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A non-technical introduction to the question of modeling with time-varying parameters, using the beta coefficient from Financial Economics as the main example. After a brief introduction to this coefficient for those not versed in finance, the book presents a number of rather well known tests for constant coefficients and then performs these tests on data from the Stockholm Exchange. The Kalman filter is then introduced and a simple example is used to demonstrate the power of the filter. The filter is then used to estimate the market model with time-varying betas. The book concludes with further examples of how the Kalman filter may be used in estimation models used in analyzing other aspects of finance. Since both the programs and the data used in the book are available for downloading, the book is especially valuable for students and other researchers interested in learning the art of modeling with time varying coefficients

SummaryOur final comments can be relatively brief. In assessing the empirical importance of expectations variables in macroeconomic behavioural equations, a variety of "expectations models" should be used. To date, the Muth‐rational expectations approach has dominated the empirical literature. A major drawback, however, is the lack of an explicit optimal learning process by agents. We have attempted to remedy this by bringing together various diverse strands in the expectations, statistics and engineering literature to formalize models that embody "optimal information extraction" by agents faced with a stochastic environment. The Khan filter provides a unified method of approaching these problems and in this paper we presented the Kalman filter in terms of the usual least squares approach familiar to applied economists. Relatively inexpensive econometric software which utilizes recursive estimation techniques has recently become available. It is hoped that this paper has provided a framework favourable to its use by applied economists particularly in investigating the role of expectations variables in economic models.

Missiles are military rocket weapons having an automatic control system to locate its targets or adjust its direction. Indonesia itself, which is a country of archipelago, covers air area of its largest territory, followed by sea area and land area. Logically, the existence of missile defense equipment (the main weapon system) or precisely the type of long-range missile is acceptable to support the defense and security of the Republic of Indonesia, but its consequences to be operated in the territory of Indonesia itself, in case of an occufanct of an error in targeting the target, will fall on of harm to its own national territory. Therefore, trajectory estimation for guided missiles is the basic requirement for guided missiles to be aimed at the precise targets. The trajectory is used as a guide to direct that the missile reach the target by following the given path. To maintain the accuracy of the trajectory continuously, the missile trajectory estimation was made by using Unscented Kalman Filter (UKF) Algorithm. This algorithm was used to estimate nonlinear dynamic models The simulation results showed that the UKF method was effective, showing the accuracy of 97% by the UKF method

Unmanned aerial vehicles (UAVs) are increasingly used in military and scientific research. Some miniaturized UAVs rely entirely on the global positioning system (GPS) for navigation. GPS is vulnerable to accidental or deliberate interference that can cause it to fail. It is not unusual, even in a benign environment, for a GPS outage to occur for periods of seconds to minutes. For UAVs relying solely on GPS for navigation such an event can be catastrophic. This paper proposes an extended Kalman filter approach to estimate the location of a UAV when its GPS connection is lost, using inter-UAV distance measurements. The results from a recent trial conducted by DSTO in Australia with three UAVs are presented. It is shown that the location of a manoeuvering UAV that has lost the GPS signal can be determined to an accuracy of within 40m of its true location simply by measuring the range to two other UAVs at known location, where the range measurement error has a zero mean and a standard deviation of 10m.

Unmanned aerial vehicles (UAVs) are increasingly used in military and scientific research. Some miniaturized UAVs rely entirely on the global positioning system (GPS) for navigation. GPS is vulnerable to accidental or deliberate interference that can cause it to fail. It is not unusual, even in a benign environment, for a GPS outage to occur for periods of seconds to minutes. For UAVs relying solely on GPS for navigation such an event can be catastrophic. This paper proposes an extended Kalman filter approach to estimate the location of a UAV when its GPS connection is lost, using inter-UAV distance measurements. The results from a recent trial conducted by DSTO in Australia with three UAVs are presented. It is shown that the location of a manoeuvering UAV that has lost the GPS signal can be determined to an accuracy of within 40m of its true location simply by measuring the range to two other UAVs at known location, where the range measurement error has a zero mean and a standard deviation of 10m.

Global Positioning System (GPS) technology is widely used today in the areas of geodesy and topography as well as in aeronautics mainly for military purposes. Due to the military usage of GPS, full access and use of this technology is being denied to the civilian user who must then work with a less accurate version. In this paper we focus on the estimation of the receiver coordinates ( X, Y, Z ) and its clock bias ( δtr ) of a fixed point based on pseudorange measurements of a single GPS receiver. Utilizing the instantaneous coordinates of just 4 satellites and their clock offsets, by taking into account the atmospheric delays, we are able to derive a set of pseudorange equations. The estimation of the four unknowns ( X, Y, Z , δtr ) is achieved by introducing an extended Kalman filter that processes, off-line, all the data collected from the receiver. Higher performance of position accuracy is attained by appropriate tuning of the filter noise parameters and by including other forms of biases.