Lab on GNSS Signal Processing Part II

Transcription

1 JRC SUMMERSCHOOL GNSS Lab on GNSS Signal Processing Part II Daniele Borio European Commission Joint Research Centre Davos, Switzerland, July 15-25, 2013

2 INTRODUCTION Second Part of the Lab: Introduction to tracking loops Summary of the tracking process o Basic functional blocks o Loop filter design (concept of loop order and bandwidth) The tracking loop script Exercise 1: Loop parameters 2

3 THE TRACKING PROCESS (RECAP) Acquisition: determine the signal presence and provide raw estimates of the signal parameters (code delay and Doppler frequency) Tracking: precisely estimate the signal parameters (code delay, Doppler frequency and carrier phase) and track their variations over time Use of two coupled loops: Delay Lock Loop (DLL) code Phase Lock Loop (PLL)* carrier Input signal Code wipe-off DLL PLL * a Frequency Lock Loop (FLL) could also be used Carrier wipe-off 3

4 TRACKING LOOPS: FUNCTIONAL BLOCKS All tracking loops share a common structure: r[ n] Input signal (to be read from the binary file) Update of the parameter to be estimated and signal replica generation Correlation 1 N n ( ) Local signal replica (Several signal replicas may be required) NCO Derivative of the parameter to be estimated Several correlators may be evaluated Non-Linear Discriminator Loop Filter Discriminator output 4

5 PLL: BASIC SCHEME The code has been removed using the local replica from the DLL Only 1 correlator: Prompt Extract the residual phase error r[ n] Input signal Correlation 1 N n ( ) Non-Linear Discriminator Complex Carrier replica Carrier NCO Loop Filter Discriminator output 5

6 DLL: BASIC SCHEME The carrier has been removed using the local replica from the PLL r[ n] Input signal 1 N n ( ) 1 N n ( ) 1 N n ( ) 3 correlators: Early, Prompt, Late Non-Linear Discriminator Extract the residual delay error Discriminator output Code NCO Loop Filter 6

7 LOOP DISCRIMINATOR It is the interface between the correlation and the parameter domain In the PLL case and in the absence of noise Prompt correlator P = Aexp{ j ϕ} Phase discriminator arctan I{ P} R{ P} Discriminator output ϕ Residual carrier phase error (this is not the carrier phase itself, but a correction with respect to the previous carrier phase estimate) In general, the discriminator output is an odd function of the residual parameter error ( ) ( 3 ϕ ϕ + ϕ ) D = f G O out odd d If the residual error is small, D out is approximately proportional to φ G d is the discriminator gain 7

8 LOOP FILTERS (I/II) Reduce the impact of noise on the discriminator output They are a linear combination of integrators of different orders (why?) ω 0 The number of integrators determine the order of the loop: 1st order loop: the loop filter is just a gain 2 ω 0 a2ω 0 1 s Analog integrator 2nd order loop: a single integrator is adopted The order determines the ability of the loop to cope with the signal dynamics From Kaplan E. D. and C.J. Hegarty (2006), Understanding GPS Principles and Applications, Artech House 8

9 LOOP FILTERS (II/II) In the digital domain, analog integrators are replaced by digital approximations For a third order loop: Recurrence relation implemented in the code H ( z) = a z + a z ( 1 z ) + a y[ n] = a x[ n 2] + a x[ n 1] + a x[ n] y[ n 1] y[ n 2] 3 ω 0 2 a3ω 0 1 s 1 s b3ω 0 9

10 TRACKING LOOP AS A FILTER A tracking loop can be approximated by an equivalent linear device (filter). The approximation is valid for small tracking errors, i.e., when the discriminator acts in its linear region Useful signal Noise Tracking loop - Equivalent filter Estimate of the signal parameter Noise The quantity of noise transferred from the input signal to the final estimate determines the loop bandwidth Coherent integration time B eq = 1 2T c σ σ 2 OUT 2 IN Variance of the output noise Variance of the input noise 10

11 LOOP BANDWIDTH The loop bandwidth is a property of the whole loop (not only of the loop filter) Narrow bandwidth: reduced output noise, difficulties in following the signal variations Wide bandwidth: higher output noise, suitable for high dynamic applications The loop bandwidth is controlled by the loop filter parameters and the discriminator gain Loop filter design formulas assume that the discriminator output has been normalized to 1 11

12 LOOP FILTER DESIGN FORMULAS Loop Order Noise Bandwidth B n (Hz) Typical Filter Values Steady State Error First ω 0 4 Bn = 0.25ω 0 Sensitive to velocity stress Second 2 ( 1 a 2 ) ω + 0 4a 2 B n a ω = 0.53 ω 0 = 1.414ω Sensitive to acceleration stress Third 2 2 ( a b a b ) ω ( a b ) B n b ω a ω = ω = 2. 4ω = 1. 1ω Sensitive to jerk stress From Kaplan E. D. and C.J. Hegarty (2006), Understanding GPS Principles and Applications, Artech House 12

13 STRUCTURE OF THE CODE Initialization Main processing loop: at each epoch 1 ms of data is read and processed Read 1 ms of data (1 code period) NCO: generate the local code and carrier Compute the 1 ms correlator outputs Is bit-synched? Yes Accumulate over 20 ms No Update the loop (Signal parameters) 13

14 INITIALIZATION Several variables and vectors are defined and initialized The main script ( mytracking.m ) computes a series of parameters (correlator outputs, code and carrier discriminator outputs, loop filter outputs, ). These values are stored in circular buffers. When the buffers are full, the values are dumped to file (writetodisk routine) Loop filter design: Generation of the local code (at the chipping rate, bi-polar form) 14

15 LOOP FILTER DESIGN The filter is implemented using the struct: (see SetLoopCoefficients ) Standard formulas (see slide 12) are used to set the loop coefficients The integration time (Tc) is used for the conversion between analog and digital integrators The LoopFilter struct is designed to easily perform the filtering operation: y[ n] = a x[ n 2] + a x[ n 1] + a x[ n] + 2 y[ n 1] y[ n 2] Filtering in implemented in LoopFilter 15

16 MAIN PROCESSING LOOP For each processing epoch Data Loading: same as in the acquisition script NCO: generate the local codes and carrier Integrate & Dump: the input samples are down-converted to baseband and integrated over the integration time, T c Discriminator and Filter Update If required: save the results to disk ( writetodisk ) 16

17 NCO OPERATIONS A tracking loop also estimates the code rate (~ output of the loop filter) Local codes need to be generated at the same rate as the incoming signal For each correlator define the time scale (in chips) and resample the local code (stored in the vector ca ) Propagate the delay of the local code (this is a form of integration) Do something similar for the local carrier 17

18 DISCRIMINATOR AND FILTER UPDATE All data are stored in circular buffer At each update, the index of the circular buffer needs to be updated Loop filters are memory devices Their memory needs to be updated 18

19 EXPECTED RESULTS 19

20 Loop Bandwidth and Order EXERCISE 1 Experiment with the different loop parameters and investigate the impact of the loop order and bandwidth on the tracking performance Suggestion: process the input signal using different parameters Plot the estimated Doppler on the same figure (modify the plotresults script) 20