CRF-Filters: Discriminative Particle Filters for Sequential State Estimation

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Technology

Published on September 23, 2008

Author: cijat

Source: slideshare.net

Description

Seminar talk on the paper by Limketkai, Fox and Liao.

CRF-F: D P F  S S E B L, D F  L L Hannes Schulz University of Freiburg, ACS Feb 2008

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

Intro Transformation of Directed Model to CRF Application Experimental Results C: S E C D M A  S E ut−2 ut−1 xt−2 xt−1 xt ... ... n 1 2 n zt−1 1 zt 2 zt zt zt−1 zt−1 P (xt |u1:t −1 , z1:t ) = ηP (zt |xt ) P (xt |ut −1 , xt −1 )P (xt −1 |u1:t −2 , z1:t −1 ) dxt −1

Intro Transformation of Directed Model to CRF Application Experimental Results D  D M P p (zt |xt ) = n i =1 p (zti |xt ) p (xt +1 |xt , u)

Intro Transformation of Directed Model to CRF Application Experimental Results D  D M P p (zt |xt ) = n i =1 p (zti |xt ) p (xt +1 |xt , u) i P (zt |xt) ˆi zt zmax zrand

Intro Transformation of Directed Model to CRF Application Experimental Results D  D M P p (zt |xt ) = n i =1 p (zti |xt ) p (xt +1 |xt , u) i P (zt |xt) ˆi zt zmax zrand

Intro Transformation of Directed Model to CRF Application Experimental Results D  D M P p (zt |xt ) = n i =1 p (zti |xt ) p (xt +1 |xt , u) i P (zt |xt) ˆi zt zmax δrot2 zrand xt δtrans δrot1 xt−1 u = (δrot1 , δrot2 , δtrans ) executed with gaussian noise

Intro Transformation of Directed Model to CRF Application Experimental Results A P   D A p (zti |xt ) are not cond. independent zt xt

Intro Transformation of Directed Model to CRF Application Experimental Results A P   D A ut−2 ut−1 xt−2 xt−1 xt p (zti |xt ) are not cond. independent Sensor models can only be ... ... n 1 2 n zt−1 1 2 zt zt−1 zt−1 zt zt generated seperatly for each beam i P (zt |xt) ˆi zt zmax zrand

Intro Transformation of Directed Model to CRF Application Experimental Results A P   D A ut−2 ut−1 xt−2 xt−1 xt p (zti |xt ) are not cond. independent Sensor models can only be ... ... n 1 2 n zt−1 1 2 zt zt−1 zt−1 zt zt generated seperatly for each beam Assumption that measurements are independent: “Works i P (zt |xt) ˆi zt zmax surprisingly well”. . . if. . . zrand

Intro Transformation of Directed Model to CRF Application Experimental Results A P   D A ut−2 ut−1 xt−2 xt−1 xt p (zti |xt ) are not cond. independent Sensor models can only be ... ... n 1 2 n zt−1 1 2 zt zt−1 zt−1 zt zt generated seperatly for each beam Assumption that measurements are independent: “Works i P (zt |xt) ˆi zt zmax surprisingly well”. . . if. . . increasing uncertainty (tweaking) using every 10th measurement zrand ...

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

Intro Transformation of Directed Model to CRF Application Experimental Results I: CRF Undirected graphical models ut−2 ut−1 xt−2 xt−1 xt zt−1 zt

Intro Transformation of Directed Model to CRF Application Experimental Results I: CRF Undirected graphical models Every (possible) dependency ut−2 ut−1 represented by edge xt−2 xt−1 xt zt−1 zt

Intro Transformation of Directed Model to CRF Application Experimental Results I: CRF Undirected graphical models Every (possible) dependency ut−2 ut−1 represented by edge Distribution defined over products xt−2 xt−1 xt of functions over cliques zt−1 zt

Intro Transformation of Directed Model to CRF Application Experimental Results I: CRF Undirected graphical models Every (possible) dependency ut−2 ut−1 represented by edge Distribution defined over products xt−2 xt−1 xt of functions over cliques zt−1 zt Functions are called clique potentials

Intro Transformation of Directed Model to CRF Application Experimental Results I: CRF Undirected graphical models Every (possible) dependency ut−2 ut−1 represented by edge Distribution defined over products xt−2 xt−1 xt of functions over cliques zt−1 zt Functions are called clique potentials Clique potentials represent compatibility of their variables

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

Intro Transformation of Directed Model to CRF Application Experimental Results CRF-M  S E ut−2 ut−1 xt−2 xt−1 xt zt−1 zt T 1 p (x0:T |z1:T , u0:T −1 ) = ϕp (xt , xt −1 , ut −1 )ϕm (xt , zt ) Z (z1:T , u1:T −1 ) t =1

Intro Transformation of Directed Model to CRF Application Experimental Results CRF-M  S E ut−2 ut−1 xt−2 xt−1 xt zt−1 zt T 1 p (x0:T |z1:T , u0:T −1 ) = ϕp (xt , xt −1 , ut −1 )ϕm (xt , zt ) Z (z1:T , u1:T −1 ) t =1 Z (·): all trajectories ϕp (·)ϕm (·)

Intro Transformation of Directed Model to CRF Application Experimental Results CRF-M  S E ut−2 ut−1 xt−2 xt−1 xt zt−1 zt T 1 p (x0:T |z1:T , u0:T −1 ) = ϕp (xt , xt −1 , ut −1 )ϕm (xt , zt ) Z (z1:T , u1:T −1 ) t =1 Z (·): all trajectories ϕp (·)ϕm (·) How to define ϕp (·) and ϕm (·)?

Intro Transformation of Directed Model to CRF Application Experimental Results T P P φp ut −1 = (δrot1 , δtrans , δrot2 ) odometry ut −1 = (δrot1 , δtrans , δrot2 ) derived odometry ˆ ˆ ˆ ˆ δrot2 2 Before: Gaussian noise N uti −1 , σi xt δtrans δrot1 xt−1

Intro Transformation of Directed Model to CRF Application Experimental Results T P P φp ut −1 = (δrot1 , δtrans , δrot2 ) odometry ut −1 = (δrot1 , δtrans , δrot2 ) derived odometry ˆ ˆ ˆ ˆ δrot2 2 Before: Gaussian noise N uti −1 , σi xt  (δrot1 − δrot1 )2 ˆ      δtrans   fp (xt , xt −1 , ut −1 ) =  (δtrans − δtrans )2       ˆ      3 features   (δrot2 − δrot2 )2 ˆ     δrot1 xt−1

Intro Transformation of Directed Model to CRF Application Experimental Results T P P φp ut −1 = (δrot1 , δtrans , δrot2 ) odometry ut −1 = (δrot1 , δtrans , δrot2 ) derived odometry ˆ ˆ ˆ ˆ δrot2 2 Before: Gaussian noise N uti −1 , σi xt  (δrot1 − δrot1 )2 ˆ      δtrans   fp (xt , xt −1 , ut −1 ) =  (δtrans − δtrans )2       ˆ      3 features   (δrot2 − δrot2 )2 ˆ     δrot1 φp (xt , xt −1 , ut −1 ) = exp wp , fp (xt , xt −1 , ut −1 ) xt−1

Intro Transformation of Directed Model to CRF Application Experimental Results T P P φp ut −1 = (δrot1 , δtrans , δrot2 ) odometry ut −1 = (δrot1 , δtrans , δrot2 ) derived odometry ˆ ˆ ˆ ˆ δrot2 2 Before: Gaussian noise N uti −1 , σi xt  (δrot1 − δrot1 )2 ˆ      δtrans   fp (xt , xt −1 , ut −1 ) =  (δtrans − δtrans )2       ˆ      3 features   (δrot2 − δrot2 )2 ˆ     δrot1 φp (xt , xt −1 , ut −1 ) = exp wp , fp (xt , xt −1 , ut −1 ) xt−1 1 (a − a )2 ˆ N a, = exp − σ2 2σ2 Gaussian noise N uti −1 , 1 −2wpi if wp < 0 i

Intro Transformation of Directed Model to CRF Application Experimental Results R: S M   N¨ B A  i P (zt |xt) ˆi zt zmax zrand n p (zt |xt ) = p (zti |xt ) i =1

Intro Transformation of Directed Model to CRF Application Experimental Results M P φm i P (zt |xt) ˆi zt zmax n     φm (xt , zt ) = exp  wm , fm (zt , xt )  i         i =0 zrand (¬mti ∧ ¬mti )cti (zti − zti )2 ˆ ˆ         i i i        ˆ (¬mt ∧ ¬mt )¬ct      fm (zt , xt ) =  i   (¬mti ∧ mti ) ˆ            ( mti ∧ ¬mti )        ˆ        ( mti ∧ mti ) ˆ  

Intro Transformation of Directed Model to CRF Application Experimental Results M P φm i P (zt |xt) ˆi zt zmax n     φm (xt , zt ) = exp  wm , fm (zt , xt )  i         i =0 zrand (¬mti ∧ ¬mti )cti (zti − zti )2 ˆ ˆ         i i i        ˆ (¬mt ∧ ¬mt )¬ct      fm (zt , xt ) =  i   (¬mti ∧ mti ) ˆ            ( mti ∧ ¬mti )        ˆ        ( mti ∧ mti ) ˆ   mti ∈ {1, 0} measured zmax

Intro Transformation of Directed Model to CRF Application Experimental Results M P φm i P (zt |xt) ˆi zt zmax n     φm (xt , zt ) = exp  wm , fm (zt , xt )  i         i =0 zrand (¬mti ∧ ¬mti )cti (zti − zti )2 ˆ ˆ         i i i        ˆ (¬mt ∧ ¬mt )¬ct      fm (zt , xt ) =  i   (¬mti ∧ mti ) ˆ            ( mti ∧ ¬mti )        ˆ        ( mti ∧ mti ) ˆ   mti ∈ {1, 0} measured zmax mti ∈ {1, 0} expected zmax ˆ

Intro Transformation of Directed Model to CRF Application Experimental Results M P φm i P (zt |xt) ˆi zt zmax n     φm (xt , zt ) = exp  wm , fm (zt , xt )  i         i =0 zrand (¬mti ∧ ¬mti )cti (zti − zti )2 ˆ ˆ         i i i        ˆ (¬mt ∧ ¬mt )¬ct      fm (zt , xt ) =  i   (¬mti ∧ mti ) ˆ            ( mti ∧ ¬mti )        ˆ        ( mti ∧ mti ) ˆ   mti ∈ {1, 0} measured zmax mti ∈ {1, 0} expected zmax ˆ cti ∈ {1, 0} zti − zti < 20cm ˆ

Intro Transformation of Directed Model to CRF Application Experimental Results M P φm i P (zt |xt) ˆi zt zmax n     φm (xt , zt ) = exp  wm , fm (zt , xt )  i         i =0 zrand (¬mti ∧ ¬mti )cti (zti − zti )2 ˆ ˆ         i i i        ˆ (¬mt ∧ ¬mt )¬ct      fm (zt , xt ) =  i   (¬mti ∧ mti ) ˆ            ( mti ∧ ¬mti )        ˆ        ( mti ∧ mti ) ˆ   mti ∈ {1, 0} measured zmax mti ∈ {1, 0} expected zmax ˆ cti ∈ {1, 0} zti − zti < 20cm ˆ

Intro Transformation of Directed Model to CRF Application Experimental Results M P φm i P (zt |xt) ˆi zt zmax n     φm (xt , zt ) = exp  wm , fm (zt , xt )  i         i =0 zrand (¬mti ∧ ¬mti )cti (zti − zti )2 ˆ ˆ         i i i        ˆ (¬mt ∧ ¬mt )¬ct      fm (zt , xt ) =  i   (¬mti ∧ mti ) ˆ            ( mti ∧ ¬mti )        ˆ        ( mti ∧ mti ) ˆ   mti ∈ {1, 0} measured zmax mti ∈ {1, 0} expected zmax ˆ cti ∈ {1, 0} zti − zti < 20cm ˆ

Intro Transformation of Directed Model to CRF Application Experimental Results M P φm i P (zt |xt) ˆi zt zmax n     φm (xt , zt ) = exp  wm , fm (zt , xt )  i         i =0 zrand (¬mti ∧ ¬mti )cti (zti − zti )2 ˆ ˆ         i i i        ˆ (¬mt ∧ ¬mt )¬ct      fm (zt , xt ) =  i   (¬mti ∧ mti ) ˆ            ( mti ∧ ¬mti )        ˆ        ( mti ∧ mti ) ˆ   mti ∈ {1, 0} measured zmax mti ∈ {1, 0} expected zmax ˆ cti ∈ {1, 0} zti − zti < 20cm ˆ

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

Intro Transformation of Directed Model to CRF Application Experimental Results U  CRF    P F At each time step t: Prediction Move particles according to gaussian noise determined by wp Same as sampling from N uti −1 , ˆ 1 i −2wp Correction Particle at xt gets weight φm (xt , zt ) Resample (includes normalization)

Intro Transformation of Directed Model to CRF Application Experimental Results U  CRF    P F At each time step t: Prediction Move particles according to gaussian noise determined by wp u Same as sampling from N uti −1 , ˆ 1 i −2wp Correction Particle at xt gets weight φm (xt , zt ) Resample (includes normalization)

Intro Transformation of Directed Model to CRF Application Experimental Results U  CRF    P F At each time step t: Prediction Move particles according to gaussian noise determined by wp moved Same as sampling from N uti −1 , ˆ 1 −2wpi particles Correction Particle at xt gets weight φm (xt , zt ) Resample (includes normalization)

Intro Transformation of Directed Model to CRF Application Experimental Results U  CRF    P F At each time step t: Prediction Move particles according to gaussian noise determined by wp added Same as sampling from N uti −1 , noise 1 ˆ −2wpi Correction Particle at xt gets weight φm (xt , zt ) Resample (includes normalization)

Intro Transformation of Directed Model to CRF Application Experimental Results U  CRF    P F At each time step t: Prediction Move particles according to gaussian noise determined by wp ...sense... Same as sampling from N uti −1 , ˆ 1 −2wpi Correction Particle at xt gets weight φm (xt , zt ) Resample (includes normalization)

Intro Transformation of Directed Model to CRF Application Experimental Results U  CRF    P F At each time step t: Prediction Move particles according to gaussian noise determined by wp weights Same as sampling from N uti −1 , ˆ 1 −2wpi Correction Particle at xt gets weight φm (xt , zt ) Resample (includes normalization)

Intro Transformation of Directed Model to CRF Application Experimental Results U  CRF    P F At each time step t: Prediction Move particles according to gaussian noise determined by wp resample Same as sampling from N uti −1 , ˆ 1 i −2wp Correction Particle at xt gets weight φm (xt , zt ) Resample (includes normalization)

O 1 I: S E U D M 2 T  D M  CRF Short Introduction to CRF CRF-Model for State Estimation 3 A CRF-Filter Algorithm Learning the Parameters 4 E R

Intro Transformation of Directed Model to CRF Application Experimental Results D     wp  wm Drive around in test area

Intro Transformation of Directed Model to CRF Application Experimental Results D     wp  wm Drive around in test area Use high-quality scanmatcher to generate “ground truth” trajectory x∗

Intro Transformation of Directed Model to CRF Application Experimental Results D     wp  wm Drive around in test area Use high-quality scanmatcher to generate “ground truth” trajectory x∗ ˆ Using arbitrary weights, generate trajectory x with CRF-filter

Intro Transformation of Directed Model to CRF Application Experimental Results D     wp  wm Drive around in test area Use high-quality scanmatcher to generate “ground truth” trajectory x∗ ˆ Using arbitrary weights, generate trajectory x with CRF-filter Use difference of summed features as weight update(−) : wk = wk −1 + α ( f (x∗ , u, z) − f (x, u, z)) ˆ

Intro Transformation of Directed Model to CRF Application Experimental Results D     wp  wm Drive around in test area Use high-quality scanmatcher to generate “ground truth” trajectory x∗ ˆ Using arbitrary weights, generate trajectory x with CRF-filter Use difference of summed features as weight update(−) : wk = wk −1 + α ( f (x∗ , u, z) − f (x, u, z)) ˆ Decrease α if new Filter cannot track

Intro Transformation of Directed Model to CRF Application Experimental Results D     wp  wm Drive around in test area Use high-quality scanmatcher to generate “ground truth” trajectory x∗ ˆ Using arbitrary weights, generate trajectory x with CRF-filter Use difference of summed features as weight update(−) : wk = wk −1 + α ( f (x∗ , u, z) − f (x, u, z)) ˆ Decrease α if new Filter cannot track loop Adapts weights to task, sensor dependencies/environment, sensor noise, particle filter parameters

Intro Transformation of Directed Model to CRF Application Experimental Results L A Averaged Perceptron Algorithm (Collins 2002) for tagging w k = w k −1 + α f (x∗ , u, z) − f (x, u, z)

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