vision.KalmanFilter
Correction of measurement, state, and state estimation error covariance
Description
The Kalman filter object is designed for tracking. You can use it to predict a physical object's future location, to reduce noise in the detected location, or to help associate multiple physical objects with their corresponding tracks. A Kalman filter object can be configured for each physical object for multiple object tracking. To use the Kalman filter, the object must be moving at constant velocity or constant acceleration.
Creation
The Kalman filter algorithm involves two steps, prediction and correction (also known as the update step). The first step uses previous states to predict the current state. The second step uses the current measurement, such as object location, to correct the state. The Kalman filter implements a discrete time, linear State-Space System.
Note
To make configuring a Kalman filter easier, you can use theconfigureKalmanFilterobject to configure a Kalman filter. It sets up the filter for tracking a physical object in a Cartesian coordinate system, moving with constant velocity or constant acceleration. The statistics are the same along all dimensions. If you need to configure a Kalman filter with different assumptions, do not use the function, use this object directly.
In the state space system, the state transition model,A, and the measurement model,H, are set as follows:
| Variable | Value |
|---|---|
| A | [1 1 0 0; 0 1 0 0; 0 0 1 1; 0 0 0 1] |
| H | [1 0 0 0; 0 0 1 0] |
Syntax
Description
kalmanFilter= Vision.KalmanFilter
kalmanFilter= Vision.KalmanFilter(StateTransitionModel,MeasurementModel)
kalmanFilter= Vision.KalmanFilter(StateTransitionModel,MeasurementModel,ControlModel,Name,Value)Name,Valuepair arguments. Unspecified properties have default values.
Properties
Object Functions
Use thepredictandcorrectfunctions based on detection results. Use thedistancefunction to find the best matches.
检测到跟踪对象时，请使用
predictandcorrectfunctions with the Kalman filter object and the detection measurement. Call the functions in the following order:[...] = predict(
kalmanFilter）；[...] =正确（kalmanFilter,measurement）；When the tracked object is not detected, call the
predictfunction, but not thecorrectfunction. When the tracked object is missing or occluded, no measurement is available. Set the functions up with the following logic:[...] = predict(
kalmanFilter）；Ifmeasurementexists [...] = correct(kalmanFilter,measurement）；endIf the tracked object becomes available after missing for the pastt-1 contiguous time steps, you can call the
predictfunctionttimes. This syntax is particularly useful to process asynchronous video.. For example,for i = 1:k [...] = predict(kalmanFilter); end [...] = correct(kalmanFilter,measurement)
Examples
Track Location of An Object
跟踪物理对象向一个方向移动的位置。
Generate synthetic data which mimics the 1-D location of a physical object moving at a constant speed.
detectedLocations = num2cell(2*randn(1,40) + (1:40));
Simulate missing detections by setting some elements to empty.
detectedLocations{1} = [];foridx = 16: 25 detectedLocations{idx} = [];end
Create a figure to show the location of detections and the results of using the Kalman filter for tracking.
figure; holdon;ylabel ('地点'）；ylim([0,50]); xlabel('Time'）；xlim（[0，长度（检测到）]）;
Create a 1-D, constant speed Kalman filter when the physical object is first detected. Predict the location of the object based on previous states. If the object is detected at the current time step, use its location to correct the states.
kalman = [];foridx = 1: length(detectedLocations) location = detectedLocations{idx};ifisempty(kalman)if~isempty(location) stateModel = [1 1;0 1]; measurementModel = [1 0]; kalman = vision.KalmanFilter(stateModel,measurementModel,'ProcessNoise',1e-4,'MeasurementNoise',4); kalman.State = [location, 0];endelsetrackedLocation = predict(kalman);if~isempty(location) plot(idx, location,'k+'）；d = distance(kalman,location); title(sprintf('Distance:%f', d)); trackedLocation = correct(kalman,location);elsetitle('Missing detection'）；endpause(0.2); plot(idx,trackedLocation,'ro'）；endendlegend('Detected locations','Predicted/corrected locations'）；
Remove Noise From a Signal
Use Kalman filter to remove noise from a random signal corrupted by a zero-mean Gaussian noise.
Synthesize a random signal that has value of 1 and is corrupted by a zero-mean Gaussian noise with standard deviation of 0.1.
x = 1; len = 100; z = x + 0.1 * randn(1,len);
Remove noise from the signal by using a Kalman filter. The state is expected to be constant, and the measurement is the same as state.
stateTransitionModel = 1; measurementModel = 1; obj = vision.KalmanFilter(stateTransitionModel,measurementModel,“StateCovariance”,1,'ProcessNoise'，1E-5，'MeasurementNoise',1e-2); z_corr = zeros(1,len);foridx = 1: len predict(obj); z_corr(idx) = correct(obj,z(idx));end
情节结果。
图，图（x *一个（1，len），'g-'）；holdon;plot(1:len,z,'b+',1:len,z_corr,'r-'）；legend('Original signal','Noisy signal','Filtered signal'）；
Algorithms
参考
[1] Welch, Greg, and Gary Bishop,An Introduction to the Kalman Filter, TR 95–041. University of North Carolina at Chapel Hill, Department of Computer Science.
[2] Blackman, S.带有雷达应用的多目标跟踪。Artech House, Inc., pp. 93, 1986.
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