EXPANDING-MEMORY (GROWING-MEMORY) POLYNOMIAL FILTERS INTRODUCTION The fixed-memory flter described in Chapter 5 has two important disadvantages. First, all the data obtained over the last L þ 1 observations have to be stored. This can result in excessive memory requirements in some instances. Second, at each new observation the last L þ 1 data samples have to be reprocessed to obtain the update estimate with no use being made of the previous estimate calculations. This can lead to a large computer load. When these disadvantages are not a problem, the fixed-memory filter would be used generally. Two filters that do not. | Tracking and Kalman Filtering Made Easy. Eli Brookner Copyright 1998 John Wiley Sons Inc. ISBNs 0-471-18407-1 Hardback 0-471-22419-7 Electronic 6 EXPANDING-MEMORY GROWING-MEMORY POLYNOMIAL FILTERS INTRODUCTION The fixed-memory flter described in Chapter 5 has two important disadvantages. First all the data obtained over the last L 1 observations have to be stored. This can result in excessive memory requirements in some instances. Second at each new observation the last L 1 data samples have to be reprocessed to obtain the update estimate with no use being made of the previous estimate calculations. This can lead to a large computer load. When these disadvantages are not a problem the fixed-memory filter would be used generally. Two filters that do not have these two disadvantages are the expanding-memory filter and the fading memory filter. The expanding memory filter is as discussed in Section and later in Section suitable for track initiation and will be covered in detail in this chapter. The fading memory filter as discussed in Chapter 1 is used for steady state tracking as is the fixed-memory filter and will be covered in detail in Chapter 7. Before proceeding it is important to highlight the advantages of the fixed-memory filter. First if bad data is acquired the effect on the filter will only last for a finite time because the filter has a finite memory of duration L 1 that is the fixed-memory filter has a finite transient response. Second fixed-memory filters of short duration have the advantage of allowing simple processor models to be used when the actual process model is complex or even unknown because simple models can be used over short observation intervals. These two advantages are also obtained when using a short memory for the fading-memory filter discussed in Chapter 7. 233 234 EXPANDING-MEMORY GROWING-MEMORY POLYNOMIAL FILTERS EXTRAPOLATION FROM FIXED-MEMORY FILTER RESULTS All the results given in Chapter 5 for the fixed-memory
