We provide a tutorial-like description of Kalman filter and extended Kalman filter. This chapter aims for those who need to teach Kalman filters to others, or for those who do not have a strong background in estimation theory. Following a problem definition of state estimation, filtering algorithms will be presented with supporting examples to help readers easily grasp how the Kalman filters work. Implementations on INS/GNSS navigation, target tracking, and terrain-referenced navigation (TRN) are given. In each example, we discuss how to choose, implement, tune, and modify the algorithms for real world practices. Source codes for implementing the examples are also provided. In conclusion, this chapter will become a prerequisite for other contents in the book.

This paper focuses on maximizing the percent coverage and minimizing the revisit time for a small satellite constellation with limited coverage. A target area represented by a polygon defined by grid points is chosen instead of using a target point only. The constellation consists of nonsymmetric and circular Low Earth Orbit (LEO) satellites. A global optimization method, Genetic Algorithm (GA), is chosen due to its ability to locate a global optimum solution for nonlinear multiobjective problems. From six orbital elements, five elements (semimajor axis, inclination, argument of perigee, longitude of ascending node, and mean anomaly) are varied as optimization design variables. A multiobjective optimization study is conducted in this study with percent coverage and revisit time as the two main parameters to analyze the performance of the constellation. Some efforts are made to improve the objective function and to minimize the computational load. A semianalytical approach is implemented to speed up the guessing of initial orbital elements. To determine the best parametric operator combinations, the fitness value and the computational time from each study cases are compared.

This paper proposes a novel method to cope with local measurement ambiguity problem in particle filtering. The ambiguity of the measurement has been attributed as a crucial cause of filter degradation and divergence. Given the observation that the ambiguous measurement update is contributed by not only the shape of the measurement model but also the prior distribution of the filter estimate, we adopt a solution to the outof- sequence measurement (OOSM) problem on the framework of the particle filter with sequential importance resampling (SIR). Once an ambiguous measurement update is detected, the proposed method skips the measurement update at the time step and utilizes the measurement later when the particle distribution becomes adequate for the measurement update. This strategy provides a remedy to the ambiguity problem to obtain accurate current position estimate with lower covariance. Numerical simulation is presented to demonstrate effectiveness and performance of the proposed method. Compared to other methods such as the standard particle filter, the auxiliary particle filter, the mixture particle filter, and the receding-horizon Kalman filter, the proposed method shows better performance in terms of root-mean-square error and estimated covariance.

This paper addresses measurement models in a particle filter for application in terrain‐referenced navigation using an interferometric radar altimeter (IRA). We propose a novel method for utilizing an IRA in a terrain‐referenced navigation system based on the fact that an IRA provides accurate three‐dimensional measurement of the closest target point on the ground. The proposed measurement model searches for the closest point on an on‐board digital elevation model and constructs an estimated measurement to calculate the measurement residual. Comparative simulation analysis with an existing method shows the proposed method provides outstanding navigation performance in terms of root mean square position error. The proposed method yields positioning solutions with an average root mean square error less than 3 m whereas that of the existing method is more than 11 m using a virtual digital elevation model fulfilling the HRTI‐3 specification. Simulation results on the effects of terrain roughness, cruising altitude, sampling frequency, and magnitudes of inertial navigation system/barometer biases are also presented. © 2018 Institute of Navigation

This paper presents a scalable deep learning approach for short-term traffic prediction based on historical traffic data in a vehicular road network. Capturing the spatio-temporal relationship of the big data often requires a significant amount of computational burden or an ad-hoc design aiming for a specific type of road network. To tackle the problem, we combine a road network graph with recurrent neural networks (RNNs) to construct a structural RNN (SRNN). The SRNN employs a spatio-temporal graph to infer the interaction between adjacent road segments as well as the temporal dynamics of the time series data. The model is scalable thanks to two key aspects. First, the proposed SRNN architecture is built by using the semantic similarity of the spatio-temporal dynamic interactions of all segments. Second, we design the architecture to deal with fixed-length tensors regardless of the graph topology. With the real traffic speed data measured in the city of Santander, we demonstrate the proposed SRNN outperforms the image-based approaches using the capsule network (CapsNet) by 14.1% and the convolutional neural network (CNN) by 5.87%, respectively, in terms of root mean squared error (RMSE). Moreover, we show that the proposed model is scalable. The SRNN model trained with data of a road network is able to predict traffic speed of different road networks, with the fixed number of parameters to train.