Kalman Filter to Estimate the state of a Maneuvering Aircraft Prepared By Kevin Meier Alok Desai 11292011 ECEn 670 Stochastic Process 1 ECEn 670 Stochastic Process Instructor ID: 249744
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Using the Kalman Filter to Estimate the state of a Maneuvering Aircraft
Prepared By: Kevin Meier Alok Desai
11/29/2011
ECEn -670 Stochastic Process
1
ECEn -670 Stochastic Process
Instructor:
Dr. Brian
MazzeoSlide2
OutlinesKalman filterCorrelation Between the Process and Measurement NoiseApplication of KF for estimating Bearing and RangeSimulation results 11/29/2011
ECEn -670 Stochastic Process 2Slide3
Kalman Filter Purpose: It is to use measurements observed over time, containing noise (random variations) and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated values.
When system model and measurement model equations are linear, then to estimate the state vector recursively.11/29/2011ECEn -670 Stochastic Process 3Slide4
Estimating States11/29/2011ECEn -670 Stochastic Process 4
System dynamic model: Measurement model: Slide5
Kalman Filter Estimation11/29/2011ECEn -670 Stochastic Process 5Slide6
Kalman Filter (Cont.)State estimation: Error covariance (a priori): Kalman Gain:Error covariance update (a posteriori):State estimate update:
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Correlation Between the Process and Measurement NoiseCorrelation be given byPrediction equation remain unchanged.Measurement equation 11/29/2011
ECEn -670 Stochastic Process 7
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Range and Bearing Estimation Radars are used to track aircraft.11/29/2011ECEn -670 Stochastic Process
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Range = ct/211/29/2011ECEn -670 Stochastic Process
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How the Kalman filter applies to RadarRadar is used to track the state of an aircraftThe state is the range, range rate, bearing and bearing rate11/29/2011
ECEn -670 Stochastic Process 10Slide11
How to model the aircraft with no acceleration dataModel the acceleration as a uniform random variable using the singer model. Where the acceleration is correlated from sample to sample11/29/2011ECEn -670 Stochastic Process
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How the Kalman filter applies to RadarThe radar uses sensors to measure the Range and Bearing angle. In this process there is sensor measurement noise11/29/2011ECEn -670 Stochastic Process
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How the Kalman filter applies to RadarThe process and measurement noise are zero-mean white Gaussian random variables11/29/2011ECEn -670 Stochastic Process
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Error Covariance for Range11/29/2011ECEn -670 Stochastic Process
15Error covariance (One prediction)
Error covariance (Multiple prediction)Slide16
Error Covariance of Bearing11/29/2011
ECEn -670 Stochastic Process 16Error covariance (One prediction)
Error covariance (Multiple prediction)Slide17
Bearing Angle11/29/2011ECEn -670 Stochastic Process 17
Bearing Angle (One prediction)Bearing Angle (Multiple prediction)Slide18
Vehicle Range11/29/2011ECEn -670 Stochastic Process 18
Vehicle Range (One Prediction)Vehicle Range (Multiple Prediction)Slide19
Range Error11/29/2011ECEn -670 Stochastic Process 19
Range Error (One Prediction)cVehicle Range (Multiple Prediction)Slide20
Bearing Rate11/29/2011ECEn -670 Stochastic Process 20
Bearing ( one prediction )Bearing (multiple prediction )Slide21
Range11/29/2011ECEn -670 Stochastic Process
21Range (One prediction )Range (Multiple prediction )Slide22
Range Error and Range Ratewith correlated noise11/29/2011ECEn -670 Stochastic Process
22Range ErrorRange RateSlide23
Questions??Thank you !
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