Global RTK Positioning in Graphical State Space

For simultaneous localization and mapping (SLAM) in large-scale scenarios, the influence of long-distance and high-speed motion cannot be ignored because the risk of huge odometry drift will increase. To solve this problem, we propose the LiDAR -inertial odometry (LIO) method via Kalman filter and factor graph optimization (LIO-FILO), which provides real-time, high-frequency, and high-precision odometry. The LIO system consisting of three modules is established to fit various application scenarios. The state estimation module provides the pose states to be optimized and receives timely feedback from the pose optimization module. In the loop closure module, LIO-FILO constructs a multilayer structure loop closure detection method, including different schemes of detection, and the loop closure factor is constructed by the pose transformation matrix calculated by ICP. In the pose optimization module, the fast-build adjacent constraint factors and the loop closure factors are added to the factor graph to get the optimized result based on the GTSAM library. The real-world experiments show that LIO-FILO can mitigate the odometry drift to achieve accurate mapping results and obtain higher precision odometry compared with the existing advanced SLAM methods.

Global navigation satellite systems (GNSSs) applied to intelligent transport systems in urban areas suffer from multipath and non-line-of-sight (NLOS) effects due to the signal reflections from high-rise buildings, which seriously degrade the accuracy and reliability of vehicles in real-time applications. Accordingly, the integration between GNSS and inertial navigation systems (INSs) could be utilized to improve positioning performance. However, the fixed GNSS solution uncertainty of the conventional integration method cannot determine the fluctuating GNSS reliability in fast-changing urban environments. This weakness becomes solvable using a deep learning model for sensing the ambient environment intelligently, and it can be further mitigated using factor graph optimization (FGO), which is capable of generating robust solutions based on historical data. This paper mainly develops the adaptive GNSS/INS loosely coupled system on FGO, along with the fixed-gain Kalman filter (KF) and adaptive KF (AKF) being taken as comparisons. The adaptation is aided by a convolutional neural network (CNN), and the feasibility is verified using data from different grades of receivers. Compared with the integration using fixed-gain KF, the proposed adaptive FGO (AFGO) maintains the 100% positioning availability and reduces the overall 2D positioning error by up to 70% in the aspects of both root mean square error (RMSE) and standard deviation (STD).

Multi-sensor fusion and precise point positioning real-time kinematic (PPP-RTK) techniques are gaining popularity in vehicle navigation studies. The integration of the Global Navigation Satellite System (GNSS), inertial navigation system (INS), and vision can significantly improve the accuracy and continuity of positioning. The methods used to integrate different measurements are usually divided into an extended Kalman filter and factor graph optimization (FGO). We propose an integration method of PPP-RTK/INS/Vision that utilizes both the square-root information filter (SRIF) and FGO, combining the merits of the two algorithms. The proposed PPP-RTK/INS/Vision integration consists of two parts: the first is reweighted PPP-RTK/INS tightly coupled integration based on SRIF, and the second is GNSS/INS/Vision integration based on a two-step FGO method with feature selection in the vision component. The first positioning result is integrated with the FGO-based visual INS with uniform depth distribution to generate the final navigation information. The real-world experiment, carried out in an urban area, includes many GNSS-challenged environments, such as high buildings, tunnels, and viaducts. The results demonstrate that the proposed method achieves a root mean square of 0.57, 0.65, and 0.86 m in the north, east, and down components of the entire trajectory, respectively. Compared to the PPP-RTK/INS/Vision tightly coupled integration with a multi-state constrained Kalman filter, it shows an 11.0% improvement in vertical accuracy and comparable horizontal accuracy. Moreover, in the GNSS-challenged environment, the performance of the proposed method is more outstanding in the vertical component, with an improvement of 83.0% in the vertical direction and similar horizontal accuracy. Our study provides a novel approach to integrating both measurements and optimal estimation methods.

In environments where GNSS is unavailable or not useful for positioning, the use of low cost MEMS-based inertial sensors has paved a way to a more cost effective solution. Of particular interest is a foot mounted pedestrian navigation system, where zero velocity updates (ZUPT) are used with the standard strapdown navigation algorithm in a Kalman filter to restrict the error growth of the low cost inertial sensors. However heading drift still remains despite using ZUPT measurements since the heading error is unobservable. External sensors such as magnetometers are normally used to mitigate this problem, but the reliability of such an approach is questionable because of the existence of magnetic disturbances that are often very difficult to predict. Hence there is a need to eliminate the heading drift problem for such a low cost system without relying on external sensors to give a possible stand-alone low cost inertial navigation system. In this paper, a novel and effective algorithm for generating heading measurements from basic knowledge of the orientation of the building in which the pedestrian is walking is proposed to overcome this problem. The effectiveness of this approach is demonstrated through three field trials using only a forward Kalman filter that can work in real-time without any external sensors. This resulted in position accuracy better than 5 m during a 40 minutes walk, about 0·1% in position error of the total distance. Due to its simplistic algorithm, this simple yet very effective solution is appealing for a promising future autonomous low cost inertial navigation system.

For autonomous systems, the smoothness of estimated trajectories is essential to ensure robust and performant vehicle control. Unfortunately, approaches for state estimation using Kalman filters are sensitive to measurement outliers that can diverge dramatically. We propose a state-estimation algorithm using factor graph optimization (FGO) in continuous-time for GNSS/INS navigation systems to track this problem. The focus is on the smoothness of the estimated trajectory in environments where the GNSS observations become temporarily unreliable. Therefore, an inland shipping scenario with bridge crossings is selected as an application example. To estimate the trajectory in continuous-time, we integrate a White-Noise-On-Acceleration (WNOA) motion prior factor based on Gaussian process regression between successive states. Our results show a 30% improvement in accuracy and increased smoothness of the estimated trajectory with FGO compared to Kalman filtering.

Multisource information fusion is a major area of interest within the field of unmanned technology. In comparison with utilizing the Kalman filter (KF)-based method, the factor graph optimization (FGO)-based method has recently been proposed as an innovative approach. However, the traditional FGO-based inertial measurement unit (IMU) preintegration process is designed for low-accuracy inertial sensors, which leads to insufficient utilization of information and a decrease in positioning accuracy, in the case of tactical-grade or higher accuracy IMUs. Therefore, this article refines the process on the manifold model and utilizes the equivalent rotation vector to accumulate IMU measurements. The main contribution of our work is the refined on-manifold IMU preintegration theory and the application of the multisample algorithm based on the equivalent rotation vector for obtaining more precise preintegrated IMU measurements. The refined on-manifold IMU preintegration theory is applied based on the FGO algorithm in the global navigation satellite system (GNSS)/inertial navigation system (INS) loosely integrated navigation system. The experiments based on simulated and real-world data were conducted and demonstrate that, compared to a high-precision extended KF (EKF) algorithm and optimization methods, the proposed method achieves more accuracy in a dynamic environment.

As the demand for indoor services relying on location information grows, achieving precise indoor positioning is becoming an urgent issue to address. The ultra-wide band (UWB) accuracy can reach centimeter level, but is susceptible to non-line-of-sight (NLOS) effects. The inertial navigation system (INS) is not affected by the environment, but the error will diverge over time. Therefore, this paper focuses on the UWB/INS combined positioning system, which can combine the advantages of both. We propose a loosely-coupled INS/UWB indoor localization scheme based on factor graph optimization (FGO). Firstly, an agglomerative hierarchical clustering based NLOS mitigation method is applied to preprocess the UWB raw measurement data. The position estimates under UWB are then obtained using an improved extended Kalman filter to mitigate NLOS errors and provide more accurate location data for combined navigation. Then, we build the IMU preintegration factor and the zero-bias factor. Finally, FGO is used to fuse the information to get the final location. Designed experiments demonstrate the superiority of the algorithm. The simulation and experimental results show that the proposed scheme outperforms the comparison algorithms.

This paper describes an algorithm that identifies a state-space model and an associated steady-state Kalman filter gain from noise-corrupted input–output data. The model structure involves two Kalman filters where a second Kalman filter accounts for the error in the estimated residual of the first Kalman filter. Both Kalman filter gains and the system state-space model are identified simultaneously. Knowledge of the noise covariances is not required.

Modeling physical systems is an essential skill for engineers, since it enables to achieve a deep understanding of their dynamic behavior and, consequently, to develop effective control strategies. The first part of this paper provides a recap of the fundamental principles and properties of the Power-Oriented Graphs (POG) modeling technique, by also referring to a case study to consolidate them. The POG technique is then compared with the other two main graphical modeling techniques available in the literature, namely Bond Graph (BG) and Energetic Macroscopic Representation (EMR). The second part of this paper introduces the new Fast Modeling POG (FMPOG) procedure. The FMPOG, which operates in the POG framework, is a methodical step-by-step procedure that enables the readers to quickly derive the power-oriented graphical model of physical systems starting from their schematics. From the power-oriented graphical model, the state-space model can then be directly determined. To ensure the FMPOG procedure is easily usable by the entire community, we apply it to three examples in different energetic domains in this paper, guiding the reader step-by-step through the derivation of the physical systems models. A freely available Matlab/Simulink program is provided in a repository, allowing the users to automatically apply the FMPOG procedure to various classes of physical systems. This program allows to convert the physical systems schematics into the corresponding POG block schemes and, ultimately, into the state-space mathematical models.

In this chapter, the state space model is thoroughly discussed. After defining the general state space model, the Kalman filter is derived. The square root covariance and the information filter are described. The topics of likelihood evaluation, forecasting, smoothing and covariance-based filters are discussed. Markov processes and the backwards Kalman filter are presented. The last part of the chapter is devoted to the handling of state space models with constant bias and incompletely specified initial conditions. The two-stage Kalman filter and the square root information form of the bias filter are described. Several algorithms for likelihood evaluation, forecasting and smoothing are given.

PurposeThis paper aims to find out whether lagging problems exist within Hong Kong's office values.Design/methodology/approachA State Space Model with the Kalman filter is deployed in detecting the extent of lagging errors in Hong Kong's office price indices, proffered by the ratings and valuation department (RVD).FindingsThe findings suggest that about one year of lagging errors exists in RVD's office price indices compared with the stock market property indices. Also, the finding suggests that the Kalman filter provides a more efficient form of estimates for real estate values and returns.Originality/valueWhile most studies investigating lagging problems of appraisal‐based returns concentrate on the US real estate market, studies in this regard for Asian countries (or cities) are few and far between. Hong Kong, in particular, is worth studying, considering its established role as a financial centre in South East Asia. This paper also provides some insights for further studies on the prediction of future real estate values, in particular those with fewer transactions.

In today's global market, a critical issue for companies to survive the increasing competition is how to handle uncertainty in their supply network. In this paper, we explore the application of Kalman filtering to estimate the dynamic states in a supply network. Two state-space models are developed. The first one focuses on processing each individual order which includes both waiting time and value-added processing time. Considering the correlation of consecutive orders, the second one enhances the state-space model by employing autoregressive model of waiting time. To signal potential abnormal events, the estimates from the models are further used in control charts with control limits being updated at each monitoring stage according to the related estimation error. A supply network case example is studied and we conclude in the benchmark model (without using Kalman filtering) and the first state-space model, the data collected from the bottleneck stage turns out to be most valuable for increased accuracy in detecting tardy orders. The second state-space model consistently outperforms both the benchmark model and the first state-space model for robustly early detection of abnormalities at all stages, especially the stages before the bottleneck stage, of the system.

In this paper we develop and validate a procedure for testing against a shift in mean in the observa-tions and hidden state sequence of state space models with Gaussian noise. State space models are popular for modelling stochastic networks as they allow to take into account that observations of the true state of a sys-tem may be corrupted by measurement noise (usually, a Gaussian noise process is assumed). Although state space models are very general, they are still relatively tractable in that the true system state can be estimated efficiently by a recursive procedure known as Kalman filtering. State space models can be regarded as a special type of hidden Markov model. As such, they are a flexible modelling tool that has been found useful, for example, for modelling road networks (Stathopoulos and Karlaftis, 2003) to account for uncertainty in the measurement of travel times. For instance, we may assume that travel times have to be estimated from flow and occupancy data. An increase in the unobserved mean travel time can be caused by traffic congestion; a shift in the mean value of the observations on the other hand could indicate a bias of the sensors. State space models can also be used to model communication networks: Suppose that the current state of a channel (e.g. measured by the probability of packet loss) is not observed directly, but has to be inferred from the received package flow. A change in the mean value of the hidden state sequence, or a change in the mean value of the received package flow can deteriorate the performance of the network if it remains unrecognised. This motivates us to investigate procedures for testing against a shift in mean in the observations and hidden state sequence of state space models. The objective is to detect a change as quickly as possible while keeping the ratio of false alarms at a pre-specified low level. Since the observations are generally not independent, in (Basseville and Nikiforov, 1993) a cumulative sum (CUSUM) procedure is applied to the (independent) sequence of innovations, which is obtained as a byproduct from Kalman filter estimation of the hidden states. That is, a log-likelihood ratio (LLR) test statistic is used and an alarm is raised as soon as this test statistic exceeds a certain threshold that is assumed to be given. Change point detection for state space models has also been considered in (Lai and Shan, 1999) for the case where the size of the mean shift is unknown, in which case a generalized LLR test can be applied. In this paper we tackle the question of how the threshold of the sequential LLR test can be chosen when the shift size is assumed to be known. In practice, the latter assumption can be dealt with by realizing that typically there will be a minimum change size that is of interest from an engineering perspective, and that can thus be used as input for the model. Based on this assumption we can identify the appropriate level of the threshold based on approximations of the false alarm probability - essentially the probability that a random walk process exceeds a given threshold on an interval. A persistent change in the mean value of the observations results in a dynamic change in the mean value of the innovations, which are therefore not identically distributed after the change point. However, it follows from the stability properties of the Kalman filter that under weak conditions the magnitude of the shift converges to a constant. This allows for large-deviations (LD) approximations as well as approximations motivated by a functional central limit theorem (CLT). LD approximations to the false alarm probability have been considered in (Bucklew, 1985; Ellens et al., 2013; Kuhn et al., 2014) for testing i.i.d. and vector autoregressive moving average (VARMA) models. CLT approximations were motivated, for example, in Siegmund (1985). We compare the numerical performance of the tests under both types of limiting regimes with respect to the false alarm probability and the detection delay.

While exploring unknown territory on search and rescue missions, fusing multiple sensors is vital for the precise on-line localization of mobile robots. The Extended Kalman filter (EKF) with stochastic cloning is well suited for this purpose and allows to directly integrate multiple absolute and relative state measurements. The latter measure differences between a past state and the current state, thus introducing correlations. These inter-dependencies are modeled by stochastic cloning, which performs a state augmentation by cloning the respective state estimates connected by a relative measurement. Different approaches to feed back information from absolute updates to the cloned state are presented and compared to a SLAM algorithm based on factor graph optimization.

Multibody dynamics comprises methodologies for the design and analysis of mechanical systems, with Kalman filters being the principal state estimation methods. The Kalman filters are generally formulated for unconstrained systems, the dynamics of which are described by ordinary differential equations in state-space models. However, multibody systems are constrained systems, and the commonly used method to describe their dynamics involves using differential algebraic equations (DAEs) comprising differential and algebraic equations. The differential equations also include the Lagrange multipliers. Hence, incorporating multibody systems, described by DAEs into the scheme of Kalman filters, cannot be achieved straightforwardly, which facilitates different strategies being addressed. This study develops a novel method for converting DAEs into a state-space model. A transition model of the time derivatives of Lagrange multipliers and a Lagrange multiplier constraint vector are devised and used in the state and output equations, respectively. The continuous- and discrete-time extended Kalman filters (CEKF and DEKF) are constructed using the proposed state-space model, and state estimations are simulated on the benchmark planar four- and five-bar linkages. Further, a demonstration of system observability is conducted, and sensitivity to the initial state estimates is studied. These tests demonstrate that the proposed state-space model achieves observable systems and that both the CEKF and DEKF, constructed using the proposed state-space model, can estimate the states with a wide range of initial conditions.