenge to compute the minimum number of PMUs and their optimal distribution in the power systems for achieving full monitoring. The coronavirus herd immunity optimizer (CHIO) is a novel optimization algorithm that emulates the flock immunity strategies for the elimination of the coronavirus pandemic. In this research, the CHIO is adapted for the OPP problem for full fault observability. The proposed algorithm is implemented on power systems considering the zero injection bus impacts. A program is created in MATLAB® environment to implement the proposed algorithm. The algorithm is applied to different test systems including; IEEE 9-bus, 14-bus, 30-bus, 118-bus, 300-bus, New England 39-bus and Polish 2383-bus. The proposed CHIO-based OPP is compared to some exact and metaheuristic-based OPP techniques. Compared to these techniques, the promising results have proved the effectiveness and robustness of the proposed CHIO to solve the OPP problem for full fault observability.

Mobile Sensor Path Planning for Kalman Filter Spatiotemporal Estimation.

The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. In this paper, we consider the use of mobile sensors for estimating spatiotemporal data via Kalman filtering. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy algorithms and low-rank subspace projection to provide model-free, data-driven estimates. Alternatively, Kalman filter estimation balances model-based information and sparsely observed measurements to collectively make better estimation with limited sensors. It is especially important with mobile sensors to utilize historical measurements. We show that mobile sensing along dynamic trajectories can achieve the equivalent performance of a larger number of stationary sensors, with performance gains related to three distinct timescales: (i) the timescale of the spatiotemporal dynamics, (ii) the velocity of the sensors, and (iii) the rate of sampling. Taken together, these timescales strongly influence how well-conditioned the estimation task is. We draw connections between the Kalman filter performance and the observability of the state space model and propose a greedy path planning algorithm based on minimizing the condition number of the observability matrix. This approach has better scalability and computational efficiency compared to previous works. Through a series of examples of increasing complexity, we show that mobile sensing along our paths improves Kalman filter performance in terms of better limiting estimation and faster convergence. Moreover, it is particularly effective for spatiotemporal data that contain spatially localized structures, whose features are captured along dynamic trajectories.

Revisiting the observability and identifiability properties of a popular HIV model.

This paper revisits the observability and identifiability properties of a popular ODE model commonly adopted to characterize the HIV dynamics in HIV-infected patients with antiretroviral treatment. These properties are determined by using the general analytical solution of the unknown input observability problem, introduced very recently in Martinelli (2022). This solution provides the systematic procedures able to determine the state observability and the parameter identifiability of any ODE model, in particular, even in the presence of time varying parameters. Four variants of the HIV model are investigated. They differ because some of their parameters are considered constant or time varying. Fundamental new properties, which also highlight an error in the scientific literature, are automatically determined and discussed. Additionally, for each variant, the paper provides a quantitative answer to the following practical question: What is the minimal external information (external to the available measurements of the system outputs) required to make observable the state and identifiable all the model parameters? The answer to this fundamental question is obtained by exploiting the concept of continuous symmetry, recently introduced in Martinelli (2019). This concept allows us to determine a first preliminary general result which is then applied to the HIV model. Finally, for each variant, the paper concludes by providing a redefinition of the state and of the parameters in order to obtain a full description of the system only in terms of a state which is observable and a set of parameters which are identifiable (both constant and time varying).

The security of IOT from the perspective of the observability of complex networks.

The Internet of Things (IOT) is based on the computer Internet, using RFID, wireless data communication and other technologies to construct a network covering everything in the world. It contains numerous entities such as sensors, processors, transmitters and actuators, meanwhile the interactions of which are complicated. These characteristics of IOT are consistent with those of the complex network. Motivated by this, this paper comprehends the security issue of IOT from the sight of the observability of complex network and regards the ability of reconstruction as a security threat to IOT network. We try to identify the minimum vertices whose data could reconstruct the whole data of network, in other words, we need to implement additional protective measures on these vertices to enhance the security of IOT network. By analyzing the topology of IOT network, an identification strategy is adopted and the corresponding algorithm is proposed to identify the minimum protection vertices.

Optimal linear filter design for process state and packet loss estimation in networked control systems.

Considering the effect of packet losses on the behavior of networked systems, this work is concerned with estimation of the packet loss occurrences in the input channels possibly together with the system state. For this purpose, the commonly used Markov chain model of the successive packet loss occurrences is transformed to a linear recursive model in which the packet loss occurrence variables appear as new state variables. Two methods are proposed for combining the recursive packet loss model with the plant model to obtain an overall model for the whole networked control system (NCS). In the first method, a state space model of the plant is used which allows for simultaneous estimation of the packet loss occurrences and the plant state. In the second method, an input-output model of the plant is employed which allows for estimating only the packet loss occurrences. Both the zero and the hold packet loss handling strategies are considered and stability of the filters is analyzed. The proposed methods are compared with some existing results during an example to show their advantages.

A Fast Self-Calibration Method for Dual-Axis Rotational Inertial Navigation Systems Based on Invariant Errors.

In order to ensure that dual-axis rotational inertial navigation systems (RINSs) maintain a high level of accuracy over the long term, there is a demand for periodic calibration during their service life. Traditional calibration methods for inertial measurement units (IMUs) involve removing the IMU from the equipment, which is a laborious and time-consuming process. Reinstalling the IMU after calibration may introduce new installation errors. This paper focuses on dual-axis rotational inertial navigation systems and presents a system-level self-calibration method based on invariant errors, enabling high-precision automated calibration without the need for equipment disassembly. First, navigation parameter errors in the inertial frame are expressed as invariant errors. This allows the corresponding error models to estimate initial attitude even more rapidly and accurately in cases of extreme misalignment, eliminating the need for coarse alignment. Next, by utilizing the output of a gimbal mechanism, angular velocity constraint equations are established, and the backtracking navigation is introduced to reuse sensor data, thereby reducing the calibration time. Finally, a rotation scheme for the IMU is designed to ensure that all errors are observable. The observability of the system is analyzed based on a piecewise constant system method and singular value decomposition (SVD) observability analysis. The simulation and experimental results demonstrate that this method can effectively estimate IMU errors and installation errors related to the rotation axis within 12 min, and the estimated error is less than 4%. After using this method to compensate for the calibration error, the velocity and position accuracies of a RINS are significantly improved.

Identification of Boolean control networks with time delay.

This paper investigates the identification of time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) via Cheng product. According to all admissible (input-)output sequences, definition on identifiability of the (TBCN) TBN is given. Two algorithms are designed to select suitable delay parameters of the TBN and TBCN, respectively. Based on these, the original systems are divided into several subsystems. Then by virtue of observability, the criteria for identifiability of the TBN and TBCN are obtained. Moreover, the corresponding constructing processes are presented to establish the internal structures of the TBN and TBCN. Finally, two illustrative examples are given to show the feasibility of the proposed methods.

Autonomous State Estimation and Observability Analysis for the Taiji Formation Using High-Precision Optical Sensors.

In certain observation periods of navigation missions for the Taiji formation, ground observation stations are unable to observe the spacecraft, while the state of the spacecraft can be estimated through the utilization of dynamic equations simulated on prior knowledge. However, this method cannot accurately track the spacecraft. In this paper, we focus on appropriately selecting the available onboard measurement to estimate the state of the spacecraft of the Taiji formation. We design two schemes to explore the performance of the state estimation based on the interspacecraft interferometry measurements and the measurements obtained from the Sun sensor and the radial velocity sensor. The observability of the system is numerically analyzed using the singular value decomposition method. Furthermore, we analyze error covariance propagation using the cubature Kalman filter. The results show that using high-precision interspacecraft angle measurement can improve significantly the observability of the system. The absolute position and velocity of the spacecraft can be estimated respectively with an accuracy of about 3.1 km and 0.14 m/s in the first scheme, where the prior information of the precision of the position and velocity is respectively 100 km and 1 m/s. When the measurement from the radial velocity sensor is used in the second scheme, the estimation accuracy of the velocity can be improved about 18 times better than that in the first scheme.

Assessing the Impact of Context Inference Error and Partial Observability on RL Methods for Just-In-Time Adaptive Interventions.

Just-in-Time Adaptive Interventions (JITAIs) are a class of personalized health interventions developed within the behavioral science community. JITAIs aim to provide the right type and amount of support by iteratively selecting a sequence of intervention options from a pre-defined set of components in response to each individual's time varying state. In this work, we explore the application of reinforcement learning methods to the problem of learning intervention option selection policies. We study the effect of context inference error and partial observability on the ability to learn effective policies. Our results show that the propagation of uncertainty from context inferences is critical to improving intervention efficacy as context uncertainty increases, while policy gradient algorithms can provide remarkable robustness to partially observed behavioral state information.

Virtue Discounting: Observability Reduces Moral Actors' Perceived Virtue.

Performing prosociality in public presents a paradox: only by doing so can people demonstrate their virtue and also influence others through their example, yet observers may derogate actors' behavior as mere "virtue signaling." Here we investigate the role of observability of actors' behavior as one reason that people engage in such "virtue discounting." Further, we investigate observers' motivational inferences as a mechanism of this effect, using the comparison of generosity and fairness as a case study among virtues. Across 14 studies (7 preregistered, total N = 9,360), we show that public actors are perceived as less virtuous than private actors, and that this effect is stronger for generosity compared to fairness (i.e., differential virtue discounting). Exploratory factor analysis suggests that three types of motives-principled, reputation-signaling, and norm-signaling-affect virtue discounting. Using structural equation modeling, we show that observability's effect on actors' trait virtue ratings is largely explained by inferences that actors have less principled motivations. Further, we leverage experimental evidence to provide stronger causal evidence of these effects. We discuss theoretical and practical implications of our findings, as well as future directions for research on the social perception of virtue.

A unified method for assessing the observability of dynamic complex systems.

PROBLEM: Systems theory applied to biology and medicine assumes that the complexity of a system can be described by quasi-generic models to predict the behavior of many other similar systems. To this end, the aim of various research works in systems theory is to develop inductive modeling (based on data-intensive analysis) or deductive modeling (based on the deduction of mechanistic principles) to discover patterns and identify plausible correlations between past and present events, or to connect different causal relationships of interacting elements at different scales and compute mathematical predictions. Mathematical principles assume that there are constant and observable universal causal principles that apply to all biological systems. Nowadays, there are no suitable tools to assess the soundness of these universal causal principles, especially considering that organisms not only respond to environmental stimuli (and inherent processes) across multiple scales but also integrate information about and within these scales. This implies an uncontrollable degree of uncertainty. METHODOLOGY: A method has been developed to detect the stability of causal processes by evaluating the information contained in the trajectories identified in a phase space. Time series patterns are analyzed using concepts from geometric information theory and persistent homology. In essence, recognizing these patterns in different time periods and evaluating their geometrically integrated information leads to the assessment of causal relationships. With this method, and together with the evaluation of persistent entropy in trajectories in relation to different individual systems, we have developed a method called Φ-S diagram as a complexity measure to recognize when organisms follow causal pathways leading to mechanistic responses. RESULTS: We calculated the Φ-S diagram of a deterministic dataset available in the ICU repository to test the method's interpretability. We also calculated the Φ-S diagram of time series from health data available in the same repository. This includes patients' physiological response to sport measured with wearables outside laboratory conditions. We confirmed the mechanistic nature of both datasets in both calculations. In addition, there is evidence that some individuals show a high degree of autonomous response and variability. Therefore, persistent individual variability may limit the ability to observe the cardiac response. In this study, we present the first demonstration of the concept of developing a more robust framework for representing complex biological systems.

ϵ-Controllability/ϵ-Observability of linear switched sampled-data systems with the non-equidistant time schedule.

In this work, a novel perspective is developed to investigate the property of controllability/observability of linear switched sampled-data systems under the non-equidistant sampling schedule. In this regard, two new notions are introduced as ϵ-controllability and ϵ-observability to create a feasible ground for controlling and observing linear switched sampled-data systems with any initial time chosen from outside of ϵ neighborhood of switching instants. The main motivation is to control and observe the given switched sampled-data system, which consists of a finite number of discrete-time sub-systems within each sub-system. Hence, the system requires a lower number of sampling times for ϵ-controllability and ϵ-observability compared to the original notions of controllability and observability in this context. Although the number of sampling times in a certain time interval increases whenever ϵ tends to zero, the number of sampling candidates required for ϵ-controllability and ϵ-observability becomes finite. Numerical experiments are performed on several continuous time switched linear systems, and ϵ-controllability and ϵ-observability of their corresponding switched sampled-data systems are derived for various ϵ values under constructed non-equidistant sampling patterns.

Four conservation challenges and a synthesis.

Conservation and management of biological systems involves decision-making over time, with a generic goal of sustaining systems and their capacity to function in the future. We address four persistent and difficult conservation challenges: (1) prediction of future consequences of management, (2) uncertainty about the system's structure, (3) inability to observe ecological systems fully, and (4) nonstationary system dynamics. We describe these challenges in terms of dynamic systems subject to different sources of uncertainty, and we present a basic Markovian framework that can encompass approaches to all four challenges. Finding optimal conservation strategies for each challenge requires issue-specific structural features, including adaptations of state transition models, uncertainty metrics, valuation of accumulated returns, and solution methods. Strategy valuation exhibits not only some remarkable similarities among approaches but also some important operational differences. Technical linkages among the models highlight synergies in solution approaches, as well as possibilities for combining them in particular conservation problems. As methodology and computing software advance, such an integrated conservation framework offers the potential to improve conservation outcomes with strategies to allocate management resources efficiently and avoid negative consequences.

Structural Identifiability and Observability of Microbial Community Models.

Biological communities are populations of various species interacting in a common location. Microbial communities, which are formed by microorganisms, are ubiquitous in nature and are increasingly used in biotechnological and biomedical applications. They are nonlinear systems whose dynamics can be accurately described by models of ordinary differential equations (ODEs). A number of ODE models have been proposed to describe microbial communities. However, the structural identifiability and observability of most of them-that is, the theoretical possibility of inferring their parameters and internal states by observing their output-have not been determined yet. It is important to establish whether a model possesses these properties, because, in their absence, the ability of a model to make reliable predictions may be compromised. Hence, in this paper, we analyse these properties for the main families of microbial community models. We consider several dimensions and measurements; overall, we analyse more than a hundred different configurations. We find that some of them are fully identifiable and observable, but a number of cases are structurally unidentifiable and/or unobservable under typical experimental conditions. Our results help in deciding which modelling frameworks may be used for a given purpose in this emerging area, and which ones should be avoided.

State Estimation in Partially Observable Power Systems via Graph Signal Processing Tools.

This paper considers the problem of estimating the states in an unobservable power system, where the number of measurements is not sufficiently large for conventional state estimation. Existing methods are either based on pseudo-data that is inaccurate or depends on a large amount of data that is unavailable in current systems. This study proposes novel graph signal processing (GSP) methods to overcome the lack of information. To this end, first, the graph smoothness property of the states (i.e., voltages) is validated through empirical and theoretical analysis. Then, the regularized GSP weighted least squares (GSP-WLS) state estimator is developed by utilizing the state smoothness. In addition, a sensor placement strategy that aims to optimize the estimation performance of the GSP-WLS estimator is proposed. Simulation results on the IEEE 118-bus system show that the GSP methods reduce the estimation error magnitude by up to two orders of magnitude compared to existing methods, using only 70 sampled buses, and increase of up to 30% in the probability of bad data detection for the same probability of false alarms in unobservable systems The results conclude that the proposed methods enable an accurate state estimation, even when the system is unobservable, and significantly reduce the required measurement sensors.

Angle-Only Cooperative Orbit Determination Considering Attitude Uncertainty.

In this paper, a novel concept for cooperative orbit determination (OD) using inter-spacecraft angle-only measurements is proposed. Different from the conventional cooperative OD that only estimates orbit states, the attitude of the observer spacecraft is considered by incorporating the attitude into the estimated vector. The observability of a two-spacecraft system is analyzed based on the observability matrix. Observability analysis reveals that inter-spacecraft angle-only measurements are inadequate to estimate both the attitude and the orbit states in two-body dynamics. The observability of the two-spacecraft system can be improved by considering high-order gravitational perturbation or executing an attitude maneuver on the observer spacecraft. This is the first time that we present the observability analysis and orbit estimation results for a two-spacecraft system considering attitude uncertainty for the observer. Finally, simulation results demonstrate the effectiveness of the proposed method. The results in this paper can be potentially useful for autonomous managements of a spacecraft constellation and formation.

Time varying Markov process with partially observed aggregate data: An application to coronavirus.

A major difficulty in the analysis of Covid-19 transmission is that many infected individuals are asymptomatic. For this reason, the total counts of infected individuals and of recovered immunized individuals are unknown, especially during the early phase of the epidemic. In this paper, we consider a parametric time varying Markov process of Coronavirus transmission and show how to estimate the model parameters and approximate the unobserved counts from daily data on infected and detected individuals and the total daily death counts. This model-based approach is illustrated in an application to French data, performed on April 6, 2020.

State estimation for nonlinear state-space transmission models of tuberculosis.

Given the high prevalence of tuberculosis (TB) and the mortality rate associated with the disease, numerous models, such as the Gammaitoni and Nucci (GN) model, were developed to model the risk of transmission. These models typically rely on a quanta generation rate as a measurement of infectivity. Since the quanta generation rate cannot be measured directly, the unique contribution of this work is to develop state estimators to estimate the quanta generation rate from available measurements. To estimate the quanta generation rate, the GN model is adapted into an augmented single-room GN model and a simplified two-room GN model. Both models are shown to be observable, i.e., it is theoretically possible to estimate the quanta generation rate given available measurements. Kalman filters are used to estimate the quanta generation rate. First, a continuous-time extended Kalman filter is used for both adapted models using a simulation and measurement sampling rate of 60 s. Accurate quanta generate rate estimates are achieved in both cases. A more realistic scenario is also considered with a measurement sampling rate of one day. For these estimates, a hybrid extended Kalman filter (HEKF) is used. Accurate quanta generation rate estimates are achieved for the more realistic scenario. Future work could potentially use the HEKFs, the adapted models, and real-time measurements in a control system feedback loop to reduce the transmission of TB in confined spaces such as hospitals.