Signal Processing - September 2017 - 81
106
106
MLE
ZZB
105
MLE
ZZB
105
104
104
Two−Steps
103
102
Two−Steps
DPE
103
102
101
DPE
100
24
26
101
28
30
32
34
(a)
36
38
40
42
44
100
20
25
30
(b)
35
40
FIGURE 5. Galileo E1 signal processing with (a) 4-ms and (b) 8-ms coherent integration times. DPE outperforms two-steps, as predicted by the breakdown
points of the bound.
Regardless of the signal type and integration times, DPE and
two-steps perform similarly at high C/N 0 values. However,
the breakdown point (i.e., the C/N 0 at which performance is
severely degraded due to large errors) of two-steps receivers
occurs much earlier than DPE, which is more robust to weak
signal conditions. The distance between breakdown points
is, roughly, 10 log 10 (7) . 8.5 dB as predicted by the bound.
Increasing the coherent integration time improves the performance of the methods, with DPE surpassing two-steps in all
situations thanks to its additional integration over the available
satellites. Noncoherent integration could be implemented to
further increase the positioning performances, as described,
for instance, in [11] for two-steps open-loop positioning. To
compare, Figure 6 reports results for GPS and Galileo signals
with the same integration time. Note that the Galileo E1 signal
106
MLE
ZZB
5
106
GPS L1
103
102
101
100
24
DPE
28
30
32 34 36 38
C/N0 (dB Hz)
Two−Steps
104
103
102
Galileo E1
26
MLE
105
Two−Steps
104
RMSE (ns)
RMSE (m)
10
outperforms the GPS L1 signal at high C/N 0 values. Results
regarding the receiver clock bias are also reported for this
setup in Figure 7. In the same way as it happens for the position domain, the breakdown point occurs at a lower C/N 0 for
the DPE approach. However, these results are not compared
against the bound since the Ziv-Zakai expression in (6) is derived
for the position domain only.
A second experiment considers hybrid positioning with
M = 7 satellites, four of which are from the GPS L1 constellation and the remaining three are emitting Galileo E1 signals. For
the sake of illustration, each of these satellites varies its C/N 0 at
the same time. In Figure 8, the breakdown point of DPE occurs
at lower C/N 0 as predicted by the bounds. Moreover, there is
a performance gap between both approaches at high C/N 0,
where DPE also outperforms two-steps. This is due to the lack
40
42
44
DPE
101
30
35
FIGURE 6. Positioning results for GPS L1 and Galileo E1 signals,
processed with a 4-ms coherent integration time and with M = 7 satellites
varying power at the same time.
40
C/N0 (dB Hz)
45
50
FIGURE 7. Clock offset results for the GPS L1 signal in Figure 6.
IEEE SIGNAL PROCESSING MAGAZINE
|
September 2017
|
81
Table of Contents for the Digital Edition of Signal Processing - September 2017
Signal Processing - September 2017 - Cover1
Signal Processing - September 2017 - Cover2
Signal Processing - September 2017 - 1
Signal Processing - September 2017 - 2
Signal Processing - September 2017 - 3
Signal Processing - September 2017 - 4
Signal Processing - September 2017 - 5
Signal Processing - September 2017 - 6
Signal Processing - September 2017 - 7
Signal Processing - September 2017 - 8
Signal Processing - September 2017 - 9
Signal Processing - September 2017 - 10
Signal Processing - September 2017 - 11
Signal Processing - September 2017 - 12
Signal Processing - September 2017 - 13
Signal Processing - September 2017 - 14
Signal Processing - September 2017 - 15
Signal Processing - September 2017 - 16
Signal Processing - September 2017 - 17
Signal Processing - September 2017 - 18
Signal Processing - September 2017 - 19
Signal Processing - September 2017 - 20
Signal Processing - September 2017 - 21
Signal Processing - September 2017 - 22
Signal Processing - September 2017 - 23
Signal Processing - September 2017 - 24
Signal Processing - September 2017 - 25
Signal Processing - September 2017 - 26
Signal Processing - September 2017 - 27
Signal Processing - September 2017 - 28
Signal Processing - September 2017 - 29
Signal Processing - September 2017 - 30
Signal Processing - September 2017 - 31
Signal Processing - September 2017 - 32
Signal Processing - September 2017 - 33
Signal Processing - September 2017 - 34
Signal Processing - September 2017 - 35
Signal Processing - September 2017 - 36
Signal Processing - September 2017 - 37
Signal Processing - September 2017 - 38
Signal Processing - September 2017 - 39
Signal Processing - September 2017 - 40
Signal Processing - September 2017 - 41
Signal Processing - September 2017 - 42
Signal Processing - September 2017 - 43
Signal Processing - September 2017 - 44
Signal Processing - September 2017 - 45
Signal Processing - September 2017 - 46
Signal Processing - September 2017 - 47
Signal Processing - September 2017 - 48
Signal Processing - September 2017 - 49
Signal Processing - September 2017 - 50
Signal Processing - September 2017 - 51
Signal Processing - September 2017 - 52
Signal Processing - September 2017 - 53
Signal Processing - September 2017 - 54
Signal Processing - September 2017 - 55
Signal Processing - September 2017 - 56
Signal Processing - September 2017 - 57
Signal Processing - September 2017 - 58
Signal Processing - September 2017 - 59
Signal Processing - September 2017 - 60
Signal Processing - September 2017 - 61
Signal Processing - September 2017 - 62
Signal Processing - September 2017 - 63
Signal Processing - September 2017 - 64
Signal Processing - September 2017 - 65
Signal Processing - September 2017 - 66
Signal Processing - September 2017 - 67
Signal Processing - September 2017 - 68
Signal Processing - September 2017 - 69
Signal Processing - September 2017 - 70
Signal Processing - September 2017 - 71
Signal Processing - September 2017 - 72
Signal Processing - September 2017 - 73
Signal Processing - September 2017 - 74
Signal Processing - September 2017 - 75
Signal Processing - September 2017 - 76
Signal Processing - September 2017 - 77
Signal Processing - September 2017 - 78
Signal Processing - September 2017 - 79
Signal Processing - September 2017 - 80
Signal Processing - September 2017 - 81
Signal Processing - September 2017 - 82
Signal Processing - September 2017 - 83
Signal Processing - September 2017 - 84
Signal Processing - September 2017 - 85
Signal Processing - September 2017 - 86
Signal Processing - September 2017 - 87
Signal Processing - September 2017 - 88
Signal Processing - September 2017 - 89
Signal Processing - September 2017 - 90
Signal Processing - September 2017 - 91
Signal Processing - September 2017 - 92
Signal Processing - September 2017 - 93
Signal Processing - September 2017 - 94
Signal Processing - September 2017 - 95
Signal Processing - September 2017 - 96
Signal Processing - September 2017 - 97
Signal Processing - September 2017 - 98
Signal Processing - September 2017 - 99
Signal Processing - September 2017 - 100
Signal Processing - September 2017 - 101
Signal Processing - September 2017 - 102
Signal Processing - September 2017 - 103
Signal Processing - September 2017 - 104
Signal Processing - September 2017 - 105
Signal Processing - September 2017 - 106
Signal Processing - September 2017 - 107
Signal Processing - September 2017 - 108
Signal Processing - September 2017 - 109
Signal Processing - September 2017 - 110
Signal Processing - September 2017 - 111
Signal Processing - September 2017 - 112
Signal Processing - September 2017 - 113
Signal Processing - September 2017 - 114
Signal Processing - September 2017 - 115
Signal Processing - September 2017 - 116
Signal Processing - September 2017 - 117
Signal Processing - September 2017 - 118
Signal Processing - September 2017 - 119
Signal Processing - September 2017 - 120
Signal Processing - September 2017 - 121
Signal Processing - September 2017 - 122
Signal Processing - September 2017 - 123
Signal Processing - September 2017 - 124
Signal Processing - September 2017 - 125
Signal Processing - September 2017 - 126
Signal Processing - September 2017 - 127
Signal Processing - September 2017 - 128
Signal Processing - September 2017 - 129
Signal Processing - September 2017 - 130
Signal Processing - September 2017 - 131
Signal Processing - September 2017 - 132
Signal Processing - September 2017 - 133
Signal Processing - September 2017 - 134
Signal Processing - September 2017 - 135
Signal Processing - September 2017 - 136
Signal Processing - September 2017 - 137
Signal Processing - September 2017 - 138
Signal Processing - September 2017 - 139
Signal Processing - September 2017 - 140
Signal Processing - September 2017 - 141
Signal Processing - September 2017 - 142
Signal Processing - September 2017 - 143
Signal Processing - September 2017 - 144
Signal Processing - September 2017 - 145
Signal Processing - September 2017 - 146
Signal Processing - September 2017 - 147
Signal Processing - September 2017 - 148
Signal Processing - September 2017 - 149
Signal Processing - September 2017 - 150
Signal Processing - September 2017 - 151
Signal Processing - September 2017 - 152
Signal Processing - September 2017 - 153
Signal Processing - September 2017 - 154
Signal Processing - September 2017 - 155
Signal Processing - September 2017 - 156
Signal Processing - September 2017 - 157
Signal Processing - September 2017 - 158
Signal Processing - September 2017 - 159
Signal Processing - September 2017 - 160
Signal Processing - September 2017 - 161
Signal Processing - September 2017 - 162
Signal Processing - September 2017 - 163
Signal Processing - September 2017 - 164
Signal Processing - September 2017 - 165
Signal Processing - September 2017 - 166
Signal Processing - September 2017 - 167
Signal Processing - September 2017 - 168
Signal Processing - September 2017 - 169
Signal Processing - September 2017 - 170
Signal Processing - September 2017 - 171
Signal Processing - September 2017 - 172
Signal Processing - September 2017 - 173
Signal Processing - September 2017 - 174
Signal Processing - September 2017 - 175
Signal Processing - September 2017 - 176
Signal Processing - September 2017 - 177
Signal Processing - September 2017 - 178
Signal Processing - September 2017 - 179
Signal Processing - September 2017 - 180
Signal Processing - September 2017 - 181
Signal Processing - September 2017 - 182
Signal Processing - September 2017 - 183
Signal Processing - September 2017 - 184
Signal Processing - September 2017 - 185
Signal Processing - September 2017 - 186
Signal Processing - September 2017 - 187
Signal Processing - September 2017 - 188
Signal Processing - September 2017 - 189
Signal Processing - September 2017 - 190
Signal Processing - September 2017 - 191
Signal Processing - September 2017 - 192
Signal Processing - September 2017 - 193
Signal Processing - September 2017 - 194
Signal Processing - September 2017 - 195
Signal Processing - September 2017 - 196
Signal Processing - September 2017 - Cover3
Signal Processing - September 2017 - Cover4
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