Tightly coupled INS/GPS system using particle filter

D0928- system architecture and math

functions

Part A - Final presentation

Students: Royzman Danny Peleg Nati

Supervisor: Fiksman Evgeni

•Math functions▫Overview

▫Trigonometric ▫Exp{-x}▫SQRT

▫Implementation▫Performance

•Infrastructure – Phase1▫Main difficulties▫Block diagram▫Controllers diagram

•Gantt Chart

Agenda

Math functions - Overview

sine & Cosine

exp

sqrt

Particle propagationRevaluation

GPS update + Neff

Dk computation

Reweight

Math functions - guidelines

The following guidelines were defined for function

implementation:

• I/O format : signed fixed point.

• Maximum flexibility.

• Low FPGA resource usage.

• Reasonable accuracy.

Math functions – OverviewInitial proposal

Initially proposed implementation based on CORDIC

algorithm

• Iterative algorithm.

• I/O format : variable width signed fixed point.

• Low HW requirements.

• Easily adjustable and easily implementable .

• Allows a generic unified core, for all the functions needed.

• Rough accuracy estimation is one bit for each iteration.

Math functions – OverviewCORDIC R&D

FunctionIssues

TrigonometricPre and post processing units

needed to cover ±Π

ExponentialVery large convergence zone

needed, impractical for CORDIC use

Square rootVery large IO format needed,

impractical for CORDIC use

• See project book for more details

Math functions – OverviewAlgorithm adjustments

FunctionAlgorithm

Trigonometric CORDIC algorithm

Exponential“Invariants” method

Square root“A non-restoring square root “

algorithm

Math functions – ImplementationTrigonometric functions

• Variable-width variable-pipeline CORDIC algorithm.

▫ Sine, Cosine functions implemented in single unit.

▫ Pre & Post processing units added for broader input coverage.

▫ Pipe core contains datapath and control stages.

▫ Pipe core combined from variable (2,4..16) amount of single stages,

separated by a register.

▫ Default values: (HW cost/accuracy trade off).

Stages total amount : 32 units.

Input/output width :32 bit.

IO format 1.2.29 input, 1.0.31 output

Math functions – ImplementationTrigonometric functions

Pre-Processing

unitPipe Core

Post-Processing

unit

Default values LUT

Input

Sine

Cosine

Math functions – ImplementationTrigonometric functions

Single pipe stage

http://en.wikibooks.org/wiki/Digital_Circuits/CORDIC

Math functions – ImplementationTrigonometric functions

Pre processing unit

Math functions – ImplementationTrigonometric functions

Post processing unit

Math functions – ImplementationExponential function

• “Invariants” method will be used

▫ 17 single stages.

▫ Executing a 4-stages pipe flow.

▫ 5 unique “integer” stages.

▫ 6 unique “fractal” stages, repeated twice for better coverage.

▫ Pipe core contains datapath and control stages.

▫ IO format 0.5.27 input, 0.0.32 output.

Math functions – ImplementationExponential function

Single stage

Math functions – ImplementationSquare root function

• “A non-restoring square root” algorithm will be used

▫ Fully combinatorial implementation

▫ 48 unique iterations, can be pipelined.

▫ IO format 0.32.64 input, 0.16.32 output.

Math functions – ImplementationSquare root function

Schematic

Math functions – Performance

PerformanceResource usage

Pipe

size

Clock(MHz)Mean

accuracy(%)

Comb.ALUDedicated logic registers

Trig block2÷1625.85÷159.640.0000064148÷3585196÷1381

Exp block467.050.311706167

SQRT block07.070.0033932144

Infrastructure

Infrastructure mile stone - GPS Phase I is done

• Infrastructure – Phase1▫Main difficulties▫Block diagram▫Controllers diagram

InfrastructureMain difficulties

•Integration problems between frames.

•Hardware adjustments for debug .

•Long compilation time.

InfrastructurePhase1 - block diagram

Taken from Gadi&Eran’s D1418_BOOK

InfrastructurePhase1 - connectivity

InfrastructurePhase1 - connectivity

InfrastructurePhase1 - connectivity

InfrastructurePhase1 - controllers diagram

Main controller1 F.S.M

InfrastructurePhase1 - controllers diagram

Local controller2 F.S.M

InfrastructurePhase1 - controllers diagram

Main controller3 F.S.M

InfrastructurePhase1 - controllers diagram

Main controller4 F.S.M

InfrastructurePhase1 - From Debug

InfrastructurePhase1 - From Debug +100 cycles

InfrastructureGantt Chart

ינוארדצמברנובמבר

21285121926291623

Phase2Phase2Phase2Phase3Phase3Phase3Phase4Phase4Phase4Phase4

Q&A

Backup

CORDICאלגוריתם :סיבוב וקטור – התמרה כללית

( , )x y

( , )x y

( ', ')x y

CORDICאלגוריתם

CORDICאלגוריתם הצובר הזוויתי:

CORDICאלגוריתם

שני מצבי עבודה :• Rotation by Volder .1מצב סיבוב –

2.Vectoring מצב וקטורי –

CORDICאלגוריתם בסה"כ עבור מצב

סיבוב :

CORDICאלגוריתם

CORDICאלגוריתם

Regular single stagesAdditional single stages

Proposed HW implementationHyperbolic functions Pre Process Unit

Mathematical actions required, compared to regular single stage

• X. Hu, R. Huber, S. Bass, “Expanding the Range ofConvergence of the CORDIC Algorithm”, IEEETransactions on Computers. Vol. 40, Nº 1, pp. 13-21, Jan.1991.• Daniel R. Llamocca-Obregón,Carla P. Agurto-Ríos; A FIXED-POINT IMPLEMENTATION OF THE EXPANDED HYPERBOLICCORDIC ALGORITHM

http://www.iberchip.org/iberchip2006/ponencias/106.pdf

Back

Proposed HW implementationHyperbolic functions Pre Process Unit

C simulation results, acquired by running D0228 (Neta & Moti)

project code.

• Maximum Exponential input : 375.704604

• Minimum Exponential input : 0.12665

• Average Exponential input : 14.15504

•Convergence zone expansion:

•Total values checked : >1000000 (One million)Back

Negative stagesValues covered

0(default)1%

563%

1087%