RECORD
On the design of fixed-gain tracking filters by pole placement: Or an introduction to applied signals-and-systems theory for engineers
Systems and Control · Submitted 1 Oct 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is suggested that the arbitrary placement of closed-loop state-observer poles is a simple and intuitive way of tuning the transient and steady-state response of a fixed-gain tracking filter when prior distributions are unknown.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
The Kalman filter computes the optimal variable-gain using prior knowledge of the initial state and random (process and measurement) noise distributions, which are assumed to be Gaussian with known variance. However, when these distributions are unknown, the Kalman filter is not necessarily optimal and other simpler state-estimators, such as fixed-gain ({\alpha}, {\alpha}-\b{eta} or {\alpha}-\b{eta}-{\gamma} etc.) filters may be sufficient. When such filters are used as low-complexity state-estimators in embedded tracking systems, the fixed gain parameters are usually set equal to the steady-state gains of the corresponding Kalman filter. An alternative procedure, that does not rely prior distributions, based on Luenberger observers, is presented here. It is suggested that the arbitrary placement of closed-loop state-observer poles is a simple and intuitive way of tuning the transient and steady-state response of a fixed-gain tracking filter when prior distributions are unknown. All poles are placed inside the unit circle on the positive real axis of the complex z-plane at p for a well damped response and a configurable bandwidth. Transient bias errors, e.g. due to target manoeuvres or process modelling errors, decrease as p=0 is approached for a wider bandwidth. Steady-state random errors, e.g. due to sensor noise, decrease as p=1 is approached for a narrower bandwidth. Thus the p parameter (with 0<p<1) may be interpreted as a dimensionless smoothing factor. This tutorial-style report examines state-observer design by pole placement, which is a standard procedure for feedback controls but unusual for tracking filters, due to the success and popularity of the Kalman filter. As Bayesian trackers are designed via statistical modelling, not by pole-zero placement in the complex plane, the underlying principles of linear time-invariant signals and systems are also reviewed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Kalman filter computes the optimal variable-gain using prior knowledge of the initial state and random (process and measurement) noise distributions, which are assumed to be Gaussian with known variance. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | However, when these distributions are unknown, the Kalman filter is not necessarily optimal and other simpler state-estimators, such as fixed-gain ({\alpha}, {\alpha}-\b{eta} or {\alpha}-\b{eta}-{\gamma} etc.) filters may be sufficient. | background 0.82 | 0.06 | 0.06 | hedged possibility 0.69 |
| s2 | When such filters are used as low-complexity state-estimators in embedded tracking systems, the fixed gain parameters are usually set equal to the steady-state gains of the corresponding Kalman filter. | background 1.00 | 0.06 | 0.04 | asserted 0.95 |
| s3 | An alternative procedure, that does not rely prior distributions, based on Luenberger observers, is presented here. | contribution 0.83 | 0.76 | 0.12 | asserted 0.99 |
| s4 | It is suggested that the arbitrary placement of closed-loop state-observer poles is a simple and intuitive way of tuning the transient and steady-state response of a fixed-gain tracking filter when prior distributions are unknown. | method 0.51 | 0.41 | 0.69 | hedged possibility 0.99 |
| s5 | All poles are placed inside the unit circle on the positive real axis of the complex z-plane at p for a well damped response and a configurable bandwidth. | method 0.97 | 0.49 | 0.18 | asserted 0.99 |
| s6 | Transient bias errors, e.g. due to target manoeuvres or process modelling errors, decrease as p=0 is approached for a wider bandwidth. | result 0.91 | 0.53 | 0.10 | asserted 1.00 |
| s7 | Steady-state random errors, e.g. due to sensor noise, decrease as p=1 is approached for a narrower bandwidth. | result 0.93 | 0.50 | 0.11 | asserted 1.00 |
| s8 | Thus the p parameter (with 0<p<1) may be interpreted as a dimensionless smoothing factor. | interpretation 1.00 | 0.59 | 0.25 | hedged possibility 0.98 |
| s9 | This tutorial-style report examines state-observer design by pole placement, which is a standard procedure for feedback controls but unusual for tracking filters, due to the success and popularity of the Kalman filter. | background 0.53 | 0.23 | 0.08 | asserted 0.98 |
| s10 | As Bayesian trackers are designed via statistical modelling, not by pole-zero placement in the complex plane, the underlying principles of linear time-invariant signals and systems are also reviewed. | background 0.72 | 0.10 | 0.05 | asserted 0.98 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
The Kalman filter computes the optimal variable-gain using prior knowledge of the initial state and random (process and measurement) noise distributions, which are assumed to be Gaussian with known variance. However, when these distributions are unknown, the Kalman filter is not necessarily optimal and other simpler state-estimators, such as fixed-gain ({\alpha}, {\alpha}-\b{eta} or {\alpha}-\b{eta}-{\gamma} etc.) filters may be sufficient. When such filters are used as low-complexity state-estimators in embedded tracking systems, the fixed gain parameters are usually set equal to the steady-state gains of the corresponding Kalman filter. An alternative procedure, that does not rely prior distributions, based on Luenberger observers, is presented here. It is suggested that the arbitrary placement of closed-loop state-observer poles is a simple and intuitive way of tuning the transient and steady-state response of a fixed-gain tracking filter when prior distributions are unknown. All poles are placed inside the unit circle on the positive real axis of the complex z-plane at p for a well damped response and a configurable bandwidth. Transient bias errors, e.g. due to target manoeuvres or process modelling errors, decrease as p=0 is approached for a wider bandwidth. Steady-state random errors, e.g. due to sensor noise, decrease as p=1 is approached for a narrower bandwidth. Thus the p parameter (with 0<p<1) may be interpreted as a dimensionless smoothing factor. This tutorial-style report examines state-observer design by pole placement, which is a standard procedure for feedback controls but unusual for tracking filters, due to the success and popularity of the Kalman filter. As Bayesian trackers are designed via statistical modelling, not by pole-zero placement in the complex plane, the underlying principles of linear time-invariant signals and systems are also reviewed.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.