Address for Correspondence *1 Professor, 2 Student, HITAM, JNTUH, Hyderabad, AP, India

Transcription

1 Research Paper TARGET TRACKING SYSTEM USING KALMAN FILTER Dr. K Rameshbabu* 1, J.Swarnadurga 2, G.Archana 2, K.Menaka 2 Address for Correspondence *1 Professor, 2 Student, HITAM, JNTUH, Hyderabad, AP, India ABSTRACT Kalman filtering was very popular in the research field of navigation and aviation because of its magnificent accurate estimation characteristic. Since then, electrical engineers manipulate its advantages to useful purpose in target tracking systems. Consequently, today it had become a popular filtering technique for estimating and resolving redundant errors involves in tracing the target. This project proposes a system for tracking a target (ball) in video streams, returning its body and head bounding boxes. The proposed system comprises a variation of Stauffer s adaptive background algorithm with spacio-temporal adaptation of the learning parameters and a Kalman tracker in a feedback configuration. In the feed forward path, the adaptive background module provides object evidence to the Kalman tracker. In the feedback path, the Kalman tracker adapts the learning parameters of the adaptive background module. The first just does detection by background subtraction. This can be considered as the ground truth. The second feeds the detection output into a Kalman filter. The predicted position from the kalman filter (red) is compared against the actual ground truth position (green).target tracking systems has many applications, like surveillance, security, smart spaces, pervasive computing, and human-machine interfaces to name a few. In these applications the targets are either human bodies, or vehicles. The common property of these targets is that sooner or later they exhibit some movement which is evidence that distinguishes them from the background and identifies them as foreground targets. KEYWORDS kalman filter, tracking system, navigation, stauffer s, spacio-temporal adaption. I.INTRODUCTION In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a mathematical power tool that is playing an increasingly important role in computer graphics as we include sensing of the real world in our systems. I.1About Kalman Filter: Theoretically, the Kalman Filter is an estimator for what is called the linear quadratic problem, which focuses on estimating the instantaneous state of a linear dynamic system perturbed by white noise. Statistically, this estimator is optimal with respect to any quadratic function of estimation errors. Time Update equations and Measurement Update equations. The time update equations can also be thought of as predictor equations, while the measurement update equations can be thought of as corrector equations. This recursive nature is one of the very appealing features of the Kalman filter it makes practical implementations much more feasible than (for example) an implementation of a Wiener filter which is designed to operate on all of the data directly for each estimate. Instead, the Kalman filter recursively conditions the current estimate on all of the past measurements. Once again, notice how the time update equations in fig 1 project its state, x and covariance, p k estimates forward from time step k-1 to step k. Initial conditions for the filter are discussed in the earlier section. I.2. Probabilistic Origins of the Filter: This section is a short section describing the justification as mentioned in the previous section for this justification is rooted in the probability of a priori estimate conditioned on all prior z k measurements (Bayes rule). For now it is suffice to point out that the Kalman filter maintains the first two moments of the state distribution, I.3 Discrete Algorithm: This section will begin with a broad overview, covering the "high-level" operation of one form of the discrete Kalman filter. After presenting this highlevel view, I will narrow the focus to the specific equations and their use in this discrete version of the filter. Firstly, it the posteriori state estimate of reflects the mean (the first moment) of the state distribution it is normally distributed if the conditions are met. The posteriori estimate error covariance of reflects the variance of the state distribution estimates a process by using a form of feedback control loop whereby the filter estimates the process state at some time and then obtains feedback in the form of (noisy) measurements. As such, these equations for the Kalman filter fall into two groups: Fig: 1.1 Measurement updates equation I.4 Filter Parameters and Tuning: The measurement noise covariance R is usually measured before the operation of the filter when it comes to the actual implementation of Kalman filter. Generally, measuring the measurement noise covariance R is practically possible due to the fact that the necessary requirement to measure the process noise covariance Q (while operating the filter), therefore it should be possible to take some off-line sample measurements in order to determine the variance of the measurement noise. As for determining of the process noise covariance Q, it will be generally more difficult. This is due to the reason that the process to be estimated is unable to be directly observed. Sometimes a relatively simple (poor) process model can produce acceptable results if one "injects" enough uncertainty into the process via the selection of Q The vision and sensor fusion techniques described in the previous chapters provide a measurement of target locations for each image

2 frame. In its raw form, this information is of limited use for camera control because it is imprecise due to measurement noise; it may include false-positive detections of people; and it provides no association between new measurements and previous target locations. I.5 Coordinate Transformation: The coordinates measured by the camera system must be transformed into Cartesian coordinates for tracking and data association. This is important for measuring the distance between targets and measurements, and for using state estimation techniques based on Netwon's laws of motion. Each pixel location in a camera image represents a different azimuth and elevation with respect to the camera orientation. Adding these angles to the camera's pan and tilt position defines a line through the real world. I.6 Data Association: For the tracking system to perform properly, the most likely measured potential target location should be used to update the target's state estimator. This is generally known as the data association problem. The probability of the given measurement being correct is a distance function between the predicted state of the target and the measured state. One may measure the color histogram difference, H(I,M), between each new measured object and the previously detected target data using Swain and Ballard's histogram intersection technique. In the above equation Ij is the jth color histogram bin of an object in the current frame, and Mj is the jth color bin of a tracked object in the previous frame. In order to obtain a distance metric for data association that incorporates both the histogram intersection and position difference, we calculate the joint probability of these two measurements. This probability may be incorporated into association/tracking algorithms such as nearest-neighbour, joint probabilistic data association, and multi-hypothesis track splitting. For person-tracking, the color/position metric has been found to be good enough for a simple winner-take-all nearest-neighbour data association scheme to suffice. If one assumes equal prior probabilities for all Xi,j, one may simplify the nearest neighbour decision process to one that seeks to maximize the value Fy(Yi,j)Fz(Zi,j). For this project, a simple nearestneighbour assignment policy was used for target measurement updates.in target tracking applications, the most popular methods for updating target assumes that the dynamics of the target can be modelled, and that noise affecting the target dynamics and sensor data is stationary and zero mean The objective of using this model to remove measurement noise with a Kalman filter/state estimator. This optimal solution incorporates the target model, state disturbances, and estimates of sensor noise variance. Figure 2.2 shows the model of the target including the state disturbance noise, W(k) and the sensor noise, V(k). I.7 Estimation Update: This Kalman filter is based on a current observer state estimator that provides an estimate, q(k), of the current system state x(k), as well as a prediction,, of the state at sample k+1. From [120], the filter equations are Kalman filter design develops the observer sensor feedback matrix G(k) such that the values of G(k) lead to an optimal estimator, where the expected values of the squared estimation errors are minimized. The determination of G(k) is recursive, and must be calculated at run-time for this application since the sensor covariance Rv(k) changes depending on target position. From the following equations are used to find G(k) Here M(k) is the covariance of the prediction errors, P(k) is the covariance of the estimation errors, and B1 = B. When a new target is detected and its tracked path is initialized, the values of q(k) and q~(k) are set equal to the current sensor measurement and M(k) is set equal to the identity matrix. If the measurement error for each dimension of movement (x, y, and z) were statistically independent, then a separate Kalman filter state estimator could be used for each dimension. For this reason, the three dimensions must be combined in the vector, increasing the size of the vectors and matrices that make up the filter. The model of human motion dynamics and in Cartesian coordinates provides the basis for filtering and smoothing the sensor data. Target position data may then be used for camera control or for intelligent room applications. However, question of which target to follow and how to look for targets still remains. Target tracking is often complicated by the measurement noise. The noise must be filtered out in order to predict the true path of a moving target. In this study of linear filtering, the Kalman filter, a recursive linear filtering model, was used to estimate tracks. There are two types of noise; the measurement noise is caused by inaccuracies in the tracking device, and state noise is caused by turbulence or human error and other environmental factors. Kalman described his new approach to linear filtering, a series of recursive equations that seek to minimize error by decreasing the covariance, increasing accuracy of the filter s prediction as each position coordinate is provided by target trackers such as radars. The Kalman filter is a variant of Bayesian filters. Bayesian filters are utilized for their excellent ability to hone in on the true track of the target as more noisy input data is supplied. However, the Kalman Filter is used in most modern target tracking systems because of its computational efficiency. First of all, the filter computes without storing past data. This simplicity allows a single personal computer to track upwards of thousands of targets at once. The recursive formulas produce more confident predictions, valuing future points less heavily as compared to the experience gained (abstractly called the Kalman Gain ) from successfully decreasing the magnitude of error in its predictions. Additionally, the filter adapts to varying measurement time intervals and is able to provide error estimates.

3 Fig: 1. 2 Model of target Dynamics I.8 The kalman Filter: The Kalman Filter is a set of equations that provides a method to estimate the state of a process. This series of equations consist of two steps: Predict and Correct. These two steps of predict and correct are used recursively. In real time, the raw data would be added to the filter during the correct step. After the current data points are received, the correct step is used to estimate the state and its variances. The projected positions of the two planes were updated. Upon reaching two consecutive alerts, the program re-initializes the filter with a new set of starting parameters and conditions. The notation of means given the state of. is the prediction of the X vector at time step k+1 given the information known at time step k. Equation projects the next predicted state given the previous state. The P matrix in Equation is the state covariance matrix representing the covariance of the position coordinates and the covariance of the velocity vectors. The Q matrix in Equation is a covariance matrix of the process noise. Equation updates the state covariance matrix based on the Kalman gain and the predicted state covariance matrix. is an identity matrix. Note that the updated state covariance matrix can never be larger than the previous state covariance matrix, which means that the estimate gets more accurate. However, simply comparing the distance between the predicted point and the measured point is insufficient due to state uncertainty, as described in our state covariance matrix. Thus, in order to find the relative distance from the two points, distance must be measured in terms of relative probability, in units of standard deviations. At each time-step, we can calculate the residual in our correct procedure, enabling our filter to effectively detect sharp maneuvers. Our implementation re-initializes the filter upon detecting two consecutive data points with residuals over four standard deviations, which provides a certainty better than one in a thousand. Fig 1.3 Path of Maneuvering Target II TARGET INTERCEPTION: Though the Kalman filter can be used to predict the path of a moving target, the applications of the filter can also be useful in calculating the path of interception. To do so requires first calculating the position and velocity of the target, projecting its path, and then computing the angle of interception for the designated course. As shown below in Figure 2.1, the interceptor successfully follows the interception path of the target, ending with a successful interception. Fig: 2.1 Paths of Interceptor and Target II.1 tracking multiple targets: The Kalman Filter can be used to track the position of multiple targets. To do this, an object-oriented approach was used: a plane class was created containing the iterate method and all the data associated with the plane. Two instances of the plane class were created upon running the program, one for each target being tracked. The main class read in the data and called the iterate method in each of the plane instances, passing the data to them as parameters. The new data points were then retrieved from both planes and printed out. II.2 Collision Avoidance Systems: one of the applications of multiple-target tracking is for collision avoidance systems. Planes flying at high speeds often cannot see each other in time to communicate and maneuver to avoid a collision. Thus, tracking the position of planes and alerting them in advance when their trajectories would lead to possible future collisions is vital in air traffic control. The projected positions of the two planes were updated. Equation was then used to check if the updated distance was less than 1 mile. If so, a message was sent to both pilots alerting them of the projected point of collision. If the new projected distance was found to be greater than the previous projected distance, meaning the planes were travelling away from each other, the loop ended, as the pilots were not in danger. Otherwise, the positions were updated once more using the above equations. II.3Kalman Filtering for Motion Prediction: Kalman filtering is a technique for temporal association and integration in tracking Based on a second order kinematic model; we can model the affine motion vector evolution as a linear system with sk as the state vector describing the affine motion vector, its first derivative and its second derivative, vk as the model noise, ok as the observation (affine motion) vector and X k as the observation noise. State matrix Aand observation matrix H come from the second order kinematic model. The result will input this Kalman filter, which will output a motion prediction result from update of the state vector. This allows the filter to integrate over time the temporal information of the tracked object]. Data association is an important factor in multiple target tracking (MTT) system. An observation is assigned to the target for maintenance of the true trajectory. Nearest neighbour (NN) is the simplest one among the different data

4 assignment techniques. We propose tracking algorithm which uses genetic algorithm for data association and it tracks multiple maneuvering and nonmaneuvering targets simultaneously in the presence of dense clutter using multiple filter bank (MFB). In real world application target may be maneuvering and non-maneuvering and there is no apriori knowledge about its movement. This makes the model selection for tracking the target difficult. Along with tracking an observation is to be assigned to track for state update and predict where data assignment plays a major role for maintaining true trajectory in the presence of dense clutter. One of the important characterstic of kalman fitler is it suits for only linear dynamical systems that is the reason it is called a linear quadratic estimation algorithm(lde). If the system is nonlinear is the question that arises in terms of the usage, since usage of nonlinear systems are responsible for noise and many other disturbances an extension for kalman filter is obtained called as extended kalman filter which suits for even for nonlinear dynamical systems. The use of two channels (dark and bright images) for mean shift tracking as well as the experimental determination of the optimal window size and quantization level for mean shift tracking further enhance the performance of our technique. By experimental results, we have demonstrated that the proposed method dramatically improves the robustness and accuracy of eye tracking. II.4 The kalman Model:The Kalman Filter is modeled by utilizing a linear algebra approach using matrices Equation shows Xk+1 that is a matrix representing the updated state and Xk is a vector representing the current state, which contains position and velocity vectors. Matrix is a state transformation matrix that relates the state of one time step to the next. This recursive process includes the use of t to update the new location and velocity of the target. The variable k represents the time step. In our case, Φ is represented by this 4X4 matrix in Equation The qk vector is the process noise. In other words, it is the noise due to uncertainty in the transition. can be described as the error caused by the inaccuracy of our instruments. II.5 Types of sensors used: Locations and orientations of the various sensor types with respect to the system to be estimated. Allowable noise characteristics of the sensors. Pre-filtering methods for smoothing sensor noise. Data sampling rates for the various sensor types and the level of model simplification for reducing implementation requirements. A system designer is able to assign an error budget to subsystems of an estimation system, which this is allowed by the analytical capability of the Kalman filter formalism. Moreover, it can trade off the budget allocations to optimize cost or other measures of performance while achieving a required level of estimation accuracy. Target tracking systems has many applications, like surveillance, security, smart spaces, pervasive computing, and human-machine interfaces to name a few. In these applications the targets are either human bodies, or vehicles. The common property of these targets is that sooner or later they exhibit some movement which is evidence that distinguishes them from the background and identifies them as foreground targets. Fig:2.2 Liner filter characteristics A linear Kalman filter is employed to predict the estimated affine motion parameters based on a second order kinematic model as shown in fig 2.2. A great variety of visual tracking algorithms have been proposed, they can be classified roughly into two categories. The first is the feature-based method A typical instance in this category estimates the 3D pose of a target object to fit into the image features such as contours given a 3D geometric model of the object. The second is the region-based method. Compared to the feature-based methods the regionbased methods are more robust, insensitive to small partial occlusions. The region based methods can be subdivided into two groups: the view-based method and the parametric method. The view based method finds the best match of a region in a search area with a reference template. The parametric method assumes a parametric model of changes in the target image and computes optimal fitting of the model to pixel data in a region. III RESULTS COMPARISION: We have studied about kalman filter and results also compared with weiner filter as shown in table. The matrix Yk in Equation is a representation of the current measurement in a 2X1matrix. The H matrix is a transformation matrix Xk s 4X1 into 2X1 To do this, the H matrix must be 2x4. The rk vector is a 2X1 measurement noise vector. Measurement noise

5 Fig 3.1 position tracking face while walking Fig 3.2 tracking a pattern walking IV ADVANTAGES OF KALMAN FILTER Below are some advantages of the Kalman filter, comparing with another famous filter known as the Wiener Filter, which this filter was popular before the introduction of Kalman filter. The information below is obtained from. I. The Kalman filter algorithm is implementable on a digital computer, which this was replaced by analog circuitry for estimation and control when Kalman filter was first introduced. This implementation may be slower compared to analog filters of Wiener; however it is capable of much greater accuracy. II. Stationary properties of the Kalman filter are not required for the deterministic dynamics or random processes. Many applications of importance include non stationary stochastic III. processes. The Kalman filter is compatible with statespace formulation of optimal controllers for dynamic systems. It proves useful towards the 2 properties of estimation and control for these systems. a) The Kalman filter requires less additional mathematical preparation to learn for the modern control engineering student, compared to the Wiener filter. b) Necessary information for mathematically sound, statistically-based decision methods for detecting and rejecting anomalous measurements are provided through the use of Kalman filter. IV.1 Applications of Kalman filter: Although, the applications of Kalman filtering encompass many fields, its use as a tool is mainly for two purposes: estimation and performance analysis of estimators. Since the Kalman filter uses a complete description of the probability of its estimation errors in determining the optimal filtering gains, this probability distribution may be used in assessing its performance as a function of the design parameters of the following estimation systems: V CONCLUSION: Our project titled Target Tracking System Using Kalman Filter is performed and the results are computed. Kalman filter provides 95%efficeint output even in the noisy environment.in this thesis we have studied several estimation and data association methods for target tracking. A general method of increasing the sampling frequency of a vision sensor by using a predictive Kalman filter and partial window imaging has been introduced and has been demonstrated to work effectively. The method reduces the acquisition and processing time of an image. The acquisition time is reduced by a larger percentage than the processing time and so the image processing is the bottle neck in reducing the sampling frequency. Two processing methods were implemented. This system was not as robust but it does provide a further increase in sampling frequency. VI FUTURE SCOPE: One of the important characteristic of kalman filter is it suits for only linear dynamical systems that is the reason it is called a linear quadratic estimation algorithm (LDE).If the system is nonlinear is the question that arises in terms of the usage, since usage of nonlinear systems are responsible for noise and many other disturbances an extension for kalman filter is obtained called as extended kalman filter which suits for even for nonlinear dynamical systems. REFERENCES: 1. Havran, V.: Heuristic Ray Shooting Algorithms. PhD thesis, Faculty of Electrical Engineering, Czech Technical University in Prague (2001) 2. 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