# cumulativeTruthMetrics

Cumulative metrics for recent truths

## Syntax

``metricsTable = cumulativeTruthMetrics(errorMetrics)``

## Description

````metricsTable = cumulativeTruthMetrics(errorMetrics)` returns a table of cumulative metrics, `metricsTable`, for every truth identifier provided in the most recent update.```

## Examples

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Examine the assignments and errors for a system tracking two targets.

First, load the stored track data.

`load trackmetricex tracklog truthlog`

Create objects to analyze assignment and error metrics.

```tam = trackAssignmentMetrics; tem = trackErrorMetrics;```

Create the output variables.

```posRMSE = zeros(numel(tracklog),1); velRMSE = zeros(numel(tracklog),1); posANEES = zeros(numel(tracklog),1); velANEES = zeros(numel(tracklog),1);```

Loop over all tracks to:

• Extract the tracks and ground truth at the i th tracker update.

• Analyze and retrieve the current track-to-truth assignment.

• Analyze instantaneous error metrics over all tracks and truths.

```for i=1:numel(tracklog) tracks = tracklog{i}; truths = truthlog{i}; [trackAM,truthAM] = tam(tracks, truths); [trackIDs,truthIDs] = currentAssignment(tam); [posRMSE(i),velRMSE(i),posANEES(i),velANEES(i)] = ... tem(tracks,trackIDs,truths,truthIDs); end```

Show the track metrics table.

`trackMetricsTable(tam)`
```ans=4×15 table TrackID AssignedTruthID Surviving TotalLength DeletionStatus DeletionLength DivergenceStatus DivergenceCount DivergenceLength RedundancyStatus RedundancyCount RedundancyLength FalseTrackStatus FalseTrackLength SwapCount _______ _______________ _________ ___________ ______________ ______________ ________________ _______________ ________________ ________________ _______________ ________________ ________________ ________________ _________ 1 NaN false 1120 false 0 false 3 3 false 0 0 false 0 0 2 NaN false 1736 false 0 false 8 88 false 0 0 false 28 3 6 3 true 1138 false 0 false 4 314 false 1 28 false 0 2 8 2 true 662 false 0 false 2 29 false 1 169 false 28 0 ```

Show the truth metrics table.

`truthMetricsTable(tam)`
```ans=2×10 table TruthID AssociatedTrackID DeletionStatus TotalLength BreakStatus BreakCount BreakLength InCoverageArea EstablishmentStatus EstablishmentLength _______ _________________ ______________ ___________ ___________ __________ ___________ ______________ ___________________ ___________________ 2 8 false 2678 false 4 168 true true 56 3 6 false 2678 false 3 645 true true 84 ```

Plot the RMSE and ANEES error metrics.

```subplot(2,2,1) plot(posRMSE) title('Position Error') xlabel('tracker update') ylabel('RMSE (m)') subplot(2,2,2) plot(velRMSE) title('Velocity Error') xlabel('tracker update') ylabel('RMSE (m/s)') subplot(2,2,3) plot(posANEES) title('Position Error') xlabel('tracker update') ylabel('ANEES') subplot(2,2,4) plot(velANEES) title('Velocity Error') xlabel('tracker update') ylabel('ANEES')```

Show the current error metrics for each individual recorded track.

`currentTrackMetrics(tem)`
```ans=2×5 table TrackID posRMS velRMS posANEES velANEES _______ ______ ______ ________ ________ 6 44.712 20.988 0.05974 0.31325 8 129.26 12.739 1.6745 0.2453 ```

Show the current error metrics for each individual recorded truth object.

`currentTruthMetrics(tem)`
```ans=2×5 table TruthID posRMS velRMS posANEES velANEES _______ ______ ______ ________ ________ 2 129.26 12.739 1.6745 0.2453 3 44.712 20.988 0.05974 0.31325 ```

Show the cumulative error metrics for each individual recorded track.

`cumulativeTrackMetrics(tem)`
```ans=4×5 table TrackID posRMS velRMS posANEES velANEES _______ ______ ______ ________ ________ 1 117.69 43.951 0.58338 0.44127 2 129.7 42.8 0.81094 0.42509 6 371.35 87.083 4.5208 1.6952 8 130.45 53.914 1.0448 0.44813 ```

Show the cumulative error metrics for each individual recorded truth object.

`cumulativeTruthMetrics(tem)`
```ans=2×5 table TruthID posRMS velRMS posANEES velANEES _______ ______ ______ ________ ________ 2 258.21 65.078 2.2514 0.93359 3 134.41 48.253 0.96314 0.49183 ```

## Input Arguments

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Error metrics object, specified as a `trackErrorMetrics` System object™.

## Output Arguments

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Truth error metrics, returned as a table.

• When you set the `ErrorFunctionFormat` property of the input error metrics object to `'built-in'`, the table columns depend on the setting of the `MotionModel` property.

 Motion Model Table Columns `'constvel'` `posRMSE`, `velRMSE`, `posANEES`, `velANEES` `'constacc'` `posRMSE`, `velRMSE`, `accRMSE`, `posANEES`, `velANEES`, `accANEES` `'constturn'` `posRMSE`, `velRMSE`, `yawRateRMSE`, `posANEES`, `velANEES`, `yawRateANEES`

RMSE and ANEES denote root mean squared error and average normalized estimation error squared of a truth trajectory for the entire tracking scenario time history. Since a truth trajectory can associate with multiple tracks at a time step, the calculation of cumulative RMSE and ANEES values is each separated into two steps. For example, in the first step of the position RMSE value calculation, the function first calculates the RMSE value at a given time step t as:

`${S}_{t}=\sum _{k=1}^{{K}_{t}}‖\Delta {p}_{t,k}{‖}^{2}$`

where Kt is the number of tracks associated with the truth at time step t, and

`$\Delta {p}_{t,k}={p}_{track,t,k}-{p}_{truth,t}$`

is the position difference between the position of kth associated track and the position of the truth at time step t. In the second step, the St values of all the time steps (t = 1,2,…,N) are summed and averaged over the total number of associated tracks (denoted by R) to obtained the cumulative position RMSE value as:

`$\text{posRMSE}=\sqrt{\frac{1}{\sum _{t=1}^{N}{K}_{t}}\sum _{t=1}^{N}\sum _{k=1}^{{K}_{t}}‖\Delta {p}_{t,k}{‖}^{2}}$`

where the total number of associated tracks, R, is given by

`$R=\sum _{t=1}^{N}{K}_{t}.$`

The cumulative RMSE values for other states (`vel`, `pos`, `acc`, and `yawRate`) are defined similarly.

The calculation of the cumulative position ANEES value, `posANEES`, for a truth trajectory can also be separated into two steps. In the first step, the function calculates the ANEES value at a given time step t as:

`${Q}_{t}=\sum _{k=1}^{{K}_{t}}\Delta {p}_{t,k}{}^{T}{C}_{p,t,k}^{-1}\Delta {p}_{t,k}$`

where Cp,t,k is the covariance corresponding to the position of the kth associated track at time step t. In the second step, the Qt values for all the time steps (t = 1,2,…,N) are summed and averaged over the total number of associated tracks (denoted by R) to obtained the cumulative position ANEES value as:

`$posANEES=\frac{1}{\sum _{t=1}^{N}{K}_{t}}\sum _{t=1}^{N}\sum _{k=1}^{{K}_{t}}\Delta {p}_{t,k}{}^{T}{C}_{p,t,k}^{-1}\Delta {p}_{t,k}$`

The cumulative ANEES values for other states (`vel`, `pos`, `acc`, and `yawRate`) are defined similarly.

• When you set the `ErrorFunctionFormat` property to `'custom'`, the table contains the arithmetically averaged values of the custom metrics output from the error function.

Introduced in R2018b