Misc. Information on Multi-Target Tracking: Algorithm Comparisons

Any information on IMM-SD?

• Theoretically IMM-SD and IMM-MHT should provide equivalent performance in tracking
  • Can be considered as an implementation of IMM-MHT
• However, simulation shows that IMM-SD performs better.

How can IMM-SD achieve better performance than IMM-MHT?

• IMM-SD finds the global optimal where IMM-MHT finds current optimum (as I could understand, however, further verification is required)
• Global optimum through the enumeration of current IMM-MHT

What else does IMM-SD use to find the global optimum?

• Lagrange relaxation method is used to get approximate optimal global hypothesis

References:

Academic Press Library in Signal Processing: Communications and Radar Signals

What is IMM-JIPDA?

• Interactive multiple model – Joint integrated Probabilistic Data Association

What are some other related algorithms to IMM-JIPDA?

• IMM-IPDA, IMM-LMIPDA, PDA is the common concept here

What is the common approach that all of the above algorithms use?

• Integrates IMM to PDA
• Each of them models a posterior state estimation – PDF using a single Gaussian pdf.
• Recursively updates the probability of target existence – IMM style
  • Can be used for false track discrimination

Does IMM-PDA track multiple targets?

• No, it is to track one target

What are the multi-target tracking algorithms among the names mentioned before?

• IMM-JIPDA, IMM-LMIPDA

How does IMM-JIPDA work?

• Calculates a posterior probabilities to all measurements to track allocations
• The number of measurement to track allocations grows exponentially
• Hence, IMM-JIPDA can be used for small number of crossing targets
  • Also in low clutter measurement density

How does IMM-LMIPDA work?

• Integrates linear multi-target method methods with IMM-IPDA
• When one track is updated with LM
  • The other tracks modulate the clutter measurement density
  • And are subsequently ignored

  References:

  A research paper. I could not locate the paper at this time. Will update, if I come across again

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Performance Measurement Metrics for Target (Aeroplanes, People) Tracking

By Sayed Ahmed

Let’s see, you want to track the aeroplanes in the sky using some radar and tracking algorithms. You have written simulation software for that. How will you measure that your software and algorithm is doing a great job. Even in real life, how will you know that your aero plane tracking is working well?

You can define some metrics for that i.e. to measure the performance.

T: Tracks : your decision/finding of the aero plane trajectory

L: Truths : The actual trajectory of the aero planes

M: Measures: your radar measurements

What is the general performance metric? What does it mean?

• p = g (M, L, T )

What are performance categories?

• Sensor Related: Independent of tracking result (Cramer Rao Lower Bound, Sensor Characteristics)
• Tracker Related : Tracking Result, Tracker Type, application of interest

What are the subdivisions of Tracker Dependent Metrics?

• Algorithm free: Based on Available Truth and Unavailable Truth (tracking and truth)
• Algorithm dependent : application dependent : For MHT, Dynamic Programming

Algorithm Free

• Cardinality Measures, based on some numbers
  • Count of Valid Tracks, false tracks, missed tracks, spurious tracks, completeness, broken tracks, swaps in tracks
• Time Measures: Performance based on Time Measures
  • Rate of false alarm, redundant track ratio, probability of detection, fragmentation rate, track latency
• Available Truths
  • Truth to Track Association -> association matrix at each scan and monte carlo run
  • Distance metric -> between truths and tracks

• Unavailable Truths:
  • Consistency of estimations -> To innovation of estimation
• Track Cardinality Measures
  • Track result and Truth Data
  • Valid Tracks: A target is assigned to one track, the target is not assigned to any other
  • Missed Tracks: If a target is not assigned to any tracks
  • False Tracks: No target is assigned to that track, only false alarms for example
  • Spurious Tracks: A track is assigned to multiple targets
  • Completeness: Number of valid tracks per truth
  • Swaps in Tracks: Track Crossings by targets. Count of track segments for each target over the total time
  • Broken Tracks: For each timestamp, there is no track assigned to the truth. Count B (l, m) : l_th truth, m_th run. Count of broken tracks

• Time Measures
  • Track Latency
    • Confirmation latency: does it mean target start to track confirmation
    • Termination Latency : does it mean target disappear to termination time
      • Timestamp i.e. time required
  • Rate of False Alarm:
    • Average number of false tracks per time
  • Track Probability of Detection
    • ( duration l th target is assigned to a valid track) / (l th track last scan time – l th track first scan time)
• Accuracy Measures
  • RMSE:
  • kth scan, l th target, M monte carlo run : Mth monte carlo

• Average Euclidean Error:
  • RMSE without Square Root, no square in the error
• Geometric Average Error:
  • Average Euclidean Error, just sum of log
• Harmonic: 1/(sum(1/error)/Cont_monte_carlo_run )

Sensor Metrics

• Probability of detection: within scenario, within FOV
• Coverage: Average, minimum, maximum
• Detection Gap: Average, Minimum, Maximum

Estimator Consistency

• Normalized Estimation Error Squared

Selected Metrics:

• Number of false tracks,
• track probability of detection,
• fragmentation rate,
• track latency (confirmation, deletion),
• swap count,
• RMSE

Score:

Un-normalized score, Normalized Score, Best = 1.00 , worst = 0.0

References:

A. A. Gorji ; R. Tharmarasa ; T. Kirubarajan: Performance measures for multiple target tracking problems

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What are the two types of tracking measures?

• Measures of performance (MOP)
• measures of effectiveness (MOE)

What are the two broad categories for MOP and MOE?

• Sensor-related
  • sensor characteristics
• Tracker-related
  • algorithm-free and algorithm-dependent

Give some information on Algorithm and Algorithm Free

• Algorithm Dependent
  • Track scores in the Multiple Hypothesis tracker
• Algorithm Free
  • Applicable to any tracker

What are different types of Tracker

• Single-hypothesis tracker
• Multiple-hypothesis tracker
• Probabilistic data association tracker

What is a great way to track maneuvering targets better?

• Estimate the motion of the targets by using various models

What are some objectives of target tracking? What are some of the concerns that tracking wants to answer?

“

• How many objects are there?
• Where are the objects located in space?
• What is their speed and direction of motion?
• How do the objects maneuver relative to each other?

“

What is one challenge in detecting/tracking closely separated targets?

• If the targets are in one sensor resolution cell, then only one target will be reported

What is the simplest choice for multi-target tracking?

• Single-hypothesis tracker like the GNN

How does interacting multiple-model (IMM) help in tracking?

• IMM can help to find the correct motion models of the targets

What can help with broken tracks?

• a multiple-hypothesis tracker (MHT)

How does MHT help with this?

• It can create and maintain multiple tracks for ambiguous situations and
• then resolves for ambiguity for better tracking
• MHT can improve the tracking when the targets turn (and go away from one another)

Compare JPDA and MHT

• MHT can be slower than JPDA
• JPDA can be thought of sub-optimal tracking where MHT is more optimal tracking
• MHT is usually slower

How does JPDA work and how is this different from MHT?

• “JPDA allows a single detection to be used for updating multiple tracks in its vicinity. Moreover, multiple detections can be clustered together with several tracks and update each of those tracks. This resolves the issue of the broken track.”

How is track status kept in JPDA for ambiguous regions?

• Confirmed

Can IMM be used with JPDA?

• Yes

How does IMM with JPDA help?

• Provides better before turn tracking
• the turn before the ambiguity region is better addressed

Are GNN and JPDA faster than MHT?

• Yes

Give an example when the Constant Velocity model does not give better tracking?

• Maneuvering targets
• How can that be improved
  • Use IMM

The algorithms as discussed which one is the best overall and in general

• JPDA

Still JPDA is faster and great, can there be a scenario where JPDA is not appropriate?

• Too much ambiguity where JPDA or GNN cannot give proper tracking

References: The fusion example TrackingCloselySpacedTargetsUnderAmbiguityExample in Matlab document

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Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
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