An Overview of Recent Developments in Target Tracking, in the Active Airbone Sonar Networks Domain

Francis Martineri and Sebastian Brisson, 1993

ABSTRACT

1. Address Target Tracking problem from the measurements made on a passive sonars activated by an active sonars (multistatic networks)
2. recalls on principles of classic tracking approaches in the specific context of distributed sensors measuring range, doppler, and azimuth
3. Include improvements on simultaneous tracking of a target and calibration of the sensor field
4. Introduce improvement on 'recently introduced approach in target tracking' and target motion analysis which is based on a non-deterministic modelisation of the target evolution.
   
5. Method based on Hidden Markov Modelling leads to multiple and maneuvering target tracking with few Hypotheses

CASE INTRODUCTION

• The increase in level of difficulties in detection and localisation from basic sensor due to low level of submarine radiated noise, develop interest in distributed sonar networks.
• Network consist of active sonar acting as a transmitter/receiver, and N passive sensors acting as receiver
• Sensors and targets assume to be at the same plane
• Targets are characterised by position and speed in Cartesian coordinates
• X(t) = (x(t),y(t),vx(t),vy(t))
• Sensor positions are known Xs = ( (xs1,ys1), ... , (xsN,ysN)
• False alarm assumed uniform
• Measurements carried in discrete time: a signal emitted by the active sensor will give rise to detection on the passive sensor after it has impinged the targets.
• The range, doppler, or azimuth measurements corresponding to a detection on sensor are extracted. (equations given)
  

CLASSIC APPROACHES IN TRACKING

• Come from a classic data association and tracking method and based on 2 steps

1. Extracting and Data Association
• Extracting the measurement corresponding to each single target received from the sensors. Usually Extraction perform by track formation at the sensor level. (Based on the block diagram of track extraction, I presume they use a centralized fusion techniques)
  
• Track to track association where tracks from different sensors corresponding to the same targets have to be associated.
  
• often perform manually by an operator. However at this point automatic algorithms based on Generalized Likelihood Ratio Test have been developed and validated
2. Target Parameter Estimate

• M = M ( X(t), Xs ) + B where
  
• M is a global vector of measure corresponding to the same target
• M ( X(t), Xs ) composed of measurements at the various time instant computed according the range, doppler, or azimuth equations.
• B is a zero mean Gaussian noise vector of known covariance ∑B.
• Assuming target motion model in known (in most cases rectilinear unaccelerated), the target characteristic are next derived from the measurement vector M with the help of maximum likelihood estimators (MLE)
• MLE are based on the identification of the target characteristic which minimize a least square criterion on the measurements. In this case is as follow

• J = [M-M(X(t),Xs),Xs]^T∙∑B∙[M-M(X(t),Xs)] + [Xs-Xap]^T∙∑ap∙[Xs-Xap]
• Xap represents supposed sensor position
• ∑ap represents the covariance of this uncertainty

• J take into account the imperfect knowledge of the sonar position, therefore calibration of the network can be perform simultaneously to the target characteristic estimation by considering Xs as an unknown and Xap as a parameter.
• Classic MLE - Gaussian Newton (GN) algorithm and EKF are extended to this case with few modification.
• Difficulties occur for EKF when the initial parameter is to be set.
• Results of measuring range and azimuth for both methods are provided.
• EKF able to track maneuvering target provided the target noise model covariance is well chosen
• GN algorithm is significantly degraded due to the fact that it is implicitly non adaptive
• Accurate calibration is performed jointly with an unbiased target motion estimation provided at least one sensor position is exactly known and azimuth measurements are made by at least one sensor.
• Classic approach has limitation on maneuvering targets
  

THE DIAMANT ALGORITHM

• DIAMANT ( DIscrete Association, Motion ANalysis and Tracking) differs compare to classic sonar tracking method.
• Use Hidden Markov Chain method

Note: No further reading has been made. (seem irrelevant at a.t.m)

Overview of Problems and Techniques in Target Tracking

Wolfgang Koch

SENSOR SYSTEM

• Sensing hardware of sensor or sensor networks collecting information on time varying quantities (waveform). This information is a series of sensor data set (also called scans or data frames) that received at discrete instants of time.
  
• Via a detector device, the data go through a data rate reduction process and forwarded for signal processing.
  
• This data set is used to estimate the state of a stochastically driven dynamical system. Therefore the signal processing results in estimates of the waveform parameters and produced the final sensor reports (measured quantities) and become the input of tracking system

TRACKING SYSTEM

• Tracking results from the data association and estimation algorithm techniques (sensor data processing) which used to exploit efficiently the data from sensor resources and also to obtain information that not directly produce by the sensor reports.
• i.e: tracks mean estimate of state trajectories which statistically represent the quantities or object considered along with their temporal history.
• Sensor reports that can be associated to existing tracks are used for track maintenance
• While remaining reports that non-associated to any existing track are used to initiate new track or multiple frame track extraction.(track initiation)
  
• Both track initiation and track maintenance required a prior knowledge of the sensor performance, object characteristic and object environment. This prior knowledge available in the form of statistical modeling assumptions.
• Plot-to-track unit is important when dealing with multiple target tracking system
  
• Stored data (in Track File Storage) is extracted during track processing and used for track termination /conformation, object classification/identification, and track to track fusion (fusion of track representing identical information).
• Results are displayed through man-machined interface. Other purpose is for interaction function where available information on sensor, object of interest, and the environment can be specified, updated, or corrected by direct Human interaction or the track processor itself.

CHALLENGE

• High false return background. Sensor can't compress data
• Ambiguous correlation between new and existing track become a problem for closely-spaced moving object. Plus false return or unwanted object, identity of the individual object tracks might get lost
• Limited sensor resolution capability make the data association harder bcoz the closely-spaced object may continuously change from being resolved to unresolved and back again. Besides, sensor returns having poor quality, low SNR, or fading phenomena. Scan rate maybe low in certain application ex: long-range air surveillance.
• The underlying dynamics models are restricted to one particular sample out of several sets of alternatives. Sudden switches between the underlying dynamics models do occur and tracks can get lost in such critical situation.

BAYESIAN APPROACH

• Most mathematical techniques of tracking system essentially make use of Bayes' Rule
• Tracking algorithm is an iterative updating scheme for conditional probability densities that describe the object states given both the accumulated sensor data and all available prior information
• Optimal state estimators may be derived related to various risk function provided that filtering, density iteration, has been done correctly.
• Generalization of standard smoothing algorithms, retrodiction, provides a backwards iteration scheme for calculating the probability densities of the past objects states given all information accumulated up to the current scan.
• Track maintenance and data acquisition are closely related
• exist feedback of tracking information to the sensor system
• Tracking algorithm must be initiated by appropriately chosen prior densities.
  

SENSOR FUSION ASPECTS

• Network of homogeneous or heterogeneous sensors are preferred compare to single sensors
• Networks' advantages:
  
• Total coverage of suitably distributed sensors are much larger
• Low-cost sensor network
• Redundancy of overlapping fields of view increased data rates and observation under several aspect
• Multiple-sited networks provide that is on principle not available by corresponding single-sited sensor
• More robust against failure or destructive of individual components
• Centralised data fusion: sensor reports are transmitted to a processing centre without significant delay.
  
• Issue of single-sited sensor or sensor networks is irrelevant.
• Practical realization is difficult bcoz of limited data links between the sensors and the fusion centre, synchronisation problems, or misalignment errors.
• Decentralised fusion architecture or hybrid solution is proposed.
• Data of the sensor system are pre-processed at their individual sites
• Fusion centre receives higher-level information
• i.e: sensor-individual track which are to be fused with other tracks resulting in a central track.

EXPERIMENTAL EXAMPLE

• Real radar data from single-sited radar.
• Data compared using IMM-MHT Retroiction and MMSE-MHT Retrodiction
• IMM-MHT perform better especially in a verysmooth condition (accurate speed and heading information)
• Both filtering and retrodiction produce better results when using model histories more than length n = 1 (delay the frame for MMES-MHT)
  

Maneuvering Target Tracking by Using Particle Filter [N. Ikoma et al.]

Hope:A brighter light at the end of my reading. please ya Allah... the brighter the better

Simulation Based

1. Dynamics of the maneuvering target tracking model, for continuous model, is defined according to Singer 1970.
   
1. Gaussian white noise process is used as the input for system noise vector in the continuous time model.
2. After discretized, Cauchy distribution, as the typical heavy-tailed distribution, is proposed for the system noise to cater for manuvering target with an abrupt change of its acceleration.
3. Non-linear Observation model is used to represent the radar measurement process.
   
2. To estimate the non-Gaussian nonlinear state space model defined above, particle filtering (SMC) is considered as the most effective method compared to Gaussian-sum approximation and numerical representation.
1. Monte Carlo Filter (MCF) method is employed among other SMC methods, which are bootstrap and condensation (conditional density propagation).
2. State Space model: use the subset of the general class of state space reperesentation estimated byMCF.same as space model define aboved.
   
3. State Estimation: Calculate the conditional distribution from the given observation. 3 Steps: prediction, filtering, and smoothing with fixed lag.
4. MCF used an approximation of non-Gaussian distribution by particles to defined the state approximation.
   
5. Filtering procedure: Find the prediction value, then calculte the likelihood of each particle, then resample the particle.
6. Smoothing: By augmenting the particles where invoving the process of integrating past and current time (prediction and filtering) values.
7. Likelihood:The 'hyperparameter', that consist of covariance matrices of observation noise,R and system noice, Q, is determined by maximizing the log-likelihood. This 'hyperparameter' governs the performance of state estimation where if Q > R, the observation value is more reliable and state variables change quickly. While if R > Q, the state variables evolve smoothly and the observation value can be ignored.
   
3. Simulation:
1. Simulate with the assupmtion of small observation noise.
2. The simulation shows that Cauchy-MCF model can quickly follow the sudden change while Gaussian-EKF model has delayed response.
4. Future work:
1. Larger noise measurement
2. Application to real data
3. High SNR case is a real challange b'coz acceleration is much sensitive to the noise in position.
   

Object Tracking: A Survey [A. Yilmaz et al]

Object Tracking Method

We have point tracking method , kernel tracking methol, and silhouette tracking method.

Point Tracking Method

Deterministic : constrain the correspondence problem using qualitative motion heuristic
[Veenman et al. 2001]

• The combination of the constrin used are as follow:

• Proximity - constant background
• Maximum velocity - defines maximum displacement r and the circular area form from the obtained radius, r.
• Small velocity change
• Common motion - the multiple points that represent the object have similar movement.
• Rigidity - assume the object in 3D is rigid therefore the distance at time t-2, t-1, and t are the same. (confirm again)
• Proximal uniformity - combination of proximity and small velocity change.

• History

• 1987 Sethi nad Jain solve the correspondance using greedy approach based on the proximity and rigidity constrain. The algorithm consider two consecutive frame and is initialized by the nearest neighbor criterion. However this algorithm can'thandle occlusions, entries or exit.
• 1990 Salari and Sethi improve the algorithm by first establishing correspondence for the detectedpoints and then extending the tracking of the missing objects by adding a number of hypothetical points
• 1991 Rangarajan and Shah proposed greedy method using proximal uniformity constrain. Initial correxpondences are ontained by computing optical flow in the first two frames. The algorithm can't handle exit and entries. For occlusions, the problem is solved by establishing the correspondence for the detected object in the current frame and the position of the remaining object is predicted based on the constant velocity assupmtion.
• 1997 Intille et al.modified Rangarajan and Shah [1991] for matching object centroids. Object detected using background subtraction. Exit and entries handle explicitly by eximining the image region looking for a door to detect exit or entries
• 2001 Veenman et al. extend both Sethi and Jain [1987] and Rangarajan and Shah [1991] works by introducing the common motion constrain for correspondence.The algorith is initialized by generating the initial tracks using a two-pass algorithm, and cost function is minimized by Hungarian assignment algorithm in two consecutive frames. can handle occlusion and misdetection but not exit and entries.
• 2003 Shafique and Shah propose multiframe approach to preserve temporal coherency of the speed and position.Fin the best unique path for each point. [x clear sgt]

Statistical Method: take the object measurements and uncertainties into account to establish
correspondence.

Use space state approach to model the object properties such as position, velocity, and acceleration. Measurements obtained by detection mechanism which usually consist of object position in the image

Single Object State Estimation

• Kalman Filter: used to estimate the stae of linear system and have Gaussian distribution. Compose of prediction and correction steps.

• Prediction step uses the state model to predict the new state of the variables
• Correction step uses the current obzervation to update the object's state
• Matlab Toolbox: KalmanSrc

• Particle Filter: used for non Gaussian distribution [Tanizaki 1987]

• The conditional state density at time t is represented by a set of sampling particles with weight (sampling probability).
• The weight define the importance of a sample (observation frequency) [Isard and Blake 1998]
• The common sampling scheme is importance sampling

• Selection: Select N random Sample
• Prediction: Generate new sample with zero mean Gaussian Error and non-negative function
• Correction: Weight corresponding to the new sample are computed using the measurement equation which can be modeled as a Gaussian density

• Particle filter -based tracker is initialized by either using the first measurements or by training the system using sample sequences.
• maltab toolbox available at ParticleFlSrc.

Multiobject Data Association and State Estimation

Requires a joiny solution of data association and state estimation problem.
Before applying Kalman or Particle Filter one must deterministicallyassociate the most likely measurement for a particular object to that object's state.

• Joint Probability Data Association Filter (JPDAF)
• Multiple Hypothesis Tracking (MHT)

Note: will continue once have better undestanding