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	Kalman Filtering
		Kalman filtering is a relatively recent (1960) development in filtering, although it has its roots as far back as Gauss (1795).
		Kalman filtering has been applied in areas as diverse as aerospace, marine navigation, nuclear power plant instrumentation, demographic modeling, manufactring, and many others.
		Kalman filtering is a huge field whose depths we cannot hope to begin to plumb in such a brief paper as this.
	www.innovatia.com /software/papers/kalman.htm (1335 words)

	Fundamentals of Kalman Filtering
		We design the filter under the assumption that we are trying to estimate a constant bias state.
		With the a priori knowledge that the vehicle is on a particular road, the vehicle state is estimated with a constrained Kalman filter.
		The filter is designed to be robust to changes in the variance of the process noise and measurement noise.
	academic.csuohio.edu /simond/courses/kalman (816 words)

	ECS EPrints Service - Kalman Filter
		The filter requires a knowledge of the second-order statistics of the noise of process being observed and of the measurement noise in order to provide the solution that minimises the mean square error between the true state and the estimate of state.
		Kalman filtering provides a convenient means of determining the weightings (denoted as gains) to be given to input measurement data.
		Hence the Kalman filter chooses the gain sequence and estimates the estimated state's accuracy in accordance with the variations (in terms of accuracy and update rate) of input data and modelled process dynamics.
	eprints.ecs.soton.ac.uk /165 (449 words)

	Hybrid Kalman / Minimax Filtering
		Although the Kalman filter may be stable and the minimax filter may be stable, a combination of the two filters may be unstable.
		The behavior of the filter was investigated by examining its ability to track the one GPS satellite carrier phase for the first 60 seconds of the flight.
		The Kalman filter, the minimax filter, or the hybrid filter?
	www.innovatia.com /software/papers/hybrid.htm (1266 words)

	KALMAN FILTERS
		The purpose of a Kalman filter is to estimate the state of a system from meaurements which contain random errors.
		Kalman assumed that u(k) is a random number selected by picking a number from a hat.
		In later lessons we will extend the Kalman filter to cases where the dynamic equation is not linear and where u is not white noise.
	ourworld.compuserve.com /homepages/PDJoseph/kalman.htm (1171 words)

	Embedded.com - Kalman Filtering
		The Kalman filter not only works well in practice, but it is theoretically attractive because it can be shown that of all possible filters, it is the one that minimizes the variance of the estimation error.
		Kalman filters are often implemented in embedded control systems because in order to control a process, you first need an accurate estimate of the process variables.
		In order to use a Kalman filter to remove noise from a signal, the process that we are measuring must be able to be described by a linear system.
	www.embedded.com /showArticle.jhtml?articleID=9900168 (2124 words)

	Some of My Experiences with Kalman Filters
		The word recursive means that, unlike certain data processing concepts, the Kalman filter does not require all previous data to be kept in storage and reprocessed every time a new measurement is taken.
		Despite the typical connotation of a filter as a "fl box" containing electrical networks, the fact is that in most practical applications, the "filter" is just a computer program in the central processor.
		The use of the filter's error bounds on the estimate is contingent upon the accuracy of the measurement and target dynamics models.
	www.megasociety.net /noesis/138/kalman.html (885 words)

	[No title]
		Kalman Filtering is commonly used in the navigation systems of airplanes, where knowing the location accurately, and precisely if possible, is important.
		A Kalman Filter is a set of states, aka a vector, that approximately describe a real world system and a set of measurements that relate the set of states to a set of measurements.
		In a fiducial run of the filter with random spreads in the position and accelerometer inputs the time it takes to estimate the accelerometer bias is shown in Figure 1.
	www.gamasutra.com /view/feature/1494/wheres_the_wiimote_using_kalman_.php?print=1 (3000 words)

	Kalman Filters
		Kalman filters can be employed to replicate the results of the complimentary filter or to further condition the output of the complimentary filter.
		A simple Kalman filter is applied directly to the noisy output of the simulated system of a gyro, accelerometer, and complimentary filter.
		Kalman filtering can also be applied to other useful state variables such as position, or orientation.
	coecsl.ece.uiuc.edu /ge423/spring05/group3/website/kalman_info.htm (699 words)

	MARKET DATA PREDICTION WITH AN ADAPTIVE KALMAN FILTER
		If they were known, the Kalman filter could be adjusted, or tuned, to the data volatility by initially specifying the ratio of the noise variances.
		This is because the filter cannot “see” into the future and expects the data to maintain its current trend.
		Adaptive Kalman filters that have proved so useful in military applications, have been shown here to also be effective in market predictions, when used in conjunction with suitable indicators, and when properly adjusted.
	www.haikulabs.com /kalman.htm (2418 words)

	Kalman Adaptive Filter :: Blocks - Alphabetical List (Signal Processing Blockset)
		The Kalman filter assumes that there are no deterministic changes to the filter taps over time (that is, the transition matrix is identity), and that the only observable output from the system is the filter output with additive noise.
		The filter algorithm based on this constraint is also known as the random-walk Kalman filter.
		The FIR filter length parameter specifies the length of the filter that the Kalman algorithm estimates.
	www.mathworks.com /access/helpdesk/help/toolbox/dspblks/ref/kalmanadaptivefilter.html (541 words)

	Terence's HomePage
		Kalman filter has the the ability to fuse multiple sensor readings together, taking advantages of their individual strength, while gives readings with a balance of noise cancelation and adaptability.
		Now the girl comes and she is 30 mintues late (and that's how she interpret the meaning of "to the hour"), you now correct your own estimation for this current time frame, and use this new estimation to predict when she will come next time you meet her.
		They have the exact same equations, but for extended kalman filter we just have H and F as a partial derivative matrix that change with the variables, whereas for original kalman filter it is just a plain old constant matrix.
	www.ocf.berkeley.edu /~tmtong/kalman.php (2109 words)

	Kalman Filtering - Experimental Robotics
		The Kalman filter is an efficient infinite impulse responserecursive filter which estimates the state of a dynamic system from a series of incomplete and noise measurements.
		Kalman filtering is an important topic in control theory and control systems engineering.
		The Kalman filter exploits the dynamics of the target, which govern its time evolution, to remove the effects of the noise and get a good estimate of the location of the target at the present time (filtering), at a future time (prediction), or at a time in the past (interpolation or smoothing).
	cgi.cse.unsw.edu.au /~cs4411/wiki/index.php?title=Kalman_Filtering (817 words)

	mini_ker 101e manual: 4.3 Kalman filter
		At each time step the Kalman filter recomputes an estimation of the state and the variance-covariance matrix of the state.
		With the Kalman filter the dimension of estimated states, of the error on the state and of the observation, the W matrix, the observation function, the initial variance-covariance matrices on the state and the variance-covariance matrices of errors have to be given.
		This matrix is updated by the filter at each time step because the states are pertubated by some noise, and when assimilation takes place as new information reduce the error.
	www.lmd.jussieu.fr /~pdlmd/mini_ker/Kalman-filter.html (720 words)

	[No title]
		The purpose of a Kalman filter is to estimate the state of a system from measurements which contain random errors.
		The Kalman filter state variables for a specific application must include all those system dynamic variables that are measurable by the sensors used in the application.
		The Kalman gain matrix K is the crown jewel of Kalman filter.
	www.site.uottawa.ca /~rhabash/GPS9Kalmanfiltering (2032 words)

	IngentaConnect THIS ARTICLE HAS BEEN RETRACTEDThe Kalman filter for the pedologi... (Site not responding. Last check: )
		The Kalman filter is a tool designed primarily to estimate the values of the `state' of a dynamic system in time.
		For the discrete Kalman filter, discussed in this paper, the state equation is a stochastic difference equation that incorporates a random component for noise in the system and that may include external forcing.
		The Kalman filter operates recursively to predict forwards one step at a time the state of the system from the previously predicted state and the next measurement.
	www.ingentaconnect.com /content/bsc/ejss/2006/00000057/00000005/art00008 (725 words)

	JoBS: Of Point Spreads and Predictions, Using a Kalman Filter
		In this case, the filters can be used to estimate the strength of a team using a team's game-to-game progression of points scored, points allowed, whether they were at home or on the road, and who they played against.
		Kalman filters are used by NASA to predict the path of missiles and planes.
		The Kalman Filter's generality of applicability (to other fields) is great, but it also implies that it doesn't have built in a lot of the details of those fields.
	www.rawbw.com /~deano/articles/kalman.html (4092 words)

	ATI's Applications-Oriented Kalman Filtering course
		This is followed with an in-depth discussion of estimation theory and methods, concluding with the derivation of the Kalman filter algorithm.
		The remainder of the course focuses on the practical use of the Kalman filter.
		He is an expert in estimation and Kalman filtering with applications to orbit determination, multi-target tracking and real-time systems, and navigation/GPS.
	www.aticourses.com /applications-oriented_kalman_filtering.htm (562 words)

	Applications of Kalman filter in WAAS (Site not responding. Last check: )
		The Kalman filter being a multi-input, multi-output, recursive digital filter that produces estimates of states of a system, which are optimal in the mean square sense, finds application in two ways in GPS based navigation systems like WAAS.
		The Kalman filter is a multi-input, multi-output, recursive digital filter that can optimally estimate, in real time, the states of the system based on its noisy outputs.
		A brief approach of using the Kalman filter for estimation of TEC and synchronization of the atomic clocks at the RIMS is given below.
	www.gisdevelopment.net /technology/gps/techgp0033.htm (405 words)

	Kalman filtering - BaseGroup Labs
		These filters are widely used in control loops of the automatic control systems and this is where they originate from, as confirmed by such a specific term used to describe their work as ‘state space’.
		The filter’s smoothing properties are improving with increase of n, that is the precision of estimate grows.
		The growing memory filter working in accordance with the formula 6 is a particular case of a filtration algorithm known as Kalman filter.
	www.basegroup.ru /filtration/kalmanfilter.en.htm (1809 words)

	Autopilot: Kalman Filtering
		The core of the Kalman filtering algorithm is the state propagation matrix and the weights of the estimate and measurement matrices.
		The filter requires a translation matrix to translate the Euler angles to the Quaterion frame.
		The Kalman Filter update algorithm uses the measured state M, the matrix C and the gain matrix R to update the covariance matrix P and the estimated state X:
	autopilot.sourceforge.net /kalman.html (537 words)

	KalmanIntro - Portland State Aerospace Society
		Given a system model, an initial system state, and a sequence of noisy measurements, a Kalman filter can be constructed to produce a sequence of state estimates that are optimal in the sense that they minimize the expected square-error between the estimates and the true system state.
		The chief difficulty with Kalman filter theory is contained in (3.4).
		In formulating the Kalman filter the noise statistics have been defined in terms of covariance, and since elements with large covariance should be given low weight, the correct weighting matrix for this problem is the inverse of the covariance matrix.
	psas.pdx.edu /KalmanIntro (1317 words)

	Extended Kalman Filter — FloodRiskNet
		In the extended Kalman filter (EKF) for nonlinear systems (Jazwinski, 1970), approximate expressions are found for the propagation of the conditional mean and its associated covariance matrix.
		The structure of the propagation equations is similar to those of the classic Kalman filter for a linear system, as they are linearized about the conditional mean.
		Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model.
	www.floodrisknet.org.uk /methods/ExtendedKalmanFilter (503 words)

	ATI's Practical Kalman Filtering using MATLAB course
		The continuous filter is shown to be a limiting case of the discrete filter.
		For the constant gain (steady state) filter, the filter gains and the steady-state state error covariance matrix are derived from an eigenvector decomposition of the control Hamiltonian (Potter-MacFarlane) implemented in Matlab codes.
		One of the most important applications of Kalman filter methods is covariance analysis, used to predict the performance of a system using assumed system dynamics and assumed covariance models for system disturbances, measurement noise, and uncertain internal parameters of the system.
	www.aticourses.com /practical_kalman_filtering_using_matlab.htm (673 words)

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